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

International Nuclear Information System (INIS)

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.

Linear canonical transforms theory and applications

CERN Document Server

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.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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)

Daptomycin Tolerance in the Staphylococcus aureus pitA6 Mutant Is Due to Upregulation of the dlt Operon.

Science.gov (United States)

Mechler, Lukas; Bonetti, Eve-Julie; Reichert, Sebastian; Flötenmeyer, Matthias; Schrenzel, Jacques; Bertram, Ralph; François, Patrice; Götz, Friedrich

2016-05-01

Understanding the mechanisms of how bacteria become tolerant toward antibiotics during clinical therapy is a very important object. In a previous study, we showed that increased daptomycin (DAP) tolerance of Staphylococcus aureus was due to a point mutation in pitA (inorganic phosphate transporter) that led to intracellular accumulation of both inorganic phosphate (Pi) and polyphosphate (polyP). DAP tolerance in the pitA6 mutant differs from classical resistance mechanisms since there is no increase in the MIC. In this follow-up study, we demonstrate that DAP tolerance in the pitA6 mutant is not triggered by the accumulation of polyP. Transcriptome analysis revealed that 234 genes were at least 2.0-fold differentially expressed in the mutant. Particularly, genes involved in protein biosynthesis, carbohydrate and lipid metabolism, and replication and maintenance of DNA were downregulated. However, the most important change was the upregulation of the dlt operon, which is induced by the accumulation of intracellular Pi The GraXRS system, known as an activator of the dlt operon (d-alanylation of teichoic acids) and of the mprF gene (multiple peptide resistance factor), is not involved in DAP tolerance of the pitA6 mutant. In conclusion, DAP tolerance of the pitA6 mutant is due to an upregulation of the dlt operon, triggered directly or indirectly by the accumulation of Pi. Copyright © 2016, American Society for Microbiology. All Rights Reserved.

Direct Linear Transformation Method for Three-Dimensional Cinematography

Science.gov (United States)

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)

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

International Nuclear Information System (INIS)

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)

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

Science.gov (United States)

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.

Orientação exterior de um par estereoscópico Ikonos II com base no modelo não-rigoroso DLT

Directory of Open Access Journals (Sweden)

Sydney de Oliveira Dias

Full Text Available O crescente avanço tecnológico ocorrido nos últimos anos, tanto da área da Informática, Fotogrametria e também Sensoriamento Remoto, vem contribuindo significativamente para diversas pesquisas sobre extração de informações tridimensionais a partir de imagens de alta resolução. No presente trabalho, uma solução utilizando modelagem não rigorosa baseada na transformação matemática DLT (Direct Linear Transformation foi utilizada para a orientação exterior de um par estereoscópico de imagens Ikonos II e determinação de coordenadas tridimensionais por intersecção fotogramétrica. O objetivo principal foi o de avaliar o desempenho do modelo na aplicação, como também a obtenção de melhor configuração de pontos de apoio necessários na orientação exterior para fins da determinação de coordenadas tridimensionais por interseção espacial. Os experimentos realizados permitiram recomendar a configuração adequada para a distribuição dos pontos de apoio, onde a exatidão planimétrica foi equivalente a precisão teórica tolerável igual a um pixel de erro nas observações, enquanto a exatidão altimétrica ficou próxima de 1,5 pixels.

Data Transformations for Inference with Linear Regression: Clarifications and Recommendations

Science.gov (United States)

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…

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

International Nuclear Information System (INIS)

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.

The early detection and follow-up of the highly obscured Type II supernova 2016ija/DLT16am

DEFF Research Database (Denmark)

Tartaglia, L.; Sand, D. J.; Valenti, S.

2018-01-01

We present our analysis of the Type II supernova DLT16am (SN~2016ija). The object was discovered during the ongoing $\\rm{D}`edge-on nearby ($D=20.0\\pm1.9\\,\\rm{Mpc}$) galaxy NGC~1532. The subsequent prompt and high-cadenced spectroscopic and photometric follow-up revealed a highly extincted...

Seismic Linear Noise Attenuation with Use of Radial Transform

Science.gov (United States)

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.

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

Science.gov (United States)

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

Transformations between inertial and linearly accelerated frames of reference

International Nuclear Information System (INIS)

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)

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

International Nuclear Information System (INIS)

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.

Noiseless Vlasov–Poisson simulations with linearly transformed particles

Energy Technology Data Exchange (ETDEWEB)

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.

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

Science.gov (United States)

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.

LCPT: a program for finding linear canonical transformations

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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

A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

Directory of Open Access Journals (Sweden)

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.

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

OpenAIRE

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...

Identification problems in linear transformation system

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Discrete linear canonical transform computation by adaptive method.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

NARCIS (Netherlands)

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

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

International Nuclear Information System (INIS)

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)

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

International Nuclear Information System (INIS)

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

Darboux transformations and linear parabolic partial differential equations

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Identification and characterization of dwarf 62, a loss-of-function mutation in DLT/OsGRAS-32 affecting gibberellin metabolism in rice.

Science.gov (United States)

Li, Wenqiang; Wu, Jianguo; Weng, Shili; Zhang, Yujiang; Zhang, Dapeng; Shi, Chunhai

2010-11-01

A dwarf mutant, dwarf 62 (d62), was isolated from rice cultivar 93-11 by mutagenesis with γ-rays. Under normal growth conditions, the mutant had multiple abnormal phenotypes, such as dwarfism, wide and dark-green leaf blades, reduced tiller numbers, late and asynchronous heading, short roots, partial male sterility, etc. Genetic analysis indicated that the abnormal phenotypes were controlled by the recessive mutation of a single nuclear gene. Using molecular markers, the D62 gene was fine mapped in 131-kb region at the short arm of chromosome 6. Positional cloning of D62 gene revealed that it was the same locus as DLT/OsGRAS-32, which encodes a member of the GRAS family. In previous studies, the DLT/OsGRAS-32 is confirmed to play positive roles in brassinosteroid (BR) signaling. Sequence analysis showed that the d62 carried a 2-bp deletion in ORF region of D62 gene which led to a loss-of-function mutation. The function of D62 gene was confirmed by complementation experiment. RT-PCR analysis and promoter activity analysis showed that the D62 gene expressed in all tested tissues including roots, stems, leaves and panicles of rice plant. The d62 mutant exhibited decreased activity of α-amylase in endosperm and reduced content of endogenous GA(1). The expression levels of gibberellin (GA) biosynthetic genes including OsCPS1, OsKS1, OsKO1, OsKAO, OsGA20ox2/SD1 and OsGA2ox3 were significantly increased in d62 mutant. Briefly, these results demonstrated that the D62 (DLT/OsGRAS-32) not only participated in the regulation of BR signaling, but also influenced GA metabolism in rice.

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

International Nuclear Information System (INIS)

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

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

CERN Document Server

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.

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

Science.gov (United States)

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.

Discrete linear canonical transforms based on dilated Hermite functions.

Science.gov (United States)

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.

Linear-algebraic bath transformation for simulating complex open quantum systems

International Nuclear Information System (INIS)

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)

Solution of linear transport equation using Chebyshev polynomials and Laplace transform

International Nuclear Information System (INIS)

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)

A Top-Down Account of Linear Canonical Transforms

Directory of Open Access Journals (Sweden)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

Science.gov (United States)

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.

Capacitor blocks for linear transformer driver stages.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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))

Linear transform of the multi-target survival curve

Energy Technology Data Exchange (ETDEWEB)

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.

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

Science.gov (United States)

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.

Insertional inactivation of genes responsible for the D-alanylation of lipoteichoic acid in Streptococcus gordonii DL1 (Challis) affects intrageneric coaggregations.

Science.gov (United States)

Clemans, D L; Kolenbrander, P E; Debabov, D V; Zhang, Q; Lunsford, R D; Sakone, H; Whittaker, C J; Heaton, M P; Neuhaus, F C

1999-05-01

Most human oral viridans streptococci participate in intrageneric coaggregations, the cell-to-cell adherence among genetically distinct streptococci. Two genes relevant to these intrageneric coaggregations were identified by transposon Tn916 mutagenesis of Streptococcus gordonii DL1 (Challis). A 626-bp sequence flanking the left end of the transposon was homologous to dltA and dltB of Lactobacillus rhamnosus ATCC 7469 (formerly called Lactobacillus casei). A 60-kb probe based on this flanking sequence was used to identify the homologous DNA in a fosmid library of S. gordonii DL1. This DNA encoded D-alanine-D-alanyl carrier protein ligase that was expressed in Escherichia coli from the fosmid clone. The cloned streptococcal dltA was disrupted by inserting an ermAM cassette, and then it was linearized and transformed into S. gordonii DL1 for allelic replacement. Erythromycin-resistant transformants containing a single insertion in dltA exhibited a loss of D-alanyl esters in lipoteichoic acid (LTA) and a loss of intrageneric coaggregation. This phenotype was correlated with the loss of a 100-kDa surface protein reported previously to be involved in mediating intrageneric coaggregation (C. J. Whittaker, D. L. Clemans, and P. E. Kolenbrander, Infect. Immun. 64:4137-4142, 1996). The mutants retained the parental ability to participate in intergeneric coaggregation with human oral actinomyces, indicating the specificity of the mutation in altering intrageneric coaggregations. The mutants were altered morphologically and exhibited aberrant cell septa in a variety of pleomorphs. The natural DNA transformation frequency was reduced 10-fold in these mutants. Southern analysis of chromosomal DNAs from various streptococcal species with the dltA probe revealed the presence of this gene in most viridans streptococci. Thus, it is hypothesized that D-alanyl LTA may provide binding sites for the putative 100-kDa adhesin and scaffolding for the proper presentation of this adhesin to

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

Directory of Open Access Journals (Sweden)

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.

Voltage linear transformation circuit design

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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.

Square pulse linear transformer driver

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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.

Predicting birth weight with conditionally linear transformation models.

Science.gov (United States)

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.

Extended Kalman filter-based methods for pose estimation using visual, inertial and magnetic sensors: comparative analysis and performance evaluation.

Science.gov (United States)

Ligorio, Gabriele; Sabatini, Angelo Maria

2013-02-04

In this paper measurements from a monocular vision system are fused with inertial/magnetic measurements from an Inertial Measurement Unit (IMU) rigidly connected to the camera. Two Extended Kalman filters (EKFs) were developed to estimate the pose of the IMU/camera sensor moving relative to a rigid scene (ego-motion), based on a set of fiducials. The two filters were identical as for the state equation and the measurement equations of the inertial/magnetic sensors. The DLT-based EKF exploited visual estimates of the ego-motion using a variant of the Direct Linear Transformation (DLT) method; the error-driven EKF exploited pseudo-measurements based on the projection errors from measured two-dimensional point features to the corresponding three-dimensional fiducials. The two filters were off-line analyzed in different experimental conditions and compared to a purely IMU-based EKF used for estimating the orientation of the IMU/camera sensor. The DLT-based EKF was more accurate than the error-driven EKF, less robust against loss of visual features, and equivalent in terms of computational complexity. Orientation root mean square errors (RMSEs) of 1° (1.5°), and position RMSEs of 3.5 mm (10 mm) were achieved in our experiments by the DLT-based EKF (error-driven EKF); by contrast, orientation RMSEs of 1.6° were achieved by the purely IMU-based EKF.

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

Science.gov (United States)

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…

Definition of path integrals and rules for non-linear transformations

International Nuclear Information System (INIS)

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.)

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

Science.gov (United States)

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.

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

CERN Document Server

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.

Photogrammetry Applied to Wind Tunnel Testing

Science.gov (United States)

Liu, Tian-Shu; Cattafesta, L. N., III; Radeztsky, R. H.; Burner, A. W.

2000-01-01

In image-based measurements, quantitative image data must be mapped to three-dimensional object space. Analytical photogrammetric methods, which may be used to accomplish this task, are discussed from the viewpoint of experimental fluid dynamicists. The Direct Linear Transformation (DLT) for camera calibration, used in pressure sensitive paint, is summarized. An optimization method for camera calibration is developed that can be used to determine the camera calibration parameters, including those describing lens distortion, from a single image. Combined with the DLT method, this method allows a rapid and comprehensive in-situ camera calibration and therefore is particularly useful for quantitative flow visualization and other measurements such as model attitude and deformation in production wind tunnels. The paper also includes a brief description of typical photogrammetric applications to temperature- and pressure-sensitive paint measurements and model deformation measurements in wind tunnels.

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

NARCIS (Netherlands)

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

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

Directory of Open Access Journals (Sweden)

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.

Extreme non-linear elasticity and transformation optics

DEFF Research Database (Denmark)

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...

Householder transformations and optimal linear combinations

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

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.

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

International Nuclear Information System (INIS)

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

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

Directory of Open Access Journals (Sweden)

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.

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

International Nuclear Information System (INIS)

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

All-automatic swimmer tracking system based on an optimized scaled composite JTC technique

Science.gov (United States)

Benarab, D.; Napoléon, T.; Alfalou, A.; Verney, A.; Hellard, P.

2016-04-01

In this paper, an all-automatic optimized JTC based swimmer tracking system is proposed and evaluated on real video database outcome from national and international swimming competitions (French National Championship, Limoges 2015, FINA World Championships, Barcelona 2013 and Kazan 2015). First, we proposed to calibrate the swimming pool using the DLT algorithm (Direct Linear Transformation). DLT calculates the homography matrix given a sufficient set of correspondence points between pixels and metric coordinates: i.e. DLT takes into account the dimensions of the swimming pool and the type of the swim. Once the swimming pool is calibrated, we extract the lane. Then we apply a motion detection approach to detect globally the swimmer in this lane. Next, we apply our optimized Scaled Composite JTC which consists of creating an adapted input plane that contains the predicted region and the head reference image. This latter is generated using a composite filter of fin images chosen from the database. The dimension of this reference will be scaled according to the ratio between the head's dimension and the width of the swimming lane. Finally, applying the proposed approach improves the performances of our previous tracking method by adding a detection module in order to achieve an all-automatic swimmer tracking system.

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

Science.gov (United States)

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.

Linear algebra

CERN Document Server

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.

Elements of linear space

CERN Document Server

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

Solving non-linear Horn clauses using a linear Horn clause solver

DEFF Research Database (Denmark)

Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre

2016-01-01

In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....

Garbageless reversible implementation of integer linear transformations

DEFF Research Database (Denmark)

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...

New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit

Directory of Open Access Journals (Sweden)

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.

Linear algebra

CERN Document Server

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...

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

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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.

Multiview Trajectory Mapping Using Homography with Lens Distortion Correction

Directory of Open Access Journals (Sweden)

Andrea Cavallaro

2008-11-01

Full Text Available We present a trajectory mapping algorithm for a distributed camera setting that is based on statistical homography estimation accounting for the distortion introduced by camera lenses. Unlike traditional approaches based on the direct linear transformation (DLT algorithm and singular value decomposition (SVD, the planar homography estimation is derived from renormalization. In addition to this, the algorithm explicitly introduces a correction parameter to account for the nonlinear radial lens distortion, thus improving the accuracy of the transformation. We demonstrate the proposed algorithm by generating mosaics of the observed scenes and by registering the spatial locations of moving objects (trajectories from multiple cameras on the mosaics. Moreover, we objectively compare the transformed trajectories with those obtained by SVD and least mean square (LMS methods on standard datasets and demonstrate the advantages of the renormalization and the lens distortion correction.

Multiview Trajectory Mapping Using Homography with Lens Distortion Correction

Directory of Open Access Journals (Sweden)

Kayumbi Gabin

2008-01-01

Full Text Available Abstract We present a trajectory mapping algorithm for a distributed camera setting that is based on statistical homography estimation accounting for the distortion introduced by camera lenses. Unlike traditional approaches based on the direct linear transformation (DLT algorithm and singular value decomposition (SVD, the planar homography estimation is derived from renormalization. In addition to this, the algorithm explicitly introduces a correction parameter to account for the nonlinear radial lens distortion, thus improving the accuracy of the transformation. We demonstrate the proposed algorithm by generating mosaics of the observed scenes and by registering the spatial locations of moving objects (trajectories from multiple cameras on the mosaics. Moreover, we objectively compare the transformed trajectories with those obtained by SVD and least mean square (LMS methods on standard datasets and demonstrate the advantages of the renormalization and the lens distortion correction.

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

Science.gov (United States)

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.

Generalized field-transforming metamaterials

International Nuclear Information System (INIS)

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.

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

Science.gov (United States)

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.

Linear Transformer Drivers for Z-pinch Based Propulsion

Science.gov (United States)

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.

Rectangular waveform linear transformer driver module design

International Nuclear Information System (INIS)

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)

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Linear integral equations and soliton systems

International Nuclear Information System (INIS)

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.)

Shear-transformation-zone theory of linear glassy dynamics.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Development of a hybrid mode linear transformer driver stage

Science.gov (United States)

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 .

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

Science.gov (United States)

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.

A linear-time algorithm for Euclidean feature transform sets

NARCIS (Netherlands)

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

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

Science.gov (United States)

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.

Logarithmic Transformations in Regression: Do You Transform Back Correctly?

Science.gov (United States)

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…

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

Directory of Open Access Journals (Sweden)

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.

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

International Nuclear Information System (INIS)

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.

Advanced statistics: linear regression, part I: simple linear regression.

Science.gov (United States)

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.

The Bargmann transform and canonical transformations

International Nuclear Information System (INIS)

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

Linear circuit theory matrices in computer applications

CERN Document Server

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.

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

Directory of Open Access Journals (Sweden)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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)

Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis.

Science.gov (United States)

Kwon, Young-Hoo; Casebolt, Jeffrey B

2006-07-01

One of the most serious obstacles to accurate quantification of the underwater motion of a swimmer's body is image deformation caused by refraction. Refraction occurs at the water-air interface plane (glass) owing to the density difference. Camera calibration-reconstruction algorithms commonly used in aquatic research do not have the capability to correct this refraction-induced nonlinear image deformation and produce large reconstruction errors. The aim of this paper is to provide a thorough review of: the nature of the refraction-induced image deformation and its behaviour in underwater object-space plane reconstruction; the intrinsic shortcomings of the Direct Linear Transformation (DLT) method in underwater motion analysis; experimental conditions that interact with refraction; and alternative algorithms and strategies that can be used to improve the calibration-reconstruction accuracy. Although it is impossible to remove the refraction error completely in conventional camera calibration-reconstruction methods, it is possible to improve the accuracy to some extent by manipulating experimental conditions or calibration frame characteristics. Alternative algorithms, such as the localized DLT and the double-plane method are also available for error reduction. The ultimate solution for the refraction problem is to develop underwater camera calibration and reconstruction algorithms that have the capability to correct refraction.

