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Sample records for linear fractional transformation

  1. Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

    Pei, Soo-Chang; Ding, Jian-Jiun

    2005-03-01

    Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

  2. Output feedback control of linear fractional transformation systems subject to actuator saturation

    Ban, Xiaojun; Wu, Fen

    2016-11-01

    In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.

  3. Fractional finite Fourier transform.

    Khare, Kedar; George, Nicholas

    2004-07-01

    We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

  4. Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

    Hennelly, Bryan M.; Sheridan, John T.

    2005-05-01

    By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

  5. Chaos-based partial image encryption scheme based on linear fractional and lifting wavelet transforms

    Belazi, Akram; Abd El-Latif, Ahmed A.; Diaconu, Adrian-Viorel; Rhouma, Rhouma; Belghith, Safya

    2017-01-01

    In this paper, a new chaos-based partial image encryption scheme based on Substitution-boxes (S-box) constructed by chaotic system and Linear Fractional Transform (LFT) is proposed. It encrypts only the requisite parts of the sensitive information in Lifting-Wavelet Transform (LWT) frequency domain based on hybrid of chaotic maps and a new S-box. In the proposed encryption scheme, the characteristics of confusion and diffusion are accomplished in three phases: block permutation, substitution, and diffusion. Then, we used dynamic keys instead of fixed keys used in other approaches, to control the encryption process and make any attack impossible. The new S-box was constructed by mixing of chaotic map and LFT to insure the high confidentiality in the inner encryption of the proposed approach. In addition, the hybrid compound of S-box and chaotic systems strengthened the whole encryption performance and enlarged the key space required to resist the brute force attacks. Extensive experiments were conducted to evaluate the security and efficiency of the proposed approach. In comparison with previous schemes, the proposed cryptosystem scheme showed high performances and great potential for prominent prevalence in cryptographic applications.

  6. The linear canonical transformation : definition and properties

    Bastiaans, Martin J.; Alieva, Tatiana; Healy, J.J.; Kutay, M.A.; Ozaktas, H.M.; Sheridan, J.T.

    2016-01-01

    In this chapter we introduce the class of linear canonical transformations, which includes as particular cases the Fourier transformation (and its generalization: the fractional Fourier transformation), the Fresnel transformation, and magnifier, rotation and shearing operations. The basic properties

  7. Matrices and linear transformations

    Cullen, Charles G

    1990-01-01

    ""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

  8. On fractional Fourier transform moments

    Alieva, T.; Bastiaans, M.J.

    2000-01-01

    Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

  9. Thermochemical transformations of anthracite fractions

    Belkina, T.V.; Privalov, V.E.; Stepanenko, atM.A.

    1979-08-01

    Research on the nature of thermochemical transformations of anthracite fractions and the possibility of increasing their activity and identifying conditions for their use in the electrode pitch process is described. From research done on different anthracite fractions processed at varying temperatures it was concluded that accumulations of condensates from heating anthracite fractions occur significantly slower in comparison with pitch. As a result the electrode pitch process is prolonged. Thermal treatment of an anthracite fraction causes the formation and accumulation of condensates and promotes thermochemical transformations. Lastly, the use of thermally treated anthracite fractions apparently intensifies the electrode pitch process and improves its quality. (16 refs.) (In Russian)

  10. The fractional Fourier transform and applications

    Bailey, David H.; Swarztrauber, Paul N.

    1991-01-01

    This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

  11. Fractional Laplace Transforms - A Perspective

    Rudolf A. Treumann

    2014-06-01

    Full Text Available A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equations or problems in non-extensive statistical mechanics.

  12. A new fractional wavelet transform

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-03-01

    The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

  13. Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

    Oktem, Figen S; Ozaktas, Haldun M

    2010-08-01

    Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

  14. Quaternion Linear Canonical Transform Application

    Bahri, Mawardi

    2015-01-01

    Quaternion linear canonical transform (QLCT) is a generalization of the classical linear canonical transfom (LCT) using quaternion algebra. The focus of this paper is to introduce an application of the QLCT to study of generalized swept-frequency filter

  15. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

    Ai-Min Yang

    2014-01-01

    Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

  16. Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

    Bin Wang

    2015-01-01

    Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

  17. Wigner distribution and fractional Fourier transform

    Alieva, T.; Bastiaans, M.J.; Boashash, B.

    2003-01-01

    We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

  18. On the Scaled Fractional Fourier Transformation Operator

    Hong-Yi, Fan; Li-Yun, Hu

    2008-01-01

    Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched

  19. The random continued fraction transformation

    Kalle, Charlene; Kempton, Tom; Verbitskiy, Evgeny

    2017-03-01

    We introduce a random dynamical system related to continued fraction expansions. It uses random combinations of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces, as well as the dynamical properties of the system.

  20. Tunable fractional-order Fourier transformer

    Malyutin, A A

    2006-01-01

    A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

  1. Fractionalization of cyclic transformations in optics

    Alieva, T.; Bastiaans, M.J.; Calvo, M.L.

    2005-01-01

    The paper starts with some preparatory work on three types of transformations often used in information processing: a convolution, a matrix-vector multiplication, and a general linear integral transformation. In particular we represent these transformations in a diagonalized form. We then focus on

  2. Voltage linear transformation circuit design

    Sanchez, Lucas R. W.; Jin, Moon-Seob; Scott, R. Phillip; Luder, Ryan J.; Hart, Michael

    2017-09-01

    Many engineering projects require automated control of analog voltages over a specified range. We have developed a computer interface comprising custom hardware and MATLAB code to provide real-time control of a Thorlabs adaptive optics (AO) kit. The hardware interface includes an op amp cascade to linearly shift and scale a voltage range. With easy modifications, any linear transformation can be accommodated. In AO applications, the design is suitable to drive a range of different types of deformable and fast steering mirrors (FSM's). Our original motivation and application was to control an Optics in Motion (OIM) FSM which requires the customer to devise a unique interface to supply voltages to the mirror controller to set the mirror's angular deflection. The FSM is in an optical servo loop with a wave front sensor (WFS), which controls the dynamic behavior of the mirror's deflection. The code acquires wavefront data from the WFS and fits a plane, which is subsequently converted into its corresponding angular deflection. The FSM provides +/-3° optical angular deflection for a +/-10 V voltage swing. Voltages are applied to the mirror via a National Instruments digital-to-analog converter (DAC) followed by an op amp cascade circuit. This system has been integrated into our Thorlabs AO testbed which currently runs at 11 Hz, but with planned software upgrades, the system update rate is expected to improve to 500 Hz. To show that the FSM subsystem is ready for this speed, we conducted two different PID tuning runs at different step commands. Once 500 Hz is achieved, we plan to make the code and method for our interface solution freely available to the community.

  3. Wigner distribution and fractional Fourier transform

    Alieva, T.; Bastiaans, M.J.

    2001-01-01

    The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution

  4. Linear fractional diffusion-wave equation for scientists and engineers

    Povstenko, Yuriy

    2015-01-01

    This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

  5. Square pulse linear transformer driver

    A. A. Kim

    2012-04-01

    Full Text Available The linear transformer driver (LTD technological approach can result in relatively compact devices that can deliver fast, high current, and high-voltage pulses straight out of the LTD cavity without any complicated pulse forming and pulse compression network. Through multistage inductively insulated voltage adders, the output pulse, increased in voltage amplitude, can be applied directly to the load. The usual LTD architecture [A. A. Kim, M. G. Mazarakis, V. A. Sinebryukhov, B. M. Kovalchuk, V. A. Vizir, S. N Volkov, F. Bayol, A. N. Bastrikov, V. G. Durakov, S. V. Frolov, V. M. Alexeenko, D. H. McDaniel, W. E. Fowler, K. LeCheen, C. Olson, W. A. Stygar, K. W. Struve, J. Porter, and R. M. Gilgenbach, Phys. Rev. ST Accel. Beams 12, 050402 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050402; M. G. Mazarakis, W. E. Fowler, A. A. Kim, V. A. Sinebryukhov, S. T. Rogowski, R. A. Sharpe, D. H. McDaniel, C. L. Olson, J. L. Porter, K. W. Struve, W. A. Stygar, and J. R. Woodworth, Phys. Rev. ST Accel. Beams 12, 050401 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050401] provides sine shaped output pulses that may not be well suited for some applications like z-pinch drivers, flash radiography, high power microwaves, etc. A more suitable power pulse would have a flat or trapezoidal (rising or falling top. In this paper, we present the design and first test results of an LTD cavity that generates such a type of output pulse by including within its circular array a number of third harmonic bricks in addition to the main bricks. A voltage adder made out of a square pulse cavity linear array will produce the same shape output pulses provided that the timing of each cavity is synchronized with the propagation of the electromagnetic pulse.

  6. Image encryption using the fractional wavelet transform

    Vilardy, Juan M; Useche, J; Torres, C O; Mattos, L

    2011-01-01

    In this paper a technique for the coding of digital images is developed using Fractional Wavelet Transform (FWT) and random phase masks (RPMs). The digital image to encrypt is transformed with the FWT, after the coefficients resulting from the FWT (Approximation, Details: Horizontal, vertical and diagonal) are multiplied each one by different RPMs (statistically independent) and these latest results is applied an Inverse Wavelet Transform (IWT), obtaining the encrypted digital image. The decryption technique is the same encryption technique in reverse sense. This technique provides immediate advantages security compared to conventional techniques, in this technique the mother wavelet family and fractional orders associated with the FWT are additional keys that make access difficult to information to an unauthorized person (besides the RPMs used), thereby the level of encryption security is extraordinarily increased. In this work the mathematical support for the use of the FWT in the computational algorithm for the encryption is also developed.

  7. Signals and transforms in linear systems analysis

    Wasylkiwskyj, Wasyl

    2013-01-01

    Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7.  The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...

  8. Parameter optimization in the regularized kernel minimum noise fraction transformation

    Nielsen, Allan Aasbjerg; Vestergaard, Jacob Schack

    2012-01-01

    Based on the original, linear minimum noise fraction (MNF) transformation and kernel principal component analysis, a kernel version of the MNF transformation was recently introduced. Inspired by we here give a simple method for finding optimal parameters in a regularized version of kernel MNF...... analysis. We consider the model signal-to-noise ratio (SNR) as a function of the kernel parameters and the regularization parameter. In 2-4 steps of increasingly refined grid searches we find the parameters that maximize the model SNR. An example based on data from the DLR 3K camera system is given....

  9. Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

    He, Ji-Huan; Elagan, S.K.; Li, Z.B.

    2012-01-01

    The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.

  10. Fast numerical algorithm for the linear canonical transform.

    Hennelly, Bryan M; Sheridan, John T

    2005-05-01

    The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

  11. Linear transformer driver for pulse generation

    Kim, Alexander A; Mazarakis, Michael G; Sinebryukhov, Vadim A; Volkov, Sergey N; Kondratiev, Sergey S; Alexeenko, Vitaly M; Bayol, Frederic; Demol, Gauthier; Stygar, William A

    2015-04-07

    A linear transformer driver includes at least one ferrite ring positioned to accept a load. The linear transformer driver also includes a first power delivery module that includes a first charge storage devices and a first switch. The first power delivery module sends a first energy in the form of a first pulse to the load. The linear transformer driver also includes a second power delivery module including a second charge storage device and a second switch. The second power delivery module sends a second energy in the form of a second pulse to the load. The second pulse has a frequency that is approximately three times the frequency of the first pulse. The at least one ferrite ring is positioned to force the first pulse and the second pulse to the load by temporarily isolating the first pulse and the second pulse from an electrical ground.

  12. Gauge transformations with fractional winding numbers

    Abouelsaood, A.

    1996-01-01

    The role which gauge transformations of noninteger winding numbers might play in non-Abelian gauge theories is studied. The phase factor acquired by the semiclassical physical states in an arbitrary background gauge field when they undergo a gauge transformation of an arbitrary real winding number is calculated in the path integral formalism assuming that a θFF term added to the Lagrangian plays the same role as in the case of integer winding numbers. Requiring that these states provide a representation of the group of open-quote open-quote large close-quote close-quote gauge transformations, a condition on the allowed backgrounds is obtained. It is shown that this representability condition is only satisfied in the monopole sector of a spontaneously broken gauge theory, but not in the vacuum sector of an unbroken or a spontaneously broken non-Abelian gauge theory. It is further shown that the recent proof of the vanishing of the θ parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed because certain gauge transformations needed for the proof, and whose existence is assumed, are either spontaneously broken or cannot be globally defined as a result of a topological obstruction. copyright 1996 The American Physical Society

  13. An Approach for Solving Linear Fractional Programming Problems

    Andrew Oyakhobo Odior

    2012-01-01

    Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebr...

  14. Fractional Fourier transform for confluent hypergeometric beams

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-01-01

    Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

  15. An approach for solving linear fractional programming problems ...

    The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality ...

  16. Reduced differential transform method for partial differential equations within local fractional derivative operators

    Hossein Jafari

    2016-04-01

    Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

  17. Implementation of quantum and classical discrete fractional Fourier transforms

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

    2016-01-01

    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

  18. Implementation of quantum and classical discrete fractional Fourier transforms.

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

    2016-03-23

    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

  19. Linear canonical transforms theory and applications

    Kutay, M; Ozaktas, Haldun; Sheridan, John

    2016-01-01

    This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

  20. Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

    Kumar, Sanjay

    2018-01-01

    In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

  1. Integral transform method for solving time fractional systems and fractional heat equation

    Arman Aghili

    2014-01-01

    Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

  2. INTRODUCTION OF GENERALIZED LAPLACE-FRACTIONAL MELLIN TRANSFORM

    V. D. Sharma*, M. M. Thakare

    2016-01-01

    In present era, Fractional Integral Transform plays an important role in various fields of mathematics and Technology. Mellin transform has an many application in navigations, correlaters, in area of statistics, probability and also solving in differential equation. Fractional Mellin transform is integral part of mathematical modeling method because of its scale invariance property. The aim of this paper is to generalization of Laplace-Fractional Mellin Transform. Analyticity theore...

  3. Identification problems in linear transformation system

    Delforge, Jacques.

    1975-01-01

    An attempt was made to solve the theoretical and numerical difficulties involved in the identification problem relative to the linear part of P. Delattre's theory of transformation systems. The theoretical difficulties are due to the very important problem of the uniqueness of the solution, which must be demonstrated in order to justify the value of the solution found. Simple criteria have been found when measurements are possible on all the equivalence classes, but the problem remains imperfectly solved when certain evolution curves are unknown. The numerical difficulties are of two kinds: a slow convergence of iterative methods and a strong repercussion of numerical and experimental errors on the solution. In the former case a fast convergence was obtained by transformation of the parametric space, while in the latter it was possible, from sensitivity functions, to estimate the errors, to define and measure the conditioning of the identification problem then to minimize this conditioning as a function of the experimental conditions [fr

  4. Image Retrieval Algorithm Based on Discrete Fractional Transforms

    Jindal, Neeru; Singh, Kulbir

    2013-06-01

    The discrete fractional transforms is a signal processing tool which suggests computational algorithms and solutions to various sophisticated applications. In this paper, a new technique to retrieve the encrypted and scrambled image based on discrete fractional transforms has been proposed. Two-dimensional image was encrypted using discrete fractional transforms with three fractional orders and two random phase masks placed in the two intermediate planes. The significant feature of discrete fractional transforms benefits from its extra degree of freedom that is provided by its fractional orders. Security strength was enhanced (1024!)4 times by scrambling the encrypted image. In decryption process, image retrieval is sensitive for both correct fractional order keys and scrambling algorithm. The proposed approach make the brute force attack infeasible. Mean square error and relative error are the recital parameters to verify validity of proposed method.

  5. Exact solutions of time-fractional heat conduction equation by the fractional complex transform

    Li Zheng-Biao

    2012-01-01

    Full Text Available The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.

  6. On the discretization of linear fractional representations of LPV systems

    Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.

    2012-01-01

    Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a

  7. Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

    Lorenzo, C F; Hartley, T T; Malti, R

    2013-05-13

    A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

  8. Capacitor blocks for linear transformer driver stages.

    Kovalchuk, B M; Kharlov, A V; Kumpyak, E V; Smorudov, G V; Zherlitsyn, A A

    2014-01-01

    In the Linear Transformer Driver (LTD) technology, the low inductance energy storage components and switches are directly incorporated into the individual cavities (named stages) to generate a fast output voltage pulse, which is added along a vacuum coaxial line like in an inductive voltage adder. LTD stages with air insulation were recently developed, where air is used both as insulation in a primary side of the stages and as working gas in the LTD spark gap switches. A custom designed unit, referred to as a capacitor block, was developed for use as a main structural element of the transformer stages. The capacitor block incorporates two capacitors GA 35426 (40 nF, 100 kV) and multichannel multigap gas switch. Several modifications of the capacitor blocks were developed and tested on the life time and self breakdown probability. Blocks were tested both as separate units and in an assembly of capacitive module, consisting of five capacitor blocks. This paper presents detailed design of capacitor blocks, description of operation regimes, numerical simulation of electric field in the switches, and test results.

  9. Fractional order differentiation by integration: An application to fractional linear systems

    Liu, Dayan

    2013-02-04

    In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

  10. Householder transformations and optimal linear combinations

    Decell, H. P., Jr.; Smiley, W., III

    1974-01-01

    Several theorems related to the Householder transformation and separability criteria are proven. Orthogonal transformations, topology, divergence, mathematical matrices, and group theory are discussed.

  11. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

    Ahmet Bekir

    2013-01-01

    Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

  12. Fractional Hartley transform applied to optical image encryption

    Jimenez, C [Grupo GIFES. Universidad de La Guajira. Riohacha (Colombia); Torres, C; Mattos, L, E-mail: carlosj114@gmail.com [Grupo LOI. Universidad Popular del Cesar. Valledupar (Colombia)

    2011-01-01

    A new method for image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as addictional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. Computer simulations are also perfomed to confirm the possibility of proposed method.

  13. Optical image encryption with redefined fractional Hartley transform

    Zhao, Daomu; Li, Xinxin; Chen, Linfei

    2008-11-01

    A new method for optical image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as additional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.

  14. Fractional Hartley transform applied to optical image encryption

    Jimenez, C.; Torres, C.; Mattos, L.

    2011-01-01

    A new method for image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as addictional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. Computer simulations are also perfomed to confirm the possibilty of proposed method.

  15. Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

    Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

    2017-12-01

    The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

  16. Projective Synchronization of N-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

    Baogui Xin

    2012-01-01

    Full Text Available Based on linear feedback control technique, a projective synchronization scheme of N-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

  17. Rectangular waveform linear transformer driver module design

    Zhao Yue; Xie Weiping; Zhou Liangji; Chen Lin

    2014-01-01

    Linear Transformer Driver is a novel pulsed power technology, its main merits include a parallel LC discharge array and Inductive Voltage Adder. The parallel LC discharge array lowers the whole circuit equivalent inductance and the Inductive Voltage Adder unites the modules in series in order to create a high electric field grads, meanwhile, restricts the high voltage in a small space. The lower inductance in favor of LTD output a fast waveform and IVA confine high voltage in secondary cavity. In recently, some LTD-based pulsed power system has been development yet. The usual LTD architecture provides damped sine shaped output pulses that may not be suitable in flash radiography, high power microwave production, z-pinch drivers, and certain other applications. A more suitable driver output pulse would have a flat or inclined top (slightly rising or falling). In this paper, we present the design of an LTD cavity that generates this type of the output pulse by including within its circular array some number of the harmonic bricks in addition to the standard bricks according to Fourier progression theory. The parallel LC discharge array circuit formula is introduced by Kirchhoff Law, and the sum of harmonic is proofed as an analytic result, meanwhile, rationality of design is proved by simulation. Varying gas spark discharge dynamic resistance with harmonic order and switches jitter are analyzed. The results are as following: The more harmonic order is an approach to the ideal rectangular waveform, but lead to more system complexity. The capacity decreases as harmonic order increase, and gas spark discharge dynamic resistance rises with the capacity. The rising time protracts and flat is decay or even vanishes and the shot to shot reproducibility is degenerate as the switches jitter is high. (authors)

  18. Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

    Fan Hongyi; Hao Ren; Lu Hailiang

    2008-01-01

    Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible

  19. Garbageless reversible implementation of integer linear transformations

    Burignat, Stéphane; Vermeirsch, Kenneth; De Vos, Alexis

    2013-01-01

    inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide...

  20. A Solution to the Fundamental Linear Fractional Order Differential Equation

    Hartley, Tom T.; Lorenzo, Carl F.

    1998-01-01

    This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

  1. Kernel maximum autocorrelation factor and minimum noise fraction transformations

    Nielsen, Allan Aasbjerg

    2010-01-01

    in hyperspectral HyMap scanner data covering a small agricultural area, and 3) maize kernel inspection. In the cases shown, the kernel MAF/MNF transformation performs better than its linear counterpart as well as linear and kernel PCA. The leading kernel MAF/MNF variates seem to possess the ability to adapt...

  2. Solution of fractional differential equations by using differential transform method

    Arikoglu, Aytac; Ozkol, Ibrahim

    2007-01-01

    In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply

  3. Solution of fractional differential equations by using differential transform method

    Arikoglu, Aytac [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey); Ozkol, Ibrahim [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey)]. E-mail: ozkol@itu.edu.tr

    2007-12-15

    In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.

  4. Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

    Healy, John J.

    2018-01-01

    The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

  5. Solving fractal steady heat-transfer problems with the local fractional Sumudu transform

    Wang Yi

    2015-01-01

    Full Text Available In this paper the linear oscillator problem in fractal steady heat-transfer is studied within the local fractional theory. In particular, the local fractional Sumudu transform (LFST will be used to solve both the homogeneous and the non-homogeneous local fractional oscillator equations (LFOEs under fractal steady heat-transfer. It will be shown that the obtained non-differentiable solutions characterize the fractal phenomena with and without the driving force in fractal steady heat transfer at low excess temperatures.

  6. Influence of the void fraction in the linear reactivity model

    Castillo, J.A.; Ramirez, J.R.; Alonso, G.

    2003-01-01

    The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)

  7. Dual beam encoded extended fractional Fourier transform security ...

    This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...

  8. Direct Linear Transformation Method for Three-Dimensional Cinematography

    Shapiro, Robert

    1978-01-01

    The ability of Direct Linear Transformation Method for three-dimensional cinematography to locate points in space was shown to meet the accuracy requirements associated with research on human movement. (JD)

  9. Data Transformations for Inference with Linear Regression: Clarifications and Recommendations

    Pek, Jolynn; Wong, Octavia; Wong, C. M.

    2017-01-01

    Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

  10. 2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

    Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.

    2017-05-01

    The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.

  11. Solution of fractional kinetic equation by a class of integral transform of pathway type

    Kumar, Dilip

    2013-04-01

    Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.

  12. Applications of (a,b)-continued fraction transformations

    Katok, Svetlana; Ugarcovici, Ilie

    2011-01-01

    We describe a general method of arithmetic coding of geodesics on the modular surface based on a two parameter family of continued fraction transformations studied previously by the authors. The finite rectangular structure of the attractors of the natural extension maps and the corresponding "reduction theory" play an essential role. In special cases, when an (a,b)-expansion admits a so-called "dual", the coding sequences are obtained by juxtaposition of the boundary expansions of the fixed ...

  13. Paraxial diffractive elements for space-variant linear transforms

    Teiwes, Stephan; Schwarzer, Heiko; Gu, Ben-Yuan

    1998-06-01

    Optical linear transform architectures bear good potential for future developments of very powerful hybrid vision systems and neural network classifiers. The optical modules of such systems could be used as pre-processors to solve complex linear operations at very high speed in order to simplify an electronic data post-processing. However, the applicability of linear optical architectures is strongly connected with the fundamental question of how to implement a specific linear transform by optical means and physical imitations. The large majority of publications on this topic focusses on the optical implementation of space-invariant transforms by the well-known 4f-setup. Only few papers deal with approaches to implement selected space-variant transforms. In this paper, we propose a simple algebraic method to design diffractive elements for an optical architecture in order to realize arbitrary space-variant transforms. The design procedure is based on a digital model of scalar, paraxial wave theory and leads to optimal element transmission functions within the model. Its computational and physical limitations are discussed in terms of complexity measures. Finally, the design procedure is demonstrated by some examples. Firstly, diffractive elements for the realization of different rotation operations are computed and, secondly, a Hough transform element is presented. The correct optical functions of the elements are proved in computer simulation experiments.

  14. Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform

    Devendra Kumar

    2015-01-01

    Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.

  15. Rectification of aerial images using piecewise linear transformation

    Liew, L H; Lee, B Y; Wang, Y C; Cheah, W S

    2014-01-01

    Aerial images are widely used in various activities by providing visual records. This type of remotely sensed image is helpful in generating digital maps, managing ecology, monitoring crop growth and region surveying. Such images could provide insight into areas of interest that have lower altitude, particularly in regions where optical satellite imaging is prevented due to cloudiness. Aerial images captured using a non-metric cameras contain real details of the images as well as unexpected distortions. Distortions would affect the actual length, direction and shape of objects in the images. There are many sources that could cause distortions such as lens, earth curvature, topographic relief and the attitude of the aircraft that is used to carry the camera. These distortions occur differently, collectively and irregularly in the entire image. Image rectification is an essential image pre-processing step to eliminate or at least reduce the effect of distortions. In this paper, a non-parametric approach with piecewise linear transformation is investigated in rectifying distorted aerial images. The non-parametric approach requires a set of corresponding control points obtained from a reference image and a distorted image. The corresponding control points are then applied with piecewise linear transformation as geometric transformation. Piecewise linear transformation divides the image into regions by triangulation. Different linear transformations are employed separately to triangular regions instead of using a single transformation as the rectification model for the entire image. The result of rectification is evaluated using total root mean square error (RMSE). Experiments show that piecewise linear transformation could assist in improving the limitation of using global transformation to rectify images

  16. Results of fractionated stereotactic radiotherapy with linear accelerator

    Aoki, Masahiko; Watanabe, Sadao [Aomori Prefectural Central Hospital (Japan); Mariya, Yasushi [and others

    1997-03-01

    A lot of clinical data about stereotactic radiotherapy (SRT) were reported, however, standard fractionated schedules were not shown. In this paper, our clinical results of SRT, 3 fractions of 10 Gy, are reported. Between February 1992 and March 1995, we treated 41 patients with 7 arteriovenous malformations and 41 intracranial tumors using a stereotactic technique implemented by a standard 10MV X-ray linear accelerator. Average age was 47.4 years (range 3-80 years) and average follow-up time was 16.7 months (range 3.5-46.1 months). The patients received 3 fractions of 10 Gy for 3 days delivered by multiple arc narrow beams under 3 cm in width and length. A three-pieces handmade shell was used for head fixation without any anesthetic procedures. Three-dimensional treatment planning system (Focus) was applied for the dose calculation. All patients have received at least one follow-up radiographic study and one clinical examination. In four of the 7 patients with AVM the nidus has become smaller, 9 of the 21 patients with benign intracranial tumors and 9 of the 13 patients with intracranial malignant tumors have shown complete or partial response to the therapy. In 14 patients, diseases were stable or unevaluable due to the short follow-up time. In 5 patients (3 with astrocytoma, 1 each with meningioma and craniopharyngioma), diseases were progressive. Only 1 patient with falx meningioma had minor complication due to the symptomatic brain edema around the tumor. Although, further evaluation of target control (i.e. tumor and nidus) and late normal tissue damage is needed, preliminary clinical results indicate that SRT with our methods is safe and effective. (author)

  17. Linear transformer driver for pulse generation with fifth harmonic

    Mazarakis, Michael G.; Kim, Alexander A.; Sinebryukhov, Vadim A.; Volkov, Sergey N.; Kondratiev, Sergey S.; Alexeenko, Vitaly M.; Bayol, Frederic; Demol, Gauthier; Stygar, William A.; Leckbee, Joshua; Oliver, Bryan V.; Kiefer, Mark L.

    2017-03-21

    A linear transformer driver includes at least one ferrite ring positioned to accept a load. The linear transformer driver also includes a first, second, and third power delivery module. The first power delivery module sends a first energy in the form of a first pulse to the load. The second power delivery module sends a second energy in the form of a second pulse to the load. The third power delivery module sends a third energy in the form of a third pulse to the load. The linear transformer driver is configured to form a flat-top pulse by the superposition of the first, second, and third pulses. The first, second, and third pulses have different frequencies.

  18. Transformations between inertial and linearly accelerated frames of reference

    Ashworth, D.G.

    1983-01-01

    Transformation equations between inertial and linearly accelerated frames of reference are derived and these transformation equations are shown to be compatible, where applicable, with those of special relativity. The physical nature of an accelerated frame of reference is unambiguously defined by means of an equation which relates the velocity of all points within the accelerated frame of reference to measurements made in an inertial frame of reference. (author)

  19. Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform

    Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid

    2014-01-01

    We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)

  20. LCPT: a program for finding linear canonical transformations

    Char, B.W.; McNamara, B.

    1979-01-01

    This article describes a MACSYMA program to compute symbolically a canonical linear transformation between coordinate systems. The difficulties in implementation of this canonical small physics problem are also discussed, along with the implications that may be drawn from such difficulties about widespread MACSYMA usage by the community of computational/theoretical physicists

  1. Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

    Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.

    1984-09-01

    The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)

  2. Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.

    Ding, Jian-Jiun; Pei, Soo-Chang; Liu, Chun-Lin

    2012-08-01

    The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.

  3. Discrete linear canonical transforms based on dilated Hermite functions.

    Pei, Soo-Chang; Lai, Yun-Chiu

    2011-08-01

    Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time-frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time-frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

  4. Discrete linear canonical transform computation by adaptive method.

    Zhang, Feng; Tao, Ran; Wang, Yue

    2013-07-29

    The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process.

  5. The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

    Narayanamoorthy, S; Kalyani, S

    2015-01-01

    An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  6. The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

    S. Narayanamoorthy

    2015-01-01

    Full Text Available An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  7. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  8. Seismic Linear Noise Attenuation with Use of Radial Transform

    Szymańska-Małysa, Żaneta

    2018-03-01

    One of the goals of seismic data processing is to attenuate the recorded noise in order to enable correct interpretation of the image. Radial transform has been used as a very effective tool in the attenuation of various types of linear noise, both numerical and real (such as ground roll, direct waves, head waves, guided waves etc). The result of transformation from offset - time (X - T) domain into apparent velocity - time (R - T) domain is frequency separation between reflections and linear events. In this article synthetic and real seismic shot gathers were examined. One example was targeted at far offset area of dataset where reflections and noise had similar apparent velocities and frequency bands. Another example was a result of elastic modelling where linear artefacts were produced. Bandpass filtering and scaling operation executed in radial domain attenuated all discussed types of linear noise very effectively. After noise reduction all further processing steps reveal better results, especially velocity analysis, migration and stacking. In all presented cases signal-to-noise ratio was significantly increased and reflections covered previously by noise were revealed. Power spectra of filtered seismic records preserved real dynamics of reflections.

  9. Application of the fractional Fourier transform to image reconstruction in MRI.

    Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

    2012-07-01

    The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

  10. Darboux transformations and linear parabolic partial differential equations

    Arrigo, Daniel J.; Hickling, Fred

    2002-01-01

    Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor

  11. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

    Ravi Kanth, A.S.V.; Aruna, K.