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

Directory of Open Access Journals (Sweden)

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 (<T_s> 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 (<T_s>, pair together with the wet-environment surface temperature (<T_ws> and ET rate (ET_w, 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, T_s, values within the watershed. The linear transformation preserves the mean which is highly desirable. <T_ws>, in the lack of significant open water surfaces within the study watershed (Elkhorn, Nebraska, was obtained as the mean of the smallest MODIS T_s 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.

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

Science.gov (United States)

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

Level Design as Model Transformation

NARCIS (Netherlands)

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

Linear motor with contactless energy transfer

NARCIS (Netherlands)

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

Fractional finite Fourier transform.

Science.gov (United States)

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.

Optimized nonorthogonal transforms for image compression.

Science.gov (United States)

Guleryuz, O G; Orchard, M T

1997-01-01

The transform coding of images is analyzed from a common standpoint in order to generate a framework for the design of optimal transforms. It is argued that all transform coders are alike in the way they manipulate the data structure formed by transform coefficients. A general energy compaction measure is proposed to generate optimized transforms with desirable characteristics particularly suited to the simple transform coding operation of scalar quantization and entropy coding. It is shown that the optimal linear decoder (inverse transform) must be an optimal linear estimator, independent of the structure of the transform generating the coefficients. A formulation that sequentially optimizes the transforms is presented, and design equations and algorithms for its computation provided. The properties of the resulting transform systems are investigated. In particular, it is shown that the resulting basis are nonorthogonal and complete, producing energy compaction optimized, decorrelated transform coefficients. Quantization issues related to nonorthogonal expansion coefficients are addressed with a simple, efficient algorithm. Two implementations are discussed, and image coding examples are given. It is shown that the proposed design framework results in systems with superior energy compaction properties and excellent coding results.

Error Analysis on Plane-to-Plane Linear Approximate Coordinate ...

Indian Academy of Sciences (India)

Abstract. In this paper, the error analysis has been done for the linear approximate transformation between two tangent planes in celestial sphere in a simple case. The results demonstrate that the error from the linear transformation does not meet the requirement of high-precision astrometry under some conditions, so the ...

Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation

International Nuclear Information System (INIS)

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. 

Quadratic Lagrangians and Legendre transformation

International Nuclear Information System (INIS)

Magnano, G.

1988-01-01

In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor

A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

OpenAIRE

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...

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

International Nuclear Information System (INIS)

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

Fractionalization of cyclic transformations in optics

NARCIS (Netherlands)

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

An introduction to linear algebra and tensors

CERN Document Server

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.

Linear regression and the normality assumption.

Science.gov (United States)

Schmidt, Amand F; Finan, Chris

2017-12-16

Researchers often perform arbitrary outcome transformations to fulfill the normality assumption of a linear regression model. This commentary explains and illustrates that in large data settings, such transformations are often unnecessary, and worse may bias model estimates. Linear regression assumptions are illustrated using simulated data and an empirical example on the relation between time since type 2 diabetes diagnosis and glycated hemoglobin levels. Simulation results were evaluated on coverage; i.e., the number of times the 95% confidence interval included the true slope coefficient. Although outcome transformations bias point estimates, violations of the normality assumption in linear regression analyses do not. The normality assumption is necessary to unbiasedly estimate standard errors, and hence confidence intervals and P-values. However, in large sample sizes (e.g., where the number of observations per variable is >10) violations of this normality assumption often do not noticeably impact results. Contrary to this, assumptions on, the parametric model, absence of extreme observations, homoscedasticity, and independency of the errors, remain influential even in large sample size settings. Given that modern healthcare research typically includes thousands of subjects focusing on the normality assumption is often unnecessary, does not guarantee valid results, and worse may bias estimates due to the practice of outcome transformations. Copyright © 2017 Elsevier Inc. All rights reserved.

Laplace transforms essentials

CERN Document Server

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

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

International Nuclear Information System (INIS)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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.

The Symmetric Rudin-Shapiro Transform

DEFF Research Database (Denmark)

Harbo, Anders La-Cour

2003-01-01

A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, symmetric transform, the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generating large sets...... of spread spectrum signals. This presentation provides a simple definition of the symmetric RST that leads to a fast N log(N) and numerically stable implementation of the transform....

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

Science.gov (United States)

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.

Unstable intertrochanteric femur fractures in geriatric patients treated with the DLT trochanteric nail.

Science.gov (United States)

Temiz, Aytun; Durak, Aslihan; Atici, Teoman

2015-07-01

To evaluate clinical-functional and radiological results of geriatric patients with unstable intertrochanteric femur fracture treated with intramedullary nail. Thirty-two patients treated with intramedullary nail (DLT trochanteric nail) due to unstable intertrochanteric femur fractures were reviewed retrospectively. Fractures 31-A2 and 31-A3 (AO classification) were evaluated. Operation time, blood loss, and blood transfusion requirements, hospitalization period, time to fracture union were evaluated and perioperative and postoperative complications were recorded. According to the modified Baumgaertner criteria fracture reduction was analyzed radiologically, and nail tip-apex distance was measured. Femoral neck-shaft angle was also evaluated. Harris Hip Score for clinical evaluation and Kyo criteria for walking capacity were used. The mean age was 72 years (65-81), mean follow up time was 18.3 months (12-26). Nineteen patients had type 31-A2 and 13 had type 31-A3 fractures. Mean operation time was 36.3min (25-45), blood loss 185.9ml (100-250). Blood transfusion was required in 7 patients. The average hospitalization duration was 6 days (4-14) while the time to surgery from admission was 2.9 days (2-6). Radiologically, in 21 of the cases fracture reduction was well (65.6%), acceptable in 9 (28.1%), and poor in 2 (6.3%). In early postoperative period, the mean collo-diaphyseal angle was 129.1° (120-140°), mean tip-apex distance was 15.5mm (10-27). The mean Harris Hip Score was 63.4 (38-90). Two patients (6.3%) had excellent, 21 patients (65.6%) had good, 7 patients (21.8%) had moderate, and 2 patients (6.3%) had poor results. Walking capacity in the last follow-up in 20 of the cases (62.5%) was pre-fracture level. While complications were observed in seventeen patients (53.1%) (5 superficial wound infections, 5 fractures of the greater trochanter, 3 cases of secondary varus angulation and 4 cases of heterotopic ossification) none of them required additional surgery

Modelling the pulse transformer in SPICE

International Nuclear Information System (INIS)

Godlewska, Malgorzata; Górecki, Krzysztof; Górski, Krzysztof

2016-01-01

The paper is devoted to modelling pulse transformers in SPICE. It shows the character of the selected models of this element, points out their advantages and disadvantages, and presents the results of experimental verification of the considered models. These models are characterized by varying degrees of complexity - from linearly coupled linear coils to nonlinear electrothermal models. The study was conducted for transformer with ring cores made of a variety of ferromagnetic materials, while exciting the sinusoidal signal of a frequency 100 kHz and different values of load resistance. The transformers operating conditions under which the considered models ensure the acceptable accuracy of calculations are indicated

Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

International Nuclear Information System (INIS)

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.)

Multi-dimensional Laplace transforms and applications

International Nuclear Information System (INIS)

Mughrabi, T.A.

1988-01-01

In this dissertation we establish new theorems for computing certain types of multidimensional Laplace transform pairs from known one-dimensional Laplace transforms. The theorems are applied to the most commonly used special functions and so we obtain many two and three dimensional Laplace transform pairs. As applications, some boundary value problems involving linear partial differential equations are solved by the use of multi-dimensional Laplace transformation. Also we establish some relations between the Laplace transformation and other integral transformation in two variables

The Symmetric Rudin-Shapiro Transform

DEFF Research Database (Denmark)

Harbo, Anders La-Cour

2003-01-01

A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, and symmetric transform given as the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generatin...... large sets of spread spectrum signals. This presentation provides a simple definition of the symmetric RST that leads to a fast N log(N) and numerically stable implementation of the transform....

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

International Nuclear Information System (INIS)

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)

Cayley transform on Stiefel manifolds

Science.gov (United States)

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.

Aliasing in the Complex Cepstrum of Linear-Phase Signals

DEFF Research Database (Denmark)

Bysted, Tommy Kristensen

1997-01-01

Assuming linear-phase of the associated time signal, this paper presents an approximated analytical description of the unavoidable aliasing in practical use of complex cepstrums. The linear-phase assumption covers two major applications of complex cepstrums which are linear- to minimum-phase FIR......-filter transformation and minimum-phase estimation from amplitude specifications. The description is made in the cepstrum domain, the Fourier transform of the complex cepstrum and in the frequency domain. Two examples are given, one for verification of the derived equations and one using the description to reduce...... aliasing in minimum-phase estimation...

Linear problems and Baecklund transformations for the Hirota-Ohta system

International Nuclear Information System (INIS)

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.

Analytical exact solution of the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

2011-01-01

Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability

International Nuclear Information System (INIS)

Bogdanov, I I; Guterman, A E

2007-01-01

Bijective linear transformations of the matrix algebra over an arbitrary field that preserve simultaneous diagonalizability are characterized. This result is used for the characterization of bijective linear monotone transformations . Bibliography: 28 titles.

Matrices and transformations

CERN Document Server

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.

Fourier transform NMR

International Nuclear Information System (INIS)

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

Non-linear effects in the Boltzmann equation

International Nuclear Information System (INIS)

Barrachina, R.O.

1985-01-01

The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

Acoustic cloaking and transformation acoustics

International Nuclear Information System (INIS)

Chen Huanyang; Chan, C T

2010-01-01

In this review, we give a brief introduction to the application of the new technique of transformation acoustics, which draws on a correspondence between coordinate transformation and material properties. The technique is formulated for both acoustic waves and linear liquid surface waves. Some interesting conceptual devices can be designed for manipulating acoustic waves. For example, we can design acoustic cloaks that make an object invisible to acoustic waves, and the cloak can either encompass or lie outside the object to be concealed. Transformation acoustics, as an analog of transformation optics, can go beyond invisibility cloaking. As an illustration for manipulating linear liquid surface waves, we show that a liquid wave rotator can be designed and fabricated to rotate the wave front. The acoustic transformation media require acoustic materials which are anisotropic and inhomogeneous. Such materials are difficult to find in nature. However, composite materials with embedded sub-wavelength resonators can in principle be made and such 'acoustic metamaterials' can exhibit nearly arbitrary values of effective density and modulus tensors to satisfy the demanding material requirements in transformation acoustics. We introduce resonant sonic materials and Helmholtz resonators as examples of acoustic metamaterials that exhibit resonant behaviour in effective density and effective modulus. (topical review)

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

Directory of Open Access Journals (Sweden)

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.

The Transformation App Redux: The Notion of Linearity

Science.gov (United States)

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…

Effect of Image Linearization on Normalized Compression Distance

Science.gov (United States)

Mortensen, Jonathan; Wu, Jia Jie; Furst, Jacob; Rogers, John; Raicu, Daniela

Normalized Information Distance, based on Kolmogorov complexity, is an emerging metric for image similarity. It is approximated by the Normalized Compression Distance (NCD) which generates the relative distance between two strings by using standard compression algorithms to compare linear strings of information. This relative distance quantifies the degree of similarity between the two objects. NCD has been shown to measure similarity effectively on information which is already a string: genomic string comparisons have created accurate phylogeny trees and NCD has also been used to classify music. Currently, to find a similarity measure using NCD for images, the images must first be linearized into a string, and then compared. To understand how linearization of a 2D image affects the similarity measure, we perform four types of linearization on a subset of the Corel image database and compare each for a variety of image transformations. Our experiment shows that different linearization techniques produce statistically significant differences in NCD for identical spatial transformations.

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

Directory of Open Access Journals (Sweden)

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.

Magnetic bead detection using nano-transformers

Energy Technology Data Exchange (ETDEWEB)

Kim, Hyung Kwon; Ahn, Doyeol [Institute of Quantum Information Processing and Systems, University of Seoul, 90 Jeonnong, Dongdaemun, Seoul 130-743 (Korea, Republic of); Hwang, Jong Seung; Hwang, Sung Woo, E-mail: dahn@uos.ac.kr [Research Center for Time-domain Nano-functional Devices and School of Electrical Engineering, Korea University, 5-1 Anam, Sungbuk, Seoul 136-701 (Korea, Republic of)

2010-11-19

A novel scheme to detect magnetic beads using a nano-scale transformer with a femtoweber resolution is reported. We have performed a Faraday's induction experiment with the nano-transformer at room temperature. The transformer shows the linear output voltage responses to the sinusoidal input current. When magnetic beads are placed on the transformer, the output responses are increased by an amount corresponding to the added magnetic flux from the beads when compared with the case of no beads on the transformer. In this way, we could determine whether magnetic beads are on top of the transformer in a single particle level.

Magnetic bead detection using nano-transformers.

Science.gov (United States)

Kim, Hyung Kwon; Hwang, Jong Seung; Hwang, Sung Woo; Ahn, Doyeol

2010-11-19

A novel scheme to detect magnetic beads using a nano-scale transformer with a femtoweber resolution is reported. We have performed a Faraday's induction experiment with the nano-transformer at room temperature. The transformer shows the linear output voltage responses to the sinusoidal input current. When magnetic beads are placed on the transformer, the output responses are increased by an amount corresponding to the added magnetic flux from the beads when compared with the case of no beads on the transformer. In this way, we could determine whether magnetic beads are on top of the transformer in a single particle level.

On the linearization of nonlinear supersymmetry based on the commutator algebra

Energy Technology Data Exchange (ETDEWEB)

Tsuda, Motomu, E-mail: tsuda@sit.ac.jp

2017-01-10

We discuss a linearization procedure of nonlinear supersymmetry (NLSUSY) based on the closure of the commutator algebra for variations of functionals of Nambu–Goldstone fermions and their derivative terms under NLSUSY transformations in Volkov–Akulov NLSUSY theory. In the case of a set of bosonic and fermionic functionals, which leads to (massless) vector linear supermultiplets, we explicitly show that general linear SUSY transformations of basic components defined from those functionals are uniquely determined by examining the commutation relation in the NLSUSY theory.

The Baecklund transformation for isomonodromy deformation Schlesinger equations

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1980-01-01

We define the transformation of linear differential equations with rational function coefficients that fix monodromy data and change local multiplicities by any sequence of integers. This transformation that gives rise to Pade approximations, at the same time defines the Baecklund transformation of Schlesinger equations. (orig.)

Photoinduced electro-optics measurements of biosilica transformation to cristobalite

Energy Technology Data Exchange (ETDEWEB)

Fuchs, Ido [Department of Chemistry and the Institute of Nanotechnology, Bar-Ilan University, Ramat-Gan 52900 (Israel); Aluma, Yaniv; Ilan, Micha [Department of Zoology, George S. Wise Faculty of Life Sciences, Tel Aviv University, Tel Aviv 6997801 (Israel); Kityk, Iwan [Institute of Electronic Systems, Faculty of Electrical Engineering, Czestochowa University, Czestochowa 42-201 (Poland); Mastai, Yitzhak, E-mail: Yitzhak.Mastai@biu.ac.il [Department of Chemistry and the Institute of Nanotechnology, Bar-Ilan University, Ramat-Gan 52900 (Israel)

2015-03-15

In this paper we studied the photoinduced electro optics effects in the thermal transformation process of biosilica to cristobalite, at a relatively low temperature and ambient pressure. This process was characterized by a variety of standards techniques with emphasis on linear electro optic effect measurements. Overall we demonstrated that photoinduced electro optics measurements are very sensitive to the transformation from amorphous structure of silica in the natural sponge samples to laminar string morphology of cristobalite. With this technique we could probe the change in the samples chirality from achiral bio silica to chiral cristobalite structure. Furthermore it is shown that natural biosilica have photoinduced linear electro optics respond indicating the chiral natural of biosilica. - Graphical abstract: The phase transformation of biosilica from marine sponges to Cristobalite under thermal treatment was investigated using photoinduced electro optics measurements. The figure shows the changes of the electro-optic coefficient of cristobalite and biosilica. - Highlights: • We examine phase transformation of biosilica. • We report transition from amorphous biosilica to crystalline Cristobalite. • Biosilica transformation to Cristobalite at temperature of 850 °C. • Biosilica transformation is studied with photoinduced measurements. • We examine changes in the photoinduced linear electro optics properties.

Photoinduced electro-optics measurements of biosilica transformation to cristobalite

International Nuclear Information System (INIS)

Fuchs, Ido; Aluma, Yaniv; Ilan, Micha; Kityk, Iwan; Mastai, Yitzhak

2015-01-01

In this paper we studied the photoinduced electro optics effects in the thermal transformation process of biosilica to cristobalite, at a relatively low temperature and ambient pressure. This process was characterized by a variety of standards techniques with emphasis on linear electro optic effect measurements. Overall we demonstrated that photoinduced electro optics measurements are very sensitive to the transformation from amorphous structure of silica in the natural sponge samples to laminar string morphology of cristobalite. With this technique we could probe the change in the samples chirality from achiral bio silica to chiral cristobalite structure. Furthermore it is shown that natural biosilica have photoinduced linear electro optics respond indicating the chiral natural of biosilica. - Graphical abstract: The phase transformation of biosilica from marine sponges to Cristobalite under thermal treatment was investigated using photoinduced electro optics measurements. The figure shows the changes of the electro-optic coefficient of cristobalite and biosilica. - Highlights: • We examine phase transformation of biosilica. • We report transition from amorphous biosilica to crystalline Cristobalite. • Biosilica transformation to Cristobalite at temperature of 850 °C. • Biosilica transformation is studied with photoinduced measurements. • We examine changes in the photoinduced linear electro optics properties

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

Science.gov (United States)

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

Modified CT imaging by reduction factor transformations

International Nuclear Information System (INIS)

Doehring, W.; Linke, G.

1981-01-01

The possibilities of CT image modification which had existed so far for given matrix of attenuation values (window setting, highlighting, black-and-white or colour reversal and logarithmic distortion of the video signal) are supplemented by the method of attenuation value transformation. As a specific case a linear interval by interval attenuation value transformation is described. First of all, the intirety of the measured CT values is transformed into the corresponding CT quotients (CTQ) and then subdivided into 5 optional intervals. Each one freely selected CTQ value can be allocated to the first and to the last interval; the intermediate 3 intervals can be linearly transformed at random. The article discusses the influence of such a manipulation on CT image reproduction; this is of particular importance for the image visualisation of the results of quantitative organ analyses by means of computed tomography. The presented paper also points to the possibility of effecting further attenuation value transformations. (orig.) [de

Variable transformation of calibration equations for radiation dosimetry

International Nuclear Information System (INIS)

Watanabe, Yoichi

2005-01-01

For radiation dosimetry, dosimetric equipment must be calibrated by using known doses. The calibration is done to determine an equation that relates the absorbed dose to a physically measurable quantity. Since the calibration equation is accompanied by unavoidable uncertainties, the doses estimated with such equations suffer from inherent uncertainties. We presented mathematical formulation of the calibration when the calibration relation is either linear or nonlinear. We also derived equations for the uncertainty of the estimated dose as a function of the uncertainties of the parameters in the equations and the measured physical quantity. We showed that a dosimeter with a linear calibration equation with zero dose-offset enables us to perform relative dosimetry without calibration data. Furthermore, a linear equation justifies useful data manipulations such as rescaling the dose and changing the dose-offset for comparing dose distributions. Considering that some dosimeters exhibit linear response with a large dose-offset or often nonlinear response, we proposed variable transformations of the measured physical quantity, namely, linear- and log-transformation methods. The proposed methods were tested with Kodak X-Omat V radiographic film and BANG (registered) polymer gel dosimeter. We demonstrated that the variable transformation methods could lead to linear equations with zero dose-offset and could reduce the uncertainty of the estimated dose

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

Directory of Open Access Journals (Sweden)

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.

A simple transformation for converting CW-OSL curves to LM-OSL curves

DEFF Research Database (Denmark)

Bulur, E.

2000-01-01

A simple mathematical transformation is introduced to convert from OSL decay curves obtained in the conventional way to those obtained using a linear modulation technique based on a linear increase of the stimulation light intensity during OSL measurement. The validity of the transformation...... was tested by the IR-stimulated luminescence curves from feldspars, recorded using both the conventional and the linear modulation techniques. The transformation was further applied to green-light-stimulated OSL from K and Na feldspars. (C) 2000 Elsevier Science Ltd. All rights reserved....

Repair-dependent cell radiation survival and transformation: an integrated theory

International Nuclear Information System (INIS)

Sutherland, John C

2014-01-01

The repair-dependent model of cell radiation survival is extended to include radiation-induced transformations. The probability of transformation is presumed to scale with the number of potentially lethal damages that are repaired in a surviving cell or the interactions of such damages. The theory predicts that at doses corresponding to high survival, the transformation frequency is the sum of simple polynomial functions of dose; linear, quadratic, etc, essentially as described in widely used linear-quadratic expressions. At high doses, corresponding to low survival, the ratio of transformed to surviving cells asymptotically approaches an upper limit. The low dose fundamental- and high dose plateau domains are separated by a downwardly concave transition region. Published transformation data for mammalian cells show the high-dose plateaus predicted by the repair-dependent model for both ultraviolet and ionizing radiation. For the neoplastic transformation experiments that were analyzed, the data can be fit with only the repair-dependent quadratic function. At low doses, the transformation frequency is strictly quadratic, but becomes sigmodial over a wider range of doses. Inclusion of data from the transition region in a traditional linear-quadratic analysis of neoplastic transformation frequency data can exaggerate the magnitude of, or create the appearance of, a linear component. Quantitative analysis of survival and transformation data shows good agreement for ultraviolet radiation; the shapes of the transformation components can be predicted from survival data. For ionizing radiations, both neutrons and x-rays, survival data overestimate the transforming ability for low to moderate doses. The presumed cause of this difference is that, unlike UV photons, a single x-ray or neutron may generate more than one lethal damage in a cell, so the distribution of such damages in the population is not accurately described by Poisson statistics. However, the complete

Linear algebra a first course with applications

CERN Document Server

Knop, Larry E

2008-01-01

Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, this classroom-tested book gives students enough time to absorb the material by focusing on vector spaces early on and using computational sections as numerical interludes. It offers introductions to Maple™, MATLAB®, and TI-83 Plus for calculating matri

Backlund transformations and three-dimensional lattice equations

NARCIS (Netherlands)

Nijhoff, F.W.; Capel, H.W.; Wiersma, G.L.; Quispel, G.R.W.

1984-01-01

A (nonlocal) linear integral equation is studied, which allows for Bäcklund transformations in the measure. The compatibility of three of these transformations leads to an integrable nonlinear three-dimensional lattice equation. In appropriate continuum limits the two-dimensional Toda-lattice

Lifetime estimation of zirconia ceramics by linear ageing kinetics

International Nuclear Information System (INIS)

Zhang, Fei; Inokoshi, Masanao; Vanmeensel, Kim; Van Meerbeek, Bart; Naert, Ignace; Vleugels, Jef

2015-01-01

Up to now, the ageing kinetics of zirconia ceramics were mainly derived from the sigmoidal evolution of the surface phase transformation as a function of time, as quantified by means of X-ray diffraction (XRD). However, the transformation propagation into the material should be better to monitor the ageing kinetics. In this work, μ-Raman spectroscopy was used to quantitatively measure the transformation profiles in depth as a function of ageing time at 160 °C, 140 °C, 134 °C and 110 °C. A linear relationship between the transformed depth and the ageing time was observed for all investigated yttria stabilized tetragonal zirconia polycrystals (3Y-TZP). Furthermore, the μ-Raman investigation of residual stresses in the subsurface of aged 3Y-TZPs showed that the highest tensile stress was located just ahead of the transformation front, indicating the key responsibility of stress accumulation for transformation front propagating into the material. Moreover, the linear kinetics of the transformation propagation were more accurate to calculate the apparent activation energy of the ageing process and allowed a more straightforward estimation of the lifetime of 3Y-TZP at body temperature, as compared to the conventional ageing kinetic parameters obtained from the surface transformation analysis by XRD

Mathematical methods linear algebra normed spaces distributions integration

CERN Document Server

Korevaar, Jacob

1968-01-01

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector

On Darboux transformation of the supersymmetric sine-Gordon equation

International Nuclear Information System (INIS)

Siddiq, M; Hassan, M; Saleem, U

2006-01-01

Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super Baecklund transformation and is further used to obtain N super soliton solutions

RetroTransformDB: A Dataset of Generic Transforms for Retrosynthetic Analysis

Directory of Open Access Journals (Sweden)

Svetlana Avramova

2018-04-01

Full Text Available Presently, software tools for retrosynthetic analysis are widely used by organic, medicinal, and computational chemists. Rule-based systems extensively use collections of retro-reactions (transforms. While there are many public datasets with reactions in synthetic direction (usually non-generic reactions, there are no publicly-available databases with generic reactions in computer-readable format which can be used for the purposes of retrosynthetic analysis. Here we present RetroTransformDB—a dataset of transforms, compiled and coded in SMIRKS line notation by us. The collection is comprised of more than 100 records, with each one including the reaction name, SMIRKS linear notation, the functional group to be obtained, and the transform type classification. All SMIRKS transforms were tested syntactically, semantically, and from a chemical point of view in different software platforms. The overall dataset design and the retrosynthetic fitness were analyzed and curated by organic chemistry experts. The RetroTransformDB dataset may be used by open-source and commercial software packages, as well as chemoinformatics tools.

Data Compression with Linear Algebra

OpenAIRE

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.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

Science.gov (United States)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

Riccati transformations and principal solutions of discrete linear systems

International Nuclear Information System (INIS)

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

Matrix transformations and sequence spaces

International Nuclear Information System (INIS)

Nanda, S.

1983-06-01

In most cases the most general linear operator from one sequence space into another is actually given by an infinite matrix and therefore the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of general theory of matrix transformations was motivated by the special results in summability theory. This paper is a review article which gives almost all known results on matrix transformations. This also suggests a number of open problems for further study and will be very useful for research workers. (author)

The Box-Cox power transformation on nursing sensitive indicators: does it matter if structural effects are omitted during the estimation of the transformation parameter?

Science.gov (United States)

Hou, Qingjiang; Mahnken, Jonathan D; Gajewski, Byron J; Dunton, Nancy

2011-08-19

Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI® for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects.

The Box-Cox power transformation on nursing sensitive indicators: Does it matter if structural effects are omitted during the estimation of the transformation parameter?

Directory of Open Access Journals (Sweden)

Gajewski Byron J

2011-08-01

Full Text Available Abstract Background Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Methods Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI® for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a estimating the transformation parameter along with factors with potential structural effects, and b estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Results Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. Conclusions The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects.

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

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

Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2012-01-01

The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As ...

Visuo-manual tracking: does intermittent control with aperiodic sampling explain linear power and non-linear remnant without sensorimotor noise?

Science.gov (United States)

Gollee, Henrik; Gawthrop, Peter J; Lakie, Martin; Loram, Ian D

2017-11-01

A human controlling an external system is described most easily and conventionally as linearly and continuously translating sensory input to motor output, with the inevitable output remnant, non-linearly related to the input, attributed to sensorimotor noise. Recent experiments show sustained manual tracking involves repeated refractoriness (insensitivity to sensory information for a certain duration), with the temporary 200-500 ms periods of irresponsiveness to sensory input making the control process intrinsically non-linear. This evidence calls for re-examination of the extent to which random sensorimotor noise is required to explain the non-linear remnant. This investigation of manual tracking shows how the full motor output (linear component and remnant) can be explained mechanistically by aperiodic sampling triggered by prediction error thresholds. Whereas broadband physiological noise is general to all processes, aperiodic sampling is associated with sensorimotor decision making within specific frontal, striatal and parietal networks; we conclude that manual tracking utilises such slow serial decision making pathways up to several times per second. The human operator is described adequately by linear translation of sensory input to motor output. Motor output also always includes a non-linear remnant resulting from random sensorimotor noise from multiple sources, and non-linear input transformations, for example thresholds or refractory periods. Recent evidence showed that manual tracking incurs substantial, serial, refractoriness (insensitivity to sensory information of 350 and 550 ms for 1st and 2nd order systems respectively). Our two questions are: (i) What are the comparative merits of explaining the non-linear remnant using noise or non-linear transformations? (ii) Can non-linear transformations represent serial motor decision making within the sensorimotor feedback loop intrinsic to tracking? Twelve participants (instructed to act in three prescribed

A hybrid Scatter/Transform cloaking model

Directory of Open Access Journals (Sweden)

Gad Licht

2015-01-01

Full Text Available A new Scatter/Transform cloak is developed that combines the light bending of refraction characteristic of a Transform cloak with the scatter cancellation characteristic of a Scatter cloak. The hybrid cloak incorporates both Transform’s variable index of refraction with modified linear intrusions to maximize the Scatter cloak effect. Scatter/Transform improved the scattering cross-section of cloaking in a 2-dimensional space to 51.7% compared to only 39.6% or 45.1% respectively with either Scatter or Transform alone. Metamaterials developed with characteristics based on the new ST hybrid cloak will exhibit superior cloaking capabilities.

Topological defects in the second-class phase transformations

International Nuclear Information System (INIS)

Dobrowolski, T.

2002-06-01

The dynamics of systems during second-class phase transformations are presented.in a frame of quantum fields theory. It is shown that solutions of non-linear field equations generate some topological defects what result in symmetry breaking and field phase transformations

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

Science.gov (United States)

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.

The study of interferometer spectrometer based on DSP and linear CCD

Science.gov (United States)

Kang, Hua; Peng, Yuexiang; Xu, Xinchen; Xing, Xiaoqiao

2010-11-01

In this paper, general theory of Fourier-transform spectrometer and polarization interferometer is presented. A new design is proposed for Fourier-transform spectrometer based on polarization interferometer with Wollaston prisms and linear CCD. Firstly, measured light is changed into linear polarization light by polarization plate. And then the light can be split into ordinary and extraordinary lights by going through one Wollaston prism. At last, after going through another Wollaston prism and analyzer, interfering fringes can be formed on linear CCD behind the analyzer. The linear CCD is driven by CPLD to output amplitude of interfering fringes and synchronous signals of frames and pixels respectively. DSP is used to collect interference pattern signals from CCD and the digital data of interfering fringes are processed by using 2048-point-FFT. Finally, optical spectrum of measured light can be display on LCD connected to DSP with RS232. The spectrometer will possess the features of firmness, portability and the ability of real-time analyzing. The work will provide a convenient and significant foundation for application of more high accuracy of Fourier-transform spectrometer.

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

Science.gov (United States)

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.

transformation of independent variables in polynomial regression ...

African Journals Online (AJOL)

Ada

preferable when possible to work with a simple functional form in transformed variables rather than with a more complicated form in the original variables. In this paper, it is shown that linear transformations applied to independent variables in polynomial regression models affect the t ratio and hence the statistical ...

Reduced conservatism in stability robustness bounds by state transformation

Science.gov (United States)

Yedavalli, R. K.; Liang, Z.

1986-01-01

This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.

A linear process-algebraic format for probabilistic systems with data

NARCIS (Netherlands)

Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Timmer, Mark; Gomes, L.; Khomenko, V.; Fernandes, J.M.

This paper presents a novel linear process algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar

A general algorithm for computing distance transforms in linear time

NARCIS (Netherlands)

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

UV light induced DNA damages and the radiation protection effects of Lingzi mushroom extract

International Nuclear Information System (INIS)

Vo Thi Thuong Lan; Dinh Ba Tuan; Ta Bich Thuan; Tran Bang Diep; Tran Minh Quynh

2016-01-01

UV light has strongly influenced on the growth of E. coli as well as caused DNA damages. Configurations of both genomic DNA and pUC 19 plasmids extracted from E. coli were significantly changed by the exposure to UV light of 254 nm and DLT, an extract of Ganoderma lucidum Lingzi mushroom. The results also revealed the radio-protective effects of DLT to UV radiation. By adding 2% DLT to its culturing suspension, the growth of E. coli was significantly decreased, whereas a low DLT amount of about 0.5% slightly improved its growth, indicated that the DLT extract can be used as a promising protective substance against UV radiation. At the molecular level, the radio-protective effects of DLT were observed for both UV treated DNA and protein. Thus, DLT can protect DNA in vivo, but not in vitro. This effect was also observed for Taq polymerase, suggested that the radioprotection effect of DLT may due to it accelerated the degradation of radicals or species that produced in the suspensions during UV exposure. (author)

BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

Science.gov (United States)

Krogh, F. T.

1994-01-01

The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

Macroscopic and non-linear quantum games

International Nuclear Information System (INIS)

Aerts, D.; D'Hooghe, A.; Posiewnik, A.; Pykacz, J.

2005-01-01

Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)

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

International Nuclear Information System (INIS)

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.

The fractional Fourier transform and applications

Science.gov (United States)

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.

A Global Optimization Algorithm for Sum of Linear Ratios Problem

OpenAIRE

Yuelin Gao; Siqiao Jin

2013-01-01

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the c...

Linearization: Geometric, Complex, and Conditional

Directory of Open Access Journals (Sweden)

Asghar Qadir

2012-01-01

Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.

Partial Linearization of Mechanical Systems with Application to Observer Design

NARCIS (Netherlands)

Sarras, Ioannis; Venkatraman, Aneesh; Ortega, Romeo; Schaft, Arjan van der

2008-01-01

We consider general mechanical systems and establish a necessary and sufficient condition for the existence of a suitable change in the generalized momentum coordinates such that the new dynamics become linear in the transformed momenta. The class of systems which can be (partially) linearized by

The morphing of geographical features by Fourier transformation.

Science.gov (United States)

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

Science.gov (United States)

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Linear Vlasov plasma oscillations in the Fourier transformed velocity space

Czech Academy of Sciences Publication Activity Database

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

Advanced statistics: linear regression, part II: multiple linear regression.

Science.gov (United States)

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Compressor Surge Control Design Using Linear Matrix Inequality Approach

OpenAIRE

Uddin, Nur; Gravdahl, Jan Tommy

2017-01-01

A novel design for active compressor surge control system (ASCS) using linear matrix inequality (LMI) approach is presented and including a case study on piston-actuated active compressor surge control system (PAASCS). The non-linear system dynamics of the PAASCS is transformed into linear parameter varying (LPV) system dynamics. The system parameters are varying as a function of the compressor performance curve slope. A compressor surge stabilization problem is then formulated as a LMI probl...

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

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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.

On projective invariants based on non-linear connections in a Finsler space I

International Nuclear Information System (INIS)

Rastogi, S.C.

1986-05-01

The projective transformations based on linear connections in a Finsler space have been studied by Berwald, Misra, Szabo, Matsumoto, Fukai and Yamada, Rastogi and others. In almost all these papers the emphasis has been on studying Finsler spaces of scalar curvature, Finsler spaces of constant curvature and Finsler spaces of zero curvature with the help of projective curvature tensors of Weyl and Douglas. In 1981, the author studied projective transformation in a Finsler space based on non-linear connections and obtained certain projective invariants. The aim of the present paper is to study Finsler spaces of scalar curvature, constant curvature and zero curvature with the help of non-linear connections and projective invariants obtained from non-linear connections. (author)

From spiking neuron models to linear-nonlinear models.

Science.gov (United States)

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

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

International Nuclear Information System (INIS)

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

Anaerobic degradation of linear alkylbenzene sulfonate

DEFF Research Database (Denmark)

Mogensen, Anders Skibsted; Haagensen, Frank; Ahring, Birgitte Kiær

2003-01-01

Linear alkylbenzene sulfonate (LAS) found in wastewater is removed in the wastewater treatment facilities by sorption and aerobic biodegradation. The anaerobic digestion of sewage sludge has not been shown to contribute to the removal. The concentration of LAS based on dry matter typically...... increases during anaerobic stabilization due to transformation of easily degradable organic matter. Hence, LAS is regarded as resistant to biodegradation under anaerobic conditions. We present data from a lab-scale semi-continuously stirred tank reactor (CSTR) spiked with linear dodecylbenzene sulfonate (C...