    2009-01-01

    In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

  12. Noiseless Vlasov–Poisson simulations with linearly transformed particles

    Campos Pinto, Martin, E-mail: campos@ann.jussieu.fr [Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris (France); UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris (France); Sonnendrücker, Eric, E-mail: sonnen@math.unistra.fr [IRMA, UMR 7501, Université de Strasbourg and CNRS, 7 rue René Descartes, F-67084 Strasbourg Cedex (France); Project-team CALVI, INRIA Nancy Grand Est, 7 rue René Descartes, F-67084 Strasbourg Cedex (France); Friedman, Alex, E-mail: af@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States); Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Grote, David P., E-mail: grote1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States); Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Lund, Steve M., E-mail: smlund@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States); Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)

    2014-10-15

    We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

  13. Linear transform of the multi-target survival curve

    Watson, J V [Cambridge Univ. (UK). Dept. of Clinical Oncology and Radiotherapeutics

    1978-07-01

    A completely linear transform of the multi-target survival curve is presented. This enables all data, including those on the shoulder region of the curve, to be analysed. The necessity to make a subjective assessment about which data points to exclude for conventional methods of analysis is, therefore, removed. The analysis has also been adapted to include a 'Pike-Alper' method of assessing dose modification factors. For the data cited this predicts compatibility with the hypothesis of a true oxygen 'dose-modification' whereas the conventional Pike-Alper analysis does not.

  14. Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

    Belkhatir, Zehor

    2015-11-05

    This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

  15. A Top-Down Account of Linear Canonical Transforms

    Kurt Bernardo Wolf

    2012-06-01

    Full Text Available We contend that what are called Linear Canonical Transforms (LCTs should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel representation found by Collins, Moshinsky and Quesne, and the radial and hyperbolic LCTs introduced thereafter, belong to the discrete and continuous representation series of the Lorentz group in its parabolic subgroup reduction. The reduction by the elliptic and hyperbolic subgroups can also be considered to yield LCTs that act on functions, discrete or continuous in other Hilbert spaces. We gather the summation and integration kernels reported by Basu and Wolf when studiying all discrete, continuous, and mixed representations of the linear group of 2×2 real matrices. We add some comments on why all should be considered canonical.

  16. Fast and accurate algorithm for the computation of complex linear canonical transforms.

    Koç, Aykut; Ozaktas, Haldun M; Hesselink, Lambertus

    2010-09-01

    A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in approximately N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.

  17. Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

    Wu Guo-Cheng

    2017-01-01

    Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.

  18. Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays

    Tadeusz Kaczorek

    2013-06-01

    Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.

  19. Sumudu transform series expansion method for solving the local fractional Laplace equation in fractal thermal problems

    Guo Zheng-Hong

    2016-01-01

    Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.

  20. Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

    Junesang Choi

    2014-01-01

    Full Text Available A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving the Fp(α,β(·. In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functions Fp(α,β,m(·. Some interesting special cases of our main results are also considered.

  1. Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

    Tunjo Perić

    2017-01-01

    Full Text Available This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1 Taylor’s polynomial linearization approximation, (2 the method of variable change, and (3 a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a using the optimal value of the objective functions as the decision makers’ aspirations, and (b the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.

  2. Integrated reconfigurable photonic filters based on interferometric fractional Hilbert transforms.

    Sima, C; Cai, B; Liu, B; Gao, Y; Yu, Y; Gates, J C; Zervas, M N; Smith, P G R; Liu, D

    2017-10-01

    In this paper, we present integrated reconfigurable photonic filters using fractional Hilbert transformers (FrHTs) and optical phase tuning structure within the silica-on-silicon platform. The proposed structure, including grating-based FrHTs, an X-coupler, and a pair of thermal tuning filaments, is fabricated through the direct UV grating writing technique. The thermal tuning effect is realized by the controllable microheaters located on the two arms of the X-coupler. We investigate the 200 GHz maximum bandwidth photonic FrHTs based on apodized planar Bragg gratings, and analyze the reflection spectrum responses. Through device integration and thermal modulation, the device could operate as photonic notch filters with 5 GHz linewidth and controllable single sideband suppression filters with measured 12 dB suppression ratio. A 50 GHz instantaneous frequency measuring system using this device is also schematically proposed and analyzed with potential 3 dB measurement improvement. The device could be configured with these multiple functions according to need. The reconfigurable structure has great potential in ultrafast all-optical signal processing fields.

  3. On Solution of a Fractional Diffusion Equation by Homotopy Transform Method

    Salah, A.; Hassan, S.S.A.

    2012-01-01

    The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.

  4. Study on linear canonical transformation in a framework of a phase space representation of quantum mechanics

    Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.; Solofoarisina, W.C.

    2015-04-01

    We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.

  5. Predicting birth weight with conditionally linear transformation models.

    Möst, Lisa; Schmid, Matthias; Faschingbauer, Florian; Hothorn, Torsten

    2016-12-01

    Low and high birth weight (BW) are important risk factors for neonatal morbidity and mortality. Gynecologists must therefore accurately predict BW before delivery. Most prediction formulas for BW are based on prenatal ultrasound measurements carried out within one week prior to birth. Although successfully used in clinical practice, these formulas focus on point predictions of BW but do not systematically quantify uncertainty of the predictions, i.e. they result in estimates of the conditional mean of BW but do not deliver prediction intervals. To overcome this problem, we introduce conditionally linear transformation models (CLTMs) to predict BW. Instead of focusing only on the conditional mean, CLTMs model the whole conditional distribution function of BW given prenatal ultrasound parameters. Consequently, the CLTM approach delivers both point predictions of BW and fetus-specific prediction intervals. Prediction intervals constitute an easy-to-interpret measure of prediction accuracy and allow identification of fetuses subject to high prediction uncertainty. Using a data set of 8712 deliveries at the Perinatal Centre at the University Clinic Erlangen (Germany), we analyzed variants of CLTMs and compared them to standard linear regression estimation techniques used in the past and to quantile regression approaches. The best-performing CLTM variant was competitive with quantile regression and linear regression approaches in terms of conditional coverage and average length of the prediction intervals. We propose that CLTMs be used because they are able to account for possible heteroscedasticity, kurtosis, and skewness of the distribution of BWs. © The Author(s) 2014.

  6. Group formalism of Lie transformations to time-fractional partial ...

    Lie symmetry analysis; Fractional partial differential equation; Riemann–Liouville fractional derivative ... science and engineering. It is known that while ... differential equations occurring in different areas of applied science [11,14]. The Lie ...

  7. Linear Transformation of the Polarization Modes in Coiled Optical Spun-Fibers with Strong Unperturbed Linear Birefringence. I. Nonresonant Transformation

    Malykin, G. B.; Pozdnyakova, V. I.

    2018-03-01

    A linear transformation of orthogonal polarization modes in coiled optical spun-fibers with strong unperturbed linear birefringence, which causes the emergence of the dependences of the integrated elliptical birefringence and the ellipticity and azimuth of the major axis of the ellipse, as well as the polarization state of radiation (PSR), on the length of optical fiber has been considered. Optical spun-fibers are subjected to a strong mechanical twisting, which is frozen into the structure of the optical fiber upon cooling, in the process of being drawn out from the workpiece. Since the values of the local polarization parameters of coiled spunwaveguides vary according to a rather complex law, the calculations were carried out by numerical modeling of the parameters of the Jones matrices. Since the rotation speed of the axes of the birefringence is constant on a relatively short segment of a coiled optical spun-fiber in the accompanying torsion (helical) coordinate system, the so-called "Ginzburg helical polarization modes" (GHPMs)—two mutually orthogonal ellipses with the opposite directions of traversal, the axis of which rotate relative to the fixed coordinate system uniformly and unidirectionally—are approximately the local normal polarization modes of such optical fiber. It has been shown that, despite the fact that the unperturbed linear birefringence of the spun-fibers significantly exceeds the linear birefringence, which is caused by the winding on a coil, the integral birefringence of an extended segment of such a fiber coincides in order of magnitude with the linear birefringence, which is caused by the winding on the coil, and the integral polarization modes tend asymptotically to circular ones. It has been also shown that the values of the circular birefringence of twisted single-mode fibers, which were calculated in a nonrotating and torsion helical coordinate systems, differ significantly. It has been shown that the polarization phenomena occur

  8. Fractional hereditariness of lipid membranes: Instabilities and linearized evolution.

    Deseri, L; Pollaci, P; Zingales, M; Dayal, K

    2016-05-01

    In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler-Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving the Euler-Lagrange equation above exhibits time-decay and the large number of spatial oscillation slowly relaxes, thereby keeping the features of a long-tail type time-response. Copyright © 2015 Elsevier Ltd. All rights reserved.

  9. Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β

    Amal Khalaf Haydar

    2016-01-01

    Full Text Available The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<βtransforms for Riemann-Liouville and Caputo fractional derivatives about the general fractional order n-1<βfractional initial value problems (FFIVPs are solved using the above two generalizations.

  10. New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit

    Xu Guanlei

    2009-01-01

    Full Text Available The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT and the traditional Pitt's inequality, one novel Pitt's inequality in the LCT domains is obtained, which is connected with the LCT parameters a and b. Then one novel logarithmic uncertainty principle is derived from this novel Pitt's inequality in the LCT domains, which is associated with parameters of the two LCTs. Secondly, from the relation between the original function and LCT, one entropic uncertainty principle and one Heisenberg's uncertainty principle in the LCT domains are derived, which are associated with the LCT parameters a and b. The reason why the three lower bounds are only associated with LCT parameters a and b and independent of c and d is presented. The results show it is possible that the bounds tend to zeros.

  11. Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators

    Yang Zhao

    2013-01-01

    Full Text Available The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.

  12. Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating

  13. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  14. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    Belkhatir, Zehor

    2017-05-31

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  15. A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

    Tunjo Perić

    2014-12-01

    Full Text Available This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

  16. High-order fractional partial differential equation transform for molecular surface construction.

    Hu, Langhua; Chen, Duan; Wei, Guo-Wei

    2013-01-01

    Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

  17. The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

    Hasan Bulut

    2013-01-01

    Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.

  18. A unified framework for testing in the linear regression model under unknown order of fractional integration

    Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp

    We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...

  19. Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

    Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

    2017-01-01

    In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

  20. A fractional Fourier transform analysis of the scattering of ultrasonic waves

    Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

    2015-01-01

    Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

  1. From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation

    Bastiaans, M.J.; Leest, van A.J.

    1998-01-01

    Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function,

  2. Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

    Bastiaans, M.J.; Leest, van A.J.

    1998-01-01

    Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays

  3. QR code-based non-linear image encryption using Shearlet transform and spiral phase transform

    Kumar, Ravi; Bhaduri, Basanta; Hennelly, Bryan

    2018-02-01

    In this paper, we propose a new quick response (QR) code-based non-linear technique for image encryption using Shearlet transform (ST) and spiral phase transform. The input image is first converted into a QR code and then scrambled using the Arnold transform. The scrambled image is then decomposed into five coefficients using the ST and the first Shearlet coefficient, C1 is interchanged with a security key before performing the inverse ST. The output after inverse ST is then modulated with a random phase mask and further spiral phase transformed to get the final encrypted image. The first coefficient, C1 is used as a private key for decryption. The sensitivity of the security keys is analysed in terms of correlation coefficient and peak signal-to noise ratio. The robustness of the scheme is also checked against various attacks such as noise, occlusion and special attacks. Numerical simulation results are shown in support of the proposed technique and an optoelectronic set-up for encryption is also proposed.

  4. Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord

    Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University

    1993-01-01

    The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab

  5. Linear Transformer Drivers for Z-pinch Based Propulsion

    Adams, Robert; Seidler, William; Giddens, Patrick; Fabisinski, Leo; Cassibry, Jason

    2017-01-01

    The MSFC/UAH team has been developing of a novel power management and distribution system called a Linear Transformer Driver (LTD). LTD's hold the promise of dramatically reducing the required mass to drive a z-pinch by replacing the capacitor banks which constitute half the mass of the entire system. The MSFC?UAH tea, is developing this technology in hope of integrating it with the Pulsed Fission Fusion (PuFF) propulsion concept. High-Voltage pulsed power systems used for Z-Pinch experimentation have in the past largely been based on Marx Generators. Marx generators deliver the voltage and current required for the Z-Pinch, but suffer from two significant drawbacks when applied to a flight system: they are very massive, consisting of high-voltage capacitor banks insulated in oil-filled tanks and they do not lend themselves to rapid pulsing. The overall goal of Phase 2 is to demonstrate the construction of a higher voltage stack from a number of cavities each of the design proven in Phase 1 and to characterize and understand the techniques for designing the stack. The overall goal of Phase 3 is to demonstrate the feasibility of constructing a higher energy cavity from a number of smaller LTD stacks, to characterize and understand the way in which the constituent stacks combine, and to extend this demonstration LTD to serve as the basis for a 64 kJ pulse generator for Z-Pinch experiments.

  6. Development of a hybrid mode linear transformer driver stage

    Zhang, Le; Wang, Meng; Zhou, Liangji; Tian, Qing; Guo, Fan; Wang, Lingyun; Qing, Yanling; Zhao, Yue; Dai, Yingmin; Han, Wenhui; Chen, Lin; Xie, Weiping

    2018-02-01

    At present, the mainstream technologies of primary power sources of large pulse power devices adopt Marx or linear transformer driver (LTD) designs. Based on the analysis of the characteristics of these two types of circuit topologies, the concept of a hybrid mode LTD stage based on Marx branches is proposed. The analysis shows that the hybrid mode LTD stage can realize the following goals: (a) to reduce the energy and power handled by the basic components (switch and capacitor) to lengthen their lifetime; (b) to reduce the requirements of the multipath synchronous trigger system; and (c) to improve the maintainability of the LTD stage by using independent Marx generators instead of "traditional LTD bricks." To verify the technique, a hybrid mode LTD stage consisting of 50 branches (four-stage compact Marx generators) was designed, manufactured and tested. The stage has a radius of about 3.3 m and a height of 0.6 m. The single Marx circuit's load current is about 21 kA, with a rise time of ˜90 ns (10%-90%), under the conditions of capacitors charged to ±40 kV and a 6.9 Ω matched load. The whole stage's load current is ˜1 MA , with a rise time of ˜112 ns (10%-90%), when the capacitors are charged to ±45 kV and the matched load is 0.14 Ω .

  7. Topological transformation of fractional optical vortex beams using computer generated holograms

    Maji, Satyajit; Brundavanam, Maruthi M.

    2018-04-01

    Optical vortex beams with fractional topological charges (TCs) are generated by the diffraction of a Gaussian beam using computer generated holograms embedded with mixed screw-edge dislocations. When the input Gaussian beam has a finite wave-front curvature, the generated fractional vortex beams show distinct topological transformations in comparison to the integer charge optical vortices. The topological transformations at different fractional TCs are investigated through the birth and evolution of the points of phase singularity, the azimuthal momentum transformation, occurrence of critical points in the transverse momentum and the vorticity around the singular points. This study is helpful to achieve better control in optical micro-manipulation applications.

  8. Extreme non-linear elasticity and transformation optics

    Gersborg, Allan Roulund; Sigmund, Ole

    2010-01-01

    realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...

  9. Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

    Darian M. Onchiș

    2011-09-01

    Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

  10. Underprediction of human skin erythema at low doses per fraction by the linear quadratic model

    Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang

    1996-01-01

    Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model

  11. Shear-transformation-zone theory of linear glassy dynamics.

    Bouchbinder, Eran; Langer, J S

    2011-06-01

    We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.

  12. Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

    Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

    2011-01-01

    According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

  13. Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

    Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

    2012-04-20

    It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

  14. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  15. Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces

    Hong Rae Cho

    2017-01-01

    Full Text Available Let s∈R and 2≤p≤∞. We prove that the Segal-Bargmann transform B is a bounded operator from fractional Hermite-Sobolev spaces WHs,pRn to fractional Fock-Sobolev spaces FRs,p.

  16. Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

    Wu Guo-Cheng

    2012-01-01

    Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

  17. On the measurement of Wigner distribution moments in the fractional Fourier transform domain

    Bastiaans, M.J.; Alieva, T.

    2002-01-01

    It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed

  18. Evaluation of uneven fractionation radiotherapy of cervical lymph node-metastases by linear quadratic model

    Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.

    1993-01-01

    One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)

  19. A linear-time algorithm for Euclidean feature transform sets

    Hesselink, Wim H.

    2007-01-01

    The Euclidean distance transform of a binary image is the function that assigns to every pixel the Euclidean distance to the background. The Euclidean feature transform is the function that assigns to every pixel the set of background pixels with this distance. We present an algorithm to compute the

  20. The fractional finite Hankel transform and its applications in fractal space

    Jiang Xiaoyun; Xu Mingyu

    2009-01-01

    In the present work, a generalized finite Hankel transform is derived which is useful in solving equations in fractal dimension d f and involving a fractal diffusion coefficient D 0 r -θ . The corresponding inversion formula is established and some properties are given. Then, the transform is successfully used to solve a class of time-fractional diffusion equations in fractional spatial dimension with an absorbent term and Schroedinger equation in fractional-dimensional space. Green's functions and exact wave function of the above problems are found.

  1. Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

    Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

    2014-01-01

    A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

  2. A uniform law for convergence to the local times of linear fractional stable motions

    Duffy, James A.

    2016-01-01

    We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.

  3. Analysis of separation test for automatic brake adjuster based on linear radon transformation

    Luo, Zai; Jiang, Wensong; Guo, Bin; Fan, Weijun; Lu, Yi

    2015-01-01

    The linear Radon transformation is applied to extract inflection points for online test system under the noise conditions. The linear Radon transformation has a strong ability of anti-noise and anti-interference by fitting the online test curve in several parts, which makes it easy to handle consecutive inflection points. We applied the linear Radon transformation to the separation test system to solve the separating clearance of automatic brake adjuster. The experimental results show that the feature point extraction error of the gradient maximum optimal method is approximately equal to ±0.100, while the feature point extraction error of linear Radon transformation method can reach to ±0.010, which has a lower error than the former one. In addition, the linear Radon transformation is robust.

  4. Uniqueness of non-linear ground states for fractional Laplacians in R

    Frank, Rupert L.; Lenzmann, Enno

    2013-01-01

    We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 fractional Laplacian in one dimension. In particular, we answer affirmatively an open question...... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... + = (−Δ) s +1−(α+1)Q α is non-degenerate; i.e., its kernel satisfies ker L + = span{Q′}. This result about L + proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for non-linear dispersive PDEs with fractional Laplacians, such as the generalized...

  5. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

    Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

  6. Analytical approach to linear fractional partial differential equations arising in fluid mechanics

    Momani, Shaher; Odibat, Zaid

    2006-01-01

    In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

  7. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

    Liu, Da-Yan

    2015-04-30

    This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

  8. A general algorithm for computing distance transforms in linear time

    Meijster, A.; Roerdink, J.B.T.M.; Hesselink, W.H.; Goutsias, J; Vincent, L; Bloomberg, DS

    2000-01-01

    A new general algorithm fur computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the

  9. Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System

    Z.H. Wang

    2011-01-01

    Full Text Available Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots. The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.

  10. Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform

    Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun

    2018-07-01

    Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.

  11. Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory

    Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.

    2017-11-01

    This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.

  12. Real-time implementation of optimized maximum noise fraction transform for feature extraction of hyperspectral images

    Wu, Yuanfeng; Gao, Lianru; Zhang, Bing; Zhao, Haina; Li, Jun

    2014-01-01

    We present a parallel implementation of the optimized maximum noise fraction (G-OMNF) transform algorithm for feature extraction of hyperspectral images on commodity graphics processing units (GPUs). The proposed approach explored the algorithm data-level concurrency and optimized the computing flow. We first defined a three-dimensional grid, in which each thread calculates a sub-block data to easily facilitate the spatial and spectral neighborhood data searches in noise estimation, which is one of the most important steps involved in OMNF. Then, we optimized the processing flow and computed the noise covariance matrix before computing the image covariance matrix to reduce the original hyperspectral image data transmission. These optimization strategies can greatly improve the computing efficiency and can be applied to other feature extraction algorithms. The proposed parallel feature extraction algorithm was implemented on an Nvidia Tesla GPU using the compute unified device architecture and basic linear algebra subroutines library. Through the experiments on several real hyperspectral images, our GPU parallel implementation provides a significant speedup of the algorithm compared with the CPU implementation, especially for highly data parallelizable and arithmetically intensive algorithm parts, such as noise estimation. In order to further evaluate the effectiveness of G-OMNF, we used two different applications: spectral unmixing and classification for evaluation. Considering the sensor scanning rate and the data acquisition time, the proposed parallel implementation met the on-board real-time feature extraction.

  13. Linear Vlasov plasma oscillations in the Fourier transformed velocity space

    Sedláček, Zdeněk; Nocera, L.

    2002-01-01

    Roč. 296, - (2002), s. 117-124 ISSN 0375-9601 Institutional research plan: CEZ:AV0Z2043910 Keywords : linear Vlasov plasma Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.483, year: 2002

  14. The Transformation App Redux: The Notion of Linearity

    Domenick, Anthony

    2015-01-01

    The notion of linearity is perhaps the most fundamental idea in algebraic thinking. It sets the transition to functions and culminates with the instantaneous rate of change in calculus. Despite its simplicity, this concept poses complexities to a considerable number of first semester college algebra students. The purpose of this observational…

  15. Riccati transformations and principal solutions of discrete linear systems

    Ahlbrandt, C.D.; Hooker, J.W.

    1984-01-01

    Consider a second-order linear matrix difference equation. A definition of principal and anti-principal, or recessive and dominant, solutions of the equation are given and the existence of principal and anti-principal solutions and the essential uniqueness of principal solutions is proven

  16. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam.

    Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M

    2005-11-01

    The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.

  17. Numerical inverse Laplace transformation for determining the system response of linear systems in the time domain

    Friedrich, R.; Drewelow, W.

    1978-01-01

    An algorithm is described that is based on the method of breaking the Laplace transform down into partial fractions which are then inverse-transformed separately. The sum of the resulting partial functions is the wanted time function. Any problems caused by equation system forms are largely limited by appropriate normalization using an auxiliary parameter. The practical limits of program application are reached when the degree of the denominator of the Laplace transform is seven to eight.

  18. Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

    Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

    2018-05-01

    In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

  19. Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

    Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

    2009-06-01

    Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

  20. Analysis of blood pressure signal in patients with different ventricular ejection fraction using linear and non-linear methods.

    Arcentales, Andres; Rivera, Patricio; Caminal, Pere; Voss, Andreas; Bayes-Genis, Antonio; Giraldo, Beatriz F

    2016-08-01

    Changes in the left ventricle function produce alternans in the hemodynamic and electric behavior of the cardiovascular system. A total of 49 cardiomyopathy patients have been studied based on the blood pressure signal (BP), and were classified according to the left ventricular ejection fraction (LVEF) in low risk (LR: LVEF>35%, 17 patients) and high risk (HR: LVEF≤35, 32 patients) groups. We propose to characterize these patients using a linear and a nonlinear methods, based on the spectral estimation and the recurrence plot, respectively. From BP signal, we extracted each systolic time interval (STI), upward systolic slope (BPsl), and the difference between systolic and diastolic BP, defined as pulse pressure (PP). After, the best subset of parameters were obtained through the sequential feature selection (SFS) method. According to the results, the best classification was obtained using a combination of linear and nonlinear features from STI and PP parameters. For STI, the best combination was obtained considering the frequency peak and the diagonal structures of RP, with an area under the curve (AUC) of 79%. The same results were obtained when comparing PP values. Consequently, the use of combined linear and nonlinear parameters could improve the risk stratification of cardiomyopathy patients.

  1. The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions

    Reed, I. S.; Scholtz, R. A.; Welch, L. R.; Truong, T. K.

    1978-01-01

    It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.

  2. Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

    Belkhatir, Zehor

    2017-06-28

    This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input’s amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.

  3. SLFP: a stochastic linear fractional programming approach for sustainable waste management.

    Zhu, H; Huang, G H

    2011-12-01

    A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

  4. Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

    Hai Zhang

    2014-01-01

    Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

  5. High-order sliding mode observer for fractional commensurate linear systems with unknown input

    Belkhatir, Zehor

    2017-05-20

    In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

  6. High-order sliding mode observer for fractional commensurate linear systems with unknown input

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

  7. An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

    Meriem Ait Mehdi

    2014-01-01

    Full Text Available We describe an improvement of Chergui and Moulaï’s method (2008 that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

  8. A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD

    HASHEM SABERI NAJAFI

    2016-07-01

    Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.

  9. Solution of linear transport equation using Chebyshev polynomials and Laplace transform

    Cardona, A.V.; Vilhena, M.T.M.B. de

    1994-01-01

    The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)

  10. Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

    Sun Huan

    2016-01-01

    Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

  11. Configurable unitary transformations and linear logic gates using quantum memories.

    Campbell, G T; Pinel, O; Hosseini, M; Ralph, T C; Buchler, B C; Lam, P K

    2014-08-08

    We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favorable scaling with an increasing number of modes where N memories can be configured to implement arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memories are used to implement a conditional cz gate.

  12. Solving polynomial differential equations by transforming them to linear functional-differential equations

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  13. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam

    Nicolas, F.; Coëtmellec, S.; Brunel, M.; Allano, D.; Lebrun, D.; Janssen, A.J.E.M.

    2005-01-01

    The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by

  14. Rotation-type input-output relationships for Wigner distribution moments in fractional Fourier transform systems

    Bastiaans, M.J.; Alieva, T.

    2002-01-01

    It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. This general input-output relationship is then broken down into a

  15. Orthonormal mode sets for the two-dimensional fractional Fourier transformation

    Alieva, T.; Bastiaans, M.J.

    2007-01-01

    A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

  16. Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

    Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

    2010-01-01

    We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

  17. Classification of the linear canonical transformation and its associated real symplectic matrix

    Bastiaans, M.J.; Alieva, T.

    2007-01-01

    Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the

  18. A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

    Mawardi Bahri

    2016-01-01

    Full Text Available We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT. We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.

  19. A Fuzzy Approach Using Generalized Dinkelbach’s Algorithm for Multiobjective Linear Fractional Transportation Problem

    Nurdan Cetin

    2014-01-01

    Full Text Available We consider a multiobjective linear fractional transportation problem (MLFTP with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach.

  20. A non-invasive method for fractionated steriotactic irradiation of brain tumors with linear accelerator

    Hariz, M.I.; Laitinen, L.V.; Henriksson, R.; Saeterborg, N.-E.; Loefroth, P.-O.

    1990-01-01

    A new technique for fractionated stereotactic irradiation of intracranial lesions is described. The treatment is based on a versatile, non-invasive interface for stereotactic localization of the brain target imaged by computed tomography (CT), angiography or magnetic resonance tomography (MRT), and subsequent repetitive stereotactic irradiation of the target using a linear accelerator. The fractionation of the stereotactic irradiation was intended to meet the requirements of the basic principles of radiobiology. The radiophysical evaluation using phantoms, and the clinical results in a small number of patients, demonstrated a good reproducibilit between repeated positionings of the target in the isocenter of the accelerator, and a high degree of accuracy in the treatment of brain lesions. (authors). 28 refs.; 11 figs.; 1 tab

  1. Micromechanics of transformation fields in ageing linear viscoelastic composites: effects of phase dissolution or precipitation

    Honorio, Tulio

    2017-11-01

    Transformation fields, in an affine formulation characterizing mechanical behavior, describe a variety of physical phenomena regardless their origin. Different composites, notably geomaterials, present a viscoelastic behavior, which is, in some cases of industrial interest, ageing, i.e. it evolves independently with respect to time and loading time. Here, a general formulation of the micromechanics of prestressed or prestrained composites in Ageing Linear Viscoelasticity (ALV) is presented. Emphasis is put on the estimation of effective transformation fields in ALV. The result generalizes Ageing Linear Thermo- and Poro-Viscoelasticity and it can be used in approaches coping with a phase transformation. Additionally, the results are extended to the case of locally transforming materials due to non-coupled dissolution and/or precipitation of a given (elastic or viscoelastic) phase. The estimations of locally transforming composites can be made with respect to different morphologies. As an application, estimations of the coefficient of thermal expansion of a hydrating alite paste are presented.

  2. Optical Measurement of Radiocarbon below Unity Fraction Modern by Linear Absorption Spectroscopy.

    Fleisher, Adam J; Long, David A; Liu, Qingnan; Gameson, Lyn; Hodges, Joseph T

    2017-09-21

    High-precision measurements of radiocarbon ( 14 C) near or below a fraction modern 14 C of 1 (F 14 C ≤ 1) are challenging and costly. An accurate, ultrasensitive linear absorption approach to detecting 14 C would provide a simple and robust benchtop alternative to off-site accelerator mass spectrometry facilities. Here we report the quantitative measurement of 14 C in gas-phase samples of CO 2 with F 14 C radiocarbon measurement science including the study of biofuels and bioplastics, illicitly traded specimens, bomb dating, and atmospheric transport.

  3. Novel microwave photonic fractional hilbert transformer using a ring resonator-based optical all-pass filter

    Zhuang, L.; Khan, M.R.H.; Beeker, Willem; Beeker, W.P.; Leinse, Arne; Heideman, Rene; Roeloffzen, C.G.H.

    2012-01-01

    We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonatorbased optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance

  4. Image security based on iterative random phase encoding in expanded fractional Fourier transform domains

    Liu, Zhengjun; Chen, Hang; Blondel, Walter; Shen, Zhenmin; Liu, Shutian

    2018-06-01

    A novel image encryption method is proposed by using the expanded fractional Fourier transform, which is implemented with a pair of lenses. Here the centers of two lenses are separated at the cross section of axis in optical system. The encryption system is addressed with Fresnel diffraction and phase modulation for the calculation of information transmission. The iterative process with the transform unit is utilized for hiding secret image. The structure parameters of a battery of lenses can be used for additional keys. The performance of encryption method is analyzed theoretically and digitally. The results show that the security of this algorithm is enhanced markedly by the added keys.

  5. Scatter fractions from linear accelerators with x-ray energies from 6 to 24 MV.

    Taylor, P L; Rodgers, J E; Shobe, J

    1999-08-01

    Computation of shielding requirements for a linear accelerator must take into account the amount of radiation scattered from the patient to areas outside the primary beam. Currently, the most frequently used data are from NCRP 49 that only includes data for x-ray energies up to 6 MV and angles from 30 degrees to 135 degrees. In this work we have determined by Monte Carlo simulation the scattered fractions of dose for a wide range of energies and angles of clinical significance including 6, 10, 18, and 24 MV and scattering angles from 10 degrees to 150 degrees. Calculations were made for a 400 cm2 circular field size impinging onto a spherical phantom. Scattered fractions of dose were determined at 1 m from the phantom. Angles from 10 degrees to 30 degrees are of concern for higher energies where the scatter is primarily in the forward direction. An error in scatter fraction may result in too little secondary shielding near the junction with the primary barrier. The Monte Carlo code ITS (Version 3.0) developed at Sandia National Laboratory and NIST was used to simulate scatter from the patient to the barrier. Of significance was the variation of calculated scattered dose with depth of measurement within the barrier indicating that accurate values may be difficult to obtain. Mean energies of scatter x-ray spectra are presented.

  6. Visual Outcome in Meningiomas Around Anterior Visual Pathways Treated With Linear Accelerator Fractionated Stereotactic Radiotherapy

    Stiebel-Kalish, Hadas; Reich, Ehud; Gal, Lior; Rappaport, Zvi Harry; Nissim, Ouzi; Pfeffer, Raphael; Spiegelmann, Roberto

    2012-01-01

    Purpose: Meningiomas threatening the anterior visual pathways (AVPs) and not amenable for surgery are currently treated with multisession stereotactic radiotherapy. Stereotactic radiotherapy is available with a number of devices. The most ubiquitous include the gamma knife, CyberKnife, tomotherapy, and isocentric linear accelerator systems. The purpose of our study was to describe a case series of AVP meningiomas treated with linear accelerator fractionated stereotactic radiotherapy (FSRT) using the multiple, noncoplanar, dynamic conformal rotation paradigm and to compare the success and complication rates with those reported for other techniques. Patients and Methods: We included all patients with AVP meningiomas followed up at our neuro-ophthalmology unit for a minimum of 12 months after FSRT. We compared the details of the neuro-ophthalmologic examinations and tumor size before and after FSRT and at the end of follow-up. Results: Of 87 patients with AVP meningiomas, 17 had been referred for FSRT. Of the 17 patients, 16 completed >12 months of follow-up (mean 39). Of the 16 patients, 11 had undergone surgery before FSRT and 5 had undergone FSRT as first-line management. Tumor control was achieved in 14 of the 16 patients, with three meningiomas shrinking in size after RT. Two meningiomas progressed, one in an area that was outside the radiation field. The visual function had improved in 6 or stabilized in 8 of the 16 patients (88%) and worsened in 2 (12%). Conclusions: Linear accelerator fractionated RT using the multiple noncoplanar dynamic rotation conformal paradigm can be offered to patients with meningiomas that threaten the anterior visual pathways as an adjunct to surgery or as first-line treatment, with results comparable to those reported for other stereotactic RT techniques.

  7. Bianchi-Baecklund transformations, conservation laws, and linearization of various field theories

    Chau Wang, L.L.

    1980-01-01

    The discussion includes: the Sine-Gordon equation, parametric Bianchi-Baecklund transformations and the derivation of local conservation laws; chiral fields, parametric Bianchi-Baecklund transformations, local and non-local conservation laws, and linearization; super chiral fields, a parallel development similar to the chiral field; and self-dual Yang-Mills fields in 4-dimensional Euclidean space; loop-cpace chiral equations, parallel development but with subtlety

  8. The Fractional Fourier Transform and Its Application to Energy Localization Problems

    ter Morsche Hennie G

    2003-01-01

    Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

  9. Controlling the wave propagation through the medium designed by linear coordinate transformation

    Wu, Yicheng; He, Chengdong; Wang, Yuzhuo; Liu, Xuan; Zhou, Jing

    2015-01-01

    Based on the principle of transformation optics, we propose to control the wave propagating direction through the homogenous anisotropic medium designed by linear coordinate transformation. The material parameters of the medium are derived from the linear coordinate transformation applied. Keeping the space area unchanged during the linear transformation, the polarization-dependent wave control through a non-magnetic homogeneous medium can be realized. Beam benders, polarization splitter, and object illusion devices are designed, which have application prospects in micro-optics and nano-optics. The simulation results demonstrate the feasibilities and the flexibilities of the method and the properties of these devices. Design details and full-wave simulation results are provided. The work in this paper comprehensively applies the fundamental theories of electromagnetism and mathematics. The method of obtaining a new solution of the Maxwell equations in a medium from a vacuum plane wave solution and a linear coordinate transformation is introduced. These have a pedagogical value and are methodologically and motivationally appropriate for physics students and teachers at the undergraduate and graduate levels. (paper)

  10. Controlling the wave propagation through the medium designed by linear coordinate transformation

    Wu, Yicheng; He, Chengdong; Wang, Yuzhuo; Liu, Xuan; Zhou, Jing

    2015-01-01

    Based on the principle of transformation optics, we propose to control the wave propagating direction through the homogenous anisotropic medium designed by linear coordinate transformation. The material parameters of the medium are derived from the linear coordinate transformation applied. Keeping the space area unchanged during the linear transformation, the polarization-dependent wave control through a non-magnetic homogeneous medium can be realized. Beam benders, polarization splitter, and object illusion devices are designed, which have application prospects in micro-optics and nano-optics. The simulation results demonstrate the feasibilities and the flexibilities of the method and the properties of these devices. Design details and full-wave simulation results are provided. The work in this paper comprehensively applies the fundamental theories of electromagnetism and mathematics. The method of obtaining a new solution of the Maxwell equations in a medium from a vacuum plane wave solution and a linear coordinate transformation is introduced. These have a pedagogical value and are methodologically and motivationally appropriate for physics students and teachers at the undergraduate and graduate levels.

  11. Linear variable differential transformer sensor using glass-covered amorphous wires as active core

    Chiriac, H.; Hristoforou, E.; Neagu, Maria; Pieptanariu, M.

    2000-01-01

    Results concerning linear variable differential transformer (LVDT) displacement sensor using as movable core glass-covered amorphous wires are presented. The LVDT response is linear for a displacement of the movable core up to about 14 mm, with an accuracy of 1 μm. LVDT using glass-covered amorphous wire as an active core presents a high sensitivity and good mechanical and corrosion resistance

  12. Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

    Goodman, Roe W

    2016-01-01

    This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

  13. Warped linear mixed models for the genetic analysis of transformed phenotypes.

    Fusi, Nicolo; Lippert, Christoph; Lawrence, Neil D; Stegle, Oliver

    2014-09-19

    Linear mixed models (LMMs) are a powerful and established tool for studying genotype-phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction.

  14. Application of Fractional Fourier Transform to Moving Target Indication via Along-Track Interferometry

    Chiu Shen

    2005-01-01

    Full Text Available A relatively unknown yet powerful technique, the so-called fractional Fourier transform (FrFT, is applied to SAR along-track interferometry (SAR-ATI in order to estimate moving target parameters. By mapping a target's signal onto a fractional Fourier axis, the FrFT permits a constant-velocity target to be focused in the fractional Fourier domain thereby affording orders of magnitude improvement in SCR. Moving target velocity and position parameters are derived and expressed in terms of an optimum fractional angle and a measured fractional Fourier position , allowing a target to be accurately repositioned and its velocity components computed without actually forming an SAR image. The new estimation algorithm is compared with the matched filter bank approach, showing some of the advantages of the FrFT method. The proposed technique is applied to the data acquired by the two-aperture CV580 airborne radar system configured in its along-track mode. Results show that the method is effective in estimating target velocity and position parameters.

  15. Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

    Hua Wang

    2017-01-01

    Full Text Available Abstract In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators I α $I_{\\alpha}$ in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [ b , I α ] $[b,I_{\\alpha}]$ formed by b and I α $I_{\\alpha}$ are established. Also we study related problems about two-weight, weak type inequalities for I α $I_{\\alpha}$ and [ b , I α ] $[b,I_{\\alpha}]$ in the Morrey-type spaces and give partial results.

  16. Measuring the Higgs branching fraction into two photons at future linear e+e- colliders

    Boos, E.; Schreiber, H.J.; Shanidze, R.

    2001-01-01

    We examine the prospects for a measurement of the branching fraction of the γγ decay mode of a Standard Model-like Higgs boson with a mass of 120 GeV/c 2 at the future TESLA linear e + e - collider, assuming an integrated luminosity of 1 ab -1 and centre-of-mass energies of 350 GeV and 500 GeV. A relative uncertainty on BF(H→γγ) of 16% can be achieved in unpolarised e + e - collisions at √(s) = 500 GeV, while for √(s) = 350 GeV the expected precision is slightly poorer. With appropriate initial state polarisations the uncertainty can be improved to 10%. If this measurement is combined with a measurement of the total Higgs width, a precision of 10% on the Higgs boson partial width for the γγ decay mode appears feasible. (orig.)

  17. Application of the method of continued fractions for electron scattering by linear molecules

    Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF

    1995-01-01

    The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)

  18. Solving a class of generalized fractional programming problems using the feasibility of linear programs.

    Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

    2017-01-01

    This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

  19. Scattered fractions of dose from 18 and 25 MV X-ray radiotherapy linear accelerators

    Shobe, J.; Rodgers, J.E.; Taylor, P.L.; Jackson, J.; Popescu, G.

    1996-01-01

    Over the years, measurements have been made at a few energies to estimate the scattered fraction of dose from the patient in medical radiotherapy operations. This information has been a useful aid in the determination of shielding requirements for these facilities. With these measurements, known characteriztics of photons, and various other known parameters, Monte Carlo codes are being used to calculate the scattered fractions and hence the shielding requirements for the photons of other energies commonly used in radiotherapeutic applications. The National Institute of Standards and Technology (NIST) acquired a Sagittaire medical linear accelerator (linac) which was previously located at the Yale-New Haven Hospital. This linac provides an X-ray beam of 25 MV photons and electron beams with energies up to 32 MeV. The housing on the gantry was permanently removed from the accelerator during installation. A Varian Clinac 1800 linear accelerator was used to produce the 18 MV photons at the Frederick Memorial Hospital Regional Cancer Therapy Center in Frederick, MD. This paper represents a study of the photon dose scattered from a patient in typical radiation treatment situations as it relates to the dose delivered at the isocenter in water. The results of these measurements will be compared to Monte Carlo calculations. Photon spectral measurements were not made at this time. Neutron spectral measurements were made on this Sagittaire machine in its previous location and that work was not repeated here, although a brief study of the neutron component of the 18 and 25 MV linacs was performed utilizing thermoluminescent dosimetry (TLD) to determine the isotropy of the neutron dose. (author)

  20. Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

    Merrikh-Bayat, Farshad

    2011-04-01

    One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

  1. Transforming an Introductory Linear Algebra Course with a TI-92 Hand-Held Computer.

    Quesada, Antonio R.

    2003-01-01

    Describes how the introduction of the TI-92 transformed a traditional first semester linear algebra course into a matrix-oriented course that emphasized conceptual understanding, relevant applications, and numerical issues. Indicates an increase in students' overall performance as they found the calculator very useful, believed it helped them…

  2. Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

    Liang, Yingjie; Chen, Wen; Magin, Richard L.

    2016-07-01

    Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

  3. A non-linear discrete transform for pattern recognition of discrete chaotic systems

    Karanikas, C.; Proios, G.

    2003-01-01

    It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter

  4. A non-linear discrete transform for pattern recognition of discrete chaotic systems

    Karanikas, C

    2003-01-01

    It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.

  5. Non-linear gauge transformations in D=10 SYM theory and the BCJ duality

    Lee, Seungjin [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany); Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany)

    2016-03-14

    Recent progress on scattering amplitudes in super Yang-Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.

  6. New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

    Belkic, D.

    1989-01-01

    The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

  7. Study on sampling of continuous linear system based on generalized Fourier transform

    Li, Huiguang

    2003-09-01

    In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

  8. Design of fractional order differentiator using type-III and type-IV discrete cosine transform

    Manjeet Kumar

    2017-02-01

    Full Text Available In this paper, an interpolation method based on discrete cosine transform (DCT is employed for digital finite impulse response-fractional order differentiator (FIR-FOD design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.

  9. Tracking transformation processes of organic micropollutants in aquatic environments using multi-element isotope fractionation analysis

    Hofstetter, Thomas B.; Bolotin, Jakov; Skarpeli-Liati, Marita; Wijker, Reto; Kurt, Zohre; Nishino, Shirley F.; Spain, Jim C.

    2011-01-01

    The quantitative description of enzymatic or abiotic transformations of man-made organic micropollutants in rivers, lakes, and groundwaters is one of the major challenges associated with the risk assessment of water resource contamination. Compound-specific isotope analysis enables one to identify (bio)degradation pathways based on changes in the contaminants' stable isotope ratios even if multiple reactive and non-reactive processes cause concentrations to decrease. Here, we investigated how the magnitude and variability of isotope fractionation in some priority pollutants is determined by the kinetics and mechanisms of important enzymatic and abiotic redox reactions. For nitroaromatic compounds and substituted anilines, we illustrate that competing transformation pathways can be assessed via trends of N and C isotope signatures.

  10. The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

    Pedersen, Anders Filsøe; Simons, Hugh; Detlefs, Carsten

    2018-01-01

    The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing...... the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown...

  11. Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.

    Mendlovic, D; Ozaktas, H M; Lohmann, A W

    1994-09-10

    Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.

  12. Linear-algebraic bath transformation for simulating complex open quantum systems

    Huh, Joonsuk; Mostame, Sarah; Fujita, Takatoshi; Aspuru-Guzik, Alán; Yung, Man-Hong

    2014-01-01

    In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. The transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics. (paper)

  13. Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

    Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

    2015-03-01

    Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

  14. System of coefficients for charged-particle beam linear transformation by a magnetic dipole element

    Tarantin, N.I.

    1979-01-01

    A new technique for consideration of dipole magnet ion-optical effect has been developed to study the problems of commutation and monochromatization of a charged particle beam. In a new form obtained are systematized coefficients of linear transformation (CLT) of the charged particle beam for radial and axial motions in a magnetic dipole element (MDE) including a dipole magnet and two gaps without magnetic field. Given is a method of graphic determination of MDE parameters and main CLT. The new form of coefficients and conditions of the transformations feasibility considerably facilitates the choice and calculation of dipole elements

  15. Shaping the output pulse of a linear-transformer-driver module

    Long, Finis W.; McKee, G. Randall; Stoltzfus, Brian Scott; Woodworth, Joseph Ray; McKenney, John Lee; Fowler, William E.; Mazarakis, Michael Gerrassimos; Porter, John L.; Stygar, William A.; Savage, Mark Edward; LeChien, Keith R.; Van De Valde, David M.

    2008-01-01

    We demonstrate that a wide variety of current-pulse shapes can be generated using a linear-transformer-driver (LTD) module that drives an internal water-insulated transmission line. The shapes are produced by varying the timing and initial charge voltage of each of the module's cavities. The LTD-driven accelerator architecture outlined in (Phys. Rev. ST Accel. Beams 10, 030401 (2007)) provides additional pulse-shaping flexibility by allowing the modules that drive the accelerator to be triggered at different times. The module output pulses would be combined and symmetrized by water-insulated radial-transmission-line impedance transformers (Phys. Rev. ST Accel. Beams 11, 030401 (2008))

  16. Teaching stable two-mirror resonators through the fractional Fourier transform

    Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

    2010-01-01

    We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.

  17. Transformation method for the MIRD absorbed fractions as applied to various physiques

    Yamaguchi, Hiroshi

    1978-01-01

    This study concerns with the transformation method of the MIRD absorbed fraction (AF) to the AF corresponding to an individual having the dimensions different from those of the MIRD standard man. The absorbed dose of a target organ T from a source organs S, received by the administration of a radiopharmaceutical agent is expressed with the equilibrium absorbed dose constant, the cumulative activity in the S, and the specific absorbed fraction (SAF). It is dealt only with how the MIRD SAF data can be modified for estimating individual SAF values. The SAF for individuals is given for penetrating and non-penetrating radiations. In case of the penetrating radiation, the SAF is given from the corresponding MIRD SAF by using a transformation coefficient for the MIRD SAF, when the MIRD standard man is transfigured to a corresponding phantom of an individual by the scale factors selected separately for the head section, trunk section and leg section of the MIRD standard man. The obtained results were compared with the ORNL results, and showed good agreement. (Kato, T.)

  18. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  19. Optimal Operation of Distribution Electronic Power Transformer Using Linear Quadratic Regulator Method

    Mohammad Hosein Rezaei

    2011-10-01

    Full Text Available Transformers perform many functions such as voltage transformation, isolation and noise decoupling. They are indispensable components in electric power distribution system. However, at low frequencies (50 Hz, they are one of the heaviest and the most expensive equipment in an electrical distribution system. Nowadays, electronic power transformers are used instead of conventional power transformers that do voltage transformation and power delivery in power system by power electronic converter. In this paper, the structure of distribution electronic power transformer (DEPT are analized and then paid attention on the design of a linear-quadratic-regulator (LQR with integral action to improve dynamic performance of DEPT with voltage unbalance, voltage sags, voltage harmonics and voltage flicker. The presentation control strategy is simulated by MATLAB/SIMULINK. In addition, the results that are in terms of dc-link reference voltage, input and output voltages clearly show that a better dynamic performance can be achieved by using the LQR method when compared to other techniques.

  20. The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day

    Dale, R.G.

    1986-01-01

    By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)

  1. The linear transformation model with frailties for the analysis of item response times.

    Wang, Chun; Chang, Hua-Hua; Douglas, Jeffrey A

    2013-02-01

    The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi-parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non-parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non-parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees' latent speeds; whereas the non-parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box-Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two-stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non-parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested. © 2012 The British Psychological Society.

  2. Numerical analysis of non-linear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance

    Rossikhin Yury A.

    2018-01-01

    Full Text Available Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance, resulting in modal interaction, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential equations of the second order are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the combinational internal resonance. A good agreement in results is declared.

  3. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-08-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  4. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-01-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  5. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong; Jia, Wantao [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)

    2016-08-15

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  6. Quantum Optical Realization of Arbitrary Linear Transformations Allowing for Loss and Gain

    Tischler, N.; Rockstuhl, C.; Słowik, K.

    2018-04-01

    Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations, which can involve loss and gain, require a different approach. In this work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks, it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al. [Experimental Realization of Any Discrete Unitary Operator, Phys. Rev. Lett. 73, 58 (1994), 10.1103/PhysRevLett.73.58] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols.

  7. Optimizing BAO measurements with non-linear transformations of the Lyman-α forest

    Wang, Xinkang; Font-Ribera, Andreu; Seljak, Uroš, E-mail: xinkang.wang@berkeley.edu, E-mail: afont@lbl.gov, E-mail: useljak@berkeley.edu [Department of Physics, University of California, South Hall Rd, Berkeley (United States)

    2015-04-01

    We explore the effect of applying a non-linear transformation to the Lyman-α forest transmitted flux F=e{sup −τ} and the ability of analytic models to predict the resulting clustering amplitude. Both the large-scale bias of the transformed field (signal) and the amplitude of small scale fluctuations (noise) can be arbitrarily modified, but we were unable to find a transformation that increases significantly the signal-to-noise ratio on large scales using Taylor expansion up to the third order. In particular, however, we achieve a 33% improvement in signal to noise for Gaussianized field in transverse direction. On the other hand, we explore an analytic model for the large-scale biasing of the Lyα forest, and present an extension of this model to describe the biasing of the transformed fields. Using hydrodynamic simulations we show that the model works best to describe the biasing with respect to velocity gradients, but is less successful in predicting the biasing with respect to large-scale density fluctuations, especially for very nonlinear transformations.

  8. Detection of Left-Sided and Right-Sided Hearing Loss via Fractional Fourier Transform

    Shuihua Wang

    2016-05-01

    Full Text Available In order to detect hearing loss more efficiently and accurately, this study proposed a new method based on fractional Fourier transform (FRFT. Three-dimensional volumetric magnetic resonance images were obtained from 15 patients with left-sided hearing loss (LHL, 20 healthy controls (HC, and 14 patients with right-sided hearing loss (RHL. Twenty-five FRFT spectrums were reduced by principal component analysis with thresholds of 90%, 95%, and 98%, respectively. The classifier is the single-hidden-layer feed-forward neural network (SFN trained by the Levenberg–Marquardt algorithm. The results showed that the accuracies of all three classes are higher than 95%. In all, our method is promising and may raise interest from other researchers.

  9. Emotion recognition based on multiple order features using fractional Fourier transform

    Ren, Bo; Liu, Deyin; Qi, Lin

    2017-07-01

    In order to deal with the insufficiency of recently algorithms based on Two Dimensions Fractional Fourier Transform (2D-FrFT), this paper proposes a multiple order features based method for emotion recognition. Most existing methods utilize the feature of single order or a couple of orders of 2D-FrFT. However, different orders of 2D-FrFT have different contributions on the feature extraction of emotion recognition. Combination of these features can enhance the performance of an emotion recognition system. The proposed approach obtains numerous features that extracted in different orders of 2D-FrFT in the directions of x-axis and y-axis, and uses the statistical magnitudes as the final feature vectors for recognition. The Support Vector Machine (SVM) is utilized for the classification and RML Emotion database and Cohn-Kanade (CK) database are used for the experiment. The experimental results demonstrate the effectiveness of the proposed method.

  10. Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-08-01

    Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

  11. Blind third-order dispersion estimation based on fractional Fourier transformation for coherent optical communication

    Yang, Lin; Guo, Peng; Yang, Aiying; Qiao, Yaojun

    2018-02-01

    In this paper, we propose a blind third-order dispersion estimation method based on fractional Fourier transformation (FrFT) in optical fiber communication system. By measuring the chromatic dispersion (CD) at different wavelengths, this method can estimation dispersion slope and further calculate the third-order dispersion. The simulation results demonstrate that the estimation error is less than 2 % in 28GBaud dual polarization quadrature phase-shift keying (DP-QPSK) and 28GBaud dual polarization 16 quadrature amplitude modulation (DP-16QAM) system. Through simulations, the proposed third-order dispersion estimation method is shown to be robust against nonlinear and amplified spontaneous emission (ASE) noise. In addition, to reduce the computational complexity, searching step with coarse and fine granularity is chosen to search optimal order of FrFT. The third-order dispersion estimation method based on FrFT can be used to monitor the third-order dispersion in optical fiber system.

  12. Propagation of a general-type beam through a truncated fractional Fourier transform optical system.

    Zhao, Chengliang; Cai, Yangjian

    2010-03-01

    Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

  13. Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

    Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

    2018-04-01

    We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

  14. On matrix fractional differential equations

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  15. Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

    Zhao, Liang; Healy, John J.; Muniraj, Inbarasan; Cui, Xiao-Guang; Malallah, Ra'ed; Ryle, James P.; Sheridan, John T.

    2017-05-01

    The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

  16. Fractionation schedule affects transforming growth factor β expression in chronic radiation enteropathy

    Hauer-Jensen, Martin; Richter, Konrad K.; Sung, C.-C.; Langberg, Carl W.

    1995-01-01

    Purpose/Objective: The risk of intestinal obstruction from fibrotic strictures is a major dose limiting factor in abdominal radiation therapy. We have shown that chronic intestinal radiation injury (radiation enteropathy) is associated with sustained over-expression of the fibrogenic cytokine, transforming growth factor beta (TGF-β). This study used quantitative computerized image analysis to examine the relationship between TGF-β expression and specific histopathologic alterations as a function of fractionation schedule. Materials and Methods: Localized fractionated small bowel irradiation was performed in a rat model developed in our laboratory: 49 male rats were orchiectomized and a loop of small bowel was sutured to the inside of the scrotum. After 3 weeks recovery, the intestine within the artificial 'scrotal hernia' was sham-irradiated (Controls) or exposed to a total dose of 50.4 Gy orthovoltage radiation, given either as 18 daily fractions of 2.8 Gy (Group I) or as 9 daily fractions of 5.6 Gy (Group II). Groups of animals were euthanized at 2 weeks (early injury) and 26 weeks (chronic injury). Specimens were prepared for immunohistochemistry and histopathology. Extracellular TGF-β was detected with a polyclonal antibody, and protein expression was quantified by computerized image analysis. Twenty separate 40X fields per specimen were digitized, and the average number of stained pixels relative to total pixels was determined. Histopathologic injury was assessed in H+E sections with a previously validated Radiation Injury Score (RIS). Results: Irradiated animals had significantly higher levels of extracellular TGF-β immunoreactivity at both 2 weeks and 26 weeks (p<0.01). TGF-β expression correlated with RIS at both time points (p<0.001). Group II had significantly greater RIS and TGF-β expression than group I (p<0.01). TGF-β expression at 2 weeks correlated with epithelial atypia, mucosal ulceration, and subserosal thickening (p<0.01). At 26 weeks, TGF

  17. Standardizing effect size from linear regression models with log-transformed variables for meta-analysis.

    Rodríguez-Barranco, Miguel; Tobías, Aurelio; Redondo, Daniel; Molina-Portillo, Elena; Sánchez, María José

    2017-03-17

    Meta-analysis is very useful to summarize the effect of a treatment or a risk factor for a given disease. Often studies report results based on log-transformed variables in order to achieve the principal assumptions of a linear regression model. If this is the case for some, but not all studies, the effects need to be homogenized. We derived a set of formulae to transform absolute changes into relative ones, and vice versa, to allow including all results in a meta-analysis. We applied our procedure to all possible combinations of log-transformed independent or dependent variables. We also evaluated it in a simulation based on two variables either normally or asymmetrically distributed. In all the scenarios, and based on different change criteria, the effect size estimated by the derived set of formulae was equivalent to the real effect size. To avoid biased estimates of the effect, this procedure should be used with caution in the case of independent variables with asymmetric distributions that significantly differ from the normal distribution. We illustrate an application of this procedure by an application to a meta-analysis on the potential effects on neurodevelopment in children exposed to arsenic and manganese. The procedure proposed has been shown to be valid and capable of expressing the effect size of a linear regression model based on different change criteria in the variables. Homogenizing the results from different studies beforehand allows them to be combined in a meta-analysis, independently of whether the transformations had been performed on the dependent and/or independent variables.

  18. Definition of path integrals and rules for non-linear transformations

    Kerler, W.

    1978-01-01

    Functional integrals are defined as the limit of multidimensional integrals based on fundamental generating distributions. The 'lattice choice' is put into a suitable functional form. The independence of the particular choice and the necessity of this fact are shown. Various forms of the path integrals are derived and discussed. The relation to the traditional ordering problem is pointed out. The mechanism of non-linear transformations of variables is investigated and rules are given. In the case of fields it turns out that the path integrals can also be considered for space translations. (Auth.)

  19. Computation of the Short-Time Linear Canonical Transform with Dual Window

    Lei Huang

    2017-01-01

    Full Text Available The short-time linear canonical transform (STLCT, which maps the time domain signal into the joint time and frequency domain, has recently attracted some attention in the area of signal processing. However, its applications are still limited due to the fact that selection of coefficients of the short-time linear canonical series (STLCS is not unique, because time and frequency elementary functions (together known as basis function of STLCS do not constitute an orthogonal basis. To solve this problem, this paper investigates a dual window solution. First, the nonorthogonal problem that suffered from original window is fulfilled by orthogonal condition with dual window. Then based on the obtained condition, a dual window computation approach of the GT is extended to the STLCS. In addition, simulations verify the validity of the proposed condition and solutions. Furthermore, some possible applied directions are discussed.

  20. Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

    Pipkins, Daniel Scott

    Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. linear model are compared to those

  1. A Novel Fractional Fourier Transform-Based ASK-OFDM System for Underwater Acoustic Communications

    Rami Ashri

    2017-12-01

    Full Text Available A key research area in wireless transmission is underwater communications. It has a vital role in applications such as underwater sensor networks (UWSNs and disaster detection. The underwater channel is very unique as compared to other alternatives of transmission channels. It is characterized by path loss, multipath fading, Doppler spread and ambient noise. Thus, the bit error rate (BER is increased to a large extent when compared to its counterpart of cellular communications. Acoustic signals are the current best solution for underwater communications. The use of electromagnetic or optical waves obviously entails a much higher data rate. However, they suffer from high attenuation, absorption or scattering. This paper proposes a novel fractional fast Fourier transform (FrFT—orthogonal frequency division multiplexing (FrFT-OFDM system for underwater acoustic (UWA communication—which employs the amplitude shift keying (ASK modulation technique (FrFT-ASK-OFDM. Specifically, ASK achieves a better bandwidth efficiency as compared to other commonly used modulation techniques, such as quadrature amplitude modulation (QAM and phase shift keying (PSK. In particular, the system proposed in this article can achieve a very promising BER performance, and can reach higher data rates when compared to other systems proposed in the literature. The BER performance of the proposed system is evaluated numerically, and is compared to the corresponding M-ary QAM system in the UWA channel for the same channel conditions. Moreover, the performance of the proposed system is compared to the conventional fast Fourier transform (FFT-OFDM (FFT-OFDM system in the absence and presence of the effect of carrier frequency offset (CFO. Numerical results show that the proposed system outperforms the conventional FFT-based systems for UWA channels, even in channels dominated by CFO. Moreover, the spectral efficiency and data rate of the proposed system are approximately double

  2. Linear models for assessing mechanisms of sperm competition: the trouble with transformations.

    Eggert, Anne-Katrin; Reinhardt, Klaus; Sakaluk, Scott K

    2003-01-01

    Although sperm competition is a pervasive selective force shaping the reproductive tactics of males, the mechanisms underlying different patterns of sperm precedence remain obscure. Parker et al. (1990) developed a series of linear models designed to identify two of the more basic mechanisms: sperm lotteries and sperm displacement; the models can be tested experimentally by manipulating the relative numbers of sperm transferred by rival males and determining the paternity of offspring. Here we show that tests of the model derived for sperm lotteries can result in misleading inferences about the underlying mechanism of sperm precedence because the required inverse transformations may lead to a violation of fundamental assumptions of linear regression. We show that this problem can be remedied by reformulating the model using the actual numbers of offspring sired by each male, and log-transforming both sides of the resultant equation. Reassessment of data from a previous study (Sakaluk and Eggert 1996) using the corrected version of the model revealed that we should not have excluded a simple sperm lottery as a possible mechanism of sperm competition in decorated crickets, Gryllodes sigillatus.

  3. INTELLIGENT FRACTIONAL ORDER ITERATIVE LEARNING CONTROL USING FEEDBACK LINEARIZATION FOR A SINGLE-LINK ROBOT

    Iman Ghasemi

    2017-05-01

    Full Text Available In this paper, iterative learning control (ILC is combined with an optimal fractional order derivative (BBO-Da-type ILC and optimal fractional and proportional-derivative (BBO-PDa-type ILC. In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where  to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both  and  learning law i.e. proportional , derivative  and  are optimized using Biogeography-Based optimization algorithm (BBO. Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC

  4. Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

    Fu, Wei; Nijhoff, Frank W

    2017-07-01

    A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

  5. Analytical solutions of linear diffusion and wave equations in semi-infinite domains by using a new integral transform

    Gao Lin

    2017-01-01

    Full Text Available Recently, a new integral transform similar to Sumudu transform has been proposed by Yang [1]. Some of the properties of the integral transform are expanded in the present article. Meanwhile, new applications to the linear wave and diffusion equations in semi-infinite domains are discussed in detail. The proposed method provides an alternative approach to solve the partial differential equations in mathematical physics.

  6. Modular transformations and invariants in the context of fractional level sl-circumflex(2 vertical bar 1;C)

    Johnstone, Gavin

    2000-01-01

    The modular transformation properties of admissible characters of the affine superalgebra sl-circumflex(2 vertical bar 1;C) at fractional level k=1/u-1, u is a subset of N/1 are presented. All modular invariants for u=2 and u=3 are calculated explicitly and an A-series and D-series of modular invariants emerge

  7. Imaging ultrasonic dispersive guided wave energy in long bones using linear radon transform.

    Tran, Tho N H T; Nguyen, Kim-Cuong T; Sacchi, Mauricio D; Le, Lawrence H

    2014-11-01

    Multichannel analysis of dispersive ultrasonic energy requires a reliable mapping of the data from the time-distance (t-x) domain to the frequency-wavenumber (f-k) or frequency-phase velocity (f-c) domain. The mapping is usually performed with the classic 2-D Fourier transform (FT) with a subsequent substitution and interpolation via c = 2πf/k. The extracted dispersion trajectories of the guided modes lack the resolution in the transformed plane to discriminate wave modes. The resolving power associated with the FT is closely linked to the aperture of the recorded data. Here, we present a linear Radon transform (RT) to image the dispersive energies of the recorded ultrasound wave fields. The RT is posed as an inverse problem, which allows implementation of the regularization strategy to enhance the focusing power. We choose a Cauchy regularization for the high-resolution RT. Three forms of Radon transform: adjoint, damped least-squares, and high-resolution are described, and are compared with respect to robustness using simulated and cervine bone data. The RT also depends on the data aperture, but not as severely as does the FT. With the RT, the resolution of the dispersion panel could be improved up to around 300% over that of the FT. Among the Radon solutions, the high-resolution RT delineated the guided wave energy with much better imaging resolution (at least 110%) than the other two forms. The Radon operator can also accommodate unevenly spaced records. The results of the study suggest that the high-resolution RT is a valuable imaging tool to extract dispersive guided wave energies under limited aperture. Copyright © 2014 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

  8. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  9. The Non-Linear Relationship between BMI and Health Care Costs and the Resulting Cost Fraction Attributable to Obesity.