Linear waves and instabilities

International Nuclear Information System (INIS)

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.)

Comment on 'Generalization of the Darboux transformation and generalized harmonic oscillators'

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2005-01-01

The authors Song and Klauder (2003 J. Phys. A: Math. Gen. 36 8673-84) present a generalized Darboux transformation, applicable to Hamiltonians with linear terms in the momentum. We show here that this generalized Darboux transformation is just the standard Darboux transformation in different coordinates. (comment)

Nonlinear Radon Transform Using Zernike Moment for Shape Analysis

Directory of Open Access Journals (Sweden)

Ziping Ma

2013-01-01

Full Text Available We extend the linear Radon transform to a nonlinear space and propose a method by applying the nonlinear Radon transform to Zernike moments to extract shape descriptors. These descriptors are obtained by computing Zernike moment on the radial and angular coordinates of the pattern image's nonlinear Radon matrix. Theoretical and experimental results validate the effectiveness and the robustness of the method. The experimental results show the performance of the proposed method in the case of nonlinear space equals or outperforms that in the case of linear Radon.

Gauge transformations in relativistic two-particle constraint theory

International Nuclear Information System (INIS)

Jallouli, H.; Sazdjian, H.

1996-01-01

The forms of the local potentials in linear covariant gauges are investigated and relationships are found between them. The gauge transformation properties of the Green's function and of the Bethe-Salpeter wave function are reviewed. The infinitesimal gauge transformation laws of the constraint theory wave functions and potentials are determined. The case of the local approximation of potentials is considered. The general properties of the gauge transformations in the local approximation are studied. (K.A.)

The holographic dual of the Penrose transform

Science.gov (United States)

Neiman, Yasha

2018-01-01

We consider the holographic duality between type-A higher-spin gravity in AdS4 and the free U( N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these "square root" spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a "square root" of CPT.

Linear electrical circuits. Definitions - General theorems; Circuits electriques lineaires. Definitions - Theoremes generaux

Energy Technology Data Exchange (ETDEWEB)

Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)

2005-04-01

The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)

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

International Nuclear Information System (INIS)

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

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

Directory of Open Access Journals (Sweden)

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.

A linear process-algebraic format for probabilistic systems with data (extended version)

NARCIS (Netherlands)

Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Timmer, Mark

2010-01-01

This paper presents a novel linear process-algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar

An iterative method for controlling reactive power flow in boundary transformers

Energy Technology Data Exchange (ETDEWEB)

Trigo, Angel L.; Martinez, Jose L.; Riquelme, Jesus; Romero, Esther [Department of Electrical Engineering, University of Seville (Spain)

2011-02-15

This paper presents an operational tool designed to help the system operator to control the reactive power flow in transmission-subtransmission boundary transformers. The main objective is to determine the minimum number of control actions necessary to ensure that reactive power flows in transmission/subtransmission transformers remain within limits. The proposed iterative procedure combines the use of a linear programming problem and a load flow tool. The linear programming assumes a linear behaviour between dependent and control variables around an operating point, modelled with sensitivities. Experimental results regarding IEEE systems are provided comparing the performance of the proposed approach with that of a conventional optimal power flow. (author)

Positive Quasi Linear Operator Formulation

International Nuclear Information System (INIS)

Berry, L.A.; Jaeger, E.F.

2005-01-01

Expressions for the RF quasi-linear operator are biquadratic sums over the Fourier modes (or FLR equivalent) that describe the RF electric field with a kernel that is a function of the two wave vectors, k-vector L and k-vector R , in the sum. As a result of either an implicit or explicit average over field lines or flux surfaces, this kernel only depends on one parallel wave vector, conventionally k R -vector. When k-vector is an independent component of the representation for E, the sums are demonstrably positive. However, except for closed field line systems, k-vector is dependent on the local direction of the equilibrium magnetic field, and, empirically, the absorbed energy and quasi-linear diffusion coefficients are observed to have negative features. We have formally introduced an independent k-vector sum by Fourier transforming the RF electric field (assuming straight field lines) using a field-line-length coordinate. The resulting expression is positive. We have modeled this approach by calculating the quasi linear operator for 'modes' with fixed k-vector. We form these modes by discretizing k-vector and then assigning all of the Fourier components with k-vectorthat fall within a given k-vector bin to that k-vector mode. Results will be shown as a function of the number of bins. Future work will involve implementing the expressions derived from the Fourier transform and evaluating the dependence on field line length

Use of distributed ledger technology by central banks: A review

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César del Río

2017-12-01

Full Text Available This paper reviews what stage the central banks of the world’s leading economies are at in their study and adoption of distributed ledger technology (DLT to reengineer their various systems and functions. A brief description of DLT will be given, followed by an analysis of central banks’ publications and pronouncements to determine what each central bank is doing on their journey to DLT adoption. It was found that of the central banks for which information was available, all of them have expressed interest in DLT and have evaluated it to some extent. Nevertheless, no central bank has an operational DLT-based system at this point. This is because some issues remain regarding the speed, cost of processing, security, transparency and privacy, legal settlement finality, scalability and network effects of the technology. As DLT matures, the expectation is that these issues will begin to be resolved.

Double-lumen tubes and auto-PEEP during one-lung ventilation.

Science.gov (United States)

Spaeth, J; Ott, M; Karzai, W; Grimm, A; Wirth, S; Schumann, S; Loop, T

2016-01-01

Double-lumen tubes (DLT) are routinely used to enable one-lung-ventilation (OLV) during thoracic anaesthesia. The flow-dependent resistance of the DLT's bronchial limb may be high as a result of its narrow inner diameter and length, and thus potentially contribute to an unintended increase in positive end-expiratory pressure (auto-PEEP). We therefore studied the impact of adult sized DLTs on the dynamic auto-PEEP during OLV. In this prospective clinical study, dynamic auto-PEEP was determined in 72 patients undergoing thoracic surgery, with right- and left-sided DLTs of various sizes. During OLV, air trapping was provoked by increasing inspiration to expiration ratio from 1:2 to 2:1 (five steps). Based on measured flow rate, airway pressure (Paw) and bronchial pressure (Pbronch), the pressure gradient across the DLT (ΔPDLT) and the total auto-PEEP in the respiratory system (i.e. the lungs, the DLT and the ventilator circuit) were determined. Subsequently the DLT's share in total auto-PEEP was calculated. ΔPDLT was 2.3 (0.7) cm H2O over the entire breathing cycle. At the shortest expiratory time the mean total auto-PEEP was 2.9 (1.5) cm H2O (range 0-5.9 cm H2O). The DLT caused 27 to 31% of the total auto-PEEP. Size and side of the DLT's bronchial limb did not impact auto-PEEP significantly. Although the DLT contributes to the overall auto-PEEP, its contribution is small and independent of size and side of the DLT's bronchial limb. The choice of DLT does not influence the risk of auto-PEEP during OLV to a clinically relevant extent. DRKS00005648. © The Author 2015. Published by Oxford University Press on behalf of the British Journal of Anaesthesia. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Analysis of Linear Hybrid Systems in CLP

DEFF Research Database (Denmark)

Banda, Gourinath; Gallagher, John Patrick

2009-01-01

In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive...

A Global Optimization Algorithm for Sum of Linear Ratios Problem

Directory of Open Access Journals (Sweden)

Yuelin Gao

2013-01-01

Full Text Available We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space

International Nuclear Information System (INIS)

Parzen, G.

1997-01-01

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. A set of equations is given from which the 12 elements of R can be computed form the one period transfer matrix. This set of equations also allows the linear parameters, the β i , α i , i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix

Erythrocyte osmotic fragility and lipid peroxidation following chronic co-exposure of rats to chlorpyrifos and deltamethrin, and the beneficial effect of alpha-lipoic acid

Directory of Open Access Journals (Sweden)

Chidiebere Uchendu

2014-01-01

Full Text Available The present study aimed to evaluate the effect of chronic co-exposure to chlorpyrifos (CPF and deltamethrin (DLT on erythrocyte osmotic fragility, lipid peroxidation and the ameliorative effect of alpha-lipoic acid (ALA on erythrocyte fragility. Thirty-six male Wistar rats divided into six groups of six rats each were used for the study. Groups I (S/oil and II (ALA were given soya oil (2 ml/kg and ALA (60 mg/kg, respectively. Rats in group III (DLT and IV (CPF were exposed to DLT (6.25 mg/kg and CPF (4.75 mg/kg (1/20th of the previously determined LD50 of 125 mg/kg and 95 mg/kg, respectively, over a period of 48 h. Rats in group V (CPF + DLT were co-exposed to CPF (4.75 mg/kg and DLT (6.25 mg/kg, while those in group VI (ALA + CPF + DLT were pretreated with ALA (60 mg/kg and then co-exposed to CPF and DLT, 45 min later. The treatments were administered by gavage once daily for a period of 16 weeks. Blood collected at the end of the experimental period were analyzed for erythrocyte osmotic fragility and malondialdehyde (MDA concentration. The study showed that chronic co-exposure to CPF and DLT resulted in an increase in erythrocyte fragility and MDA concentration which were ameliorated by supplementation with alpha-lipoic acid. The study concluded that repeated co-exposure to CPF and DLT elevated erythrocyte fragility probably due to increased lipid peroxidation, and pretreatment with alpha-lipoic acid ameliorated these alterations.

Supersymmetry breaking in the linear representation of the dilaton

International Nuclear Information System (INIS)

Gaida, I.

1995-01-01

String effective theories with N=1 supersymmetry in 4 dimensions are subject of the discussion. These theories are effective in the sense, that they are low-energy limits of a given higher dimensional string theory after dimensional reduction and integrating out all heavy modes. At tree level the gauge coupling constant can be expressed by the vacuum expectation value of the dilaton superfield S:g 2 =2 -1 . Throughout this text S+ anti S will be denoted as the chiral representation of the dilaton. It has been shown that there exists a supersymmetric legendre transformation called supersymmetric duality, which transforms S+ anti S into a linear superfield L, where L will be called the linear representation of the dilaton. (orig.)

Conformal array design on arbitrary polygon surface with transformation optics

Energy Technology Data Exchange (ETDEWEB)

Deng, Li, E-mail: dengl@bupt.edu.cn; Hong, Weijun, E-mail: hongwj@bupt.edu.cn; Zhu, Jianfeng; Peng, Biao; Li, Shufang [Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, 100876 Beijing (China); Wu, Yongle, E-mail: wuyongle138@gmail.com [Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, 100876 Beijing (China)

2016-06-15

A transformation-optics based method to design a conformal antenna array on an arbitrary polygon surface is proposed and demonstrated in this paper. This conformal antenna array can be adjusted to behave equivalently as a uniformly spaced linear array by applying an appropriate transformation medium. An typical example of general arbitrary polygon conformal arrays, not limited to circular array, is presented, verifying the proposed approach. In summary, the novel arbitrary polygon surface conformal array can be utilized in array synthesis and beam-forming, maintaining all benefits of linear array.

Conformal array design on arbitrary polygon surface with transformation optics

International Nuclear Information System (INIS)

Deng, Li; Hong, Weijun; Zhu, Jianfeng; Peng, Biao; Li, Shufang; Wu, Yongle

2016-01-01

A transformation-optics based method to design a conformal antenna array on an arbitrary polygon surface is proposed and demonstrated in this paper. This conformal antenna array can be adjusted to behave equivalently as a uniformly spaced linear array by applying an appropriate transformation medium. An typical example of general arbitrary polygon conformal arrays, not limited to circular array, is presented, verifying the proposed approach. In summary, the novel arbitrary polygon surface conformal array can be utilized in array synthesis and beam-forming, maintaining all benefits of linear array.

Relation of deformed nonlinear algebras with linear ones

International Nuclear Information System (INIS)

Nowicki, A; Tkachuk, V M

2014-01-01

The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)

DEVELOPMENT OF A PHYSIOLOGICALLY BASED PHARMACOKINETIC MODEL FOR DELTAMETHRIN IN THE ADULT MALE SPRAGUE-DAWLEY RAT

Science.gov (United States)

Deltamethrin (DLT) is a Type II pyrethroid insecticide widely used in agriculture and public health. DLT is a potent neurotoxin that is primarily cleared from the body by metabolism. To better understand the dosimetry of DLT in the central nervous system, a physiologically based ...

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

DEFF Research Database (Denmark)

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)....

A Coordinate Transformation for Unsteady Boundary Layer Equations

Directory of Open Access Journals (Sweden)

Paul G. A. CIZMAS

2011-12-01

Full Text Available This paper presents a new coordinate transformation for unsteady, incompressible boundary layer equations that applies to both laminar and turbulent flows. A generalization of this coordinate transformation is also proposed. The unsteady boundary layer equations are subsequently derived. In addition, the boundary layer equations are derived using a time linearization approach and assuming harmonically varying small disturbances.

Automated, non-linear registration between 3-dimensional brain map and medical head image

International Nuclear Information System (INIS)

Mizuta, Shinobu; Urayama, Shin-ichi; Zoroofi, R.A.; Uyama, Chikao

1998-01-01

In this paper, we propose an automated, non-linear registration method between 3-dimensional medical head image and brain map in order to efficiently extract the regions of interest. In our method, input 3-dimensional image is registered into a reference image extracted from a brain map. The problems to be solved are automated, non-linear image matching procedure, and cost function which represents the similarity between two images. Non-linear matching is carried out by dividing the input image into connected partial regions, transforming the partial regions preserving connectivity among the adjacent images, evaluating the image similarity between the transformed regions of the input image and the correspondent regions of the reference image, and iteratively searching the optimal transformation of the partial regions. In order to measure the voxelwise similarity of multi-modal images, a cost function is introduced, which is based on the mutual information. Some experiments using MR images presented the effectiveness of the proposed method. (author)

Implementation of 2D Discrete Wavelet Transform by Number Theoretic Transform and 2D Overlap-Save Method

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Lina Yang

2014-01-01

Full Text Available To reduce the computation complexity of wavelet transform, this paper presents a novel approach to be implemented. It consists of two key techniques: (1 fast number theoretic transform(FNTT In the FNTT, linear convolution is replaced by the circular one. It can speed up the computation of 2D discrete wavelet transform. (2 In two-dimensional overlap-save method directly calculating the FNTT to the whole input sequence may meet two difficulties; namely, a big modulo obstructs the effective implementation of the FNTT and a long input sequence slows the computation of the FNTT down. To fight with such deficiencies, a new technique which is referred to as 2D overlap-save method is developed. Experiments have been conducted. The fast number theoretic transform and 2D overlap-method have been used to implement the dyadic wavelet transform and applied to contour extraction in pattern recognition.

Linear parameter varying representations for nonlinear control design

Science.gov (United States)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that

Kernel maximum autocorrelation factor and minimum noise fraction transformations

DEFF Research Database (Denmark)

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...

Road Detection by Using a Generalized Hough Transform

Directory of Open Access Journals (Sweden)

Weifeng Liu

2017-06-01

Full Text Available Road detection plays key roles for remote sensing image analytics. Hough transform (HT is one very typical method for road detection, especially for straight line road detection. Although many variants of Hough transform have been reported, it is still a great challenge to develop a low computational complexity and time-saving Hough transform algorithm. In this paper, we propose a generalized Hough transform (i.e., Radon transform implementation for road detection in remote sensing images. Specifically, we present a dictionary learning method to approximate the Radon transform. The proposed approximation method treats a Radon transform as a linear transform, which then facilitates parallel implementation of the Radon transform for multiple images. To evaluate the proposed algorithm, we conduct extensive experiments on the popular RSSCN7 database for straight road detection. The experimental results demonstrate that our method is superior to the traditional algorithms in terms of accuracy and computing complexity.

A transformation technique to treat strong vibrating absorbers

International Nuclear Information System (INIS)

Sahni, D.C.; Garis, N.S.; Pazsit, I.

1998-06-01

Calculation of the neutron noise, induced by small amplitude vibrations of a strong absorber, is a difficult task because the traditional linearization technique cannot be applied. Two methods, based on two different representations of the absorber, were developed earlier to solve the problem. In both methods the rod displacements are described by a Taylor expansion, such that the boundary condition needs only to be considered at the surface of a static rod. Only one of the methods is applicable in two dimensions. In this paper an alternative method is developed and used for the solution of the problem. The essence of the method is a variable transformation by which the moving boundary is transformed into a static one without Taylor expansion. The corresponding equations are solved in a linear manner and the solution is transformed back to the original parameter space. The method is equally applicable in one and two dimensions. The solutions are in complete agreement with those of the previous methods

Reduction of Linear Functional Systems using Fuhrmann's Equivalence

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Mohamed S. Boudellioua

2016-11-01

Full Text Available Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by Serre. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. In this paper, Fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. This equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems.

Computer-Aided Numerical Inversion of Laplace Transform

Directory of Open Access Journals (Sweden)

Umesh Kumar

2000-01-01

Full Text Available This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

Discrete Fourier Transform in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Answers to selected problems in multivariable calculus with linear algebra and series

CERN Document Server

Trench, William F

1972-01-01

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples.The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eig

A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times.

Science.gov (United States)

Molenaar, Dylan; Bolsinova, Maria

2017-05-01

In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set. © 2017 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Differential calculus in normed linear spaces

CERN Document Server

Mukherjea, Kalyan

2007-01-01

This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab ini...

Modeling digital switching circuits with linear algebra

CERN Document Server

Thornton, Mitchell A

2014-01-01

Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transf

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

Science.gov (United States)

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.

A look inside the theory of the linear approximation

OpenAIRE

Bel, Ll.

2006-01-01

We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This allows to introduce geometrical objects that are not invariant under General gauge transformations but they are under Special ones. We develop then a formalism that strengthens the analogy of the formalisms of the electromagnetic and the gravitational theo...

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

DEFF Research Database (Denmark)

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....

Non-linear realizations of supersymmetry with off-shell central charges

International Nuclear Information System (INIS)

Santos Filho, P.B.; Oliveira Rivelles, V. de.

1985-01-01

A new class of non-linear realizations of the extended supersymmetry algebra with central charges is presented. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as is the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. It is worked in two dimensions and its extension to higher dimensions is discussed. (Author) [pt

An optimized formulation for Deprit-type Lie transformations of Taylor maps for symplectic systems

International Nuclear Information System (INIS)

Shi, Jicong

1993-01-01

An optimized iterative formulation is presented for directly transforming a Taylor map of a symplectic system into a Deprit-type Lie transformation, which is a composition of a linear transfer matrix and a single Lie transformation, to an arbitrary order

Modern linear control design a time-domain approach

CERN Document Server

Caravani, Paolo

2013-01-01

This book offers a compact introduction to modern linear control design.  The simplified overview presented of linear time-domain methodology paves the road for the study of more advanced non-linear techniques. Only rudimentary knowledge of linear systems theory is assumed - no use of Laplace transforms or frequency design tools is required. Emphasis is placed on assumptions and logical implications, rather than abstract completeness; on interpretation and physical meaning, rather than theoretical formalism; on results and solutions, rather than derivation or solvability.  The topics covered include transient performance and stabilization via state or output feedback; disturbance attenuation and robust control; regional eigenvalue assignment and constraints on input or output variables; asymptotic regulation and disturbance rejection. Lyapunov theory and Linear Matrix Inequalities (LMI) are discussed as key design methods. All methods are demonstrated with MATLAB to promote practical use and comprehension. ...

Pre-Trained Neural Networks used for Non-Linear State Estimation

DEFF Research Database (Denmark)

Bayramoglu, Enis; Andersen, Nils Axel; Ravn, Ole

2011-01-01

of the paramters in the distribution. This transformation is approximated by a neural network using offline training, which is based on monte carlo sampling. In the paper, there will also be presented a method to construct a flexible distributions well suited for covering the effect of the non-linearities......The paper focuses on nonlinear state estimation assuming non-Gaussian distributions of the states and the disturbances. The posterior distribution and the aposteriori distribution is described by a chosen family of paramtric distributions. The state transformation then results in a transformation...

Wigner's little group as a gauge generator in linearized gravity theories

International Nuclear Information System (INIS)

Scaria, Tomy; Chakraborty, Biswajit

2002-01-01

We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

Picosecond, single pulse electron linear accelerator

International Nuclear Information System (INIS)

Kikuchi, Riichi; Kawanishi, Masaharu

1979-01-01

The picosecond, single pulse electron linear accelerators, are described, which were installed in the Nuclear Engineering Laboratory of the University of Tokyo and in the Nuclear Radiation Laboratory of the Osaka University. The purpose of the picosecond, single pulse electron linear accelerators is to investigate the very short time reaction of the substances, into which gamma ray or electron beam enters. When the electrons in substances receive radiation energy, the electrons get high kinetic energy, and the energy and the electric charge shift, at last to the quasi-stable state. This transient state can be experimented with these special accelerators very accurately, during picoseconds, raising the accuracy of the time of incidence of radiation and also raising the accuracy of observation time. The outline of these picosecond, single pulse electron linear accelerators of the University of Tokyo and the Osaka University, including the history, the systems and components and the output beam characteristics, are explained. For example, the maximum energy 30 -- 35 MeV, the peak current 1 -- 8 n C, the pulse width 18 -- 40 ps, the pulse repetition rate 200 -- 720 pps, the energy spectrum 1 -- 1.8% and the output beam diameter 2 -- 5 mm are shown as the output beam characteristics of the accelerators in both universities. The investigations utilizing the picosecond single pulse electron linear accelerators, such as the investigation of short life excitation state by pulsed radiation, the dosimetry study of pulsed radiation, and the investigation of the transforming mechanism and the development of the transforming technology from picosecond, single pulse electron beam to X ray, vacuum ultraviolet ray and visual ray, are described. (Nakai, Y.)

Cyclic transformation of orbital angular momentum modes

International Nuclear Information System (INIS)

Schlederer, Florian; Krenn, Mario; Fickler, Robert; Malik, Mehul; Zeilinger, Anton

2016-01-01

The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D-dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D-dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states. (paper)

Methods of Weyl representation of the phase space and canonical transformations

International Nuclear Information System (INIS)

Budanov, V.G.

1986-01-01

The author studies nonlinear canonical transformations realized in the space of Weyl symbols of quantum operators. The kernels of the transformations, the symbol of the intertwining operator of the group of inhomogeneous point transformations, an the group characters are constructed. The group of PL transformations, which is the free produce of the group of point, p, and linear, L, transformations is considered. The simplest PL complexes relating problems with different potentials, in particular, containing a general Darboux transformation of the factorization method, are constructed. The kernel of an arbitrary element of the group PL is found

A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

Directory of Open Access Journals (Sweden)

Mio Horai

2016-01-01

Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

Resource-efficient generation of linear cluster states by linear optics with postselection

International Nuclear Information System (INIS)

Uskov, D B; Alsing, P M; Fanto, M L; Szep, A; Smith, A M; Kaplan, L; Kim, R

2015-01-01

We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to (1/2) n−1 ; an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4) m−1 . (paper)

Design of Linear - and Minimum-phase FIR-equalizers

DEFF Research Database (Denmark)

Bysted, Tommy Kristensen; Jensen, K.J.; Gaunholt, Hans

1996-01-01

an error function which is quadratic in the filtercoefficients. The advantage of the quadratic function is the ability to find the optimal coefficients solving a system of linear equations without iterations.The transformation to a minimum-phase equalizer is carried out by homomorphic deconvolution...

Duality in linearized gravity

International Nuclear Information System (INIS)

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

Multimodal Image Alignment via Linear Mapping between Feature Modalities.

Science.gov (United States)

Jiang, Yanyun; Zheng, Yuanjie; Hou, Sujuan; Chang, Yuchou; Gee, James

2017-01-01

We propose a novel landmark matching based method for aligning multimodal images, which is accomplished uniquely by resolving a linear mapping between different feature modalities. This linear mapping results in a new measurement on similarity of images captured from different modalities. In addition, our method simultaneously solves this linear mapping and the landmark correspondences by minimizing a convex quadratic function. Our method can estimate complex image relationship between different modalities and nonlinear nonrigid spatial transformations even in the presence of heavy noise, as shown in our experiments carried out by using a variety of image modalities.

Disformal invariance of continuous media with linear equation of state

Energy Technology Data Exchange (ETDEWEB)

Celoria, Marco [Gran Sasso Science Institute (INFN), Viale Francesco Crispi 7, L' Aquila, I-67100 Italy (Italy); Matarrese, Sabino [Dipartimento di Fisica e Astronomia ' G. Galilei' , Università degli Studi di Padova, via Marzolo 8, Padova, I-35131 Italy (Italy); Pilo, Luigi, E-mail: marco.celoria@gssi.infn.it, E-mail: sabino.matarrese@pd.infn.it, E-mail: luigi.pilo@aquila.infn.it [Dipartimento di Fisica, Università di L' Aquila, L' Aquila, I-67010 Italy (Italy)

2017-02-01

We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form p = w ρ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of w =1/3 (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, irrotational dust (mimetic matter) and homogeneous and isotropic solids are discussed.

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

Science.gov (United States)

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.

Discrete transforms

CERN Document Server

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...

The quantum state vector in phase space and Gabor's windowed Fourier transform

International Nuclear Information System (INIS)

Bracken, A J; Watson, P

2010-01-01

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

Soliton solutions of the (2 + 1)-dimensional Harry Dym equation via Darboux transformation

International Nuclear Information System (INIS)

Halim, A.A.

2008-01-01

This work introduces solitons solutions for the (2 + 1)-dimensional Harry Dym equation using Darboux transformation. The link between the (2 + 1)-dimensional Harry Dym equation and the linear system associated with the modified Kadomtzev-Patvishvili equation is used. Namely, soliton solutions for the linear system associated with the later equation are produced using Darboux transformation. These solutions are inserted in the mentioned link to produce soliton solutions for the (2 + 1)-dimensional Harry Dym equation

Transformation lines in an Fe-Cr-Ni-Mn-Si polycrystalline shape memory alloy

International Nuclear Information System (INIS)

Tanaka, Kikuaki; Hayashi, Toshimitsu; Fischer, F.D.; Buchmayr, B.

1994-01-01

Transformation lines, the martensite/austenite start and finish conditions in the stress-temperature plane, are determined in an Fe-Cr-Ni-Mn-Si polycrystalline shape memory alloy with two different experimental procedures. The transformation lines are shown to be almost linear with nearly the same slope. The martensitic transformation zone and the reverse transformation zone do not coincide, and the reverse transformation zone is very wide; T Af -T As ∼ 180 K. The strong dependence on the preloading of the transformation lines, especially of the reverse transformation lines, is examined. (orig.)

Frequency analysis of DC tolerant current transformers

International Nuclear Information System (INIS)

Mlejnek, P; Kaspar, P

2013-01-01

This article deals with wide frequency range behaviour of DC tolerant current transformers that are usually used in modern static energy meters. In this application current transformers must comply with European and International Standards in their accuracy and DC tolerance. Therefore, the linear DC tolerant current transformers and double core current transformers are used in this field. More details about the problems of these particular types of transformers can be found in our previous works. Although these transformers are designed mainly for power distribution network frequency (50/60 Hz), it can be interesting to understand their behaviour in wider frequency range. Based on this knowledge the new generations of energy meters with measuring quality of electric energy will be produced. This solution brings better measurement of consumption of nonlinear loads or measurement of non-sinusoidal voltage and current sources such as solar cells or fuel cells. The determination of actual power consumption in such energy meters is done using particular harmonics component of current and voltage. We measured the phase and ratio errors that are the most important parameters of current transformers, to characterize several samples of current transformers of both types

Perfect observables for the hierarchical non-linear O(N)-invariant σ-model

International Nuclear Information System (INIS)

Wieczerkowski, C.; Xylander, Y.

1995-05-01

We compute moving eigenvalues and the eigenvectors of the linear renormalization group transformation for observables along the renormalized trajectory of the hierarchical non-linear O(N)-invariant σ-model by means of perturbation theory in the running coupling constant. Moving eigenvectors are defined as solutions to a Callan-Symanzik type equation. (orig.)

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

Science.gov (United States)

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.

Application of nonlinear transformations to automatic flight control

Science.gov (United States)

Meyer, G.; Su, R.; Hunt, L. R.

1984-01-01

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

The Foldy-Wouthuysen transformation

International Nuclear Information System (INIS)

Costella, J.P.; McKellar, B.H.J.

1995-01-01

The Foldy-Wouthuysen transformation of the Dirac Hamiltonian is generally taught as simply a mathematical trick that allows one to obtain a two-component theory in the low-energy limit. It is not often emphasized that the transformed representation is the only one in which one can take a meaningful classical limit, in terms of particle and antiparticles. It is recognised that there are two representations of the Dirac equation. The Dirac-Pauli representation is unique due to its linearity; it is the representation in which the charged leptons are minimally coupled. The Newton-Wigner representation is unique due to its decoupling of positive- and negative- energy states; it is the representation in which the operators of the theory correspond to their classical counterparts. 12 refs

Time-response shaping using output to input saturation transformation

Science.gov (United States)

Chambon, E.; Burlion, L.; Apkarian, P.

2018-03-01

For linear systems, the control law design is often performed so that the resulting closed loop meets specific frequency-domain requirements. However, in many cases, it may be observed that the obtained controller does not enforce time-domain requirements amongst which the objective of keeping a scalar output variable in a given interval. In this article, a transformation is proposed to convert prescribed bounds on an output variable into time-varying saturations on the synthesised linear scalar control law. This transformation uses some well-chosen time-varying coefficients so that the resulting time-varying saturation bounds do not overlap in the presence of disturbances. Using an anti-windup approach, it is obtained that the origin of the resulting closed loop is globally asymptotically stable and that the constrained output variable satisfies the time-domain constraints in the presence of an unknown finite-energy-bounded disturbance. An application to a linear ball and beam model is presented.

Generalized magnification in visual optics. Part 2: Magnification as affine transformation

Directory of Open Access Journals (Sweden)

W. F. Harris

2010-12-01

Full Text Available In astigmatic systems magnification may be different in different directions.  It may also be accompanied by rotation or reflection.  These changes from object to image are examples of generalized magnification.  They are represented by  2 2×  matrices.  Because they are linear transformations they can be called linear magnifications.  Linear magnifications account for a change in appearance without regard to position.  Mathematical structure suggests a natural further generalization to a magnification that is complete in the sense that it accountsfor change in appearance and position.  It is represented by a  3 3×  matrix with a dummy third row. The transformation is called affine in linear algebra which suggests that these generalized magnifica-tions be called affine magnifications.  The purpose of the paper is to define affine magnification in the context of astigmatic optics.  Several examples are presented and illustrated graphically. (S Afr Optom 2010 69(4 166-172

State space and input-output linear systems

CERN Document Server

Delchamps, David F

1988-01-01

It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu­ ate level linear system theory course i...

Extended Linear Models with Gaussian Priors

DEFF Research Database (Denmark)

Quinonero, Joaquin

2002-01-01

In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....

Insight into the Effects of Reinforcement Shape on Achieving Continuous Martensite Transformation in Phase Transforming Matrix Composites

Science.gov (United States)

Zhang, Xudong; Ren, Junqiang; Wang, Xiaofei; Zong, Hongxiang; Cui, Lishan; Ding, Xiangdong

2017-12-01

A continuous martensite transformation is indispensable for achieving large linear superelasticity and low modulus in phase transforming metal-based composites. However, determining how to accurately condition the residual martensite in a shape memory alloy matrix though the reinforcement shape to achieve continuous martensite transformation has been a challenge. Here, we take the finite element method to perform a comparative study of the effects of nanoinclusion shape on the interaction and martensite phase transformation in this new composite. Two typical samples are compared: one reinforced by metallic nanowires and the other by nanoparticles. We find that the residual martensite within the shape memory alloy matrix after a pretreatment can be tailored by the reinforcement shape. In particular, our results show that the shape memory alloy matrix can retain enough residual martensite phases to achieve continuous martensite transformation in the subsequent loading when the aspect ratio of nanoreinforcement is larger than 20. In contrast, the composites reinforced with spherical or low aspect ratio reinforcement show a typical nonlinear superelasticity as a result of a low stress transfer-induced discontinuous martensite transformation within the shape memory alloy matrix.

Factors affecting the efficient transformation of Colletotrichum species

Science.gov (United States)

Redman, Regina S.; Rodriguez, Rusty J.

1994-01-01

Factors affecting the efficient transformation of Colletotrichum species. Experimental Mycology, 18, 230-246. Twelve isolates representing four species of Colletotrichum were transformed either by enhanced protoplast, restriction enzyme-mediated integration (REMI), or electroporation-mediated protocols. The enhanced protoplast transformation protocol resulted in 100- and 50-fold increases in the transformation efficiencies of Colletotrichum lindemuthianum and C. magna , respectively. REMI transformation involved the use of Hin dIII and vector DNA linearized with HindIII to increase the number of integration events and potential gene disruptions in the fungal genome. Combining the enhanced protoplast and the REMI protocols resulted in a 22-fold increase in the number of hygromycin/nystatin-resistant mutants in C. lindemuthianum . Electroporation-mediated transformation was performed on mycelial fragments and spores of four Colletotrichum species, resulting in efficiencies of up to 1000 transformants/μg DNA. The pHA1.3 vector which confers hygromycin resistance contains telomeric sequences from Fusarium oxysporum , transforms by autonomous replication and genomic integration, and was essential for elevated transformation efficiencies of 100 to 10,000 transformants/μg DNA. Modifications of pHA1.3 occurred during bacterial amplification and post fungal transformation resulting in plasmids capable of significantly elevated transformation efficiencies in C. lindemuthianum.

The resonant wake field transformer (RWT)-collider

International Nuclear Information System (INIS)

Weiland, T.; Holtkamp, N.; Schuett, P.; Wanzenberg, R.

1990-01-01

Future e + e - Linear Colliders with center of mass energies of 2 TeV need average accelerating gradients of 100 MeV/m to be built within a length of 20 km. The gradients required by colliders at this energy range can be economically provided by resonant Wake Field Transformers. At the Wake Field Experiment at DESY (Deutsches Elektronen-Synchrotron) a 20 cm long transformer section was investigated and the most recent results are presented. The second part gives a short overview of the present status of research concerning the proposed next stage of a multibunch driver linac with superconducting cavities and long Wake Field Transformer sections. (author) 9 refs.; 5 figs.; 1 tab

Predictors of transformational leadership of nurse managers.

Science.gov (United States)

Echevarria, Ilia M; Patterson, Barbara J; Krouse, Anne

2017-04-01

The aim of this study was to examine the relationships among education, leadership experience, emotional intelligence and transformational leadership of nurse managers. Nursing leadership research provides limited evidence of predictors of transformational leadership style in nurse managers. A predictive correlational design was used with a sample of nurse managers (n = 148) working in varied health care settings. Data were collected using the Genos Emotional Intelligence Inventory, the Multi-factor Leadership Questionnaire and a demographic questionnaire. Simple linear and multiple regression analyses were used to examine relationships. A statistically significant relationship was found between emotional intelligence and transformational leadership (r = 0.59, P transformational leadership. Nurse managers should be well informed of the predictors of transformational leadership in order to pursue continuing education and development opportunities related to those predictors. The results of this study emphasise the need for emotional intelligence continuing education, leadership development and leader assessment programmes. © 2016 John Wiley & Sons Ltd.

An implementation problem for boson fields and quantum Girsanov transform

Energy Technology Data Exchange (ETDEWEB)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763 (Korea, Republic of); Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp [Graduate School of Information Sciences, Tohoku University, Sendai 980-8579 (Japan)

2016-08-15

We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.

An implementation problem for boson fields and quantum Girsanov transform

International Nuclear Information System (INIS)

Ji, Un Cig; Obata, Nobuaki

2016-01-01

We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.

Bäcklund transformations and Hamiltonian flows

International Nuclear Information System (INIS)

Zullo, Federico

2013-01-01

In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)

Power/response spectrum transformations in equipment qualification

International Nuclear Information System (INIS)

Unruh, J.F.; Kana, D.D.