    Laxy, Michael; Stark, Renée; Peters, Annette; Hauner, Hans; Holle, Rolf; Teuner, Christina M

    2017-08-30

    This study aims to analyse the non-linear relationship between Body Mass Index (BMI) and direct health care costs, and to quantify the resulting cost fraction attributable to obesity in Germany. Five cross-sectional surveys of cohort studies in southern Germany were pooled, resulting in data of 6757 individuals (31-96 years old). Self-reported information on health care utilisation was used to estimate direct health care costs for the year 2011. The relationship between measured BMI and annual costs was analysed using generalised additive models, and the cost fraction attributable to obesity was calculated. We found a non-linear association of BMI and health care costs with a continuously increasing slope for increasing BMI without any clear threshold. Under the consideration of the non-linear BMI-cost relationship, a shift in the BMI distribution so that the BMI of each individual is lowered by one point is associated with a 2.1% reduction of mean direct costs in the population. If obesity was eliminated, and the BMI of all obese individuals were lowered to 29.9 kg/m², this would reduce the mean direct costs by 4.0% in the population. Results show a non-linear relationship between BMI and health care costs, with very high costs for a few individuals with high BMI. This indicates that population-based interventions in combination with selective measures for very obese individuals might be the preferred strategy.

  10. The time-walk of analog constant fraction discriminators using very fast scintillator detectors with linear and non-linear energy response

    Regis, J.-M., E-mail: regis@ikp.uni-koeln.de [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Rudigier, M.; Jolie, J.; Blazhev, A.; Fransen, C.; Pascovici, G.; Warr, N. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany)

    2012-08-21

    The electronic {gamma}-{gamma} fast timing technique allows for direct nuclear lifetime determination down to the few picoseconds region by measuring the time difference between two coincident {gamma}-ray transitions. Using high resolution ultra-fast LaBr{sub 3}(Ce) scintillator detectors in combination with the recently developed mirror symmetric centroid difference method, nuclear lifetimes are measured with a time resolving power of around 5 ps. The essence of the method is to calibrate the energy dependent position (centroid) of the prompt response function of the setup which is obtained for simultaneously occurring events. This time-walk of the prompt response function induced by the analog constant fraction discriminator has been determined by systematic measurements using different photomultiplier tubes and timing adjustments of the constant fraction discriminator. We propose a universal calibration function which describes the time-walk or the combined {gamma}-{gamma} time-walk characteristics, respectively, for either a linear or a non-linear amplitude versus energy dependency of the scintillator detector output pulses.

  11. Development and tests of fast 1-MA linear transformer driver stages

    A. A. Kim

    2009-05-01

    Full Text Available In this article we present the design and test results of the most powerful, fast linear transformer driver (LTD stage developed to date. This 1-MA LTD stage consists of 40 parallel RLC (resistor R, inductor L, and capacitor C circuits called “bricks” that are triggered simultaneously; it is able to deliver ∼1  MA current pulse with a rise time of ∼100  ns into the ∼0.1-Ohm matched load. The electrical behavior of the stage can be predicted by using a simple RLC circuit, thus simplifying the designing of various LTD-based accelerators. Five 1-MA LTD stages assembled in series into a module have been successfully tested with both resistive and vacuum electron-beam diode loads.

  12. The analysis of decimation and interpolation in the linear canonical transform domain.

    Xu, Shuiqing; Chai, Yi; Hu, Youqiang; Huang, Lei; Feng, Li

    2016-01-01

    Decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. As the linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing, it is worthwhile and interesting to analyze the decimation and interpolation in the LCT domain. In this paper, the definition of equivalent filter in the LCT domain have been given at first. Then, by applying the definition, the direct implementation structure and polyphase networks for decimator and interpolator in the LCT domain have been proposed. Finally, the perfect reconstruction expressions for differential filters in the LCT domain have been presented as an application. The proposed theorems in this study are the bases for generalizations of the multirate signal processing in the LCT domain, which can advance the filter banks theorems in the LCT domain.

  13. The linear variable differential transformer (LVDT) position sensor for gravitational wave interferometer low-frequency controls

    Tariq, Hareem E-mail: htariq@ligo.caltech.edu; Takamori, Akiteru; Vetrano, Flavio; Wang Chenyang; Bertolini, Alessandro; Calamai, Giovanni; DeSalvo, Riccardo; Gennai, Alberto; Holloway, Lee; Losurdo, Giovanni; Marka, Szabolcs; Mazzoni, Massimo; Paoletti, Federico; Passuello, Diego; Sannibale, Virginio; Stanga, Ruggero

    2002-08-21

    Low-power, ultra-high-vacuum compatible, non-contacting position sensors with nanometer resolution and centimeter dynamic range have been developed, built and tested. They have been designed at Virgo as the sensors for low-frequency modal damping of Seismic Attenuation System chains in Gravitational Wave interferometers and sub-micron absolute mirror positioning. One type of these linear variable differential transformers (LVDTs) has been designed to be also insensitive to transversal displacement thus allowing 3D movement of the sensor head while still precisely reading its position along the sensitivity axis. A second LVDT geometry has been designed to measure the displacement of the vertical seismic attenuation filters from their nominal position. Unlike the commercial LVDTs, mostly based on magnetic cores, the LVDTs described here exert no force on the measured structure.

  14. Linear variable differential transformer and its uses for in-core fuel rod behavior measurements

    Wolf, J.R.

    1979-01-01

    The linear variable differential transformer (LVDT) is an electromechanical transducer which produces an ac voltage proportional to the displacement of a movable ferromagnetic core. When the core is connected to the cladding of a nuclear fuel rod, it is capable of producing extremely accurate measurements of fuel rod elongation caused by thermal expansion. The LVDT is used in the Thermal Fuels Behavior Program at the U.S. Idaho National Engineering Laboratory (INEL) for measurements of nuclear fuel rod elongation and as an indication of critical heat flux and the occurrence of departure from nucleate boiling. These types of measurements provide important information about the behavior of nuclear fuel rods under normal and abnormal operating conditions. The objective of the paper is to provide a complete account of recent advances made in LVDT design and experimental data from in-core nuclear reactor tests which use the LVDT

  15. Estimating spatially distributed monthly evapotranspiration rates by linear transformations of MODIS daytime land surface temperature data

    J. Szilagyi

    2009-05-01

    Full Text Available Under simplifying conditions catchment-scale vapor pressure at the drying land surface can be calculated as a function of its watershed-representative temperature (<Ts> by the wet-surface equation (WSE, similar to the wet-bulb equation in meteorology for calculating the dry-bulb thermometer vapor pressure of the Complementary Relationship of evaporation. The corresponding watershed ET rate, , is obtained from the Bowen ratio with the help of air temperature, humidity and percent possible sunshine data. The resulting (<Ts>, pair together with the wet-environment surface temperature (<Tws> and ET rate (ETw, obtained by the Priestley-Taylor equation, define a linear transformation on a monthly basis by which spatially distributed ET rates can be estimated as a sole function of MODIS daytime land surface temperature, Ts, values within the watershed. The linear transformation preserves the mean which is highly desirable. <Tws>, in the lack of significant open water surfaces within the study watershed (Elkhorn, Nebraska, was obtained as the mean of the smallest MODIS Ts values each month. The resulting period-averaged (2000–2007 catchment-scale ET rate of 624 mm/yr is very close to the water-balance derived ET rate of about 617 mm/yr. The latter is a somewhat uncertain value due to the effects of (a observed groundwater depletion of about 1m over the study period caused by extensive irrigation, and; (b the uncertain rate of net regional groundwater supply toward the watershed. The spatially distributed ET rates correspond well with soil/aquifer properties and the resulting land use type (i.e. rangeland versus center-pivot irrigated crops.

  16. Utility of Higher Harmonics in Electrospray Ionization Fourier Transform Electrostatic Linear Ion Trap Mass Spectrometry.

    Dziekonski, Eric T; Johnson, Joshua T; McLuckey, Scott A

    2017-04-18

    Mass resolution (M/ΔM fwhm) is observed to linearly increase with harmonic order in a Fourier transform electrostatic linear ion trap (ELIT) mass spectrometer. This behavior was predicted by Grosshans and Marshall for frequency-multiple detection in a Fourier transform ion cyclotron resonance mass spectrometer only for situations when the prominent mechanism for signal decay is ion ejection from the trap. As the analyzer pressure in our ELIT chamber is relatively high, such that collisional scattering and collision-induced dissociation are expected to underlie much of the ion loss, we sought to explore the relationship between harmonic order and mass resolution. Mass resolutions of 36 900 (fundamental), 75 850 (2nd harmonic), and 108 200 (3rd harmonic) were obtained for GdO + (avg. m/z 173.919) with a transient length of 300 ms. To demonstrate that the mass resolution was truly increasing with harmonic order, the unresolved isotopes at the fundamental distribution of cytochrome c +8 (m/z ∼ 1549) were nearly baseline, resolved at the third harmonic (mass resolution ≈ 23 000) with a transient length of only 200 ms. This experiment demonstrates that, when the ion density is sufficiently low, ions with frequency differences of less than 4 Hz remain uncoalesced. Higher harmonics can be used to increase the effective mass resolution for a fixed transient length and thereby may enable the resolution of closely spaced masses, determination of a protein ion's charge state, and study of the onset of peak coalescence when the resolution at the fundamental frequency is insufficient.

  17. Effect of selenium-enriched organic material amendment on selenium fraction transformation and bioavailability in soil.

    Wang, Dan; Dinh, Quang Toan; Anh Thu, Tran Thi; Zhou, Fei; Yang, Wenxiao; Wang, Mengke; Song, Weiwei; Liang, Dongli

    2018-05-01

    To exploit the plant byproducts from selenium (Se) biofortification and reduce environmental risk of inorganic Se fertilizer, pot experiment was conducted in this study. The effects of Se-enriched wheat (Triticum aestivum L.) straw (WS + Se) and pak choi (Brassica chinensis L.) (P + Se) amendment on organo-selenium speciation transformation in soil and its bioavailability was evaluated by pak choi uptake. The Se contents of the cultivated pak choi in treatments amended with the same amount of Se-enriched wheat straw and pak choi were 1.7 and 9.7 times in the shoots and 2.3 and 6.3 times in the roots compared with control treatment. Soil respiration rate was significantly increased after all organic material amendment in soil (p organic materials and thus resulted in soluble Se (SOL-Se), exchangeable Se (EX-Se), and fulvic acid-bound Se (FA-Se) fraction increasing by 25.2-29.2%, 9-13.8%, and 4.92-8.28%, respectively. In addition, both Pearson correlation and cluster analysis showed that EX-Se and FA-Se were better indicators for soil Se availability in organic material amendment soils. The Marquardt-Levenberg Model well described the dynamic kinetics of FA-Se content after Se-enriched organic material amendment in soil mainly because of the mineralization of organic carbon and organo-selenium. The utilization of Se in P + Se treatment was significantly higher than those in WS + Se treatment because of the different mineralization rates and the amount of FA-Se in soil. Se-enriched organic materials amendment can not only increase the availability of selenium in soil but also avoid the waste of valuable Se source. Copyright © 2018 Elsevier Ltd. All rights reserved.

  18. End Effects on the Linear Induction MHD Generator Calculated by Two-Sided Laplace Transform

    Engeln, F.; Peschka, W. [Deutsche Versuchsanstalt fuer Luft- und Raumfahrt e.V., Institut fuer Energiewandlung und Elektrische Antriebe, Stuttgart, Federal Republic of Germany (Germany)

    1966-11-15

    In induction MHD systems special problems occur where the flow enters or leaves the magnetic field. These problems are generally described as end effects. Large gradients of the magnetic field are present at the inlet and also at the outlet of an MHD induction engine, these generating electric current systems in the fluid which may spoil the performance characteristics of the generator due to the interaction with the primary field of the engine. The two-dimensional induction MHD generator of finite length, using a polyphase winding system to obtain a travelling magnetic field, is treated as a boundary value problem by two-sided Laplace transform. For simplicity incompressibility is assumed. The two- dimensional boundary value problem of the induction engine is solved for - {infinity} Less-Than-Over-Equal-To x Less-Than-Over-Equal-To {infinity}. x is parallel to the flow direction of the linear MHD generator. In the region 0 Less-Than-Over-Equal-To x Less-Than-Over-Equal-To L the magnetic travelling wave is sinusoidal with a cyclical frequency {omega} and a phase-velocity v{sub s}. At x = 0 the conducting incompressible working fluid enters the field region and leaves it at the point-x = L. Two mathematical methods can be used to solve the boundary value problem, the Fourier transform or the two-sided Laplace transform. The latter offers the advantage of representing a complex analytical function in the image space. Moreover, it is possible to obtain the characteristics of the generator in the image space (e. g. field configuration, power flow function, etc.). That implies a large simplification of mathematical treatment. The solution in the original space then is given by asymptotic expansion of the known image function. (author)

  19. Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

    Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris

    2012-11-19

    We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S21 response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

  20. Feature-space-based FMRI analysis using the optimal linear transformation.

    Sun, Fengrong; Morris, Drew; Lee, Wayne; Taylor, Margot J; Mills, Travis; Babyn, Paul S

    2010-09-01

    The optimal linear transformation (OLT), an image analysis technique of feature space, was first presented in the field of MRI. This paper proposes a method of extending OLT from MRI to functional MRI (fMRI) to improve the activation-detection performance over conventional approaches of fMRI analysis. In this method, first, ideal hemodynamic response time series for different stimuli were generated by convolving the theoretical hemodynamic response model with the stimulus timing. Second, constructing hypothetical signature vectors for different activity patterns of interest by virtue of the ideal hemodynamic responses, OLT was used to extract features of fMRI data. The resultant feature space had particular geometric clustering properties. It was then classified into different groups, each pertaining to an activity pattern of interest; the applied signature vector for each group was obtained by averaging. Third, using the applied signature vectors, OLT was applied again to generate fMRI composite images with high SNRs for the desired activity patterns. Simulations and a blocked fMRI experiment were employed for the method to be verified and compared with the general linear model (GLM)-based analysis. The simulation studies and the experimental results indicated the superiority of the proposed method over the GLM-based analysis in detecting brain activities.

  1. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

    Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

    2016-06-27

    We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

  2. The role of transforming growth factor β1 in fractional laser resurfacing with a carbon dioxide laser.

    Jiang, Xia; Ge, Hongmei; Zhou, Chuanqing; Chai, Xinyu; Deng, Hui

    2014-03-01

    The aim of this study was to investigate the role of transforming growth factor β1 in mechanisms of cutaneous remodeling induced by fractional carbon dioxide laser treatment. The dorsal skin of Kunming mice was exposed to a single-pass fractional CO2 laser treatment. Biopsies were taken at 1 h and at 1, 3, 7, 14, 21, 28, and 56 days after treatment. Transforming growth factor (TGF) β1 expression in skin samples was evaluated by ELISA, dermal thickness by hematoxylin-eosin staining, collagen and elastic fibers by Ponceau S and Victoria blue double staining, and types I and III collagens by ELISA. The level of TGF β1 in the laser-treated areas of skin was significantly increased compared with that in the control areas on days 1 (p skin of the laser-treated areas had increased significantly (p resurfacing.

  3. Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

    Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

    1990-01-01

    Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

  4. Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation

    Edinson Fuentes

    2015-06-01

    Full Text Available In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szeg´´o transformation. A similar perturbation is analyzed through the inverse Szeg´´o transformation. In both cases, we show that the applied perturbation can be expressed in terms of the singular part of the measures, and also in terms of the corresponding sequences of moments. Resumen. En el presente trabajo, analizamos las perturbaciones a una sucesión de momentos asociada a un funcional lineal de ortogonalidad que se representa por una medida positiva con soporte en [−1, 1]. En particular, dada una cierta perturbación a dicha medida en la recta real, analizamos la perturbación obtenida en la correspondiente medida en la circunferencia unidad, cuando dichas medidas están relacionadas por la transformación de Szeg´´o. También se analiza una perturbación similar a través de la transformación inversa de Szeg´´o. En ambos casos, se muestra que la perturbación aplicada puede ser expresada en términos de la parte singular de las medidas, y también a través de las correspondientes sucesiones de momentos.

  5. The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

    Bates, Jason H T; Sobel, Burton E

    2003-05-01

    This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

  6. Circuit models and three-dimensional electromagnetic simulations of a 1-MA linear transformer driver stage

    D. V. Rose

    2010-09-01

    Full Text Available A 3D fully electromagnetic (EM model of the principal pulsed-power components of a high-current linear transformer driver (LTD has been developed. LTD systems are a relatively new modular and compact pulsed-power technology based on high-energy density capacitors and low-inductance switches located within a linear-induction cavity. We model 1-MA, 100-kV, 100-ns rise-time LTD cavities [A. A. Kim et al., Phys. Rev. ST Accel. Beams 12, 050402 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050402] which can be used to drive z-pinch and material dynamics experiments. The model simulates the generation and propagation of electromagnetic power from individual capacitors and triggered gas switches to a radially symmetric output line. Multiple cavities, combined to provide voltage addition, drive a water-filled coaxial transmission line. A 3D fully EM model of a single 1-MA 100-kV LTD cavity driving a simple resistive load is presented and compared to electrical measurements. A new model of the current loss through the ferromagnetic cores is developed for use both in circuit representations of an LTD cavity and in the 3D EM simulations. Good agreement between the measured core current, a simple circuit model, and the 3D simulation model is obtained. A 3D EM model of an idealized ten-cavity LTD accelerator is also developed. The model results demonstrate efficient voltage addition when driving a matched impedance load, in good agreement with an idealized circuit model.

  7. High current, 0.5-MA, fast, 100-ns, linear transformer driver experiments

    Michael G. Mazarakis

    2009-05-01

    Full Text Available The linear transformer driver (LTD is a new method for constructing high current, high-voltage pulsed accelerators. The salient feature of the approach is switching and inductively adding the pulses at low voltage straight out of the capacitors through low inductance transfer and soft iron core isolation. Sandia National Laboratories are actively pursuing the development of a new class of accelerator based on the LTD technology. Presently, the high current LTD experimental research is concentrated on two aspects: first, to study the repetition rate capabilities, reliability, reproducibility of the output pulses, switch prefires, jitter, electrical power and energy efficiency, and lifetime measurements of the cavity active components; second, to study how a multicavity linear array performs in a voltage adder configuration relative to current transmission, energy and power addition, and wall plug to output pulse electrical efficiency. Here we report the repetition rate and lifetime studies performed in the Sandia High Current LTD Laboratory. We first utilized the prototype ∼0.4-MA, LTD I cavity which could be reliably operated up to ±90-kV capacitor charging. Later we obtained an improved 0.5-MA, LTD II version that can be operated at ±100  kV maximum charging voltage. The experimental results presented here were obtained with both cavities and pertain to evaluating the maximum achievable repetition rate and LTD cavity performance. The voltage adder experiments with a series of double sized cavities (1 MA, ±100  kV will be reported in future publications.

  8. A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty

    Zhang, Chenglong; Guo, Ping

    2017-10-01

    The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.

  9. On the moments of the Wigner distribution and the fractional Fourier transform

    Alieva, T.; Bastiaans, M.J.; Veen, J.P.

    2000-01-01

    A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when

  10. Criterion of magnetic saturation and simulation of nonlinear magnetization for a linear multi-core pulse transformer

    Zeng Zhengzhong; Kuai Bin; Sun Fengju; Cong Peitian; Qiu Aici

    2002-01-01

    The linear multi-core pulse transformer is an important primary driving source used in pulsed power apparatus for the production of dense plasm owing to its compact, relatively low-cost and easy-to-handle characteristics. The evaluation of the magnetic saturation of the transformer cores is essential to the transformer design, because the energy transfer efficiency of the transformer will degrade significantly after magnetic saturation. This work proposes analytical formulas of the criterion of magnetic saturation for the cores when the transformer drives practical loads. Furthermore, an electric circuit model based on a dependent source treatment for simulating the electric behavior of the cores related to their nonlinear magnetization is developed using the initial magnetization curve of the cores. The numerical simulation with the model is used to evaluate the validity of the criterion. Both the criterion and the model are found to be in agreement with the experimental data

  11. On a finite moment perturbation of linear functionals and the inverse Szegö transformation

    Edinson Fuentes

    2016-05-01

    Full Text Available Given a sequence of moments $\\{c_{n}\\}_{n\\in\\ze}$ associated with an Hermitian linear functional $\\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\\mathcal{L}_{\\Omega}$ which is a perturbation of $\\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\\mathcal{L}_{\\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\\mathcal{L}_{\\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szegö transformation. Resumen. Dada una sucesión de momentos $\\{c_{n}\\}_{n\\in\\ze}$ asociada a un funcional lineal hermitiano $\\mathcal{L}$ definido en el espacio de los polinomios de Laurent, estudiamos un nuevo funcional $\\mathcal{L}_{\\Omega}$ que consiste en una perturbación de $\\mathcal{L}$ de tal forma que se perturba un número finito de momentos de la sucesión. Se encuentran condiciones necesarias y suficientes para la regularidad de $\\mathcal{L}_{\\Omega}$, y se obtiene una fórmula de conexión que relaciona las familias de polinomios ortogonales correspondientes. Por otro lado, suponiendo que $\\mathcal{L}_{\\Omega}$ es definido positivo, se analiza la perturbación mediante de la transformación inversa de Szegö.

  12. Basic design of radiation-resistant LVDTs: Linear Variable Differential Transformer

    Sohn, J. M.; Park, S. J.; Kang, Y. H. (and others)

    2008-02-15

    A LVDT(Linear Variable Differential Transformer) for measuring the pressure level was used to measure the pressure of a nuclear fuel rod during the neutron irradiation test in a research reactor. A LVDT for measuring the elongation was also used to measure the elongation of nuclear fuels, and the creep and fatigue of materials during a neutron irradiation test in a research reactor. In this report, the basic design of two radiation-resistant LVDTs for measuring the pressure level and elongation are described. These LVDTs are used a under radiation environment such as a research reactor. In the basic design step, we analyzed the domestic and foreign technical status for radiation-resistant LVDTs, made part and assembly drawings and established simple procedures for their assembling. Only a few companies in the world can produce radiation-resistant LVDTs. Not only these are extremely expensive, but the prices are continuously rising. Also, it takes a long time to procure a LVDT, as it can only be bought about by an order-production. The localization of radiation-resistant LVDTs is necessary in order to provide them quickly and at a low cost. These radiation-resistant LVDTs will be used at neutron irradiation devices such as instrumented fuel capsules, special purpose capsules and a fuel test loop in research reactors. We expect that the use of neutron irradiation tests will be revitalized by the localization of radiation-resistant LVDTs.

  13. A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range

    Wei Wang

    2016-09-01

    Full Text Available A Fourier transform spectrometer (FTS that incorporates a closed-loop controlled, electrothermally actuated microelectromechanical systems (MEMS micromirror is proposed and experimentally verified. The scan range and the tilting angle of the mirror plate are the two critical parameters for MEMS-based FTS. In this work, the MEMS mirror with a footprint of 4.3 mm × 3.1 mm is based on a modified lateral-shift-free (LSF bimorph actuator design with large piston and reduced tilting. Combined with a position-sensitive device (PSD for tilt angle sensing, the feedback controlled MEMS mirror generates a 430 µm stable linear piston scan with the mirror plate tilting angle less than ±0.002°. The usable piston scan range is increased to 78% of the MEMS mirror’s full scan capability, and a spectral resolution of 0.55 nm at 531.9 nm wavelength, has been achieved. It is a significant improvement compared to the prior work.

  14. The high current, fast, 100ns, Linear Transformer Driver (LTD) developmental project at Sandia National Laboratories

    Ward, Kevin S.; Long, Finis W.; Sinebryukhov, Vadim A.; Kim, Alexandre A.; Wakeland, Peter Eric; McKee, G. Randall; Woodworth, Joseph Ray; McDaniel, Dillon Heirman; Fowler, William E.; Mazarakis, Michael Gerrassimos; Porter, John Larry Jr.; Struve, Kenneth William; Stygar, William A.; LeChien, Keith R.; Matzen, Maurice Keith

    2010-01-01

    Sandia National Laboratories, Albuquerque, N.M., USA, in collaboration with the High Current Electronic Institute (HCEI), Tomsk, Russia, is developing a new paradigm in pulsed power technology: the Linear Transformer Driver (LTD) technology. This technological approach can provide very compact devices that can deliver very fast high current and high voltage pulses straight out of the cavity with out any complicated pulse forming and pulse compression network. Through multistage inductively insulated voltage adders, the output pulse, increased in voltage amplitude, can be applied directly to the load. The load may be a vacuum electron diode, a z-pinch wire array, a gas puff, a liner, an isentropic compression load (ICE) to study material behavior under very high magnetic fields, or a fusion energy (IFE) target. This is because the output pulse rise time and width can be easily tailored to the specific application needs. In this paper we briefly summarize the developmental work done in Sandia and HCEI during the last few years, and describe our new MYKONOS Sandia High Current LTD Laboratory.

  15. Optical colour image watermarking based on phase-truncated linear canonical transform and image decomposition

    Su, Yonggang; Tang, Chen; Li, Biyuan; Lei, Zhenkun

    2018-05-01

    This paper presents a novel optical colour image watermarking scheme based on phase-truncated linear canonical transform (PT-LCT) and image decomposition (ID). In this proposed scheme, a PT-LCT-based asymmetric cryptography is designed to encode the colour watermark into a noise-like pattern, and an ID-based multilevel embedding method is constructed to embed the encoded colour watermark into a colour host image. The PT-LCT-based asymmetric cryptography, which can be optically implemented by double random phase encoding with a quadratic phase system, can provide a higher security to resist various common cryptographic attacks. And the ID-based multilevel embedding method, which can be digitally implemented by a computer, can make the information of the colour watermark disperse better in the colour host image. The proposed colour image watermarking scheme possesses high security and can achieve a higher robustness while preserving the watermark’s invisibility. The good performance of the proposed scheme has been demonstrated by extensive experiments and comparison with other relevant schemes.

  16. SOIL NITROGEN TRANSFORMATIONS AND ROLE OF LIGHT FRACTION ORGANIC MATTER IN FOREST SOILS

    Depletion of soil organic matter through cultivation may alter substrate availability for microbes, altering the dynamic balance between nitrogen (N) immobilization and mineralization. Soil light fraction (LF) organic matter is an active pool that decreases upon cultivation, and...

  17. A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

    Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

    2018-04-01

    In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

  18. Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems

    Abdel-Halim Hassan, I.H.

    2008-01-01

    In this paper, we will compare the differential transformation method DTM and Adomian decomposition method ADM to solve partial differential equations (PDEs). The definition and operations of differential transform method was introduced by Zhou [Zhou JK. Differential transformation and its application for electrical circuits. Wuuhahn, China: Huarjung University Press; 1986 [in Chinese

  19. Nelson's syndrome: single centre experience using the linear accelerator (LINAC) for stereotactic radiosurgery and fractionated stereotactic radiotherapy.

    Wilson, Peter J; Williams, Janet R; Smee, Robert I

    2014-09-01

    Nelson's syndrome is a unique clinical phenomenon of growth of a pituitary adenoma following bilateral adrenalectomies for the control of Cushing's disease. Primary management is surgical, with limited effective medical therapies available. We report our own institution's series of this pathology managed with radiation: prior to 1990, 12 patients were managed with conventional radiotherapy, and between 1990 and 2007, five patients underwent stereotactic radiosurgery (SRS) and two patients fractionated stereotactic radiotherapy (FSRT), both using the linear accelerator (LINAC). Tumour control was equivocal, with two of the five SRS patients having a reduction in tumour volume, one patient remaining unchanged, and two patients having an increase in volume. In the FSRT group, one patient had a decrease in tumour volume whilst the other had an increase in volume. Treatment related morbidity was low. Nelson's syndrome is a challenging clinical scenario, with a highly variable response to radiation in our series. Copyright © 2014 Elsevier Ltd. All rights reserved.

  20. Cushing's disease: a single centre's experience using the linear accelerator (LINAC) for stereotactic radiosurgery and fractionated stereotactic radiotherapy.

    Wilson, P J; Williams, J R; Smee, R I

    2014-01-01

    Cushing's disease is hypercortisolaemia secondary to an adrenocorticotrophic hormone secreting pituitary adenoma. Primary management is almost always surgical, with limited effective medical interventions available. Adjuvant therapy in the form of radiation is gaining popularity, with the bulk of the literature related to the Gamma Knife. We present the results from our own institution using the linear accelerator (LINAC) since 1990. Thirty-six patients who underwent stereotactic radiosurgery (SRS), one patient who underwent fractionated stereotactic radiotherapy (FSRT) and for the purposes of comparison, 13 patients who had undergone conventional radiotherapy prior to 1990, were included in the analysis. Serum cortisol levels improved in nine of 36 (25%) SRS patients and 24 hour urinary free cortisol levels improved in 13 of 36 patients (36.1%). Tumour volume control was excellent in the SRS group with deterioration in only one patient (3%). The patient who underwent FSRT had a highly aggressive tumour refractory to radiation. Published by Elsevier Ltd.

  1. Electrode erosion properties of gas spark switches for fast linear transformer drivers

    Li, Xiaoang; Pei, Zhehao; Zhang, Yuzhao; Liu, Xuandong; Li, Yongdong; Zhang, Qiaogen

    2017-12-01

    Fast linear transformer drivers (FLTDs) are a popular and potential route for high-power devices employing multiple "bricks" in series and parallel, but they put extremely stringent demands on gas switches. Electrode erosion of FLTD gas switches is a restrictive and unavoidable factor that degrades performance and limits stability. In this paper, we systematically investigated the electrode erosion characteristics of a three-electrode field distortion gas switch under the typical working conditions of FLTD switches, and the discharge current was 7-46 kA with 46-300 ns rise time. A high speed frame camera and a spectrograph were used to capture the expansion process and the spectral emission of the spark channel was used to estimate the current density and the spark temperature, and then the energy fluxes and the external forces on the electrode surface were calculated. A tens of kilo-ampere nanosecond pulse could generate a 1011 W/m2 energy flux injection and 1.3-3.5 MPa external pressure on the electrode surface, resulting in a millimeter-sized erosion crater with the maximum peak height Rz reaching 100 μm magnitude. According to the morphological images by a laser scanning confocal microscope, the erosion crater of a FLTD switch contained three kinds of local morphologies, namely a center boiling region, an overflow region and a sputtering region. In addition, the crater size, the surface roughness, and the mass loss were highly dependent on the current amplitude and the transferred charge. We also observed Morphology Type I and Type II, respectively, with different pulse parameters, which had an obvious influence on surface roughness and mass loss. Finally, the quantitative relationship between the electrode mass loss and the pulse parameter was clarified. The transferred charge and the current amplitude were proved to be the main factors determining the electrode mass loss of a FLTD switch, and a least squares fitting expression for mass loss was also obtained.

  2. Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators

    Koornwinder, T.H.

    2015-01-01

    For each of the eight n-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential

  3. Relationship between metallothioneins and metals in a natural population of the clam Ruditapes decussatus from Sfax coast: a non-linear model using Box-Cox transformation.