1985-01-01

Since its introduction a few years ago the use of the power/response spectrum transformation has gained considerable interest and acceptance, and a number of new applications of the transformation have been developed in the equipment qualification area. A brief review of the power/response spectrum transformation is given with a discussion of the input/output relationships for linear systems required for elevated power spectrum generation. Frequency content of earthquakelike signals is discussed with emphasis on the resolution given by the PSD. The problem of excessive ZPA due to inconsistent spectra enveloping and mechanical nonlinearities is also discussed. The PSD/RS transformation is applied to the problems of combining various dynamic load events, developing bounding spectra, and developing damping consistent test spectra. Development of elevated component spectra corrected for base overtest and generation from in-situ measurements is reviewed

Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy

Directory of Open Access Journals (Sweden)

Yongfei Gao

2014-01-01

Full Text Available This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation. Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006.

Transforming to Lorentz gauge on de Sitter

NARCIS (Netherlands)

Miao, S. P.; Tsamis, N.C.; Woodard, R.P.

2009-01-01

We demonstrate that certain gauge fixing functionals cannot be added to the action on backgrounds such as de Sitter, in which a linearization instability is present. We also construct the field-dependent gauge transformation that carries the electromagnetic vector potential from a convenient, non-de

On data transformations and evidence of nonlinearity

NARCIS (Netherlands)

P. de Bruin (Paul); Ph.H.B.F. Franses (Philip Hans)

1998-01-01

textabstractIn this paper we examine the interaction between data transformation and the empirical evidence obtained when testing for (non-)linearity. For this purpose we examine nonlinear features in 64 monthly and 53 quarterly US macroeconomic variables for a range of Box-Cox data

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

Energy Technology Data Exchange (ETDEWEB)

Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)

2014-06-19

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Two-dimensional linear and nonlinear Talbot effect from rogue waves.

Science.gov (United States)

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.

A novel approach to the generation of seamless constructs for plant transformation

DEFF Research Database (Denmark)

Kronbak, Remy; Ingvardsen, Christina R.; Madsen, Claus K.

2014-01-01

Background: When creating plant transformation vectors, full control of nucleotides flanking the insert in the final construct may be desirable. Modern ligase-independent methods for DNA-recombination are based on linearization by classical type II restriction endonucleases (REs) alone or in comb......Background: When creating plant transformation vectors, full control of nucleotides flanking the insert in the final construct may be desirable. Modern ligase-independent methods for DNA-recombination are based on linearization by classical type II restriction endonucleases (REs) alone...... on wheat and barley endosperm cells for transient gfp expression.Conclusions: All nucleotides flanking an insert in a biolistic plant transformation vector can be customized by means of SRL in combination with SLIC. Especially type IIS REs promote an efficient cloning result. Based on our findings, we...

On the problem of linear calibration for a reading system of measuring devices

International Nuclear Information System (INIS)

Shigaev, V.N.

1978-01-01

The problem of gauging the frame of reference of a measuring device has been giVen a general approach which consists in finding an approximated inverse transformation on the basis of a partial diagram of a direct transformation which is defined on a given set, D, within the limits of the device measuring range. The following linear models of frame of reference are discussed: a general oblique system; a rectangular system with axes having different scales; a rectangular system with similar scale axes. Linear distortion for two rectangular models has been assessed. It is pointed out that the best approximation to the reduction operation should be found over the D set

On a representation of linear differential equations

Czech Academy of Sciences Publication Activity Database

Neuman, František

2010-01-01

Roč. 52, 1-2 (2010), s. 355-360 ISSN 0895-7177 Grant - others:GA ČR(CZ) GA201/08/0469 Institutional research plan: CEZ:AV0Z10190503 Keywords : Brandt and Ehresmann groupoinds * transformations * canonical forms * linear differential equations Subject RIV: BA - General Mathematics Impact factor: 1.066, year: 2010 http://www.sciencedirect.com/science/article/pii/S0895717710001184

Generalized Cole–Hopf transformations for generalized Burgers ...

Indian Academy of Sciences (India)

2015-10-15

Oct 15, 2015 ... Cole–Hopf transformations; Burgers equation; invariance analysis. ... was to generate nonlinear parabolic equations from a linear parabolic equation via a ..... BMV acknowledges the financial support to attend the NMI Workshop ... [16] P J Olver, Applications of Lie Groups to differential equations, Graduate ...

Methodology and Applications in Non-linear Model-based Geostatistics

DEFF Research Database (Denmark)

Christensen, Ole Fredslund

that are approximately Gaussian. Parameter estimation and prediction for the transformed Gaussian model is studied. In some cases a transformation cannot possibly render the data Gaussian. A methodology for analysing such data was introduced by Diggle, Tawn and Moyeed (1998): The generalised linear spatial model...... priors for Bayesian inference is discussed. Procedures for parameter estimation and prediction are studied. Theoretical properties of Markov chain Monte Carlo algorithms are investigated, and different algorithms are compared. In addition, the thesis contains a manual for an R-package, geoRglmm, which...

Perturbative Gaussianizing transforms for cosmological fields

Science.gov (United States)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

CPS Transformation of Flow Information, Part II

DEFF Research Database (Denmark)

Damian, D.; Danvy, Olivier

2003-01-01

consider the administrative reductions of a Plotkin-style transformation into Continuation-Passing Style (CPS), and how they affect the result of a constraint-based control-flow analysis and, in particular, the least element in the space of solutions. We show that administrative reductions preserve...... the least solution. Preservation of least solutions solves a problem that was left open in Palsberg and Wand's article ‘CPS Transformation of Flow Information.’ Together, Palsberg and Wand's article and the present article show how to map in linear time the least solution of the flow constraints...... of a program into the least solution of the flow constraints of the CPS counterpart of this program, after administrative reductions. Furthermore, we show how to CPS transform control-flow information in one pass....

New binary linear codes which are dual transforms of good codes

NARCIS (Netherlands)

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

Incremental Closed-loop Identification of Linear Parameter Varying Systems

DEFF Research Database (Denmark)

Bendtsen, Jan Dimon; Trangbæk, Klaus

2011-01-01

, closed-loop system identification is more difficult than open-loop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can be extended...

Configurable unitary transformations and linear logic gates using quantum memories.

Science.gov (United States)

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.

Linear and quadratic exponential modulation of the solutions of the paraxial wave equation

International Nuclear Information System (INIS)

Torre, A

2010-01-01

A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes

Ultrabroadband optical chirp linearization for precision metrology applications.

Science.gov (United States)

Roos, Peter A; Reibel, Randy R; Berg, Trenton; Kaylor, Brant; Barber, Zeb W; Babbitt, Wm Randall

2009-12-01

We demonstrate precise linearization of ultrabroadband laser frequency chirps via a fiber-based self-heterodyne technique to enable extremely high-resolution, frequency-modulated cw laser-radar (LADAR) and a wide range of other metrology applications. Our frequency chirps cover bandwidths up to nearly 5 THz with frequency errors as low as 170 kHz, relative to linearity. We show that this performance enables 31-mum transform-limited LADAR range resolution (FWHM) and 86 nm range precisions over a 1.5 m range baseline. Much longer range baselines are possible but are limited by atmospheric turbulence and fiber dispersion.

Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS

Energy Technology Data Exchange (ETDEWEB)

Adamopoulou, Panagiota, E-mail: p.adamopoulou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Doikou, Anastasia, E-mail: a.doikou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Papamikos, Georgios, E-mail: g.papamikos@reading.ac.uk [Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX (United Kingdom)

2017-05-15

We consider the discrete and continuous vector non-linear Schrödinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux–Bäcklund transformation. Within this spirit we then explicitly work out the generic Bäcklund transformation and the dressing associated to both discrete and continuous spectrum, i.e. the Darboux transformation is expressed in the matrix and integral representation respectively.

Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS

International Nuclear Information System (INIS)

Adamopoulou, Panagiota; Doikou, Anastasia; Papamikos, Georgios

2017-01-01

We consider the discrete and continuous vector non-linear Schrödinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux–Bäcklund transformation. Within this spirit we then explicitly work out the generic Bäcklund transformation and the dressing associated to both discrete and continuous spectrum, i.e. the Darboux transformation is expressed in the matrix and integral representation respectively.

Box-Cox transformation of firm size data in statistical analysis

Science.gov (United States)

Chen, Ting Ting; Takaishi, Tetsuya

2014-03-01

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions.

Box-Cox transformation of firm size data in statistical analysis

International Nuclear Information System (INIS)

Chen, Ting Ting; Takaishi, Tetsuya

2014-01-01

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions

The role of the dorsolateral tegmentum in the control of male sexual behavior: a reevaluation.

Science.gov (United States)

Romero-Carbente, J C; Camacho, F J; Paredes, R G

2006-06-30

The medial preoptic area/anterior hypothalamus (MPOA/AH) plays a key role in the control of male sexual behavior. Independently of the type, MPOA/AH lesions permanently eliminate male sexual behavior in the rat. The MPOA/AH projects among other structures to the dorsolateral tegmentum (DLT). Bilateral electrolytic lesions of the DLT or the unilateral electrolytic destruction of the MPOA/HA combined with a contralateral electrolytic lesion of the DLT eliminate male sexual behavior. In the present experiment, we evaluated if neurotoxic lesions of the DLT produce the same behavioral deficits as those observed after electrolytic lesions. This would allow us to evaluate if neurons of the DLT or the fibers passing through this area are important in the control of male sexual behavior. To this aim, sexually experience male rats were tested for socio-sexual behavior, partner preference and motor execution in order to determine if the possible behavioral changes could be attributed to alterations in sexual motivation or motor execution. One week after the bilateral DLT lesions the animals were evaluated in the same behavioral tests. The lesions were identified by glial fibrillary acidic protein (GFAP) and neuronal nuclear protein (Neu-N) immunohistochemistry. No significant consistent effects upon sexual behavior were observed in any of the groups, including the group with clear bilateral damage of the DLT. A reduction in the percentage of males displaying ejaculation in the first post-lesion test was observed for all groups injected with quinolinic acid. No effects upon partner preference or motor coordination were observed after the lesion in any of the groups. The lack of effect of DLT neurotoxic lesions upon mating suggests that neurons of this structure are not involved in the control of male sexual behavior.

Kac-Moody algebras derived from linearization systems using Zsub(N) reduction and extended to supersymmetry

International Nuclear Information System (INIS)

Bohr, H.; Roy Chowdhury, A.

1984-10-01

The hidden symmetries in various integrable models are derived by applying a newly developed method that uses the Riemann-Hilbert transform in a Zsub(N)-reduction of the linearization systems. The method is extended to linearization systems with higher algebras and with supersymmetry. (author)

Methods of Weyl representation of the phase space and canonical transformations. 1

International Nuclear Information System (INIS)

Budanov, V.G.

1984-01-01

The kernel structure of canonical transformation and differential equation for the intertwining operator is found. The Weyl symbol of operators producing linear canonical transformations is associated with the Cayley transformation of classical canonical transformation. Due to the invariance of the Weyl formalism a complete study of singularity and factorization of these symbols is manageable. In particular, one can study the symbols of Green functions and elements of Lie groups and find the spectra of arbitrary stationary quadratic Hamiltonians with the help of the known classification of the spectra of classical systems

Non-Linear Dynamics of Saturn's Rings

Science.gov (United States)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

An {Mathematical expression} iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming

NARCIS (Netherlands)

J.F. Sturm; J. Zhang (Shuzhong)

1996-01-01

textabstractIn this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993;

Esscher transforms and the minimal entropy martingale measure for exponential Lévy models

DEFF Research Database (Denmark)

Hubalek, Friedrich; Sgarra, C.

In this paper we offer a systematic survey and comparison of the Esscher martingale transform for linear processes, the Esscher martingale transform for exponential processes, and the minimal entropy martingale measure for exponential lévy models and present some new results in order to give...

Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation

Science.gov (United States)

Bonelli, Antonio; Ruffo, Stefano

Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the "ordered" and "chaotic" distribution of such pairs by solving the eigenvalue problem for two-dimensional modular transformations over integers. We conjecture that the optimal uniformity for pair distribution is obtained when the slope of linear modular eigenspaces takes the value n opt =maxint (p/√ {p-1}), where p is a prime number. We then propose a new generator of pairs of independent pseudo-random numbers, which realizes an optimal uniform distribution (in the "statistical" sense) of points on the unit square (0, 1] × (0, 1]. The method can be easily generalized to the generation of k-tuples of random numbers (with k>2).

Transformation techniques for cross-sectional and longitudinal endocrine data: application to salivary cortisol concentrations.

Science.gov (United States)

Miller, Robert; Plessow, Franziska

2013-06-01

Endocrine time series often lack normality and homoscedasticity most likely due to the non-linear dynamics of their natural determinants and the immanent characteristics of the biochemical analysis tools, respectively. As a consequence, data transformation (e.g., log-transformation) is frequently applied to enable general linear model-based analyses. However, to date, data transformation techniques substantially vary across studies and the question of which is the optimum power transformation remains to be addressed. The present report aims to provide a common solution for the analysis of endocrine time series by systematically comparing different power transformations with regard to their impact on data normality and homoscedasticity. For this, a variety of power transformations of the Box-Cox family were applied to salivary cortisol data of 309 healthy participants sampled in temporal proximity to a psychosocial stressor (the Trier Social Stress Test). Whereas our analyses show that un- as well as log-transformed data are inferior in terms of meeting normality and homoscedasticity, they also provide optimum transformations for both, cross-sectional cortisol samples reflecting the distributional concentration equilibrium and longitudinal cortisol time series comprising systematically altered hormone distributions that result from simultaneously elicited pulsatile change and continuous elimination processes. Considering these dynamics of endocrine oscillations, data transformation prior to testing GLMs seems mandatory to minimize biased results. Copyright © 2012 Elsevier Ltd. All rights reserved.

Design techniques for large scale linear measurement systems

International Nuclear Information System (INIS)

Candy, J.V.

1979-03-01

Techniques to design measurement schemes for systems modeled by large scale linear time invariant systems, i.e., physical systems modeled by a large number (> 5) of ordinary differential equations, are described. The techniques are based on transforming the physical system model to a coordinate system facilitating the design and then transforming back to the original coordinates. An example of a three-stage, four-species, extraction column used in the reprocessing of spent nuclear fuel elements is presented. The basic ideas are briefly discussed in the case of noisy measurements. An example using a plutonium nitrate storage vessel (reprocessing) with measurement uncertainty is also presented

Transport properties of a piecewise linear transformation and deterministic Levy flights

International Nuclear Information System (INIS)

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)

Feedback Linearization Based Arc Length Control for Gas Metal Arc Welding

DEFF Research Database (Denmark)

Thomsen, Jesper Sandberg

2005-01-01

a linear system to be controlled by linear state feedback control. The advantage of using a nonlinear approach as feedback linearization is the ability of this method to cope with nonlinearities and different operating points. However, the model describing the GMAW process is not exact, and therefore......In this paper a feedback linearization based arc length controller for gas metal arc welding (GMAW) is described. A nonlinear model describing the dynamic arc length is transformed into a system where nonlinearities can be cancelled by a nonlinear state feedback control part, and thus, leaving only......, the cancellation of nonlinear terms might give rise to problems with respect to robustness. Robustness of the closed loop system is therefore nvestigated by simulation....

The Importance of Nonlinear Transformations Use in Medical Data Analysis.

Science.gov (United States)

Shachar, Netta; Mitelpunkt, Alexis; Kozlovski, Tal; Galili, Tal; Frostig, Tzviel; Brill, Barak; Marcus-Kalish, Mira; Benjamini, Yoav

2018-05-11

The accumulation of data and its accessibility through easier-to-use platforms will allow data scientists and practitioners who are less sophisticated data analysts to get answers by using big data for many purposes in multiple ways. Data scientists working with medical data are aware of the importance of preprocessing, yet in many cases, the potential benefits of using nonlinear transformations is overlooked. Our aim is to present a semi-automated approach of symmetry-aiming transformations tailored for medical data analysis and its advantages. We describe 10 commonly encountered data types used in the medical field and the relevant transformations for each data type. Data from the Alzheimer's Disease Neuroimaging Initiative study, Parkinson's disease hospital cohort, and disease-simulating data were used to demonstrate the approach and its benefits. Symmetry-targeted monotone transformations were applied, and the advantages gained in variance, stability, linearity, and clustering are demonstrated. An open source application implementing the described methods was developed. Both linearity of relationships and increase of stability of variability improved after applying proper nonlinear transformation. Clustering simulated nonsymmetric data gave low agreement to the generating clusters (Rand value=0.681), while capturing the original structure after applying nonlinear transformation to symmetry (Rand value=0.986). This work presents the use of nonlinear transformations for medical data and the importance of their semi-automated choice. Using the described approach, the data analyst increases the ability to create simpler, more robust and translational models, thereby facilitating the interpretation and implementation of the analysis by medical practitioners. Applying nonlinear transformations as part of the preprocessing is essential to the quality and interpretability of results. ©Netta Shachar, Alexis Mitelpunkt, Tal Kozlovski, Tal Galili, Tzviel Frostig, Barak

Application of the numerical Laplace transform inversion to neutron transport theory

International Nuclear Information System (INIS)

Ganapol, B.D.

1989-01-01

A numerical Laplace transform inversion is developed using the Hurwitz-Zweifel method of evaluating the Fourier cosine integral coupled with an Euler-Knopp transformation. The numerical inversion is then applied to problems in linear transport theory concerning slowing down, time-dependence and featuring the determination of the interior scalar flux solution to the one-group stationary transport equation in half-space geometry

Analysis of a rectangular ceramic plate in electrically forced thickness-twist vibration as a piezoelectric transformer.

Science.gov (United States)

Yang, Jiashi; Liu, Jinjin; Li, Jiangyu

2007-04-01

A rectangular ceramic plate with appropriate electrical load and operating mode is analyzed for piezoelectric transformer application. An exact solution from the three-dimensional equations of linear piezoelectricity is obtained. The solution simulates the real operating situation of a transformer as a vibrating piezoelectric body connected to a circuit. Transforming ratio, input admittance, and efficiency of the transformer are obtained.