    Hamza-Chaffai, A; Amiard, J C; Cosson, R P

    1999-06-01

    Cadmium, copper and zinc were determined concomitantly with metallothionein-like proteins (MTLPs) in the subcellular fractions of Ruditapes decussatus digestive gland. This study covered 4 months and aimed to evaluate the effect of metal pollution and other factors such as sex, size and reproductive state on MTLP levels. Copper concentrations did not vary with month, however Cd and Zn concentrations showed high levels during August. Organisms showing low cadmium concentrations presented the highest cadmium percentages in the soluble fraction (SF) containing MTLPs. However for high cadmium concentrations, the insoluble fraction (IF) was implicated in cadmium association. MTLP levels varied according to the month, the sex and the size of the organisms. A non-linear model based on the Box-Cox transformation, was proposed to describe a positive and a significant relationship between MTLPs and the studied metals. A model including sex and size showed that these two factors affected MTLP levels, but were less important than metals. Males of R. decussatus showed higher significant correlations between MTLP levels and cadmium than females. Moreover, the effect of size and reproductive state on MTLP levels was less perceptible in males than in females. As a result, MTLPs in males of R. decussatus could be proposed as suitable biomarker for detecting metal contamination.

  4. Devil’s Vortex Phase Structure as Frequency Plane Mask for Image Encryption Using the Fractional Mellin Transform

    Sunanda Vashisth

    2014-01-01

    Full Text Available A frequency plane phase mask based on Devil’s vortex structure has been used for image encryption using the fractional Mellin transform. The phase key for decryption is obtained by an iterative phase retrieval algorithm. The proposed scheme has been validated for grayscale secret target images, by numerical simulation. The efficacy of the scheme has been evaluated by computing mean-squared-error between the secret target image and the decrypted image. Sensitivity analysis of the decryption process to variations in various encryption parameters has been carried out. The proposed encryption scheme has been seen to exhibit reasonable robustness against occlusion attack.

  5. Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain.

    Haldar, Justin P; Leahy, Richard M

    2013-05-01

    This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors. Copyright © 2013 Elsevier Inc. All rights reserved.

  6. Multi-linear model of transformation of runoff in river-basins

    Szolgay, J.; Kubes, R.

    2005-01-01

    The component part of atmospheric precipitations-runoff model of Hron River is a individual model of transformation of flows in river network, too, which transforms runoff from separate partial catchment basin into terminal profile. This component of precipitations-runoff model can also be used as individual hydrologic transformation model of runoff waves in river-basin. Identification and calibration of this model is realised independently on precipitations-runoff model of Hron River, which is described in this chapter in detail.

  7. On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

    Hossein Jafari

    2016-04-01

    Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

  8. A Model for Analyzing a Five-Phase Fractional-Slot Permanent Magnet Tubular Linear Motor with Modified Winding Function Approach

    Bo Zhang

    2016-01-01

    Full Text Available This paper presents a model for analyzing a five-phase fractional-slot permanent magnet tubular linear motor (FSPMTLM with the modified winding function approach (MWFA. MWFA is a fast modeling method and it gives deep insight into the calculations of the following parameters: air-gap magnetic field, inductances, flux linkages, and detent force, which are essential in modeling the motor. First, using a magnetic circuit model, the air-gap magnetic density is computed from stator magnetomotive force (MMF, flux barrier, and mover geometry. Second, the inductances, flux linkages, and detent force are analytically calculated using modified winding function and the air-gap magnetic density. Finally, a model has been established with the five-phase Park transformation and simulated. The calculations of detent force reveal that the end-effect force is the main component of the detent force. This is also proven by finite element analysis on the motor. The accuracy of the model is validated by comparing with the results obtained using semianalytical method (SAM and measurements to analyze the motor’s transient characteristics. In addition, the proposed method requires less computation time.

  9. Production of gasoline fraction from bio-oil under atmospheric conditions by an integrated catalytic transformation process

    Zhang, Zhaoxia; Bi, Peiyan; Jiang, Peiwen; Fan, Minghui; Deng, Shumei; Zhai, Qi; Li, Quanxin

    2015-01-01

    This work aimed to develop an integrated process for production of gasoline fraction bio-fuels from bio-oil under atmospheric conditions. This novel transformation process included the catalytic cracking of bio-oil to light olefins and the subsequent synthesis of liquid hydrocarbon bio-fuels from light olefins with two reactors in series. The yield of bio-fuel was up to 193.8 g/(kg bio-oil) along with a very low oxygen content, high RONs (research octane numbers), high LHVs (lower heating values) and low benzene content under the optimizing reaction conditions. Coke deposition seems to be the main cause of catalyst deactivation in view of the fact that the deactivated catalysts was almost recovered by on-line treating the used catalyst with oxygen. The integrated transformation potentially provides a useful way for the development of gasoline range hydrocarbon fuels using renewable lignocellulose biomass. - Graphical abstract: An integrated process for production of gasoline fraction bio-fuels from bio-oil through the catalytic cracking of bio-oil to light olefins followed by the synthesis of liquid hydrocarbon bio-fuels from light olefins in series. - Highlights: • A new route for production of gasoline-range bio-fuels from bio-oil was achieved. • The process was an integrated catalytic transformation at atmospheric pressure. • Bio-oil is converted into light olefins and then converted to biofuel in series. • C_6–C_1_0 bio-fuels derived from bio-oil had high RONs and LHVs.

  10. Linear problems and Baecklund transformations for the Hirota-Ohta system

    Adler, V.E.; Postnikov, V.V.

    2011-01-01

    The auxiliary linear problems are presented for all discretization levels of the Hirota-Ohta system. The structure of these linear problems coincides essentially with the structure of Nonlinear Schroedinger hierarchy. The squared eigenfunction constraints are found which relate Hirota-Ohta and Kulish-Sklyanin vectorial NLS hierarchies.

  11. Microbial respiration, but not biomass, responded linearly to increasing light fraction organic matter input: Consequences for carbon sequestration.

    Rui, Yichao; Murphy, Daniel V; Wang, Xiaoli; Hoyle, Frances C

    2016-10-18

    Rebuilding 'lost' soil carbon (C) is a priority in mitigating climate change and underpinning key soil functions that support ecosystem services. Microorganisms determine if fresh C input is converted into stable soil organic matter (SOM) or lost as CO 2 . Here we quantified if microbial biomass and respiration responded positively to addition of light fraction organic matter (LFOM, representing recent inputs of plant residue) in an infertile semi-arid agricultural soil. Field trial soil with different historical plant residue inputs [soil C content: control (tilled) = 9.6 t C ha -1 versus tilled + plant residue treatment (tilled + OM) = 18.0 t C ha -1 ] were incubated in the laboratory with a gradient of LFOM equivalent to 0 to 3.8 t C ha -1 (0 to 500% LFOM). Microbial biomass C significantly declined under increased rates of LFOM addition while microbial respiration increased linearly, leading to a decrease in the microbial C use efficiency. We hypothesise this was due to insufficient nutrients to form new microbial biomass as LFOM input increased the ratio of C to nitrogen, phosphorus and sulphur of soil. Increased CO 2 efflux but constrained microbial growth in response to LFOM input demonstrated the difficulty for C storage in this environment.

  12. An invariance property of the common trends under linear transformations of the data

    Johansen, Søren; Juselius, Katarina

    It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order...... VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t)....

  13. An Invariance Property of the Common Trends under Linear Transformations of the Data

    Johansen, Søren; Juselius, Katarina

    It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order...... VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis...... of the term structure of interest rates....

  14. ENHANCING NETWORK SECURITY USING 'LEARNING-FROM-SIGNALS' AND FRACTIONAL FOURIER TRANSFORM BASED RF-DNA FINGERPRINTS

    Buckner, Mark A [ORNL; Bobrek, Miljko [ORNL; Farquhar, Ethan [ORNL; Harmer, Paul K [Air Force Institute of Technology; Temple, Michael A [Air Force Institute of Technology

    2011-01-01

    Wireless Access Points (WAP) remain one of the top 10 network security threats. This research is part of an effort to develop a physical (PHY) layer aware Radio Frequency (RF) air monitoring system with multi-factor authentication to provide a first-line of defense for network security--stopping attackers before they can gain access to critical infrastructure networks through vulnerable WAPs. This paper presents early results on the identification of OFDM-based 802.11a WiFi devices using RF Distinct Native Attribute (RF-DNA) fingerprints produced by the Fractional Fourier Transform (FRFT). These fingerprints are input to a "Learning from Signals" (LFS) classifier which uses hybrid Differential Evolution/Conjugate Gradient (DECG) optimization to determine the optimal features for a low-rank model to be used for future predictions. Results are presented for devices under the most challenging conditions of intra-manufacturer classification, i.e., same-manufacturer, same-model, differing only in serial number. The results of Fractional Fourier Domain (FRFD) RF-DNA fingerprints demonstrate significant improvement over results based on Time Domain (TD), Spectral Domain (SD) and even Wavelet Domain (WD) fingerprints.

  15. Single-centre experience of stereotactic radiosurgery and fractionated stereotactic radiotherapy for prolactinomas with the linear accelerator.

    Wilson, Peter J; Williams, Janet Rosemary; Smee, Robert Ian

    2015-06-01

    Primary management of prolactinomas is usually medical, with surgery a secondary option where necessary. This study is a review of a single centre's experience with focused radiotherapy where benefit was not gained by medical or surgical approaches. Radiotherapy as an alternative and adjuvant treatment for prolactinomas has been performed at our institution with the linear accelerator since 1990. We present a retrospective review of 13 patients managed with stereotactic radiosurgery (SRS) and 5 managed with fractionated stereotactic radiotherapy (FSRT), as well as 5 managed with conventional radiotherapy, at the Prince of Wales Hospital. Patients with a histopathologically diagnosed prolactinoma were eligible. Those patients who had a confirmed pathological diagnosis of prolactinoma following surgical intervention, a prolactin level elevated above 500 μg/L, or a prolactin level persistently elevated above 200 μg/L with exclusion of other causes were represented in this review. At the end of documented follow-up (SRS median 6 years, FSRT median 2 years), no SRS patients showed an increase in tumour volume. After FSRT, 1 patient showed an increase in size, 2 showed a decrease in size and 2 patients showed no change. Prolactin levels trended towards improvement after SRS and FSRT, but no patients achieved the remission level of <20 μg/L. Seven of 13 patients in the SRS group achieved a level of <500 μg/L, whereas no patients reached this target after FSRT. A reduction in prolactin level is frequent after SRS and FSRT for prolactinomas; however, true biochemical remission is uncommon. Tumour volume control in this series was excellent, but this may be related to the natural history of the disease. Morbidity and mortality after stereotactic radiation were very low in this series. © 2014 The Royal Australian and New Zealand College of Radiologists.

  16. Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator.

    Shahoei, Hiva; Dumais, Patrick; Yao, Jianping

    2014-05-01

    We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

  17. Transformation of Summary Statistics from Linear Mixed Model Association on All-or-None Traits to Odds Ratio.

    Lloyd-Jones, Luke R; Robinson, Matthew R; Yang, Jian; Visscher, Peter M

    2018-04-01

    Genome-wide association studies (GWAS) have identified thousands of loci that are robustly associated with complex diseases. The use of linear mixed model (LMM) methodology for GWAS is becoming more prevalent due to its ability to control for population structure and cryptic relatedness and to increase power. The odds ratio (OR) is a common measure of the association of a disease with an exposure ( e.g. , a genetic variant) and is readably available from logistic regression. However, when the LMM is applied to all-or-none traits it provides estimates of genetic effects on the observed 0-1 scale, a different scale to that in logistic regression. This limits the comparability of results across studies, for example in a meta-analysis, and makes the interpretation of the magnitude of an effect from an LMM GWAS difficult. In this study, we derived transformations from the genetic effects estimated under the LMM to the OR that only rely on summary statistics. To test the proposed transformations, we used real genotypes from two large, publicly available data sets to simulate all-or-none phenotypes for a set of scenarios that differ in underlying model, disease prevalence, and heritability. Furthermore, we applied these transformations to GWAS summary statistics for type 2 diabetes generated from 108,042 individuals in the UK Biobank. In both simulation and real-data application, we observed very high concordance between the transformed OR from the LMM and either the simulated truth or estimates from logistic regression. The transformations derived and validated in this study improve the comparability of results from prospective and already performed LMM GWAS on complex diseases by providing a reliable transformation to a common comparative scale for the genetic effects. Copyright © 2018 by the Genetics Society of America.

  18. Stable isotope (C, O) and monovalent cation fractionation upon synthesis of carbonate-bearing hydroxyl apatite (CHAP) via calcite transformation

    Böttcher, Michael E.; Schmiedinger, Iris; Wacker, Ulrike; Conrad, Anika C.; Grathoff, Georg; Schmidt, Burkhard; Bahlo, Rainer; Gehlken, Peer-L.; Fiebig, Jens

    2016-04-01

    Carbonate-bearing hydroxyl-apatite (CHAP) is of fundamental and applied interest to the (bio)geochemical, paleontological, medical and material science communities, since it forms the basic mineral phase in human and animal teeth and bones. In addition, it is found in non-biogenic phosphate deposits. The stable isotope and foreign element composition of biogenic CHAP is widely used to estimate the formation conditions. This requires careful experimental calibration under well-defined boundary conditions. Within the DFG project EXCALIBOR, synthesis of carbonate-bearing hydroxyapatite was conducted via the transformation of synthetic calcite powder in aqueous solution as a function of time, pH, and temperature using batch-type experiments. The aqueous solution was analyzed for the carbon isotope composition of dissolved inorganic carbonate (gas irmMS), the oxygen isotope composition of water (LCRDS), and the cationic composition. The solid was characterized by powder X-ray diffraction, micro Raman and FTIR spectroscopy, SEM-EDX, elemental analysis (EA, ICP-OES) and gas irmMS. Temperature was found to significantly impact the transformation rate of calcite to CHAP. Upon complete transformation, CHAP was found to contain up to 5% dwt carbonate, depending on the solution composition (e.g., pH), both incorporated on the A and B type position of the crystal lattice. The oxygen isotope fractionation between water and CHAP decreased with increasing temperature with a tentative slope shallower than those reported in the literature for apatite, calcite or aragonite. In addition, the presence of dissolved NH4+, K+ or Na+ in aqueous solution led to partial incorporation into the CHAP lattice. How these distortions of the crystal lattice may impact stable isotope discrimination is subject of future investigations.

  19. Electron beam instabilities in unmagnetized plasmas via the Stieltjes transform (linear theory and nonlinear mode coupling)

    Krishan, S.

    2007-01-01

    The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment

  20. A 1–2 GHz high linearity transformer-feedback power-to-current LNA

    Li, X.; Serdijn, W.A.; Woestenburg, B.E.M.; Bij de Vaate, J.G.

    2009-01-01

    This paper demonstrates that a double-loop transformer-feedback power-to-current low noise amplifier, to be implemented in a 0.2 lm GaAs p-HEMT IC process, is able to obtain a noise figure less than 0.8 dB, an input return loss less than -12 dB, a flat voltage-to-current signal transfer of 180 mS,

  1. Digital simulation of staining in histopathology multispectral images: enhancement and linear transformation of spectral transmittance.

    Bautista, Pinky A; Yagi, Yukako

    2012-05-01

    Hematoxylin and eosin (H&E) stain is currently the most popular for routine histopathology staining. Special and/or immuno-histochemical (IHC) staining is often requested to further corroborate the initial diagnosis on H&E stained tissue sections. Digital simulation of staining (or digital staining) can be a very valuable tool to produce the desired stained images from the H&E stained tissue sections instantaneously. We present an approach to digital staining of histopathology multispectral images by combining the effects of spectral enhancement and spectral transformation. Spectral enhancement is accomplished by shifting the N-band original spectrum of the multispectral pixel with the weighted difference between the pixel's original and estimated spectrum; the spectrum is estimated using M transformed to the spectral configuration associated to its reaction to a specific stain by utilizing an N × N transformation matrix, which is derived through application of least mean squares method to the enhanced and target spectral transmittance samples of the different tissue components found in the image. Results of our experiments on the digital conversion of an H&E stained multispectral image to its Masson's trichrome stained equivalent show the viability of the method.

  2. Experience of micromultileaf collimator linear accelerator based single fraction stereotactic radiosurgery: Tumor dose inhomogeneity, conformity, and dose fall off

    Hong, Linda X.; Garg, Madhur; Lasala, Patrick; Kim, Mimi; Mah, Dennis; Chen, Chin-Cheng; Yaparpalvi, Ravindra; Mynampati, Dinesh; Kuo, Hsiang-Chi; Guha, Chandan; Kalnicki, Shalom [Department of Radiation Oncology, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States); Department of Neurosurgery, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States); Department of Epidemiology and Population Health, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States); Department of Radiation Oncology, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States)

    2011-03-15

    Purpose: Sharp dose fall off outside a tumor is essential for high dose single fraction stereotactic radiosurgery (SRS) plans. This study explores the relationship among tumor dose inhomogeneity, conformity, and dose fall off in normal tissues for micromultileaf collimator (mMLC) linear accelerator (LINAC) based cranial SRS plans. Methods: Between January 2007 and July 2009, 65 patients with single cranial lesions were treated with LINAC-based SRS. Among them, tumors had maximum diameters {<=}20 mm: 31; between 20 and 30 mm: 21; and >30 mm: 13. All patients were treated with 6 MV photons on a Trilogy linear accelerator (Varian Medical Systems, Palo Alto, CA) with a tertiary m3 high-resolution mMLC (Brainlab, Feldkirchen, Germany), using either noncoplanar conformal fixed fields or dynamic conformal arcs. The authors also created retrospective study plans with identical beam arrangement as the treated plan but with different tumor dose inhomogeneity by varying the beam margins around the planning target volume (PTV). All retrospective study plans were normalized so that the minimum PTV dose was the prescription dose (PD). Isocenter dose, mean PTV dose, RTOG conformity index (CI), RTOG homogeneity index (HI), dose gradient index R{sub 50}-R{sub 100} (defined as the difference between equivalent sphere radius of 50% isodose volume and prescription isodose volume), and normal tissue volume (as a ratio to PTV volume) receiving 50% prescription dose (NTV{sub 50}) were calculated. Results: HI was inversely related to the beam margins around the PTV. CI had a ''V'' shaped relationship with HI, reaching a minimum when HI was approximately 1.3. Isocenter dose and mean PTV dose (as percentage of PD) increased linearly with HI. R{sub 50}-R{sub 100} and NTV{sub 50} initially declined with HI and then reached a plateau when HI was approximately 1.3. These trends also held when tumors were grouped according to their maximum diameters. The smallest tumor group

  3. New binary linear codes which are dual transforms of good codes

    Jaffe, D.B.; Simonis, J.

    1999-01-01

    If C is a binary linear code, one may choose a subset S of C, and form a new code CST which is the row space of the matrix having the elements of S as its columns. One way of picking S is to choose a subgroup H of Aut(C) and let S be some H-stable subset of C. Using (primarily) this method for

  4. Transport properties of a piecewise linear transformation and deterministic Levy flights

    Miyaguchi, Tomoshige

    2006-01-01

    The transport properties of a 1-dimensional piecewise linear dynamical system are investigated through the spectrum of its Frobenius-Perron operator. For a class of initial densities, eigenvalues and eigenfunctions of the Frobenius-Perron operator are obtained explicitly. It is also found that in the long length wave limit, this system exhibits normal diffusion and super diffusion called Levy flight. The diffusion constant and stable index are derived from the eigenvalues. (author)

  5. Linear and nonlinear thermodynamics of a kinetic heat engine with fast transformations

    Cerino, Luca; Puglisi, Andrea; Vulpiani, Angelo

    2016-04-01

    We investigate a kinetic heat engine model composed of particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period τ : their relative excursions, δ and ɛ , respectively, constitute the thermodynamic forces dragging the system out of equilibrium. The analysis of the entropy production of the system allows us to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small δ and ɛ the fluxes are linear in the forces through a τ -dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which—in the linear regime—yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e., outside of the linear regime. In all our analysis the adiabatic limit τ →∞ and the the small-force limit δ ,ɛ →0 are not directly related.

  6. Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

    Stamova, Ivanka; Stamov, Gani

    2017-12-01

    In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

  7. Submicrosecond linear pulse transformer for 800 kV voltage with modular low-inductance primary power supply

    Bykov, Yu. A.; Krastelev, E. G., E-mail: ekrastelev@yandex.ru; Popov, G. V.; Sedin, A. A.; Feduschak, V. F. [Russian Academy of Sciences, Joint Institute for High Temperatures (Russian Federation)

    2016-12-15

    A pulsed power source with voltage amplitude up to 800 kV for fast charging (350–400 ns) of the forming line of a high-current nanosecond accelerator is developed. The source includes capacitive energy storage and a linear pulse transformer. The linear transformer consists of a set of 20 inductors with circular ferromagnetic cores surrounded by primary windings inside of which a common stock adder of voltage with film-glycerol insulation is placed. The primary energy storage consists of ten modules, each of which is a low-inductance assembly of two capacitors with a capacitance of 0.35 μF and one gas switch mounted in the same frame. The total energy stored in capacitors is 5.5 kJ at the operating voltage of 40 kV. According to test results, the parameters of the equivalent circuit of the source are the following: shock capacitance = 17.5 nF, inductance = 2 μH, resistance = 3.2 Ω.

  8. Correction of the significance level when attempting multiple transformations of an explanatory variable in generalized linear models

    2013-01-01

    Background In statistical modeling, finding the most favorable coding for an exploratory quantitative variable involves many tests. This process involves multiple testing problems and requires the correction of the significance level. Methods For each coding, a test on the nullity of the coefficient associated with the new coded variable is computed. The selected coding corresponds to that associated with the largest statistical test (or equivalently the smallest pvalue). In the context of the Generalized Linear Model, Liquet and Commenges (Stat Probability Lett,71:33–38,2005) proposed an asymptotic correction of the significance level. This procedure, based on the score test, has been developed for dichotomous and Box-Cox transformations. In this paper, we suggest the use of resampling methods to estimate the significance level for categorical transformations with more than two levels and, by definition those that involve more than one parameter in the model. The categorical transformation is a more flexible way to explore the unknown shape of the effect between an explanatory and a dependent variable. Results The simulations we ran in this study showed good performances of the proposed methods. These methods were illustrated using the data from a study of the relationship between cholesterol and dementia. Conclusion The algorithms were implemented using R, and the associated CPMCGLM R package is available on the CRAN. PMID:23758852

  9. The Wigner-Ville Distribution Based on the Linear Canonical Transform and Its Applications for QFM Signal Parameters Estimation

    Yu-E Song

    2014-01-01

    Full Text Available The Wigner-Ville distribution (WVD based on the linear canonical transform (LCT (WDL not only has the advantages of the LCT but also has the good properties of WVD. In this paper, some new and important properties of the WDL are derived, and the relationships between WDL and some other time-frequency distributions are discussed, such as the ambiguity function based on LCT (LCTAF, the short-time Fourier transform (STFT, and the wavelet transform (WT. The WDLs of some signals are also deduced. A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL is proposed and its applications in the estimation of parameters for QFM signals are also discussed. The GWDL of the QFM signal generates an impulse and the third-order phase coefficient of QFM signal can be estimated in accordance with the position information of such impulse. The proposed algorithm is fast because it only requires 1-dimensional maximization. Also the new algorithm only has fourth-order nonlinearity thus it has accurate estimation and low signal-to-noise ratio (SNR threshold. The simulation results are provided to support the theoretical results.

  10. On the prolongation structure and Backlund transformation for new non-linear Klein-Gordon equations

    Roy Chowdhury, A.; Mukherjee, J.

    1986-07-01

    We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual Sine-Gordon and Sinh-Gordon equations. The first one is of non-autonomous version of Sinh-Gordon system and the second is closely related to the usual Sine-Gordon theory. The first problem indicates how (x,t) dependent non-linear equations can be treated in the prolongation theory and how a Backlund map can be constructed. The second one is a variation of the usual Sine-Gordon equation and suggests that there may be other equations (similar to Sine-Gordon) which are completely integrable. In both cases we have been able to construct the Lax pair. We then construct an auto-Backlund map by following the idea of Konno and Wadati, for the generation of multisolution states. (author)

  11. Transformation

    Bock, Lars Nicolai

    2011-01-01

    Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi.......Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi....

  12. TRANSFORMATION

    LACKS,S.A.

    2003-10-09

    Transformation, which alters the genetic makeup of an individual, is a concept that intrigues the human imagination. In Streptococcus pneumoniae such transformation was first demonstrated. Perhaps our fascination with genetics derived from our ancestors observing their own progeny, with its retention and assortment of parental traits, but such interest must have been accelerated after the dawn of agriculture. It was in pea plants that Gregor Mendel in the late 1800s examined inherited traits and found them to be determined by physical elements, or genes, passed from parents to progeny. In our day, the material basis of these genetic determinants was revealed to be DNA by the lowly bacteria, in particular, the pneumococcus. For this species, transformation by free DNA is a sexual process that enables cells to sport new combinations of genes and traits. Genetic transformation of the type found in S. pneumoniae occurs naturally in many species of bacteria (70), but, initially only a few other transformable species were found, namely, Haemophilus influenzae, Neisseria meningitides, Neisseria gonorrheae, and Bacillus subtilis (96). Natural transformation, which requires a set of genes evolved for the purpose, contrasts with artificial transformation, which is accomplished by shocking cells either electrically, as in electroporation, or by ionic and temperature shifts. Although such artificial treatments can introduce very small amounts of DNA into virtually any type of cell, the amounts introduced by natural transformation are a million-fold greater, and S. pneumoniae can take up as much as 10% of its cellular DNA content (40).

  13. Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain

    Sui, Liansheng; Lu, Haiwei; Ning, Xiaojuan; Wang, Yinghui

    2014-02-01

    A double-image encryption scheme is proposed based on an asymmetric technique, in which the encryption and decryption processes are different and the encryption keys are not identical to the decryption ones. First, a phase-only function (POF) of each plain image is retrieved by using an iterative process and then encoded into an interim matrix. Two interim matrices are directly modulated into a complex image by using the convolution operation in the fractional Fourier transform (FrFT) domain. Second, the complex image is encrypted into the gray scale ciphertext with stationary white-noise distribution by using the FrFT. In the encryption process, three random phase functions are used as encryption keys to retrieve the POFs of plain images. Simultaneously, two decryption keys are generated in the encryption process, which make the optical implementation of the decryption process convenient and efficient. The proposed encryption scheme has high robustness to various attacks, such as brute-force attack, known plaintext attack, cipher-only attack, and specific attack. Numerical simulations demonstrate the validity and security of the proposed method.

  14. Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegó transformation

    Edinson Fuentes

    2015-01-01

    Full Text Available En el presente trabajo, analizamos las perturbaciones a una sucesión de momentos asociada a un funcional lineal de ortogonalidad que se representa por una medida positiva con soporte en [ − 1 , 1] . En particular, dada una cierta perturbación a dicha medida en la recta real, analizamos la p erturbación obtenida en la correspondiente medida en la circunferencia unidad, cuando dichas medidas están relacionadas por la transformación de Szeg ́ ́o. También se analiza una perturbación similar a través de la transform ación inversa de Szeg ́ ́o. En ambos casos, se muestra que la perturbación apli cada puede ser expresada en términos de la parte singular de las medidas, y t ambién a través de las correspondientes sucesiones de momentos.

  15. Dose fractionation effects in plateau-phase cultures of C3H 10T1/2 cells and their transformed counterparts

    Zeman, E.M.; Bedford, J.S.

    1985-01-01

    A comparison of γ-ray dose fractionation effects was made using plateau-phase cultures of C3H 10T1/2 cells and their transformed counterparts in an attempt to simulate basically similar populations of cells that differ primarily in their turnover rates. The status of cell populations with respect to their turnover rates may be an important factor influencing dose fractionation effects in early- and late-responding tissues. In this cell culture system, the rate of cell turnover was approximately three times higher for the plateau-phase transformed cultures. While the single acute dose survival curves for log-phase cells were indistinguishable, there were significant differences between the survival curves for plateau-phase cultures of the two cell types. Both cell lines had a similar capacity for repair of sublethal damage, but untransformed cells had a much greater capacity to repair potentially lethal damage in plateau phase. Multifraction survival curves were determined for both cell lines for doses per fraction ranging from 9.0 to 0.8 Gy, and from these isoeffect curves of log total dose versus dose per fraction were derived. The isoeffect curve for the slowly cycling, untransformed cells was found to be appreciably steeper than that for the more rapidly cycling transformed cells, a finding consistent with previously reported differences in dose fractionation isoeffect curves for early- and late-responding tissues in vivo

  16. Propagation of ultrashort laser pulses in water: linear absorption and onset of nonlinear spectral transformation.

    Sokolov, Alexei V; Naveira, Lucas M; Poudel, Milan P; Strohaber, James; Trendafilova, Cynthia S; Buck, William C; Wang, Jieyu; Strycker, Benjamin D; Wang, Chao; Schuessler, Hans; Kolomenskii, Alexandre; Kattawar, George W

    2010-01-20

    We study propagation of short laser pulses through water and use a spectral hole filling technique to essentially perform a sensitive balanced comparison of absorption coefficients for pulses of different duration. This study is motivated by an alleged violation of the Bouguer-Lambert-Beer law at low light intensities, where the pulse propagation is expected to be linear, and by a possible observation of femtosecond optical precursors in water. We find that at low intensities, absorption of laser light is determined solely by its spectrum and does not directly depend on the pulse duration, in agreement with our earlier work and in contradiction to some work of others. However, as the laser fluence is increased, interaction of light with water becomes nonlinear, causing energy exchange among the pulse's spectral components and resulting in peak-intensity dependent (and therefore pulse-duration dependent) transmission. For 30 fs pulses at 800 nm center wavelength, we determine the onset of nonlinear propagation effects to occur at a peak value of about 0.12 mJ/cm(2) of input laser energy fluence.

  17. TRANSFORMER

    Baker, W.R.

    1959-08-25

    Transformers of a type adapted for use with extreme high power vacuum tubes where current requirements may be of the order of 2,000 to 200,000 amperes are described. The transformer casing has the form of a re-entrant section being extended through an opening in one end of the cylinder to form a coaxial terminal arrangement. A toroidal multi-turn primary winding is disposed within the casing in coaxial relationship therein. In a second embodiment, means are provided for forming the casing as a multi-turn secondary. The transformer is characterized by minimized resistance heating, minimized external magnetic flux, and an economical construction.

  18. The Mechanism of Rh-Catalyzed Transformation of Fatty Acids to Linear Alpha olefins

    Sondre H. Hopen Eliasson

    2017-12-01

    Full Text Available Linear alpha olefins (LAOs are key commodity chemicals and petrochemical intermediates that are currently produced from fossil resources. Fatty acids are the obvious renewable starting material for LAOs, which can be obtained via transition-metal-catalyzed decarbonylative dehydration. However, even the best catalysts that have been obtained to date, which are based on palladium, are not active and stable enough for industrial use. To provide insight for design of better catalysts, we here present the first computationally derived mechanism for another attractive transition-metal for this reaction, rhodium. By comparing the calculated mechanisms and free energy profiles for the two metals, Pd and Rh, we single out important factors for a facile, low-barrier reaction and for a stable catalyst. While the olefin formation is rate limiting for both of the metals, the rate-determining intermediate for Rh is, in contrast to Pd, the starting complex, (PPh32Rh(COCl. This complex largely draws its stability from the strength of the Rh(I–CO bond. CO is a much less suitable ligand for the high-oxidation state Rh(III. However, for steric reasons, rhodium dissociates a bulkier triphenylphosphine and keeps the carbonyl during the oxidative addition, which is less favorable than for Pd. When compared to Pd, which dissociates two phosphine ligands at the start of the reaction, the catalytic activity of Rh also appears to be hampered by its preference for high coordination numbers. The remaining ancillary ligands leave less space for the metal to mediate the reaction.

  19. Digital signals processing using non-linear orthogonal transformation in frequency domain

    Ivanichenko E.V.

    2017-12-01

    domain is proposed, using some properties of nonlinear orthogonal transformations. The theoretical bases of this method and the results of the statistical modeling, proving its efficacy in suppressing concentrated interference in the communication channels.

  20. Application of linear discriminant analysis and Attenuated Total Reflectance Fourier Transform Infrared microspectroscopy for diagnosis of colon cancer.

    Khanmohammadi, Mohammadreza; Bagheri Garmarudi, Amir; Samani, Simin; Ghasemi, Keyvan; Ashuri, Ahmad

    2011-06-01

    Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) microspectroscopy was applied for detection of colon cancer according to the spectral features of colon tissues. Supervised classification models can be trained to identify the tissue type based on the spectroscopic fingerprint. A total of 78 colon tissues were used in spectroscopy studies. Major spectral differences were observed in 1,740-900 cm(-1) spectral region. Several chemometric methods such as analysis of variance (ANOVA), cluster analysis (CA) and linear discriminate analysis (LDA) were applied for classification of IR spectra. Utilizing the chemometric techniques, clear and reproducible differences were observed between the spectra of normal and cancer cases, suggesting that infrared microspectroscopy in conjunction with spectral data processing would be useful for diagnostic classification. Using LDA technique, the spectra were classified into cancer and normal tissue classes with an accuracy of 95.8%. The sensitivity and specificity was 100 and 93.1%, respectively.

  1. Variations on the planar Landau problem: canonical transformations, a purely linear potential and the half-plane

    Govaerts, Jan; Hounkonnou, M Norbert; Mweene, Habatwa V

    2009-01-01

    The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well.

  2. Investigating the performances of a 1 MV high pulsed power linear transformer driver: from beam dynamics to x radiation

    Maisonny, R.; Ribière, M.; Toury, M.; Plewa, J. M.; Caron, M.; Auriel, G.; d'Almeida, T.

    2016-12-01

    The performance of a 1 MV pulsed high-power linear transformer driver accelerator were extensively investigated based on a numerical approach which utilizes both electromagnetic and Monte Carlo simulations. Particle-in-cell calculations were employed to examine the beam dynamics throughout the magnetically insulated transmission line which governs the coupling between the generator and the electron diode. Based on the information provided by the study of the beam dynamics, and using Monte Carlo methods, the main properties of the resulting x radiation were predicted. Good agreement was found between these simulations and experimental results. This work provides a detailed understanding of mechanisms affecting the performances of this type of high current, high-voltage pulsed accelerator, which are very promising for a growing number of applications.

  3. Variations on the planar Landau problem: canonical transformations, a purely linear potential and the half-plane

    Govaerts, Jan [Center for Particle Physics and Phenomenology (CP3), Institut de Physique Nucleaire, Universite catholique de Louvain (UCL), 2, Chemin du Cyclotron, B-1348 Louvain-la Neuve (Belgium); Hounkonnou, M Norbert [International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, 072 BP 50, Cotonou (Benin); Mweene, Habatwa V [Physics Department, University of Zambia, PO Box 32379, Lusaka (Zambia)], E-mail: Jan.Govaerts@uclouvain.be, E-mail: hounkonnou@yahoo.fr, E-mail: norbert.hounkonnou@cipma.uac.bj, E-mail: habatwamweene@yahoo.com, E-mail: hmweene@unza.zm

    2009-12-04

    The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well.

  4. Dynamic flow-through sequential extraction for assessment of fractional transformation and inter-element associations of arsenic in stabilized soil and sludge

    Buanuam, Janya; Wennrich, Rainer

    2010-01-01

    A dynamic flow-through extraction system was applied for the first time to ascertain the fractional transformation and inter-element associations of arsenic in stabilized environmental solids, as exemplified by the partitioning of soil and sludge stabilized with three additives, namely MnO 2 , Ca(OH) 2 and FeSO 4 . The extraction system used not only gave fractionation data, but also the extraction profiles (extractograms) which were used for investigation of the breaking down of phases, kinetic releasing of As and elemental association between As and inorganic additives. Five geochemical fractions of As were elucidated by accommodation in the flow manifold of a modified Wenzel's sequential extraction scheme, well established for fractionation of arsenic. The results revealed that MnO 2 and FeSO 4 have a slight effect on As phase transformation for soil and sludge samples amended for one week whereas the addition of Ca(OH) 2 increases As mobility due to the desorption of As from the solid Fe-oxides phase. The significant change in fractional transformation after 8 weeks of incubation can be seen in MnO 2 -treated soil. There was an increase of 17% in the non-mobilizable As fraction in MnO 2 -treated soil. From extractograms, arsenic in untreated soil was found to be rapidly leached and concurrently released with Fe. This may be evidence that the release of As is dependent on the dissolution of amorphous Fe oxides. In MnO 2 -treated soil, a strong affinity was observed between Mn and As in the amorphous Fe/Al oxides fraction, and this plays an important role in slowing down the kinetics of As releasing.

  5. Investigation of switch designs for the dynamic load current multiplier scheme on the SPHYNX microsecond linear transformer driver

    Maysonnave, T.; Bayol, F.; Demol, G.; Almeida, T. d'; Lassalle, F.; Morell, A.; Grunenwald, J.; Chuvatin, A.S.; Pecastaing, L.; De Ferron, A.S.

    2014-01-01

    SPHINX is a microsecond linear transformer driver LTD, used essentially for implosion of Z-pinch loads in direct drive mode. It can deliver a 6-MA current pulse within 800 ns into a Z-pinch load. The dynamic load current multiplier concept enables the current pulse to be modified by increasing its amplitude while reducing its rise time before being delivered to the load. This compact system is made up of concentric electrodes (auto transformer), a dynamic flux extruder (cylindrical wire array), a vacuum convolute (eight post-holes), and a vacuum closing switch, which is the key component of the system. Several different schemes are investigated for designing a vacuum switch suitable for operating the dynamic load current multiplier on the SPHINX generator for various applications, including isentropic compression experiments and Z-pinch radiation effects studies. In particular, the design of a compact vacuum surface switch and a multichannel vacuum switch, located upstream of the load are studied. Electrostatic simulations supporting the switch designs are presented along with test bed experiments. Initial results from shots on the SPHINX driver are also presented. (authors)

  6. Influence of the void fraction in the linear reactivity model; Influencia de la fraccion de vacios en el modelo de reactividad lineal

    Castillo, J.A.; Ramirez, J.R.; Alonso, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)]. e-mail: jacm@nuclear.inin.mx

    2003-07-01

    The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)

  7. Dose fractionated gamma knife radiosurgery for large arteriovenous malformations on daily or alternate day schedule outside the linear quadratic model: Proof of concept and early results. A substitute to volume fractionation.

    Mukherjee, Kanchan Kumar; Kumar, Narendra; Tripathi, Manjul; Oinam, Arun S; Ahuja, Chirag K; Dhandapani, Sivashanmugam; Kapoor, Rakesh; Ghoshal, Sushmita; Kaur, Rupinder; Bhatt, Sandeep

    2017-01-01

    To evaluate the feasibility, safety and efficacy of dose fractionated gamma knife radiosurgery (DFGKRS) on a daily schedule beyond the linear quadratic (LQ) model, for large volume arteriovenous malformations (AVMs). Between 2012-16, 14 patients of large AVMs (median volume 26.5 cc) unsuitable for surgery or embolization were treated in 2-3 of DFGKRS sessions. The Leksell G frame was kept in situ during the whole procedure. 86% (n = 12) patients had radiologic evidence of bleed, and 43% (n = 6) had presented with a history of seizures. 57% (n = 8) patients received a daily treatment for 3 days and 43% (n = 6) were on an alternate day (2 fractions) regimen. The marginal dose was split into 2 or 3 fractions of the ideal prescription dose of a single fraction of 23-25 Gy. The median follow up period was 35.6 months (8-57 months). In the three-fraction scheme, the marginal dose ranged from 8.9-11.5 Gy, while in the two-fraction scheme, the marginal dose ranged from 11.3-15 Gy at 50% per fraction. Headache (43%, n = 6) was the most common early postoperative complication, which was controlled with short course steroids. Follow up evaluation of at least three years was achieved in seven patients, who have shown complete nidus obliteration in 43% patients while the obliteration has been in the range of 50-99% in rest of the patients. Overall, there was a 67.8% reduction in the AVM volume at 3 years. Nidus obliteration at 3 years showed a significant rank order correlation with the cumulative prescription dose (p 0.95, P value 0.01), with attainment of near-total (more than 95%) obliteration rates beyond 29 Gy of the cumulative prescription dose. No patient receiving a cumulative prescription dose of less than 31 Gy had any severe adverse reaction. In co-variate adjusted ordinal regression, only the cumulative prescription dose had a significant correlation with common terminology criteria for adverse events (CTCAE) severity (P value 0.04), independent of age, AVM volume

  8. Linear algebra

    Shilov, Georgi E

    1977-01-01

    Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

  9. Fractional approximations for linear first order differential equation with polynomial coefficients-application to E1(x) and Z(s)

    Martin, P.; Zamudio-Cristi, J.

    1982-01-01

    A method is described to obtain fractional approximations for linear first order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the highest and lowest power of the variable after the sustitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Pade method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which give three exact digits for most of the real values of the variable. Approximations of higher accuracy and of the same degree than other authors are also obtained. (Author) [pt

  10. Calculated fraction of an incident current pulse that will be accelerated by an electron linear accelerator and comparisons with experimental data

    Alsmiller, R.G. Jr.; Alsmiller, F.S.; Lewis, T.A.

    1986-05-01

    In a series of previous papers, calculated results obtained using a one-dimensional ballistic model were presented to aid in the design of a prebuncher for the Oak Ridge Electron Linear Accelerator. As part of this work, a model was developed to provide limits on the fraction of an incident current pulse that would be accelerated by the existing accelerator. In this paper experimental data on this fraction are presented and the validity of the model developed previously is tested by comparing calculated and experimental data. Part of the experimental data is used to fix the physical parameters in the model and then good agreement between the calculated results and the rest of the experimental data is obtained

  11. On the motion of non-linear oscillators with a fractional-order restoring force and time variable parameters

    Kovacic, Ivana

    2009-01-01

    An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov-Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results.

  12. Radiation-induced transformation of SV40-immortalized human thyroid epithelial cells by single and fractionated exposure to γ-irradiation in vitro

    Riches, A.C.; Herceg, Z.; Bryant, P.E.; Wynford-Thomas, D.

    1994-01-01

    Radiation-induced transformation of a human thyroid epithelial cell line (HTori-3) has been investigated following exposure to single and fractionated doses of γ-irradiation. The human epithelial cells were irradiated in vitro and following passaging, transplanted to the athymic nude mouse. Following a single exposure to γ-irradiation in the range 0.5-4Gy, 22 tumours were observed in 45 recipients and following three equal fractions in the range 0.5-4Gy per fraction, 18 tumours were observed in 31 recipients. Tumours were undifferentiated carcinomas and were observed from 7 to 20 weeks after transplantation. They occurred after similar radiation doses to those received by the children in the Belarus region of Ukraine, who developed thyroid tumours. The number of tumours observed, in each group receiving cells irradiated with a single dose of γ-irradiation in the range 0.5-4 Gy, was similar. Cell lines were established from some tumours and the tumorigenicity confirmed by retransplantation. These tumour cell lines were more radiosensitive than the human thyroid epithelial cell line they were derived from. This indicates that transformed cells were not being selected from a subpopulation within the parent cell line but that radiation-induced transformants were being induced de novo. The human origin of the tumours was established by karyotyping, immunocytochemical demonstration of human epithelial cytokeratins and p53 analysis. DNA fingerprinting confirmed that the tumours were derived from the original cell line. (author)

  13. An optimized regulating method for composting phosphorus fractions transformation based on biochar addition and phosphate-solubilizing bacteria inoculation.

    Wei, Yuquan; Zhao, Yue; Wang, Huan; Lu, Qian; Cao, Zhenyu; Cui, Hongyang; Zhu, Longji; Wei, Zimin

    2016-12-01

    The study was conducted to investigate the influence of biochar and/or phosphate-solubilizing bacteria (PSB) inoculants on microbial biomass, bacterial community composition and phosphorus (P) fractions during kitchen waste composting amended with rock phosphate (RP). There were distinct differences in the physic-chemical parameters, the proportion of P fractions and bacterial diversity in different treatments. The contribution of available P fractions increased during composting especially in the treatment with the addition of PSB and biochar. Redundancy analysis showed that bacterial compositions were significantly influenced by P content, inoculation and biochar. Variance partitioning further showed that synergy of inoculated PSB and indigenous bacterial communities and the joint effect between biochar and bacteria explained the largest two proportion of the variation in P fractions. Therefore, the combined application of PSB and biochar to improve the inoculation effect and an optimized regulating method were suggested based on the distribution of P fractions. Copyright © 2016 Elsevier Ltd. All rights reserved.

  14. NTCP modelling of lung toxicity after SBRT comparing the universal survival curve and the linear quadratic model for fractionation correction

    Wennberg, Berit M.; Baumann, Pia; Gagliardi, Giovanna

    2011-01-01

    Background. In SBRT of lung tumours no established relationship between dose-volume parameters and the incidence of lung toxicity is found. The aim of this study is to compare the LQ model and the universal survival curve (USC) to calculate biologically equivalent doses in SBRT to see if this will improve knowledge on this relationship. Material and methods. Toxicity data on radiation pneumonitis grade 2 or more (RP2+) from 57 patients were used, 10.5% were diagnosed with RP2+. The lung DVHs were corrected for fractionation (LQ and USC) and analysed with the Lyman- Kutcher-Burman (LKB) model. In the LQ-correction α/β = 3 Gy was used and the USC parameters used were: α/β = 3 Gy, D 0 = 1.0 Gy, n = 10, α 0.206 Gy-1 and d T = 5.8 Gy. In order to understand the relative contribution of different dose levels to the calculated NTCP the concept of fractional NTCP was used. This might give an insight to the questions of whether 'high doses to small volumes' or 'low doses to large volumes' are most important for lung toxicity. Results and Discussion. NTCP analysis with the LKB-model using parameters m = 0.4, D50 = 30 Gy resulted for the volume dependence parameter (n) with LQ correction n = 0.87 and with USC correction n = 0.71. Using parameters m = 0.3, D 50 = 20 Gy n = 0.93 with LQ correction and n 0.83 with USC correction. In SBRT of lung tumours, NTCP modelling of lung toxicity comparing models (LQ,USC) for fractionation correction, shows that low dose contribute less and high dose more to the NTCP when using the USC-model. Comparing NTCP modelling of SBRT data and data from breast cancer, lung cancer and whole lung irradiation implies that the response of the lung is treatment specific. More data are however needed in order to have a more reliable modelling

  15. Design of a 7-MV Linear Transformer Driver (LTD) for down-hole flash x-ray radiography

    Cordova, Steve Ray; Welch, Dale Robert; Oliver, Bryan Velten; Rose, David Vincent; Johnson, David Lee; Bruner, Nichelle Lee; Leckbee, Joshua J.

    2008-01-01

    Pulsed power driven flash x-ray radiography is a valuable diagnostic for subcritical experiments at the Nevada Test Site. The existing dual-axis Cygnus system produces images using a 2.25 MV electron beam diode to produce intense x-rays from a small source. Future hydrodynamic experiments will likely use objects with higher areal mass, requiring increased x-ray dose and higher voltages while maintaining small source spot size. A linear transformer driver (LTD) is a compact pulsed power technology with applications ranging from pulsed power flash x-ray radiography to high current Z-pinch accelerators. This report describes the design of a 7-MV dual-axis system that occupies the same lab space as the Cygnus accelerators. The work builds on a design proposed in a previous report [1]. This new design provides increased diode voltage from a lower impedance accelerator to improve coupling to low impedance diodes such as the self magnetic pinch (SMP) diode. The design also improves the predicted reliability by operating at a lower charge voltage and removing components that have proven vulnerable to failure. Simulations of the new design and experimental results of the 1-MV prototype are presented

  16. Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

    Sifeu Takougang Kingni

    2017-01-01

    Full Text Available A linear resistive-capacitive-inductance shunted junction (LRCLSJ model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.

  17. Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls

    S. Alonso-Quesada

    2010-01-01

    Full Text Available This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant (LTI continuous-time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced-order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast-sampled control signal. A suitable on-line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy.

  18. An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.

    Jamshad Ahmad

    Full Text Available In this paper, a fractional complex transform (FCT is used to convert the given fractional partial differential equations (FPDEs into corresponding partial differential equations (PDEs and subsequently Reduced Differential Transform Method (RDTM is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.

  19. Free microparticles—An inducing mechanism of pre-firing in high pressure gas switches for fast linear transformer drivers

    Li, Xiaoang; Pei, Zhehao; Wu, Zhicheng; Zhang, Yuzhao; Liu, Xuandong; Li, Yongdong; Zhang, Qiaogen

    2018-03-01

    Microparticle initiated pre-firing of high pressure gas switches for fast linear transformer drivers (FLTDs) is experimentally and theoretically verified. First, a dual-electrode gas switch equipped with poly-methyl methacrylate baffles is used to capture and collect the microparticles. By analyzing the electrode surfaces and the collecting baffles by a laser scanning confocal microscope, microparticles ranging in size from tens of micrometers to over 100 μm are observed under the typical working conditions of FLTDs. The charging and movement of free microparticles in switch cavity are studied, and the strong DC electric field drives the microparticles to bounce off the electrode. Three different modes of free microparticle motion appear to be responsible for switch pre-firing. (i) Microparticles adhere to the electrode surface and act as a fixed protrusion which distorts the local electric field and initiates the breakdown in the gap. (ii) One particle escapes toward the opposite electrode and causes a near-electrode microdischarge, inducing the breakdown of the residual gap. (iii) Multiple moving microparticles are occasionally in cascade, leading to pre-firing. Finally, as experimental verification, repetitive discharges at ±90 kV are conducted in a three-electrode field-distortion gas switch, with two 8 mm gaps and pressurized with nitrogen. An ultrasonic probe is employed to monitor the bounce signals. In pre-firing incidents, the bounce is detected shortly before the collapse of the voltage waveform, which demonstrates that free microparticles contribute significantly to the mechanism that induces pre-firing in FLTD gas switches.

  20. Design of a 5-MA 100-ns linear-transformer-driver accelerator for wire array Z-pinch experiments

    Zhou, Lin; Li, Zhenghong; Wang, Zhen; Liang, Chuan; Li, Mingjia; Qi, Jianmin; Chu, Yanyun

    2016-03-01

    The linear-transformer-driver (LTD) is a recently developed pulsed-power technology that shows great promise for a number of applications. These include a Z -pinch-driven fission-fusion-hybrid reactor that is being developed by the Chinese Academy of Engineering Physics. In support of the reactor development effort, we are planning to build an LTD-based accelerator that is optimized for driving wire-array Z -pinch loads. The accelerator comprises six modules in parallel, each of which has eight series 0.8-MA LTD cavities in a voltage-adder configuration. Vacuum transmission lines are used from the interior of the adder to the central vacuum chamber where the load is placed. Thus the traditional stack-flashover problem is eliminated. The machine is 3.2 m tall and 12 m in outer diameter including supports. A prototype cavity was built and tested for more than 6000 shots intermittently at a repetition rate of 0.1 Hz. A novel trigger, in which only one input trigger pulse is needed by utilizing an internal trigger brick, was developed and successfully verified in these shots. A full circuit modeling was conducted for the accelerator. The simulation result shows that a current pulse rising to 5.2 MA in 91 ns (10%-90%) can be delivered to the wire-array load, which is 1.5 cm in height, 1.2 cm in initial radius, and 1 mg in mass. The maximum implosion velocity of the load is 32 cm /μ s when compressed to 0.1 of the initial radius. The maximum kinetic energy is 78 kJ, which is 11.7% of the electric energy stored in the capacitors. This accelerator is supposed to enable a radiation energy efficiency of 20%-30%, providing a high efficient facility for research on the fast Z pinch and technologies for repetition-rate-operated accelerators.

  1. Free microparticles-An inducing mechanism of pre-firing in high pressure gas switches for fast linear transformer drivers.

    Li, Xiaoang; Pei, Zhehao; Wu, Zhicheng; Zhang, Yuzhao; Liu, Xuandong; Li, Yongdong; Zhang, Qiaogen

    2018-03-01

    Microparticle initiated pre-firing of high pressure gas switches for fast linear transformer drivers (FLTDs) is experimentally and theoretically verified. First, a dual-electrode gas switch equipped with poly-methyl methacrylate baffles is used to capture and collect the microparticles. By analyzing the electrode surfaces and the collecting baffles by a laser scanning confocal microscope, microparticles ranging in size from tens of micrometers to over 100 μm are observed under the typical working conditions of FLTDs. The charging and movement of free microparticles in switch cavity are studied, and the strong DC electric field drives the microparticles to bounce off the electrode. Three different modes of free microparticle motion appear to be responsible for switch pre-firing. (i) Microparticles adhere to the electrode surface and act as a fixed protrusion which distorts the local electric field and initiates the breakdown in the gap. (ii) One particle escapes toward the opposite electrode and causes a near-electrode microdischarge, inducing the breakdown of the residual gap. (iii) Multiple moving microparticles are occasionally in cascade, leading to pre-firing. Finally, as experimental verification, repetitive discharges at ±90 kV are conducted in a three-electrode field-distortion gas switch, with two 8 mm gaps and pressurized with nitrogen. An ultrasonic probe is employed to monitor the bounce signals. In pre-firing incidents, the bounce is detected shortly before the collapse of the voltage waveform, which demonstrates that free microparticles contribute significantly to the mechanism that induces pre-firing in FLTD gas switches.

  2. Sample handling and contamination encountered when coupling offline normal phase high performance liquid chromatography fraction collection of petroleum samples to Fourier transform ion cyclotron resonance mass spectrometry.

    Oro, Nicole E; Whittal, Randy M; Lucy, Charles A

    2012-09-05

    Normal phase high performance liquid chromatography (HPLC) is used to separate a gas oil petroleum sample, and the fractions are collected offline and analyzed on a high resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometer (FT-ICR MS). The separation prior to MS analysis dilutes the sample significantly; therefore the fractions need to be prepared properly to achieve the best signal possible. The methods used to prepare the HPLC fractions for MS analysis are described, with emphasis placed on increasing the concentration of analyte species. The dilution effect also means that contamination in the MS spectra needs to be minimized. The contamination from molecular sieves, plastics, soap, etc. and interferences encountered during the offline fraction collection process are described and eliminated. A previously unreported MS contamination of iron formate clusters with a 0.8 mass defect in positive mode electrospray is also described. This interference resulted from the stainless steel tubing in the HPLC system. Contamination resulting from what has tentatively been assigned as palmitoylglycerol and stearoylglycerol was also observed; these compounds have not previously been reported as contaminant peaks. Copyright © 2012 Elsevier B.V. All rights reserved.

  3. Barium isotope fractionation during the experimental transformation of aragonite to witherite and of gypsum to barite, and the effect of ion (de)solvation.

    Böttcher, Michael E; Neubert, Nadja; von Allmen, Katja; Samankassou, Elias; Nägler, Thomas F

    2018-06-01

    In this study, we present the experimental results for stable barium (Ba) isotope fractionation ( 137 Ba/ 134 Ba) during the transformation of aragonite (CaCO 3 ) and gypsum (CaSO 4 ·2H 2 O) in Ba-bearing aqueous solution to witherite (BaCO 3 ) and barite (BaSO 4 ), respectively. The process was studied at three temperatures between 4 and 60 °C. In all cases, the transformation leads to a relative enrichment of the lighter 134 Ba isotope in the solid compared to the aqueous solution, with 137/134 Ba enrichment factors between -0.11 and -0.17 ‰ for BaCO 3 , and -0.21 and -0.26 ‰ for BaSO 4 . The corresponding mass-dependent 138/134 Ba enrichment factors are -0.15 to -0.23 ‰ for BaCO 3 , and -0.28 to -0.35 ‰ for BaSO 4 . The magnitude of isotope fractionation is within the range of recent reports for witherite and barite formation, as well as trace Ba incorporation into orthorhombic aragonite, and no substantial impact of temperature can be found between 4 and 80 °C. In previous studies, ion (de)solvation has been suggested to impact both the crystallization process of Ba-bearing solids and associated Ba isotope fractionation. Precipitation experiments of BaSO 4 and BaCO 3 using an methanol-containing aqueous solution indicate only a minor effect of ion and crystal surface (de)solvation on the overall Ba isotope fractionation process.

  4. A no-key-exchange secure image sharing scheme based on Shamir's three-pass cryptography protocol and the multiple-parameter fractional Fourier transform.

    Lang, Jun

    2012-01-30

    In this paper, we propose a novel secure image sharing scheme based on Shamir's three-pass protocol and the multiple-parameter fractional Fourier transform (MPFRFT), which can safely exchange information with no advance distribution of either secret keys or public keys between users. The image is encrypted directly by the MPFRFT spectrum without the use of phase keys, and information can be shared by transmitting the encrypted image (or message) three times between users. Numerical simulation results are given to verify the performance of the proposed algorithm.

  5. A Simulation-Based Linear Fractional Programming Model for Adaptable Water Allocation Planning in the Main Stream of The Songhua River Basin, China

    Qiang Fu

    2018-05-01

    Full Text Available The potential influence of natural variations in a climate system on global warming can change the hydrological cycle and threaten current strategies of water management. A simulation-based linear fractional programming (SLFP model, which integrates a runoff simulation model (RSM into a linear fractional programming (LFP framework, is developed for optimal water resource planning. The SLFP model has multiple objectives such as benefit maximization and water supply minimization, balancing water conflicts among various water demand sectors, and addressing complexities of water resource allocation system. Lingo and Excel programming solutions were used to solve the model. Water resources in the main stream basin of the Songhua River are allocated for 4 water demand sectors in 8 regions during two planning periods under different scenarios. Results show that the increase or decrease of water supply to the domestic sector is related to the change in population density at different regions in different target years. In 2030, the water allocation in the industrial sector decreased by 1.03–3.52% compared with that in 2020, while the water allocation in the environmental sector increased by 0.12–1.29%. Agricultural water supply accounts for 54.79–77.68% of total water supply in different regions. These changes in water resource allocation for various sectors were affected by different scenarios in 2020; however, water resource allocation for each sector was relatively stable under different scenarios in 2030. These results suggest that the developed SLFP model can help to improve the adjustment of water use structure and water utilization efficiency.

  6. Design of a 5-MA 100-ns linear-transformer-driver accelerator for wire array Z-pinch experiments

    Zhou Lin

    2016-03-01

    Full Text Available The linear-transformer-driver (LTD is a recently developed pulsed-power technology that shows great promise for a number of applications. These include a Z-pinch-driven fission-fusion-hybrid reactor that is being developed by the Chinese Academy of Engineering Physics. In support of the reactor development effort, we are planning to build an LTD-based accelerator that is optimized for driving wire-array Z-pinch loads. The accelerator comprises six modules in parallel, each of which has eight series 0.8-MA LTD cavities in a voltage-adder configuration. Vacuum transmission lines are used from the interior of the adder to the central vacuum chamber where the load is placed. Thus the traditional stack-flashover problem is eliminated. The machine is 3.2 m tall and 12 m in outer diameter including supports. A prototype cavity was built and tested for more than 6000 shots intermittently at a repetition rate of 0.1 Hz. A novel trigger, in which only one input trigger pulse is needed by utilizing an internal trigger brick, was developed and successfully verified in these shots. A full circuit modeling was conducted for the accelerator. The simulation result shows that a current pulse rising to 5.2 MA in 91 ns (10%–90% can be delivered to the wire-array load, which is 1.5 cm in height, 1.2 cm in initial radius, and 1 mg in mass. The maximum implosion velocity of the load is 32  cm/μs when compressed to 0.1 of the initial radius. The maximum kinetic energy is 78 kJ, which is 11.7% of the electric energy stored in the capacitors. This accelerator is supposed to enable a radiation energy efficiency of 20%–30%, providing a high efficient facility for research on the fast Z pinch and technologies for repetition-rate-operated accelerators.

  7. The high current, fast, 100ns, Linear Transformer Driver (LTD) developmental project at Sandia Laboratories and HCEI

    Ward, Kevin S.; Long, Finis W.; Sinebryukhov, Vadim A.; Kim, Alexandre A.; Wakeland, Peter Eric; McKee, G. Randall; Woodworth, Joseph Ray; McDaniel, Dillon Heirman; Fowler, William E.; Mazarakis, Michael Gerrassimos; Porter, John Larry Jr.; Struve, Kenneth William; Savage, Mark Edward; Stygar, William A.; LeChien, Keith R.; Matzen, Maurice Keith

    2010-01-01

    Sandia National Laboratories, Albuquerque, N.M., USA, in collaboration with the High Current Electronic Institute (HCEI), Tomsk, Russia, is developing a new paradigm in pulsed power technology: the Linear Transformer Driver (LTD) technology. This technological approach can provide very compact devices that can deliver very fast high current and high voltage pulses straight out of the cavity with out any complicated pulse forming and pulse compression network. Through multistage inductively insulated voltage adders, the output pulse, increased in voltage amplitude, can be applied directly to the load. The load may be a vacuum electron diode, a z-pinch wire array, a gas puff, a liner, an isentropic compression load (ICE) to study material behavior under very high magnetic fields, or a fusion energy (IFE) target. This is because the output pulse rise time and width can be easily tailored to the specific application needs. In this paper we briefly summarize the developmental work done in Sandia and HCEI during the last few years, and describe our new MYKONOS Sandia High Current LTD Laboratory. An extensive evaluation of the LTD technology is being performed at SNL and the High Current Electronic Institute (HCEI) in Tomsk Russia. Two types of High Current LTD cavities (LTD I-II, and 1-MA LTD) were constructed and tested individually and in a voltage adder configuration (1-MA cavity only). All cavities performed remarkably well and the experimental results are in full agreement with analytical and numerical calculation predictions. A two-cavity voltage adder is been assembled and currently undergoes evaluation. This is the first step towards the completion of the 10-cavity, 1-TW module. This MYKONOS voltage adder will be the first ever IVA built with a transmission line insulated with deionized water. The LTD II cavity renamed LTD III will serve as a test bed for evaluating a number of different types of switches, resistors, alternative capacitor configurations, cores

  8. The Risk of Radiation-Induced Tumors or Malignant Transformation After Single-Fraction Intracranial Radiosurgery: Results Based on a 25-Year Experience

    Pollock, Bruce E., E-mail: pollock.bruce@mayo.edu [Department of Neurological Surgery, Mayo Clinic College of Medicine, Rochester, Minnesota (United States); Department of Radiation Oncology, Mayo Clinic College of Medicine, Rochester, Minnesota (United States); Link, Michael J. [Department of Neurological Surgery, Mayo Clinic College of Medicine, Rochester, Minnesota (United States); Department of Otorhinolaryngology, Mayo Clinic College of Medicine, Rochester, Minnesota (United States); Stafford, Scott L. [Department of Radiation Oncology, Mayo Clinic College of Medicine, Rochester, Minnesota (United States); Parney, Ian F. [Department of Neurological Surgery, Mayo Clinic College of Medicine, Rochester, Minnesota (United States); Garces, Yolanda I.; Foote, Robert L. [Department of Radiation Oncology, Mayo Clinic College of Medicine, Rochester, Minnesota (United States)

    2017-04-01

    Purpose: To determine the risk of radiation-induced tumors or malignant transformation after single-fraction intracranial stereotactic radiosurgery (SRS). Methods and Materials: We performed a retrospective review of 1837 patients who received single-fraction SRS for arteriovenous malformation or benign tumor (meningioma, vestibular schwannoma, pituitary adenoma, glomus tumor) at a single center between 1990 and 2009. Patients were excluded if they refused research authorization (n=31), had a genetic predisposition to tumor development (n=84), received prior or concurrent radiation therapy (n=79), or had less than 5 years of imaging follow-up after SRS (n=501). The median imaging follow-up period for the remaining 1142 patients was 9.0 years (range, 5-24.9 years). Results: No radiation-induced tumors were identified in 11,264 patient-years of follow-up after SRS. The risk of a radiation-induced tumor developing after SRS was 0.0% at 5 years (95% confidence interval [CI], 0.0%-0.4%), 0.0% at 10 years (95% CI, 0.0%-0.9%), and 0.0% at 15 years (95% CI, 0.0%-2.8%). Malignant transformation occurred in 7 of 316 meningioma patients (2.2%) and 1 of 358 vestibular schwannoma patients (0.3%) at a median of 4.9 years (range, 2.8-13.8 years) after SRS. No cases of malignant transformation were noted in patients with pituitary adenomas (n=188) or glomus tumors (n=47). The 5-, 10-, and 15-year risk of malignant transformation was 0.5% (95% CI, 0.0%-0.9%), 0.8% (95% CI, 0.0%-1.8%), and 2.4% (95% CI, 0.0%-5.5%), respectively. Patients who underwent prior resection (hazard ratio, 14.56; 95% CI, 1.79-118.33; P=.01) and who had meningioma pathology (hazard ratio, 11.72; 95% CI, 1.44-96.15; P=.02) were at increased risk of malignant transformation. Conclusions: The risk of radiation-induced tumors or malignant transformation after SRS is very low and should not be used as a justification for choosing alternative treatment approaches (surgical resection, observation) over SRS

  9. The Risk of Radiation-Induced Tumors or Malignant Transformation After Single-Fraction Intracranial Radiosurgery: Results Based on a 25-Year Experience

    Pollock, Bruce E.; Link, Michael J.; Stafford, Scott L.; Parney, Ian F.; Garces, Yolanda I.; Foote, Robert L.