Oblique projections and standard-form transformations for discrete inverse problems

DEFF Research Database (Denmark)

Hansen, Per Christian

2013-01-01

This tutorial paper considers a specific computational tool for the numerical solution of discrete inverse problems, known as the standard-form transformation, by which we can treat general Tikhonov regularization problems efficiently. In the tradition of B. N. Datta's expositions of numerical li...... linear algebra, we use the close relationship between oblique projections, pseudoinverses, and matrix computations to derive a simple geometric motivation and algebraic formulation of the standard-form transformation....

A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

Science.gov (United States)

Li, Chen; Liao, Yufei

2018-03-01

Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

Maximum error-bounded Piecewise Linear Representation for online stream approximation

KAUST Repository

Xie, Qing; Pang, Chaoyi; Zhou, Xiaofang; Zhang, Xiangliang; Deng, Ke

2014-01-01

Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.

Maximum error-bounded Piecewise Linear Representation for online stream approximation

KAUST Repository

Xie, Qing

2014-04-04

Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.

Supersymmetric Yang-Mills fields as an integrable system and connections with other non-linear systems

International Nuclear Information System (INIS)

Chau, L.L.

1983-01-01

Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references

Transformations to diagonal bases in closed-loop quantum learning control experiments

International Nuclear Information System (INIS)

Cardoza, David; Trallero-Herrero, Carlos; Langhojer, Florian; Rabitz, Herschel; Weinacht, Thomas

2005-01-01

This paper discusses transformations between bases used in closed-loop learning control experiments. The goal is to transform to a basis in which the number of control parameters is minimized and in which the parameters act independently. We demonstrate a simple procedure for testing whether a unitary linear transformation (i.e., a rotation amongst the control variables) is sufficient to reduce the search problem to a set of globally independent variables. This concept is demonstrated with closed-loop molecular fragmentation experiments utilizing shaped, ultrafast laser pulses

Streamflow record extension using power transformations and application to sediment transport

Science.gov (United States)

Moog, Douglas B.; Whiting, Peter J.; Thomas, Robert B.

1999-01-01

To obtain a representative set of flow rates for a stream, it is often desirable to fill in missing data or extend measurements to a longer time period by correlation to a nearby gage with a longer record. Linear least squares regression of the logarithms of the flows is a traditional and still common technique. However, its purpose is to generate optimal estimates of each day's discharge, rather than the population of discharges, for which it tends to underestimate variance. Maintenance-of-variance-extension (MOVE) equations [Hirsch, 1982] were developed to correct this bias. This study replaces the logarithmic transformation by the more general Box-Cox scaled power transformation, generating a more linear, constant-variance relationship for the MOVE extension. Combining the Box-Cox transformation with the MOVE extension is shown to improve accuracy in estimating order statistics of flow rate, particularly for the nonextreme discharges which generally govern cumulative transport over time. This advantage is illustrated by prediction of cumulative fractions of total bed load transport.

Closed-loop Identification for Control of Linear Parameter Varying Systems

DEFF Research Database (Denmark)

Bendtsen, Jan Dimon; Trangbæk, Klaus

2014-01-01

, closed- loop system identification is more difficult than open-loop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can...

Methods in half-linear asymptotic theory

Directory of Open Access Journals (Sweden)

Pavel Rehak

2016-10-01

Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

An exemplified introduction of the Laplace transform

Directory of Open Access Journals (Sweden)

Marcel BOGDAN

2018-06-01

Full Text Available We solve a linear Cauchy problem with discontinuous perturbation two ways, by solving continuous Cauchy problems successively and by using Laplace transform. An example is given when the last one cannot be used any longer, still the Cauchy problems are solvable and the Cauchy problem with discontinuous perturbation as well.

The radon transform. Theory and implementation

International Nuclear Information System (INIS)

Toft, P.

1996-01-01

The subject of this Ph.D. thesis is the mathematical Radon transform, which is well suited for curve detection in digital images, and for reconstruction of tomography images. The thesis is divided into two main parts. Part I describes the Radon- and the Hough-transform and especially their discrete approximations with respect to curve parameter detection in digital images. The sampling relationships of the Radon transform is reviewed from a digital signal processing point of view. The discrete Radon transform is investigated for detection of curves, and aspects regarding the performance of the Radon transform assuming various types of noise is covered. Furthermore, a new fast scheme for estimating curve parameters is presented. Part II of the thesis describes the inverse Radon transform in 2D and 3D with focus on reconstruction of tomography images. Some of the direct reconstruction schemes are analyzed, including their discrete implementation. Furthermore, several iterative reconstruction schemes based on linear algebra are reviewed and applied for reconstruction of Positron Emission Tomography (PET) images. A new and very fast implementation of 2D iterative reconstruction methods is devised. In a more practical oriented chapter, the noise in PET images is modelled from a very large number of measurements. Several packagers for Radon- and Hough-transform based curve detection and direct/iterative 2D and 3D reconstruction have been developed and provided for free. (au) 140 refs

Calibration of a camera–projector measurement system and error impact analysis

International Nuclear Information System (INIS)

Huang, Junhui; Wang, Zhao; Xue, Qi; Gao, Jianmin

2012-01-01

In the camera–projector measurement system, calibration is a key to the measurement accuracy; especially, it is more difficult to obtain the same calibration accuracy for projector than camera due to the inaccurate corresponding relationship between its calibration points and imaging points. Thus, based on stereo vision measurement models of the camera and the projector, a calibration method with direct linear transformation (DLT) and bundle adjustment (BA) is introduced to adjust the corresponding relationships for better optimization purpose in this paper, which minimize the effect of inaccurate calibration points. And an integral method is presented to improve the precision of projection patterns to compensate the projector resolution limitation. Moreover impacts of system parameter and calibration points errors are evaluated when the calibration points positions change, which not only provides theoretical guidance for the rational layout of the calibration points, but also can be used for the optimization of system structure. Finally, the calibration of the system is carried out and the experiment results show that better precision can be achieved with those processes. (paper)

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

Science.gov (United States)

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.

Process identification method based on the Z transformation

International Nuclear Information System (INIS)

Zwingelstein, G.

1968-01-01

A simple method is described for identifying the transfer function of a linear retard-less system, based on the inversion of the Z transformation of the transmittance using a computer. It is assumed in this study that the signals at the entrance and at the exit of the circuit considered are of the deterministic type. The study includes: the theoretical principle of the inversion of the Z transformation, details about programming simulation, and identification of filters whose degrees vary from the first to the fifth order. (authors) [fr

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.

2017-01-01

. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

Finite element evaluation of elasto-plastic accommodation energies during solid state transformations: Coherent, spherical precipitate in finite matrix

International Nuclear Information System (INIS)

Sen, S.; Balasubramaniam, R.; Sethuraman, R.

1996-01-01

The molar volume difference between the matrix and the precipitate phases in the case of solid state phase transformations results in the creation of stain energy in the system due to the misfit strains. A finite element model based on the initial strain approach is proposed to evaluate elasto-plastic accommodation energies during solid state transformation. The three-dimensional axisymmetric model has been used to evaluate energies as a function of transformation for α-β hydrogen transformations in the Nb-H system. The transformation has been analyzed for the cases of transformation progressing both from the center to surface and from the surface to center of the system. The effect of plastic deformation has been introduced to make the model realistic, specifically to the Nb-NbH phase transformation which involves a 4% linear misfit strain. It has been observed that plastic deformation reduces the strain energies compared to the linear elastic analysis

Treatment of electrochemical noise data by the Hilbert-Huang transform

International Nuclear Information System (INIS)

Rahier, A.

2009-01-01

Most of the classical approaches for treating electro-chemical noise (ECN) data suffer from the non-linear and non steady-state character of the delivered signal. Very often, the link between time and the local corrosion events supposedly responsible for ECN data signatures is lost during treatment, as is obvious when using the classical Fourier Transform (FT), followed by an analysis of the response in the frequency domain. In this particular case, the information directly related to the corrosion events is distributed into the full spectra, thereby preventing the operator to derive clear and precise conclusions. In 2005, we suggested an alternative data treatment based on the Hilbert-Huang transform (HHT). The latter keeps track of the time variable and copes with non-linear and non steady-state behaviours of the system under examination. In 2006, we demonstrated the applicability of the newly proposed data treatment in the case of ECN data collected under BWR (Boiling Water Reactor) conditions. In 2007, we collected additional ECN data and started a preliminary investigation of two mathematical restrictions that are susceptible to impair the interpretation of the results. We discovered a possible modification of the Hilbert transform allowing generating controlled phase shifts that are different from pi/2 as is always the case for the Hilbert transform

Transforming wealth: using the inverse hyperbolic sine (IHS) and splines to predict youth's math achievement.

Science.gov (United States)

Friedline, Terri; Masa, Rainier D; Chowa, Gina A N

2015-01-01

The natural log and categorical transformations commonly applied to wealth for meeting the statistical assumptions of research may not always be appropriate for adjusting for skewness given wealth's unique properties. Finding and applying appropriate transformations is becoming increasingly important as researchers consider wealth as a predictor of well-being. We present an alternative transformation-the inverse hyperbolic sine (IHS)-for simultaneously dealing with skewness and accounting for wealth's unique properties. Using the relationship between household wealth and youth's math achievement as an example, we apply the IHS transformation to wealth data from US and Ghanaian households. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. IHS transformed wealth relates to youth's math achievement similarly when compared to categorical and natural log transformations, indicating that it is a viable alternative to other transformations commonly used in research. Non-linear relationships and accumulation thresholds emerge that predict youth's math achievement when splines are incorporated. In US households, accumulating debt relates to decreases in math achievement whereas accumulating assets relates to increases in math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles relates to increases in youth's math achievement. Copyright © 2014 Elsevier Inc. All rights reserved.

Ward identities for scale and special conformal transformations in inflation

International Nuclear Information System (INIS)

Kundu, Nilay; Shukla, Ashish; Trivedi, Sandip P.

2016-01-01

We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.

Application of non-linear discretetime feedback regulators with assignable closed-loop dynamics

Directory of Open Access Journals (Sweden)

Dubljević Stevan

2003-01-01

Full Text Available In the present work the application of a new approach is demonstrated to a discrete-time state feedback regulator synthesis with feedback linearization and pole-placement for non-linear discrete-time systems. Under the simultaneous implementation of a non-linear coordinate transformation and a non-linear state feedback law computed through the solution of a system of non-linear functional equations, both the feedback linearization and pole-placement design objectives were accomplished. The non-linear state feedback regulator synthesis method was applied to a continuous stirred tank reactor (CSTR under non-isothermal operating conditions that exhibits steady-state multiplicity. The control objective was to regulate the reactor at the middle unstable steady state by manipulating the rate of input heat in the reactor. Simulation studies were performed to evaluate the performance of the proposed non-linear state feedback regulator, as it was shown a non-linear state feedback regulator clearly outperformed a standard linear one, especially in the presence of adverse disturbance under which linear regulation at the unstable steady state was not feasible.

Quantization of the Linearized Kepler Problem

OpenAIRE

Guerrero, Julio; Perez, Jose Miguel

2003-01-01

The linearized Kepler problem is considered, as obtained from the Kustaanheimo-Stiefel (K-S)transformation, both for negative and positive energies. The symmetry group for the Kepler problem turns out to be SU(2,2). For negative energies, the Hamiltonian of Kepler problem can be realized as the sum of the energies of four harmonic oscillator with the same frequency, with a certain constrain. For positive energies, it can be realized as the sum of the energies of four repulsive oscillator with...

Linear self-focusing of continuous UV laser beam in photo-thermo-refractive glasses.

Science.gov (United States)

Sidorov, Alexander I; Gorbyak, Veronika V; Nikonorov, Nikolay V

2018-03-19

The experimental and theoretical study of continuous UV laser beam propagation through thick silver-containing photo-thermo-refractive glass is presented. It is shown for the first time that self-action of UV Gaussian beam in glass results in its self-focusing. The observed linear effect is non-reversible and is caused by the transformation of subnanosized charged silver molecular clusters to neutral state under UV laser radiation. Such transformation is accompanied by the increase of molecular clusters polarizability and the refractive index increase in irradiated area. As a result, an extended positive lens is formed in glass bulk. In a theoretical study of linear self-focusing effect, the "aberration-free" approximation was used, taking into account spatial distribution of induced absorption.

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

Science.gov (United States)

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.

Modelling the effect of non-uniform radon progeny activities on transformation frequencies in human bronchial airways

International Nuclear Information System (INIS)

Fakir, H.; Hofmann, W.; Aubineau-Laniece, I.

2006-01-01

The effects of radiological and morphological source heterogeneities in straight and Y-shaped bronchial airways on hit frequencies and Micro-dosimetric quantities in epithelial cells have been investigated previously. The goal of the present study is to relate these physical quantities to transformation frequencies in sensitive target cells and to radon-induced lung cancer risk. Based on an effect-specific track length model, computed linear energy transfer (LET) spectra were converted to corresponding transformation frequencies for different activity distributions and source - target configurations. Average transformation probabilities were considerably enhanced for radon progeny accumulations and target cells at the carinal ridge, relative to uniform activity distributions and target cells located along the curved and straight airway portions at the same exposure level. Although uncorrelated transformation probabilities produce a linear dose - effect relationship, correlated transformations first increase depending on the LET, but then decrease significantly when exceeding a defined number of hits or cumulative exposure level. (authors)

Discriminative Elastic-Net Regularized Linear Regression.

Science.gov (United States)

Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

2017-03-01

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

Coreless Linear Induction Motor (LIM) for Space-borne Electro-magnetic Mass Driver Applications

Data.gov (United States)

National Aeronautics and Space Administration — Large scale linear induction motors use ferromagnetic cores, but at high speed these cores choke the system’s ability to transform electrical energy into mechanical...

Alloying effect on martensite transformation in stainless steels

International Nuclear Information System (INIS)

Gulyaev, A.P.; Shlyamnev, A.P.; Sorokina, N.A.

1975-01-01

The effect of cobalt, nickel, molybdenum on the martensite transformation kinetics in stainless steels containing 9 to 13% Cr has been studied. Cobalt in Fe-Cr base alloys decreases the temperature of the Msub(in) and Msub(fin) points without a considerable decrease of the martensite phase amount after the transformation. Nickel reduces the martensite transformation temperature range, the nickel effect being enhanced in the presence of cobalt, which is characterized by a change of the linear dependence Msub(in)=f(%Ni) for a quadratic one. Molybdenum decreases the temperature of the Msub(in) and Msub(fin) points intensively, thus, substantially increasing the residual austenite amount. In the steels investigated Ni and Co decrease, whereas Mo increases, to some extent, the temperature of the reverse a-γ-transformation. The reduction of chromium content from 13 to 9% stimulates the martensite transformation initiation, that is why, in alloys containing 9% Cr, the increase in the contents of Ni, Co., Mo with the martensite structure maintained is possible. A further alloying of steel containing 13% Cr with these elements is rather limited due to the inhibition of the martensite transformation

Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

Science.gov (United States)

2017-08-01

Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array

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

NARCIS (Netherlands)

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,

Post-transplant survival in idiopathic pulmonary fibrosis patients concurrently listed for single and double lung transplantation.

Science.gov (United States)

Chauhan, Dhaval; Karanam, Ashwin B; Merlo, Aurelie; Tom Bozzay, P A; Zucker, Mark J; Seethamraju, Harish; Shariati, Nazly; Russo, Mark J

2016-05-01

Lung transplantation is a widely accepted treatment for patients with end-stage lung disease related to idiopathic pulmonary fibrosis (IPF). However, there are conflicting data on whether double lung transplant (DLT) or single lung transplant (SLT) is the superior therapy in these patients. The purpose of this study was to determine whether actuarial post-transplant graft survival among IPF patients concurrently listed for DLT and SLT is greater for recipients undergoing the former or the latter. The United Network for Organ Sharing provided de-identified patient-level data. Analysis included lung transplant candidates with IPF listed between January 1, 2001 and December 31, 2009 (n = 3,411). The study population included 1,001 (29.3%) lung transplant recipients concurrently listed for DLT and SLT, all ≥18 years of age. The primary outcome measure was actuarial post-transplant graft survival, expressed in years. Among the study population, 433 (43.26%) recipients underwent SLT and 568 (56.74%) recipients underwent DLT. The analysis included 2,722.5 years at risk, with median graft survival of 5.31 years. On univariate (p = 0.317) and multivariate (p = 0.415) regression analyses, there was no difference in graft survival between DLT and SLT. Among IPF recipients concurrently listed for DLT and SLT, there is no statistical difference in actuarial graft survival between recipients undergoing DLT vs SLT. This analysis suggests that increased use of SLT for IPF patients may increase the availability of organs to other candidates, and thus increase the net benefit of these organs, without measurably compromising outcomes. Copyright © 2016 International Society for Heart and Lung Transplantation. Published by Elsevier Inc. All rights reserved.

Linear Power-Flow Models in Multiphase Distribution Networks: Preprint

Energy Technology Data Exchange (ETDEWEB)

Bernstein, Andrey; Dall' Anese, Emiliano

2017-05-26

This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- from advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.

Holographic Transformation, Belief Propagation and Loop Calculus for Generalized Probabilistic Theories

OpenAIRE

Mori, Ryuhei

2015-01-01

The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is represented by an inner product of two high-dimensional vectors both of which can be decomposed to tensor products of low-dimensional vectors. On the representation, the holographic transformation is clearly understood by using adjoint linear maps. Furthermore, on th...

Constitutive modelling and identification of parameters of the plastic strain-induced martensitic transformation in 316L stainless steel at cryogenic temperatures

CERN Document Server

Garion, C; Sgobba, Stefano

2006-01-01

The present paper is focused on constitutive modelling and identification of parameters of the relevant model of plastic strain- induced martensitic transformation in austenitic stainless steels at low temperatures. The model used to describe the FCCrightward arrow BCC phase transformation in austenitic stainless steels is based on the assumption of linearization of the most intensive part of the transformation curve. The kinetics of phase transformation is described by three parameters: transformation threshold (p/sub xi/), slope (A) and saturation level (xi/sub L/). It is assumed that the phase transformation is driven by the accumulated plastic strain p. In addition, the intensity of plastic deformation is strongly coupled to the phase transformation via the description of mixed kinematic /isotropic linear plastic hardening based on the Mori-Tanaka homogenization. The theory of small strains is applied. Small strain fields, corresponding to phase transformation, are decomposed into the volumic and the shea...