    2017-01-01

    Purpose: To determine the risk of radiation-induced tumors or malignant transformation after single-fraction intracranial stereotactic radiosurgery (SRS). Methods and Materials: We performed a retrospective review of 1837 patients who received single-fraction SRS for arteriovenous malformation or benign tumor (meningioma, vestibular schwannoma, pituitary adenoma, glomus tumor) at a single center between 1990 and 2009. Patients were excluded if they refused research authorization (n=31), had a genetic predisposition to tumor development (n=84), received prior or concurrent radiation therapy (n=79), or had less than 5 years of imaging follow-up after SRS (n=501). The median imaging follow-up period for the remaining 1142 patients was 9.0 years (range, 5-24.9 years). Results: No radiation-induced tumors were identified in 11,264 patient-years of follow-up after SRS. The risk of a radiation-induced tumor developing after SRS was 0.0% at 5 years (95% confidence interval [CI], 0.0%-0.4%), 0.0% at 10 years (95% CI, 0.0%-0.9%), and 0.0% at 15 years (95% CI, 0.0%-2.8%). Malignant transformation occurred in 7 of 316 meningioma patients (2.2%) and 1 of 358 vestibular schwannoma patients (0.3%) at a median of 4.9 years (range, 2.8-13.8 years) after SRS. No cases of malignant transformation were noted in patients with pituitary adenomas (n=188) or glomus tumors (n=47). The 5-, 10-, and 15-year risk of malignant transformation was 0.5% (95% CI, 0.0%-0.9%), 0.8% (95% CI, 0.0%-1.8%), and 2.4% (95% CI, 0.0%-5.5%), respectively. Patients who underwent prior resection (hazard ratio, 14.56; 95% CI, 1.79-118.33; P=.01) and who had meningioma pathology (hazard ratio, 11.72; 95% CI, 1.44-96.15; P=.02) were at increased risk of malignant transformation. Conclusions: The risk of radiation-induced tumors or malignant transformation after SRS is very low and should not be used as a justification for choosing alternative treatment approaches (surgical resection, observation) over SRS

  10. On generalized fractional vibration equation

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  11. Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

    Das, R.N.

    1980-01-01

    The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)

  12. Fractional charges

    Saminadayar, L.

    2001-01-01

    20 years ago fractional charges were imagined to explain values of conductivity in some materials. Recent experiments have proved the existence of charges whose value is the third of the electron charge. This article presents the experimental facts that have led theorists to predict the existence of fractional charges from the motion of quasi-particles in a linear chain of poly-acetylene to the quantum Hall effect. According to the latest theories, fractional charges are neither bosons nor fermions but anyons, they are submitted to an exclusive principle that is less stringent than that for fermions. (A.C.)

  13. Asphalt chemical fractionation

    Obando P, Klever N.

    1998-01-01

    Asphalt fractionation were carried out in the Esmeraldas Oil Refinery using n-pentane, SiO 2 and different mixture of benzene- methane. The fractions obtained were analyzed by Fourier's Transformed Infrared Spectrophotometry (FTIR)

  14. Transformer-assisted PWM zero-voltage switching pole inverter with high output bandwidth applied to linear motor drives

    Myrzik, J.M.A.; Duarte, J.L.; Haardt, de P.; Vissers, J.

    2002-01-01

    An application of the transformer-assisted PWM zero-voltage switching pole inverter (TRAP) is described in this paper. The TRAP is based on the auxiliary resonant commutated pole inverter (ARCP), but avoids its disadvantages. This paper describes the converter functionality and its applicability

  15. Baeklund transformations, conservation laws and linearization of the self-dual Yang-Mills and chiral fields

    Wang, L.C.

    1980-01-01

    Baecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure

  16. Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation

    Schurkus, Henry F.; Ochsenfeld, Christian

    2016-01-01

    An atomic-orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling to linear, so that large systems can be studied on simple desktop computers with fully numerically controlled accuracy. Our AO-RPA formulation introduces a contracted double-Laplace transform and employs the overlap-metric resolution-of-the-identity. First timings of our pilot code illustrate the reduced scaling with systems comprising up to 1262 atoms and 10 090 basis functions. 

  17. Linear algebra

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

  18. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

    Harry H. Hilton

    2012-01-01

    Full Text Available Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

  19. Non-invasive Estimation of Metabolic Uptake Rate of Glucose using F18-FDG PET and Linear Transformation of Outputs

    Christensen, Anders Nymark; Reichkendler, M.; Auerback, P.

    For quantitative analysis and kinetic modeling of dynamic PET-data an input function is needed. Normally this is obtained by arterial blood sampling, potentially an unpleasant experience for the patient and laborious for the staff. Aim: To validate methods for determination of the metabolic uptake...... rate (Km) of glucose from dynamic FDG-PET scans using Image Derived Input Functions (IDIF) without blood sampling. Method: We performed 24 dynamic FDG-PET scans of the thigh of 14 healthy young male volunteers during a hyperinsulinemic isoglycemic clamp. Ten of the subjects were scanned twice 11 weeks...... artery diameter in the material, the method should also be applicable to women and people of other ages, but used with caution in the elderly due to variance in intramuscular adipose distribution. If only Km and no other kinetic parameters are needed, the described method with transformation...

  20. Space-bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms.

    Healy, John J; Sheridan, John T

    2011-05-01

    The product of the spatial and spatial frequency extents of a wave field has proven useful in the analysis of the sampling requirements of numerical simulations. We propose that the ratio of these quantities is also illuminating. We have shown that the distance at which the so-called "direct method" becomes more efficient than the so-called "spectral method" for simulations of Fresnel transforms may be written in terms of this space-bandwidth ratio. We have proposed generalizations of these algorithms for numerical simulations of general ABCD systems and derived expressions for the "transition space-bandwidth ratio," above which the generalization of the spectral method is the more efficient algorithm and below which the generalization of the direct method is preferable.

  1. SU-E-T-480: Radiobiological Dose Comparison of Single Fraction SRS, Multi-Fraction SRT and Multi-Stage SRS of Large Target Volumes Using the Linear-Quadratic Formula

    Ding, C; Hrycushko, B; Jiang, S; Meyer, J; Timmerman, R

    2014-01-01

    Purpose: To compare the radiobiological effect on large tumors and surrounding normal tissues from single fraction SRS, multi-fractionated SRT, and multi-staged SRS treatment. Methods: An anthropomorphic head phantom with a centrally located large volume target (18.2 cm 3 ) was scanned using a 16 slice large bore CT simulator. Scans were imported to the Multiplan treatment planning system where a total prescription dose of 20Gy was used for a single, three staged and three fractionated treatment. Cyber Knife treatment plans were inversely optimized for the target volume to achieve at least 95% coverage of the prescription dose. For the multistage plan, the target was segmented into three subtargets having similar volume and shape. Staged plans for individual subtargets were generated based on a planning technique where the beam MUs of the original plan on the total target volume are changed by weighting the MUs based on projected beam lengths within each subtarget. Dose matrices for each plan were export in DICOM format and used to calculate equivalent dose distributions in 2Gy fractions using an alpha beta ratio of 10 for the target and 3 for normal tissue. Results: Singe fraction SRS, multi-stage plan and multi-fractionated SRT plans had an average 2Gy dose equivalent to the target of 62.89Gy, 37.91Gy and 33.68Gy, respectively. The normal tissue within 12Gy physical dose region had an average 2Gy dose equivalent of 29.55Gy, 16.08Gy and 13.93Gy, respectively. Conclusion: The single fraction SRS plan had the largest predicted biological effect for the target and the surrounding normal tissue. The multi-stage treatment provided for a more potent biologically effect on target compared to the multi-fraction SRT treatments with less biological normal tissue than single-fraction SRS treatment

  2. On the singular perturbations for fractional differential equation.

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  3. On the Singular Perturbations for Fractional Differential Equation

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  4. Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

    Ma, Q.; Boulet, C.; Tipping, R. H.

    2014-01-01

    The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

  5. The overlap Dirac operator as a continued fraction

    Wenger, U.; Deutsches Elektronen-Synchrotron

    2004-03-01

    We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. (orig.)

  6. Some Families of the Incomplete H-Functions and the Incomplete \\overline H -Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications

    Srivastava, H. M.; Saxena, R. K.; Parmar, R. K.

    2018-01-01

    Our present investigation is inspired by the recent interesting extensions (by Srivastava et al. [35]) of a pair of the Mellin-Barnes type contour integral representations of their incomplete generalized hypergeometric functions p γ q and p Γ q by means of the incomplete gamma functions γ( s, x) and Γ( s, x). Here, in this sequel, we introduce a family of the relatively more general incomplete H-functions γ p,q m,n ( z) and Γ p,q m,n ( z) as well as their such special cases as the incomplete Fox-Wright generalized hypergeometric functions p Ψ q (γ) [ z] and p Ψ q (Γ) [ z]. The main object of this paper is to study and investigate several interesting properties of these incomplete H-functions, including (for example) decomposition and reduction formulas, derivative formulas, various integral transforms, computational representations, and so on. We apply some substantially general Riemann-Liouville and Weyl type fractional integral operators to each of these incomplete H-functions. We indicate the easilyderivable extensions of the results presented here that hold for the corresponding incomplete \\overline H -functions as well. Potential applications of many of these incomplete special functions involving (for example) probability theory are also indicated.

  7. The use of linear fractional analogues of rheological models in the problem of approximating the experimental data on the stretch polyvinylchloride elastron

    Luiza G. Ungarova

    2016-12-01

    Full Text Available We considere and analyze the uniaxial phenomenological models of viscoelastic deformation based on fractional analogues of Scott Blair, Voigt, Maxwell, Kelvin and Zener rheological models. Analytical solutions of the corresponding differential equations are obtained with fractional Riemann–Liouville operators under constant stress with further unloading, that are written by the generalized (two-parameter fractional exponential function and contains from two to four parameters depending on the type of model. A method for identifying the model parameters based on the background information for the experimental creep curves with constant stresses was developed. Nonlinear problem of parametric identification is solved by two-step iterative method. The first stage uses the characteristic data points diagrams and features in the behavior of the models under unrestricted growth of time and the initial approximation of parameters are determined. At the second stage, the refinement of these parameters by coordinate descent (the Hooke–Jeeves's method and minimizing the functional standard deviation for calculated and experimental values is made. Method of identification is realized for all the considered models on the basis of the known experimental data uniaxial viscoelastic deformation of Polyvinylchloride Elastron at a temperature of 20∘C and five the tensile stress levels. Table-valued parameters for all models are given. The errors analysis of constructed phenomenological models is made to experimental data over the entire ensemble of curves viscoelastic deformation. It was found that the approximation errors for the Scott Blair fractional model is 14.17 %, for the Voigt fractional model is 11.13 %, for the Maxvell fractional model is 13.02 %, for the Kelvin fractional model 10.56 %, for the Zener fractional model is 11.06 %. The graphs of the calculated and experimental dependences of viscoelastic deformation of Polyvinylchloride

  8. Investigating the performances of a 1 MV high pulsed power linear transformer driver: from beam dynamics to x radiation

    R. Maisonny

    2016-12-01

    Full Text Available The performance of a 1 MV pulsed high-power linear transformer driver accelerator were extensively investigated based on a numerical approach which utilizes both electromagnetic and Monte Carlo simulations. Particle-in-cell calculations were employed to examine the beam dynamics throughout the magnetically insulated transmission line which governs the coupling between the generator and the electron diode. Based on the information provided by the study of the beam dynamics, and using Monte Carlo methods, the main properties of the resulting x radiation were predicted. Good agreement was found between these simulations and experimental results. This work provides a detailed understanding of mechanisms affecting the performances of this type of high current, high-voltage pulsed accelerator, which are very promising for a growing number of applications.

  9. SU-F-T-02: Estimation of Radiobiological Doses (BED and EQD2) of Single Fraction Electronic Brachytherapy That Equivalent to I-125 Eye Plaque: By Using Linear-Quadratic and Universal Survival Curve Models

    Kim, Y; Waldron, T; Pennington, E

    2016-01-01

    Purpose: To test the radiobiological impact of hypofractionated choroidal melanoma brachytherapy, we calculated single fraction equivalent doses (SFED) of the tumor that equivalent to 85 Gy of I125-BT for 20 patients. Corresponding organs-at-risks (OARs) doses were estimated. Methods: Twenty patients treated with I125-BT were retrospectively examined. The tumor SFED values were calculated from tumor BED using a conventional linear-quadratic (L-Q) model and an universal survival curve (USC). The opposite retina (α/β = 2.58), macula (2.58), optic disc (1.75), and lens (1.2) were examined. The % doses of OARs over tumor doses were assumed to be the same as for a single fraction delivery. The OAR SFED values were converted into BED and equivalent dose in 2 Gy fraction (EQD2) by using both L-Q and USC models, then compared to I125-BT. Results: The USC-based BED and EQD2 doses of the macula, optic disc, and the lens were on average 118 ± 46% (p 14 Gy). Conclusion: The estimated single fraction doses were feasible to be delivered within 1 hour using a high dose rate source such as electronic brachytherapy (eBT). However, the estimated OAR doses using eBT were 112 ∼ 118% higher than when using the I125-BT technique. Continued exploration of alternative dose rate or fractionation schedules should be followed.

  10. Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

    Man, Yiu-Kwong

    2012-01-01

    Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

  11. Distribución de las transformaciones lineales de los residuos mínimos cuadrados studentizados internamente = Distribution of linear transformations of internally studentized least squares residuals

    Seppo Pynnönem

    2012-03-01

    that the resulting ratio, U/S, has a distribution that is free of from the nuisance unknown scale parameter. External Studentization refers to a ratio in which the nominator and denominator are independent, while internal Studentization refers to a ratio in which these are dependent. The advantage of the internal Studentization is that typically one can use a single common scale estimator, while in the external Studentization every single residual is scaled by different scale estimator to gain the independence. With normal regression errors the joint distribution of an arbitrary (linearly independent subset of internally Studentized residuals is well documented. However, in some applications a linear combination of internally Studentized residuals may be useful. The boundedness of them is well documented, but the distribution seems not be derived in the literature. This paper contributes to the existing literature by deriving the joint distribution of an arbitrary linear transformation of internally Studentized residuals from ordinary least squares regression with spherical error distribution. All major versions of commonly utilized internally Studentized regression residuals in literature are obtained as special cases of the linear transformation

  12. A Monte Carlo simulation study comparing linear regression, beta regression, variable-dispersion beta regression and fractional logit regression at recovering average difference measures in a two sample design.

    Meaney, Christopher; Moineddin, Rahim

    2014-01-24

    In biomedical research, response variables are often encountered which have bounded support on the open unit interval--(0,1). Traditionally, researchers have attempted to estimate covariate effects on these types of response data using linear regression. Alternative modelling strategies may include: beta regression, variable-dispersion beta regression, and fractional logit regression models. This study employs a Monte Carlo simulation design to compare the statistical properties of the linear regression model to that of the more novel beta regression, variable-dispersion beta regression, and fractional logit regression models. In the Monte Carlo experiment we assume a simple two sample design. We assume observations are realizations of independent draws from their respective probability models. The randomly simulated draws from the various probability models are chosen to emulate average proportion/percentage/rate differences of pre-specified magnitudes. Following simulation of the experimental data we estimate average proportion/percentage/rate differences. We compare the estimators in terms of bias, variance, type-1 error and power. Estimates of Monte Carlo error associated with these quantities are provided. If response data are beta distributed with constant dispersion parameters across the two samples, then all models are unbiased and have reasonable type-1 error rates and power profiles. If the response data in the two samples have different dispersion parameters, then the simple beta regression model is biased. When the sample size is small (N0 = N1 = 25) linear regression has superior type-1 error rates compared to the other models. Small sample type-1 error rates can be improved in beta regression models using bias correction/reduction methods. In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models. Similar results were observed if the

  13. A differentially pumped argon plasma in the linear plasma generator Magnum-PSI: gas flow and dynamics of the ionized fraction

    Eck, van H.J.N.; Hansen, T.A.R.; Kleyn, A.W.; Meiden, van der H.J.; Schram, D.C.; Zeijlmans van Emmichoven, P.A.

    2011-01-01

    Magnum-PSI is a linear plasma generator designed to reach the plasma–surface interaction (PSI) regime of ITER and nuclear fusion reactors beyond ITER. To reach this regime, the influx of cold neutrals from the source must be significantly lower than the plasma flux reaching the target. This is

  14. A differentially pumped argon plasma in the linear plasma generator Magnum-PSI: gas flow and dynamics of the ionized fraction

    van Eck, H.J.N.; Hansen, T.A.R.; Kleyn, A.W.; van der Meiden, H.J.; Schram, D.C.; Zeijlmans van Emmichoven, P.A.

    2011-01-01

    Magnum-PSI is a linear plasma generator designed to reach the plasma-surface interaction (PSI) regime of ITER and nuclear fusion reactors beyond ITER. To reach this regime, the influx of cold neutrals from the source must be significantly lower than the plasma flux reaching the target. This is

  15. SU-F-T-02: Estimation of Radiobiological Doses (BED and EQD2) of Single Fraction Electronic Brachytherapy That Equivalent to I-125 Eye Plaque: By Using Linear-Quadratic and Universal Survival Curve Models

    Kim, Y; Waldron, T; Pennington, E [University Of Iowa, College of Medicine, Iowa City, IA (United States)

    2016-06-15

    Purpose: To test the radiobiological impact of hypofractionated choroidal melanoma brachytherapy, we calculated single fraction equivalent doses (SFED) of the tumor that equivalent to 85 Gy of I125-BT for 20 patients. Corresponding organs-at-risks (OARs) doses were estimated. Methods: Twenty patients treated with I125-BT were retrospectively examined. The tumor SFED values were calculated from tumor BED using a conventional linear-quadratic (L-Q) model and an universal survival curve (USC). The opposite retina (α/β = 2.58), macula (2.58), optic disc (1.75), and lens (1.2) were examined. The % doses of OARs over tumor doses were assumed to be the same as for a single fraction delivery. The OAR SFED values were converted into BED and equivalent dose in 2 Gy fraction (EQD2) by using both L-Q and USC models, then compared to I125-BT. Results: The USC-based BED and EQD2 doses of the macula, optic disc, and the lens were on average 118 ± 46% (p < 0.0527), 126 ± 43% (p < 0.0354), and 112 ± 32% (p < 0.0265) higher than those of I125-BT, respectively. The BED and EQD2 doses of the opposite retina were 52 ± 9% lower than I125-BT. The tumor SFED values were 25.2 ± 3.3 Gy and 29.1 ± 2.5 Gy when using USC and LQ models which can be delivered within 1 hour. All BED and EQD2 values using L-Q model were significantly larger when compared to the USC model (p < 0.0274) due to its large single fraction size (> 14 Gy). Conclusion: The estimated single fraction doses were feasible to be delivered within 1 hour using a high dose rate source such as electronic brachytherapy (eBT). However, the estimated OAR doses using eBT were 112 ∼ 118% higher than when using the I125-BT technique. Continued exploration of alternative dose rate or fractionation schedules should be followed.

  16. Comparison of the levels of bioactive benzoxazinoids in different wheat and rye fractions and the transformation of these compounds in homemade foods

    Tanwir, Fariha; Fredholm, Maria; Gregersen, Per L.

    2013-01-01

    -benzoxazin-3-one (HBOA-glc-hexose) were the predominant compounds found in the different wheat and rye seed fractions followed by DIBOA-glc and DIBOA. The soaking and boiling of three rye-based breakfast cereals resulted in considerable changes in the benzoxazinoid contents. The soaking of pearled rye...

  17. Transformations in occluded light fraction organic matter in a clayey oxisol; evidence from 13C-CCPMAS-NMR and &13C signature

    Roscoe, R.; Buurman, P.; Lagen, van B.; Velthorst, E.J.

    2004-01-01

    We hypothesised that, during occlusion inside granular aggregates of oxide-rich soils, the light fraction organic matter would Undergo a strong process of decomposition, either due to the slow process of aggregate formation and stabilisation or due to digestion in the macro- and meso-fauna guts.

  18. Recyclable transmission line (RTL) and linear transformer driver (LTD) development for Z-pinch inertial fusion energy (Z-IFE) and high yield

    Sharpe, Robin Arthur; Kingsep, Alexander S.; Smith, David Lewis; Olson, Craig Lee; Ottinger, Paul F.; Schumer, Joseph Wade; Welch, Dale Robert; Kim, Alexander; Kulcinski, Gerald L.; Kammer, Daniel C.; Rose, David Vincent; Nedoseev, Sergei L.; Pointon, Timothy David; Smirnov, Valentin P.; Turgeon, Matthew C.; Kalinin, Yuri G.; Bruner, Nichelle

    2007-01-01

    Z-Pinch Inertial Fusion Energy (Z-IFE) complements and extends the single-shot z-pinch fusion program on Z to a repetitive, high-yield, power plant scenario that can be used for the production of electricity, transmutation of nuclear waste, and hydrogen production, all with no CO 2 production and no long-lived radioactive nuclear waste. The Z-IFE concept uses a Linear Transformer Driver (LTD) accelerator, and a Recyclable Transmission Line (RTL) to connect the LTD driver to a high-yield fusion target inside a thick-liquid-wall power plant chamber. Results of RTL and LTD research are reported here, that include: (1) The key physics issues for RTLs involve the power flow at the high linear current densities that occur near the target (up to 5 MA/cm). These issues include surface heating, melting, ablation, plasma formation, electron flow, magnetic insulation, conductivity changes, magnetic field diffusion changes, possible ion flow, and RTL mass motion. These issues are studied theoretically, computationally (with the ALEGRA and LSP codes), and will work at 5 MA/cm or higher, with anode-cathode gaps as small as 2 mm. (2) An RTL misalignment sensitivity study has been performed using a 3D circuit model. Results show very small load current variations for significant RTL misalignments. (3) The key structural issues for RTLs involve optimizing the RTL strength (varying shape, ribs, etc.) while minimizing the RTL mass. Optimization studies show RTL mass reductions by factors of three or more. (4) Fabrication and pressure testing of Z-PoP (Proof-of-Principle) size RTLs are successfully reported here. (5) Modeling of the effect of initial RTL imperfections on the buckling pressure has been performed. Results show that the curved RTL offers a much greater buckling pressure as well as less sensitivity to imperfections than three other RTL designs. (6) Repetitive operation of a 0.5 MA, 100 kV, 100 ns, LTD cavity with gas purging between shots and automated operation is

  19. Recyclable transmission line (RTL) and linear transformer driver (LTD) development for Z-pinch inertial fusion energy (Z-IFE) and high yield.

    Sharpe, Robin Arthur; Kingsep, Alexander S. (Kurchatov Institute, Moscow, Russia); Smith, David Lewis; Olson, Craig Lee; Ottinger, Paul F. (Naval Research Laboratory, Washington, DC); Schumer, Joseph Wade (Naval Research Laboratory, Washington, DC); Welch, Dale Robert (Voss Scientific, Albuquerque, NM); Kim, Alexander (High Currents Institute, Tomsk, Russia); Kulcinski, Gerald L. (University of Wisconsin, Madison, WI); Kammer, Daniel C. (University of Wisconsin, Madison, WI); Rose, David Vincent (Voss Scientific, Albuquerque, NM); Nedoseev, Sergei L. (Kurchatov Institute, Moscow, Russia); Pointon, Timothy David; Smirnov, Valentin P. (Kurchatov Institute, Moscow, Russia); Turgeon, Matthew C.; Kalinin, Yuri G. (Kurchatov Institute, Moscow, Russia); Bruner, Nichelle " Nicki" (Voss Scientific, Albuquerque, NM); Barkey, Mark E. (University of Alabama, Tuscaloosa, AL); Guthrie, Michael (University of Wisconsin, Madison, WI); Thoma, Carsten (Voss Scientific, Albuquerque, NM); Genoni, Tom C. (Voss Scientific, Albuquerque, NM); Langston, William L.; Fowler, William E.; Mazarakis, Michael Gerrassimos

    2007-01-01

    Z-Pinch Inertial Fusion Energy (Z-IFE) complements and extends the single-shot z-pinch fusion program on Z to a repetitive, high-yield, power plant scenario that can be used for the production of electricity, transmutation of nuclear waste, and hydrogen production, all with no CO{sub 2} production and no long-lived radioactive nuclear waste. The Z-IFE concept uses a Linear Transformer Driver (LTD) accelerator, and a Recyclable Transmission Line (RTL) to connect the LTD driver to a high-yield fusion target inside a thick-liquid-wall power plant chamber. Results of RTL and LTD research are reported here, that include: (1) The key physics issues for RTLs involve the power flow at the high linear current densities that occur near the target (up to 5 MA/cm). These issues include surface heating, melting, ablation, plasma formation, electron flow, magnetic insulation, conductivity changes, magnetic field diffusion changes, possible ion flow, and RTL mass motion. These issues are studied theoretically, computationally (with the ALEGRA and LSP codes), and will work at 5 MA/cm or higher, with anode-cathode gaps as small as 2 mm. (2) An RTL misalignment sensitivity study has been performed using a 3D circuit model. Results show very small load current variations for significant RTL misalignments. (3) The key structural issues for RTLs involve optimizing the RTL strength (varying shape, ribs, etc.) while minimizing the RTL mass. Optimization studies show RTL mass reductions by factors of three or more. (4) Fabrication and pressure testing of Z-PoP (Proof-of-Principle) size RTLs are successfully reported here. (5) Modeling of the effect of initial RTL imperfections on the buckling pressure has been performed. Results show that the curved RTL offers a much greater buckling pressure as well as less sensitivity to imperfections than three other RTL designs. (6) Repetitive operation of a 0.5 MA, 100 kV, 100 ns, LTD cavity with gas purging between shots and automated operation is

  20. Integral transformations applied to image encryption

    Vilardy, Juan M.; Torres, Cesar O.; Perez, Ronal

    2017-01-01

    In this paper we consider the application of the integral transformations for image encryption through optical systems, a mathematical algorithm under Matlab platform using fractional Fourier transform (FrFT) and Random Phase Mask (RPM) for digital images encryption is implemented. The FrFT can be related to others integral transforms, such as: Fourier transform, Sine and Cosine transforms, Radial Hilbert transform, fractional Sine transform, fractional Cosine transform, fractional Hartley transform, fractional Wavelet transform and Gyrator transform, among other transforms. The encryption scheme is based on the use of the FrFT, the joint transform correlator and two RPMs, which provide security and robustness to the implemented security system. One of the RPMs used during encryption-decryption and the fractional order of the FrFT are the keys to improve security and make the system more resistant against security attacks. (paper)

  1. The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations

    Zhao, Jianping; Tang, Bo; Kumar, Sunil; Hou, Yanren

    2012-01-01

    An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powe...

  2. Hipergeometric solutions to some nonhomogeneous equations of fractional order

    Olivares, Jorge; Martin, Pablo; Maass, Fernando

    2017-12-01

    In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

  3. Elements of linear space

    Amir-Moez, A R; Sneddon, I N

    1962-01-01

    Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given.Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices a

  4. Fractional Number Operator and Associated Fractional Diffusion Equations

    Rguigui, Hafedh

    2018-03-01

    In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

  5. On matrix fractional differential equations

    Adem Kılıçman; Wasan Ajeel Ahmood

    2017-01-01

    The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...

  6. Generalized fractional Schroedinger equation with space-time fractional derivatives

    Wang Shaowei; Xu Mingyu

    2007-01-01

    In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum

  7. On a connection between the limit set of the Moebius-Klein transformation, periodic continued fractions, El Naschie's topological theory of high energy particle physics and the possibility of a new axion-like particle

    Marek-Crnjac, L.

    2004-01-01

    In the present work we first give a general representation of the derivatives of the irrational number phi, for instance ((1)/(phi)), ((1)/(phi 2 )), ((1)/(phi 3 )) etc., as periodic continued fractions. Any irrational number can then be expanded in an infinite continued fraction. The limit set of the Kleinian transformation acting on the E-infinity Cantorian spacetime turned out to be this set of periodic continued fractions, consequently the vacuum of the E-infinity is described by this limit set. As discussed by El Naschie, every particle can be interpreted geometrically as a scaling of another. This is done using the topology of hyperbolic Kleinian space of VAK, which is nothing but our limit set. Here we will present the ratios of the theoretical masses of certain elementary particles to that of some chosen particles in term of phi. Many of these masses are quite close to integer multiples of the mass of a chosen particle. Finally we discuss the possibility of new transfinite, axion-like particles as discussed recently by Krauss and El Naschie [Quintessence, Vintage, London, 1999

  8. Phosphorus transformation in poultry litter and litter-treated Oxisol of Brazil assessed by 31P-NMR and wet chemical fractionation

    César Roriz de Souza

    2012-11-01

    Full Text Available Large quantities of poultry litter are being produced in Brazil, which contain appreciable amounts of phosphorus (P that could be of environmental concern. To assess the immediate environmental threat, five poultry litters composed of diverse bedding material were incubated for 43 days under greenhouse conditions. The litters consisted of: coffee bean husk (CH; wood chips (WC; rice husk (RH; ground corn cobs (CC and ground napier grass (NG (Pennisetum purpureum Schum., in which the change in forms of soluble P was evaluated using 31P NMR spectroscopy. On average, 80.2 and 19.8 % of the total P in the extract, respectively, accounted for the inorganic and organic forms before incubation and 48 % of the organic P was mineralized to inorganic P in 43 days of incubation. Wide variation in the organic P mineralization rate (from 82 % -WC to 4 % - NG was observed among litters. Inorganic orthophosphate (99.9 % and pyrophosphate (0.1 % were the only inorganic P forms, whereas the organic P forms orthophosphate monoesters (76.3 % and diester (23.7 % were detected. Diester P compounds were mineralized almost completely in all litters, except in the CH litter, within the incubation period. Pyrophosphates contributed with less than 0.5% and remained unaltered during the incubation period. Wood-chip litter had a higher organic P (40 % content and a higher diester: monoester ratio; it was therefore mineralized rapidly, within the first 15 days, achieving steady state by the 29th day. Distinct mineralization patterns were observed in the litter when incubated with a clayey Oxisol. The substantial decrease observed in the organic P fraction (Po of the litter types followed the order: CH (45 % > CC (25 % > RH (13 % ≈ NG (12 % > WC (5 %, whereas the Pi fraction increased. Incubation of RH litter in soil slowed down the mineralization of organic P.

  9. FRACTIONAL BANKING

    Maria Klimikova

    2010-01-01

    Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.

  10. Fractional thermoelasticity

    Povstenko, Yuriy

    2015-01-01

    This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research.  The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators.  This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ...

  11. Mathematical algorithm to transform digital biomass distribution maps into linear programming networks in order to optimize bio-energy delivery chains

    Velazquez-Marti, B.; Annevelink, E.

    2008-01-01

    Many linear programming models have been developed to model the logistics of bio-energy chains. These models help to determine the best set-up of bio-energy chains. Most of them use network structures built up from nodes with one or more depots, and arcs connecting these depots. Each depot is source

  12. On the fractional calculus of Besicovitch function

    Liang Yongshun

    2009-01-01

    Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

  13. Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

    Nagy, Péter R.; Kállay, Mihály

    2017-06-01

    An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.

  14. Generalized Functions for the Fractional Calculus

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

  15. Fractional Processes and Fractional-Order Signal Processing Techniques and Applications

    Sheng, Hu; Qiu, TianShuang

    2012-01-01

    Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: • presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; • introduces FOSP techniques and the fractional signals and fractional systems point of view; • details real-world-application examples of FOSP techniques to demonstr...

  16. Transformation of fractions into simple fractions in divisive meadows

    Bergstra, J.A.; Middelburg, C.A.

    Meadows are alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Divisive meadows are meadows with the multiplicative inverse

  17. On the identifiability and the identification of linear models: examples of application within the frame of the theory of transformation systems

    Delforge, Jacques

    1984-01-01

    In its first part, this research thesis which is the result of studies of the effects of radiations on molecular structures, addresses the search for guiding principles for the elaboration of a model with the best as possible justification (model justification is based on five criteria: rational consistency, refutability, adjustment to experimental data, justification of all model characteristics, uniqueness), recalls the main principles of the theory of transformation systems, and proposes a procedure of model search. The second part addresses mathematical methods. The third part addresses the problem of identifiability of parameters and the fourth part reports examples of model development: study of the effects of gamma irradiation on unicellular algae, study of the effects of radiations on the stem cells of rat gonads. This last part also reports the elaboration of pharmacokinetic model with 21 parameters, and the study of two models of nuclear medicine (assessment of the actual lung volume of hypoxemic patients, study of the methionine brain metabolism)

  18. Financial Planning with Fractional Goals

    Goedhart, Marc; Spronk, Jaap

    1995-01-01

    textabstractWhen solving financial planning problems with multiple goals by means of multiple objective programming, the presence of fractional goals leads to technical difficulties. In this paper we present a straightforward interactive approach for solving such linear fractional programs with multiple goal variables. The approach is illustrated by means of an example in financial planning.

  19. Toward lattice fractional vector calculus

    Tarasov, Vasily E.

    2014-09-01

    An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

  20. Fractional fermions

    Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

    1984-01-01

    The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)

  1. linear-quadratic-linear model

    Tanwiwat Jaikuna

    2017-02-01

    Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

  2. The Bargmann transform and canonical transformations

    Villegas-Blas, Carlos

    2002-01-01

    This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480-5505 (1995)]--when the configuration space is the two-sphere S 2 and for a Bargmann transform that we introduce for the three-sphere S 3 . It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C 3 or C 4 . We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141-1148 (1977)] and the other quantizations are related to the work of Guillemin [Integ. Eq. Operator Theory 7, 145-205 (1984)]. Since suitable infinite linear combinations of powers of the generating functions are coherent states for L 2 (S 2 ) or L 2 (S 3 ), we show finally that the studied Bargmann transforms are actually coherent states transforms

  3. Discrete transforms

    Firth, Jean M

    1992-01-01

    The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen­ tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...

  4. Mystery Fractions

    Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max

    2016-01-01

    Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

  5. Matrices and transformations

    Pettofrezzo, Anthony J

    1978-01-01

    Elementary, concrete approach: fundamentals of matrix algebra, linear transformation of the plane, application of properties of eigenvalues and eigenvectors to study of conics. Includes proofs of most theorems. Answers to odd-numbered exercises.

  6. Damping behavior of polymer composites with high volume fraction of NiMnGa powders

    Sun, Xiaogang; Song, Jie; Jiang, Hong; Zhang, Xiaoning; Xie, Chaoying

    2011-03-01

    Polymer composites inserted with high volume fraction (up to 70 Vol%) of NiMnGa powders were fabricated and their damping behavior was investigated by dynamic mechanical analysis. It is found that the polymer matrix has little influence on the transformation temperatures of NiMnGa powders. A damping peak appears for NiMnGa/epoxy resin (EP) composites accompanying with the martensitic transformation or reverse martensitic transformation of NiMnGa powders during cooling or heating. The damping capacity for NiMnGa/EP composites increases linearly with the increase of volume fraction of NiMnGa powders and, decreases dramatically as the test frequency increases. The fracture strain of NiMnGa/EP composites decrease with the increase of NiMnGa powders.

  7. Fraction Reduction through Continued Fractions

    Carley, Holly

    2011-01-01

    This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

  8. Ferroelectric Fractional-Order Capacitors

    Agambayev, Agamyrat

    2017-07-25

    Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

  9. Ferroelectric Fractional-Order Capacitors

    Agambayev, Agamyrat; Patole, Shashikant P.; Farhat, Mohamed; Elwakil, Ahmed; Bagci, Hakan; Salama, Khaled N.

    2017-01-01

    Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

  10. Orbit Representations from Linear mod 1 Transformations

    Carlos Correia Ramos

    2012-05-01

    Full Text Available We show that every point $x_0in [0,1]$ carries a representationof a $C^*$-algebra that encodes the orbit structure of thelinear mod 1 interval map $f_{eta,alpha}(x=eta x +alpha$. Such $C^*$-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map $f_{eta,alpha}$. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every $alphain [0,1[$ and $etageq 1$.

  11. The synchronization of three fractional differential systems

    Li Changpin; Yan Jianping

    2007-01-01

    In this paper, a new method is proposed and applied to the synchronization of fractional differential systems (or 'differential systems with fractional orders'), where both drive and response systems have the same dimensionality and are coupled by the driving signal. The present technique is based on the stability criterion of linear fractional systems. This method is implemented in (chaos) synchronization of the fractional Lorenz system, Chen system and Chua circuit. Numerical simulations show the present synchronization method works well

  12. An introduction to linear algebra and tensors

    Akivis, M A; Silverman, Richard A

    1978-01-01

    Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.

  13. Linear gate

    Suwono.

    1978-01-01

    A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)

  14. Linear Accelerators

    Vretenar, M

    2014-01-01

    The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics

  15. A Fractionally Integrated Wishart Stochastic Volatility Model

    M. Asai (Manabu); M.J. McAleer (Michael)

    2013-01-01

    textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

  16. Linearization Method and Linear Complexity

    Tanaka, Hidema

    We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

  17. Linear systems optimal and robust control

    Sinha, Alok

    2007-01-01

    Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...

  18. Level Design as Model Transformation

    Dormans, Joris

    2011-01-01

    This paper frames the process of designing a level in a game as a series of model transformations. The transformations correspond to the application of particular design principles, such as the use of locks and keys to transform a linear mission into a branching space. It shows that by using rewrite

  19. expansion method for solving nonlinear space–time fractional

    2016-07-06

    Jul 6, 2016 ... Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey. ∗ ... of fractional calculus dates back to three hundred years ago. ... tions by fractional complex transformation [12,13].

  20. Linear algebra

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  1. Linear programming

    Solow, Daniel

    2014-01-01

    This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.

  2. Linear algebra

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  3. Linear algebra

    Berberian, Sterling K

    2014-01-01

    Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.

  4. Linear Models

    Searle, Shayle R

    2012-01-01

    This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

  5. LINEAR ACCELERATOR

    Christofilos, N.C.; Polk, I.J.

    1959-02-17

    Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.

  6. Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

    Bekir Ahmet; Güner Özkan

    2013-01-01

    In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

  7. Toward lattice fractional vector calculus

    Tarasov, Vasily E

    2014-01-01

    An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)

  8. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J [Intelligent System Research Group, Faculty of Electrical and Computer Engineering, Babol, Noushirvani University of Technology, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Department of Mathematics, Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com

    2009-10-15

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  9. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J; Ranjbar, A; Momani, S

    2009-01-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  10. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

    2009-10-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  11. Fractional vector calculus for fractional advection dispersion

    Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

    2006-07-01

    We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

  12. Fractional Schroedinger equation

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  13. Meadow based Fraction Theory

    Bergstra, Jan A.

    2015-01-01

    In the context of an involutive meadow a precise definition of fractions is formulated and on that basis formal definitions of various classes of fractions are given. The definitions follow the fractions as terms paradigm. That paradigm is compared with two competing paradigms for storytelling on fractions: fractions as values and fractions as pairs.

  14. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  15. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    N'Doye, Ibrahima

    2015-07-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  16. Linear regression

    Olive, David J

    2017-01-01

    This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...

  17. Linear Colliders

    Alcaraz, J.

    2001-01-01

    After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs

  18. Linear algebra

    Edwards, Harold M

    1995-01-01

    In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

  19. On fractal space-time and fractional calculus

    Hu Yue

    2016-01-01

    Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.

  20. On Fractional Order Hybrid Differential Equations

    Mohamed A. E. Herzallah

    2014-01-01

    Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

  1. Generalized field-transforming metamaterials

    Tretyakov, Sergei A; Nefedov, Igor S; Alitalo, Pekka

    2008-01-01

    In this paper, we introduce a generalized concept of field-transforming metamaterials, which perform field transformations defined as linear relations between the original and transformed fields. These artificial media change the fields in a prescribed fashion in the volume occupied by the medium. We show what electromagnetic properties of transforming medium are required. The coefficients of these linear functions can be arbitrary scalar functions of position and frequency, which makes the approach quite general and opens a possibility to realize various unusual devices.

  2. Laplace transforms essentials

    Shafii-Mousavi, Morteza

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Laplace Transforms includes the Laplace transform, the inverse Laplace transform, special functions and properties, applications to ordinary linear differential equations, Fourier tr

  3. Fourier transform NMR

    Hallenga, K.

    1991-01-01

    This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs

  4. Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel

    Xiaoyi Guo

    2017-11-01

    Full Text Available The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed.

  5. Predicting blood β-hydroxybutyrate using milk Fourier transform infrared spectrum, milk composition, and producer-reported variables with multiple linear regression, partial least squares regression, and artificial neural network.

    Pralle, R S; Weigel, K W; White, H M

    2018-05-01

    Prediction of postpartum hyperketonemia (HYK) using Fourier transform infrared (FTIR) spectrometry analysis could be a practical diagnostic option for farms because these data are now available from routine milk analysis during Dairy Herd Improvement testing. The objectives of this study were to (1) develop and evaluate blood β-hydroxybutyrate (BHB) prediction models using multivariate linear regression (MLR), partial least squares regression (PLS), and artificial neural network (ANN) methods and (2) evaluate whether milk FTIR spectrum (mFTIR)-based models are improved with the inclusion of test-day variables (mTest; milk composition and producer-reported data). Paired blood and milk samples were collected from multiparous cows 5 to 18 d postpartum at 3 Wisconsin farms (3,629 observations from 1,013 cows). Blood BHB concentration was determined by a Precision Xtra meter (Abbot Diabetes Care, Alameda, CA), and milk samples were analyzed by a privately owned laboratory (AgSource, Menomonie, WI) for components and FTIR spectrum absorbance. Producer-recorded variables were extracted from farm management software. A blood BHB ≥1.2 mmol/L was considered HYK. The data set was divided into a training set (n = 3,020) and an external testing set (n = 609). Model fitting was implemented with JMP 12 (SAS Institute, Cary, NC). A 5-fold cross-validation was performed on the training data set for the MLR, PLS, and ANN prediction methods, with square root of blood BHB as the dependent variable. Each method was fitted using 3 combinations of variables: mFTIR, mTest, or mTest + mFTIR variables. Models were evaluated based on coefficient of determination, root mean squared error, and area under the receiver operating characteristic curve. Four models (PLS-mTest + mFTIR, ANN-mFTIR, ANN-mTest, and ANN-mTest + mFTIR) were chosen for further evaluation in the testing set after fitting to the full training set. In the cross-validation analysis, model fit was greatest for ANN, followed

  6. Pitchfork bifurcation and vibrational resonance in a fractional-order ...

    The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms ...

  7. Fractional Vector Calculus and Fractional Special Function

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2010-01-01

    Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

  8. Linear circuit theory matrices in computer applications

    Vlach, Jiri

    2014-01-01

    Basic ConceptsNodal and Mesh AnalysisMatrix MethodsDependent SourcesNetwork TransformationsCapacitors and InductorsNetworks with Capacitors and InductorsFrequency DomainLaplace TransformationTime DomainNetwork FunctionsActive NetworksTwo-PortsTransformersModeling and Numerical MethodsSensitivitiesModified Nodal FormulationFourier Series and TransformationAppendix: Scaling of Linear Networks.

  9. Two-dimensional linear and nonlinear Talbot effect from rogue waves.

    Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng

    2015-03-01

    We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.

  10. Linear programming

    Karloff, Howard

    1991-01-01

    To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...

  11. Logarithmic Transformations in Regression: Do You Transform Back Correctly?

    Dambolena, Ismael G.; Eriksen, Steven E.; Kopcso, David P.

    2009-01-01

    The logarithmic transformation is often used in regression analysis for a variety of purposes such as the linearization of a nonlinear relationship between two or more variables. We have noticed that when this transformation is applied to the response variable, the computation of the point estimate of the conditional mean of the original response…

  12. Duality in linearized gravity

    Henneaux, Marc; Teitelboim, Claudio

    2005-01-01

    We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two superpotentials, one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons-like structure, as in the Maxwell case

  13. Linear waves and instabilities

    Bers, A.

    1975-01-01

    The electrodynamic equations for small-amplitude waves and their dispersion relation in a homogeneous plasma are outlined. For such waves, energy and momentum, and their flow and transformation, are described. Perturbation theory of waves is treated and applied to linear coupling of waves, and the resulting instabilities from such interactions between active and passive waves. Linear stability analysis in time and space is described where the time-asymptotic, time-space Green's function for an arbitrary dispersion relation is developed. The perturbation theory of waves is applied to nonlinear coupling, with particular emphasis on pump-driven interactions of waves. Details of the time--space evolution of instabilities due to coupling are given. (U.S.)

  14. Exact solutions to the time-fractional differential equations via local fractional derivatives

    Guner, Ozkan; Bekir, Ahmet

    2018-01-01

    This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

  15. Fractional RC and LC Electrical Circuits

    Gómez-Aguilar José Francisco

    2014-04-01

    Full Text Available In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ɣ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative ɣ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of ɣ. The classical cases are recovered by taking the limit when ɣ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations.

  16. Cayley transform on Stiefel manifolds

    Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel

    2018-01-01

    The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.

  17. Transformative Learning

    Wang, Victor C. X.; Cranton, Patricia

    2011-01-01

    The theory of transformative learning has been explored by different theorists and scholars. However, few scholars have made an attempt to make a comparison between transformative learning and Confucianism or between transformative learning and andragogy. The authors of this article address these comparisons to develop new and different insights…

  18. Advanced statistics: linear regression, part I: simple linear regression.

    Marill, Keith A

    2004-01-01

    Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

  19. Reduction of Linear Programming to Linear Approximation

    Vaserstein, Leonid N.

    2006-01-01

    It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

  20. Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

    Liu, Yingyi

    2017-09-08

    Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

  1. Fractional quantum mechanics

    Laskin, Nick

    2018-01-01

    Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...

  2. Data Compression with Linear Algebra

    Etler, David

    2015-01-01

    A presentation on the applications of linear algebra to image compression. Covers entropy, the discrete cosine transform, thresholding, quantization, and examples of images compressed with DCT. Given in Spring 2015 at Ocean County College as part of the honors program.

  3. Fractional vector calculus and fractional Maxwell's equations

    Tarasov, Vasily E.

    2008-01-01

    The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

  4. Fractional statistics and fractional quantized Hall effect

    Tao, R.; Wu, Y.S.

    1985-01-01

    The authors suggest that the origin of the odd-denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which govern quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics do not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus, no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references

  5. Backlund transformations as canonical transformations

    Villani, A.; Zimerman, A.H.

    1977-01-01

    Toda and Wadati as well as Kodama and Wadati have shown that the Backlund transformations, for the exponential lattice equation, sine-Gordon equation, K-dV (Korteweg de Vries) equation and modifies K-dV equation, are canonical transformation. It is shown that the Backlund transformation for the Boussinesq equation, for a generalized K-dV equation, for a model equation for shallow water waves and for the nonlinear Schroedinger equation are also canonical transformations [pt

  6. The fundamental solutions for fractional evolution equations of parabolic type

    Mahmoud M. El-Borai

    2004-01-01

    Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

  7. Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids

    Wang, Xiaoping; Qi, Haitao; Yu, Bo; Xiong, Zhen; Xu, Huanying

    2017-09-01

    This work investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate micro-channel under combined influence of electroosmotic and pressure gradient forcings with asymmetric zeta potentials at the walls. The generalized second grade fluid with fractional derivative was used for the constitutive equation. The Navier slip model with different slip coefficients at both walls was also considered. By employing the Debye-Hückel linearization and the Laplace and sin-cos-Fourier transforms, the analytical solutions for the velocity distribution are derived. And the finite difference method for this problem was also given. Finally, the influence of pertinent parameters on the generation of flow is presented graphically.

  8. Initialized Fractional Calculus

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

  9. Adaption of optical Fresnel transform to optical Wigner transform

    Lv Cuihong; Fan Hongyi

    2010-01-01

    Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.

  10. Tempered fractional calculus

    Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)

    2015-07-15

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  11. Tempered fractional calculus

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-07-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  12. Tempered fractional calculus

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-01-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series

  13. Exp-function method for solving fractional partial differential equations.

    Zheng, Bin

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

  14. The Investigation of Strain-Induced Martensite Reverse Transformation in AISI 304 Austenitic Stainless Steel

    Cios, G.; Tokarski, T.; Żywczak, A.; Dziurka, R.; Stępień, M.; Gondek, Ł.; Marciszko, M.; Pawłowski, B.; Wieczerzak, K.; Bała, P.

    2017-10-01

    This paper presents a comprehensive study on the strain-induced martensitic transformation and reversion transformation of the strain-induced martensite in AISI 304 stainless steel using a number of complementary techniques such as dilatometry, calorimetry, magnetometry, and in-situ X-ray diffraction, coupled with high-resolution microstructural transmission Kikuchi diffraction analysis. Tensile deformation was applied at temperatures between room temperature and 213 K (-60 °C) in order to obtain a different volume fraction of strain-induced martensite (up to 70 pct). The volume fraction of the strain-induced martensite, measured by the magnetometric method, was correlated with the total elongation, hardness, and linear thermal expansion coefficient. The thermal expansion coefficient, as well as the hardness of the strain-induced martensitic phase was evaluated. The in-situ thermal treatment experiments showed unusual changes in the kinetics of the reverse transformation (α' → γ). The X-ray diffraction analysis revealed that the reverse transformation may be stress assisted—strains inherited from the martensitic transformation may increase its kinetics at the lower annealing temperature range. More importantly, the transmission Kikuchi diffraction measurements showed that the reverse transformation of the strain-induced martensite proceeds through a displacive, diffusionless mechanism, maintaining the Kurdjumov-Sachs crystallographic relationship between the martensite and the reverted austenite. This finding is in contradiction to the results reported by other researchers for a similar alloy composition.

  15. Higher fractions theory of fractional hall effect

    Kostadinov, I.Z.; Popov, V.N.

    1985-07-01

    A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author)

  16. Stability Analysis of Fractional-Order Nonlinear Systems with Delay

    Yu Wang

    2014-01-01

    Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

  17. Lecture notes on wavelet transforms

    Debnath, Lokenath

    2017-01-01

    This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor.  These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these ...

  18. Hadamard Transforms

    Agaian, Sos; Egiazarian, Karen; Astola, Jaakko

    2011-01-01

    The Hadamard matrix and Hadamard transform are fundamental problem-solving tools in a wide spectrum of scientific disciplines and technologies, such as communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), digital logic (Boolean function analysis and synthesis), and fault-tolerant system design. Hadamard Transforms intends to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Each chapter begins with the basics of the theory, progresses to more advanced

  19. Linear integral equations and soliton systems

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  20. LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections

    2007-01-01

    1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table

  1. Linear motor with contactless energy transfer

    2014-01-01

    An integrated electromagnetic energy conversions device is provided that includes a synchronous or brushless linear (SoBL) motor, and a transformer, where the transformer is integrated electromagnetically and topologically with the SoBL motor, where an electromagnetic field orientation of the

  2. The Value Proposition for Fractionated Space Architectures

    2006-09-01

    fractionation “mass penalty” assumptions , the expected launch costs are nearly a factor of two lower for the fractionated system than for the monolith...humidity variations which may affect fire propagation speed. 23 The Capital Asset Pricing Model ( CAPM ...spacecraft, can be very significant. In any event, however, the assumption that spacecraft cost scales roughly linearly with its mass is an artifact of

  3. SU-E-J-105: Stromal-Epithelial Responses to Fractionated Radiotherapy

    Qayyum, M

    2014-01-01

    Purpose: The stromal-epithelial-cell interactions that are responsible for directing normal breast-tissue development and maintenance play a central role in the progression of breast cancer. In the present study, we developed three-dimensional (3-D) cell co-cultures used to study cancerous mammary cell responses to fractionated radiotherapy. In particular, we focused on the role of the reactive stroma in determining the therapeutic ratio for postsurgical treatment. Methods: Cancerous human mammary epithelial cells were cultured in a 3-D collagen matrix with human fibroblasts stimulated by various concentrations of transforming growth factor beta 1 (TGF-β1). These culture samples were designed to model the post-lumpectomy mammary stroma in the presence of residual cancer cells. We tracked over time the changes in medium stiffness, fibroblast-cell activation (conversion to cancer activated fibroblasts (CAF)), and proliferation of both cell types under a variety of fractionated radiotherapy protocols. Samples were exposed to 6 MV X-rays from a linear accelerator in daily fraction sizes of 90, 180 and 360 cGy over five days in a manner consistent with irradiation exposure during radiotherapy. Results: We found in fractionation studies with fibroblasts and CAF that higher doses per fraction may be more effective early on in deactivating cancer-harboring cellular environments. Higher-dose fraction schemes inhibit contractility in CAF and prevent differentiation of fibroblasts, thereby metabolically uncoupling tumor cells from their surrounding stroma. Yet, over a longer time period, the higher dose fractions may slow wound healing and increase ECM stiffening that could stimulate proliferation of surviving cancer cells. Conclusion: The findings suggest that dose escalation to the region with residual disease can deactivate the reactive stroma, thus minimizing the cancer promoting features of the cellular environment. Large-fraction irradiation may be used to sterilize

  4. SU-E-J-105: Stromal-Epithelial Responses to Fractionated Radiotherapy

    Qayyum, M [Little Company of Mary Hospital, Ever Green Park, IL (United States)

    2014-06-01

    Purpose: The stromal-epithelial-cell interactions that are responsible for directing normal breast-tissue development and maintenance play a central role in the progression of breast cancer. In the present study, we developed three-dimensional (3-D) cell co-cultures used to study cancerous mammary cell responses to fractionated radiotherapy. In particular, we focused on the role of the reactive stroma in determining the therapeutic ratio for postsurgical treatment. Methods: Cancerous human mammary epithelial cells were cultured in a 3-D collagen matrix with human fibroblasts stimulated by various concentrations of transforming growth factor beta 1 (TGF-β1). These culture samples were designed to model the post-lumpectomy mammary stroma in the presence of residual cancer cells. We tracked over time the changes in medium stiffness, fibroblast-cell activation (conversion to cancer activated fibroblasts (CAF)), and proliferation of both cell types under a variety of fractionated radiotherapy protocols. Samples were exposed to 6 MV X-rays from a linear accelerator in daily fraction sizes of 90, 180 and 360 cGy over five days in a manner consistent with irradiation exposure during radiotherapy. Results: We found in fractionation studies with fibroblasts and CAF that higher doses per fraction may be more effective early on in deactivating cancer-harboring cellular environments. Higher-dose fraction schemes inhibit contractility in CAF and prevent differentiation of fibroblasts, thereby metabolically uncoupling tumor cells from their surrounding stroma. Yet, over a longer time period, the higher dose fractions may slow wound healing and increase ECM stiffening that could stimulate proliferation of surviving cancer cells. Conclusion: The findings suggest that dose escalation to the region with residual disease can deactivate the reactive stroma, thus minimizing the cancer promoting features of the cellular environment. Large-fraction irradiation may be used to sterilize

  5. Visualizing Transformation

    Pedersen, Pia

    2012-01-01

    Transformation, defined as the step of extracting, arranging and simplifying data into visual form (M. Neurath, 1974), was developed in connection with ISOTYPE (International System Of TYpographic Picture Education) and might well be the most important legacy of Isotype to the field of graphic...... design. Recently transformation has attracted renewed interest because of the book The Transformer written by Robin Kinross and Marie Neurath. My on-going research project, summarized in this paper, identifies and depicts the essential principles of data visualization underlying the process...... of transformation with reference to Marie Neurath’s sketches on the Bilston Project. The material has been collected at the Otto and Marie Neurath Collection housed at the University of Reading, UK. By using data visualization as a research method to look directly into the process of transformation, the project...

  6. What next in fractionated radiotherapy

    Fowler, J.F.

    1984-01-01

    Trends in models for predicting the total dose required to produce tolerable normal-tissue injury can be seen by the progression from the ''cube root law'', through Strandqvist's slope of 0.22, to NSD, TDF and CRE which have separate time and fraction number exponents, to even better approximations now available. The dose-response formulae that can be used to define the effect of fraction size (and number) include (1) the linear quadratic (LQ) model (2) the two-component (TC) multi-target model and (3) repair-misrepair models. The LQ model offers considerable convenience, requires only two parameters to be determined, and emphasizes the difference between late and early normal-tissue dependence on dose per fraction first shown by exponents greater than the NSD slope of 0.24. Exponents of overall time, e.g. Tsup(0.11), yield the wrong shape of time curve, suggesting that most proliferating occurs early, although it really occurs after a delay depending on the turnover time of the tissue. Improved clinical results are being sought by hyperfractionation, accelerated fractionation, or continuous low dose rate irradiation as in interstitial implants. (U.K.)

  7. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    N U+02BC Doye, Ibrahima

    2018-02-13

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  8. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

    2018-01-01

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  9. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Mohammadtaghi Hamidi Beheshti

    2010-01-01

    Full Text Available We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  10. Numerical solution of large sparse linear systems

    Meurant, Gerard; Golub, Gene.

    1982-02-01

    This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

  11. A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

    M. ZANGIABADI; H. R. MALEKI

    2007-01-01

    In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, w...

  12. Smarandache Continued Fractions

    Ibstedt, H.

    2001-01-01

    The theory of general continued fractions is developed to the extent required in order to calculate Smarandache continued fractions to a given number of decimal places. Proof is given for the fact that Smarandache general continued fractions built with positive integer Smarandache sequences baving only a finite number of terms equal to 1 is convergent. A few numerical results are given.

  13. Linear and kernel methods for multivariate change detection

    Canty, Morton J.; Nielsen, Allan Aasbjerg

    2012-01-01

    ), as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (nonlinear), may further enhance change signals relative to no-change background. IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric...... normalization, and kernel PCA/MAF/MNF transformations are presented that function as transparent and fully integrated extensions of the ENVI remote sensing image analysis environment. The train/test approach to kernel PCA is evaluated against a Hebbian learning procedure. Matlab code is also available...... that allows fast data exploration and experimentation with smaller datasets. New, multiresolution versions of IR-MAD that accelerate convergence and that further reduce no-change background noise are introduced. Computationally expensive matrix diagonalization and kernel image projections are programmed...

  14. A procedure to construct exact solutions of nonlinear fractional differential equations.

    Güner, Özkan; Cevikel, Adem C

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

  15. Fractional smith chart theory

    Shamim, Atif

    2011-03-01

    For the first time, a generalized Smith chart is introduced here to represent fractional order circuit elements. It is shown that the standard Smith chart is a special case of the generalized fractional order Smith chart. With illustrations drawn for both the conventional integer based lumped elements and the fractional elements, a graphical technique supported by the analytical method is presented to plot impedances on the fractional Smith chart. The concept is then applied towards impedance matching networks, where the fractional approach proves to be much more versatile and results in a single element matching network for a complex load as compared to the two elements in the conventional approach. © 2010 IEEE.

  16. A novel approach for solving fractional Fisher equation using ...

    Department of Engineering Sciences, Faculty of Technology and Engineering, East of ... The reliability, simplicity and cost-effectiveness of the method are confirmed by applying this ... Differential transform method; fractional Fisher equation.

  17. A novel approach for solving fractional Fisher equation using

    Differential transform method; fractional Fisher equation. ... confirmed by applying this method on different forms of functional equations. Author Affiliations. MIRZAZADEH M1. Department of Engineering Sciences, Faculty of Technology and ...

  18. Laplace-Laplace analysis of the fractional Poisson process

    Gorenflo, Rudolf; Mainardi, Francesco

    2013-01-01

    We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.

  19. On transformation shear of precipitated zirconia particles

    Zhang, J.M.; Lam, K.Y.

    1993-01-01

    A model is proposed to investigate the transformation shear of the precipitated zirconia particles which undergo a stress-induced lattice transformation from tetragonal to monoclinic symmetry. Kinematically admissible twinning planes and the corresponding twinning elements are determined according to the continuum theory of dispacive phase transformation. It is postulated that only one twinning mode prevails in each transformed particle and that the minimization of elastic strain energy change dictates the morphology of the transformed variants. The transformation shear is determined by the twinning mode and the volume fraction of the corresponding variant. Numerical calculations show that each of the six kinematically admissible twinning modes may be kinematically favorable and therefore operate in constrained particle. The actual transformation shear in a transformed particle is shown to be dependent on the transformation stress, on the particle shape as well as on the lattice orientation relative to the principal axes of the ellipsoidal particle

  20. Fractional factorial plans

    Dey, Aloke

    2009-01-01

    A one-stop reference to fractional factorials and related orthogonal arrays.Presenting one of the most dynamic areas of statistical research, this book offers a systematic, rigorous, and up-to-date treatment of fractional factorial designs and related combinatorial mathematics. Leading statisticians Aloke Dey and Rahul Mukerjee consolidate vast amounts of material from the professional literature--expertly weaving fractional replication, orthogonal arrays, and optimality aspects. They develop the basic theory of fractional factorials using the calculus of factorial arrangements, thereby providing a unified approach to the study of fractional factorial plans. An indispensable guide for statisticians in research and industry as well as for graduate students, Fractional Factorial Plans features: * Construction procedures of symmetric and asymmetric orthogonal arrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based on orthogonal arrays. * Trend-free plans...