The superspace-translation tensor and linearized N = 1 supergravities

International Nuclear Information System (INIS)

Bedding, S.P.; Lang, W.

1982-01-01

The recently proposed superspace-translation tensor is considered as the source of supergravities in the context of N = 1 supersymmetry. It is shown how the structure of this tensor leads to a complete evaluation of the linearized supervielbein in terms of unconstrained prepotentials with derived transformation laws. Connection with formulations using torsion constraints is made. (orig.)

Sarcopenic obesity: A probable risk factor for dose limiting toxicity during neo-adjuvant chemotherapy in oesophageal cancer patients.

Science.gov (United States)

Anandavadivelan, Poorna; Brismar, Torkel B; Nilsson, Magnus; Johar, Asif M; Martin, Lena

2016-06-01

Profound weight loss and malnutrition subsequent to severe dysphagia and cancer cachexia are cardinal symptoms in oesophageal cancer (OC). Low muscle mass/sarcopenia has been linked to toxicity during neo-adjuvant therapy in other cancers, with worser effects in sarcopenic obesity. In this study the association between sarcopenia and/or sarcopenic obesity and dose limiting toxicity (DLT) during cycle one chemotherapy in resectable OC patients was evaluated. Body composition was assessed from computed tomography scans of 72 consecutively diagnosed OC patients. Lean body mass and body fat mass were estimated. Patients were grouped as sarcopenic or non-sarcopenic based on pre-defined gender-specific cut-offs for sarcopenia, and as underweight/normal (BMI sarcopenia combined with overweight and obesity. DLT was defined as temporary reduction/delay or permanent discontinuation of drugs due to adverse effects. Odds ratios for developing toxicity were ascertained using multiple logistic regression. Of 72 patients, 85% (n = 61) were males. Sarcopenia and sarcopenic obesity were present in 31 (43%) and 10 (14%), respectively, prior to chemotherapy. Sarcopenic patients had significantly lower adipose tissue index (p = 0.02) compared to non-sarcopenic patients. Patients with DLT (n = 24) had lower skeletal muscle mass (p = 0.04) than those without DLT. Sarcopenic patients (OR = 2.47; 95% CI: 0.88-6.93) showed a trend towards increased DLT risk (p < 0.10). Logistic regression with BMI as an interaction term indicated higher DLT risk in sarcopenic patients with normal BMI (OR = 1.60; 95% CI 0.30-8.40), but was non-significant. In the sarcopenic obese, risk of DLT increased significantly (OR = 5.54; 95% CI 1.12-27.44). Sarcopenic and sarcopenic obese OC patients may be at a higher risk for developing DLT during chemotherapy compared to non-sarcopenic OC patients. Copyright © 2015 Elsevier Ltd and European Society for Clinical Nutrition and Metabolism. All

Radiogenic cell transformation and carcinogenesis

Science.gov (United States)

Yang, T. C.; Georgy, K. A.; Mei, M.; Durante, M.; Craise, L. M.

1995-01-01

Radiation carcinogenesis is one of the major biological effects considered important in the risk assessment for space travel. Various biological model systems, including both cultured cells and animals, have been found useful for studying the carcinogenic effects of space radiations, which consist of energetic electrons, protons and heavy ions. The development of techniques for studying neoplastic cell transformation in culture has made it possible to examine the cellular and molecular mechanisms of radiation carcinogenesis. Cultured cell systems are thus complementary to animal models. Many investigators have determined the oncogenic effects of ionizing and nonionizing radiation in cultured mammalian cells. One of the cell systems used most often for radiation transformation studies is mouse embryonic cells (C3H10T1/2), which are easy to culture and give good quantitative dose-response curves. Relative biological effectiveness (RBE) for heavy ions with various energies and linear energy transfer (LET) have been obtained with this cell system. Similar RBE and LET relationship was observed by investigators for other cell systems. In addition to RBE measurements, fundamental questions on repair of sub- and potential oncogenic lesions, direct and indirect effect, primary target and lesion, the importance of cell-cell interaction and the role of oncogenes and tumor suppressor genes in radiogenic carcinogenesis have been studied, and interesting results have been found. Recently several human epithelial cell systems have been developed, and ionizing radiation have been shown to transform these cells. Oncogenic transformation of these cells, however, requires a long expression time and/or multiple radiation exposures. Limited experimental data indicate high-LET heavy ions can be more effective than low-LET radiation in inducing cell transformation. Cytogenetic and molecular analyses can be performed with cloned transformants to provide insights into basic genetic

Non-Linear Dynamics of Saturn’s Rings

Science.gov (United States)

Esposito, Larry W.

2015-11-01

Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects

Factorization of a class of almost linear second-order differential equations

International Nuclear Information System (INIS)

Estevez, P G; Kuru, S; Negro, J; Nieto, L M

2007-01-01

A general type of almost linear second-order differential equations, which are directly related to several interesting physical problems, is characterized. The solutions of these equations are obtained using the factorization technique, and their non-autonomous invariants are also found by means of scale transformations

Cloning of the PYR3 gene of Ustilago maydis and its use in DNA transformation

Energy Technology Data Exchange (ETDEWEB)

Banks, G.R.; Taylor, S.Y. (National Institute for Medical Research, London (England))

1988-12-01

The Ustilago maydis PYR3 gene encoding dihydroorotase activity was cloned by direct complementation of Escherichia coli pyrC mutations. PYR3 transformants of E. coli pyrC mutants expressed homologous transcripts of a variety of sizes and regained dihydroorotase activity. PYR3 also complemented Saccharomyces cerevisiae ura4 mutations, and again multiple transcripts were expressed in transformants, and enzyme activity was regained. A 1.25-kilobase poly(rA)+ PYR3 transcript was detected in U. maydis itself. Linear DNA carrying the PYR3 gene transformed a U. maydis pyr3-1 pyrimidine auxotroph to prototrophy. Hybridization analysis revealed that three different types of transformants could be generated, depending on the structure of the transforming DNA used. The first type involved exchange of chromosomal mutant gene sequences with the cloned wild-type plasmid sequences. A second type had integrated linear transforming DNA at the chromosomal PYR3 locus, probably via a single crossover event. The third type had integrated transforming DNA sequences at multiple sites in the U. maydis genome. In the last two types, tandemly reiterated copies of the transforming DNA were found to have been integrated. All three types had lost the sensitivity of the parental pyr3-1 mutant to UV irradiation. They had also regained dihydroorotase activity, although its level did not correlate with the PYR3 gene copy number.

Linear algebraic analyses of structures with one predominant type of anomalous scatterer

International Nuclear Information System (INIS)

Karle, J.

1989-01-01

Further studies have been made of the information content of the exact linear equations for analyzing anomalous dispersion data in one-wavelength experiments. The case of interest concerns structures containing atoms that essentially do not scatter anomalously and one type of anomalously scattering atoms. For this case, there are three alternative ways of writing the equations. The alternative sets of equations and the transformations for transforming one set into the other are given explicitly. Comparison calculations were made with different sets of equations. Isomorphous replacement information is readily introduced into the calculations and the advantage of doing so is clearly illustrated by the results. Another aspect of the potential of the exact linear algebraic theory is its application to multiple-wavelength experiments. Successful applications of the latter have been made by several collaborative groups of investigators. (orig.)

Input/Output linearizing control of a nuclear reactor

International Nuclear Information System (INIS)

Perez C, V.

1994-01-01

The feedback linearization technique is an approach to nonlinear control design. The basic idea is to transform, by means of algebraic methods, the dynamics of a nonlinear control system into a full or partial linear system. As a result of this linearization process, the well known basic linear control techniques can be used to obtain some desired dynamic characteristics. When full linearization is achieved, the method is referred to as input-state linearization, whereas when partial linearization is achieved, the method is referred to as input-output linearization. We will deal with the latter. By means of input-output linearization, the dynamics of a nonlinear system can be decomposed into an external part (input-output), and an internal part (unobservable). Since the external part consists of a linear relationship among the output of the plant and the auxiliary control input mentioned above, it is easy to design such an auxiliary control input so that we get the output to behave in a predetermined way. Since the internal dynamics of the system is known, we can check its dynamics behavior on order of to ensure that the internal states are bounded. The linearization method described here can be applied to systems with one-input/one-output, as well as to systems with multiple-inputs/multiple-outputs. Typical control problems such as stabilization and reference path tracking can be solved using this technique. In this work, the input/output linearization theory is presented, as well as the problem of getting the output variable to track some desired trayectories. Further, the design of an input/output control system applied to the nonlinear model of a research nuclear reactor is included, along with the results obtained by computer simulation. (Author)

Renormalization a la BRS of the non-linear σ-model

International Nuclear Information System (INIS)

Blasi, A.; Collina, R.

1987-01-01

We characterize the non-linear O(N+1) σ-model in an arbitrary parametrization with a nihilpotent BRS operator obtained from the symmetry transformation by the use of anticommuting parameters. The identity can be made compatible with the presence of a mass term in the model, so we can analyze its stability and prove that the model is anomaly free. This procedure avoids many problems encountered in the conventional analysis; in particular the introduction of an infinite number of sources coupled to the successive variations of the field is not necessary and the linear O(N) symmetry is respected as a consequence of the identity. The approach may provide useful in discussing the renormalizability of a wider class of models with non-linear symmetries. (orig.)

Non-linear realization of α0 -extended supersymmetry

International Nuclear Information System (INIS)

Nishino, Hitoshi

2000-01-01

As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the global non-linear supersymmetry. As an interesting consequence, we find a non-linear supersymmetric Born-Infeld action for a non-Abelian gauge group for arbitrary D and N , which coincides with the linearly supersymmetric Born-Infeld action in D=10 at the lowest order. For the gauge group U(N) for M(atrix)-theory, this model has N 2 -extended non-linear supersymmetries, so that its large N limit corresponds to the infinitely many (α 0 ) supersymmetries. We also perform a duality transformation from F μν into its Hodge dual N μ 1 ctdot μD-2 . We next point out that any Chern-Simons action for any (super)groups has the non-linear supersymmetry as a hidden symmetry. Subsequently, we present a superspace formulation for the component results. We further find that as long as superspace supergravity is consistent, this generalized Volkov-Akulov action can further accommodate such curved superspace backgrounds with local supersymmetry, as a super p -brane action with fermionic kappa-symmetry. We further elaborate these results to what we call 'simplified' (Supersymmetry) 2 -models, with both linear and non-linear representations of supersymmetries in superspace at the same time. Our result gives a proof that there is no restriction on D or N for global non-linear supersymmetry. We also see that the non-linear realization of supersymmetry in 'curved' space-time can be interpreted as 'non-perturbative' effect starting with the 'flat' space-time

A Laplace transform/potential-theoretic method for acoustic propagation in subsonic flows

International Nuclear Information System (INIS)

Hariharan, S.I.; Sawyer, Scott; Dane Quinn, D.

2003-01-01

This paper introduces a competitive computational approach for determining time-dependent far-field sound generated by subsonic flows around lifting airfoils. The procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil. It is assumed that the sound pressure on the boundary of this enclosed region (referred to as the Kirchhoff surface) is specified, possibly by another procedure such as solving the full Euler equations. Away from the Kirchhoff surface, the Euler equations are linearized about a uniform mean flow. It is well known that linearized Euler equations can be uncoupled into a scalar convective wave equation. However, due to the anisotropy present in the convective wave equation, it is difficult to compute solutions. In this context, direct numerical simulation of the convective wave equation requires proper numerical descriptions of far-field boundary conditions which is a non-trivial task. Moreover, if accurate far-field conditions can be formulated, the computational cost of direct simulation can be prohibitive even in a modest computational domain. In this paper, we present an alternate solution procedure. First, the problem is transformed via the Laplace transform (with appropriate initial conditions) into a reduced wave equation. The convective term in the reduced wave equation is removed using a dependent variable transformation. Then we use Gothert's rule, to obtain a Helmholtz like equation with complex wave number, which is subsequently solved using double layer potential theory. Finally upon application of numerical inverse Laplace transform techniques, far-field acoustic pressure is obtained as a function of space and time

Nonlinear Fourier transform for dual-polarization optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone

communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...

Gain scheduling for non-linear time-delay systems using approximated model

NARCIS (Netherlands)

Pham, H.T.; Lim, J.T

2012-01-01

The authors investigate a regulation problem of non-linear systems driven by an exogenous signal and time-delay in the input. In order to compensate for the input delay, they propose a reduction transformation containing the past information of the control input. Then, by utilising the Euler

Calculation of the exponential function of linear idempotent operators

International Nuclear Information System (INIS)

Chavoya-Aceves, O.; Luna, H.M.

1989-01-01

We give a method to calculate the exponential EXP[A r ] where A is a linear operator which satisfies the reaction A n =I, n is an integer and I is the identity operator. The method is generalised to operators such that A n +1=A and is applied to obtain some Lorentz transformations which generalise the notion of 'boost'. (Author)

Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems

Czech Academy of Sciences Publication Activity Database

Duintjer Tebbens, Jurjen; Tůma, Miroslav

2007-01-01

Roč. 29, č. 5 (2007), s. 1918-1941 ISSN 1064-8275 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : preconditioned iterative methods * sparse matrices * sequences of linear algebraic systems * incomplete factorizations * factorization updates * Gauss–Jordan transformations * minimum spanning tree Subject RIV: BA - General Mathematics Impact factor: 1.784, year: 2007

Similarity transformed coupled cluster response (ST-CCR) theory--a time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach.

Science.gov (United States)

Landau, Arie

2013-07-07

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Non-linear wave equations:Mathematical techniques

International Nuclear Information System (INIS)

1978-01-01

An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

Optimization design of power efficiency of exponential impedance transformer

International Nuclear Information System (INIS)

Wang Meng; Zou Wenkang; Chen Lin; Guan Yongchao; Fu Jiabin; Xie Weiping

2011-01-01

The paper investigates the optimization design of power efficiency of exponential impedance transformer with analytic method and numerical method. In numerical calculation, a sine wave Jantage with hypothesis of rising edge equivalence is regarded as the forward-going Jantage at input of transformer, and its dominant angular frequency is determined by typical rise-time of actual Jantage waveforms. At the same time, dissipative loss in water dielectric is neglected. The numerical results of three typical modes of impedance transformation, viz. linear mode, saturation mode and steep mode,are compared. Pivotal factors which affect the power efficiency of exponential impedance transformer are discussed, and a certain extent quantitative range of intermediate variables and accordance coefficients are obtained. Finally, the paper discusses some important issues in actual design, such as insulation safety factor in structure design, effects of coupling capacitance on impedance calculation, and dissipative loss in water dielectric. (authors)

The Linear Time Frequency Analysis Toolbox

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel; Torrésani, Bruno; Balazs, Peter

2011-01-01

The Linear Time Frequency Analysis Toolbox is a Matlab/Octave toolbox for computational time-frequency analysis. It is intended both as an educational and computational tool. The toolbox provides the basic Gabor, Wilson and MDCT transform along with routines for constructing windows (lter...... prototypes) and routines for manipulating coe cients. It also provides a bunch of demo scripts devoted either to demonstrating the main functions of the toolbox, or to exemplify their use in specic signal processing applications. In this paper we describe the used algorithms, their mathematical background...

A phase I trial of sorafenib combined with cisplatin/etoposide or carboplatin/pemetrexed in refractory solid tumor patients.

Science.gov (United States)

Davies, Janine M; Dhruva, Nirav S; Walko, Christine M; Socinski, Mark A; Bernard, Stephen; Hayes, D Neil; Kim, William Y; Ivanova, Anastasia; Keller, Kimberly; Hilbun, Layla R; Chiu, Michael; Dees, E Claire; Stinchcombe, Thomas E

2011-02-01

Sorafenib has demonstrated single agent activity in non-small cell (NSCLC) and small cell lung cancer (SCLC). Carboplatin/pemetrexed (CbP) and cisplatin/etoposide (PE) are commonly used in the treatment of these diseases. A phase I trial escalating doses of sorafenib in combination with fixed doses of PE (Arm A) or CbP (Arm B) was performed using a 3-patient cohort design to determine the maximum tolerated dose (MTD) and dose-limiting toxicities (DLT); DLT were assessed in the first cycle. The trial was subsequently amended with closure of Arm B and to include Arm C with a reduced dose of carboplatin. Between 9/2007 and 9/2008, 20 pts were treated on the trial; median age 62 (range 42-73), male/female ratio 12/8, PS 0/1 ratio 6/14, and median number of prior therapies 2 (range 1-4). The most common tumor types were NSCLC and SCLC. On Arm A at dose level 0 (sorafenib 200 mg BID), 2 of 4 patients experienced DLT; 2 patients were enrolled at dose level -1 (sorafenib 200 mg QD) without DLT, but this arm was closed due to slow accrual. On Arm B, 2 of 3 patients experienced DLT at dose level 0 (sorafenib 200 mg BID). On Arm C at dose level 0 (sorafenib 200 mg BID), 1 of 6 patients experienced DLT, and at dose level +1 (sorafenib 400 mg BID) 2 of 5 patients experienced a DLT. The MTD of sorafenib was 200 mg BID continuously in combination with carboplatin (AUC of 5) and pemetrexed 500 mg/m² every 3 weeks. However, only 6 patients were treated at this dose level, and the results should be interpreted cautiously. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Iterated non-linear model predictive control based on tubes and contractive constraints.

Science.gov (United States)

Murillo, M; Sánchez, G; Giovanini, L

2016-05-01

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections

International Nuclear Information System (INIS)

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

Transformations of the perturbed two-body problem to unperturbed harmonic oscillators

Energy Technology Data Exchange (ETDEWEB)

Szebehely, V; Bond, V

1983-05-01

Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations. 11 references.

Derivation of Oscillators from Biquadratic Band Pass Filters Using Circuit Transformations

Directory of Open Access Journals (Sweden)

Hung-Yu Wang

2014-09-01

Full Text Available Network transformations are the techniques to obtain new functional schemes from available circuits. They are systematic methodologies, since each transformation technique can be applied to many circuits to obtain the desired functions or characteristics. A convenient network transformation method, exploiting different circuit transformations, for deriving linear sinusoidal oscillators from biquadratic band pass filters is proposed. This method with generality can be applied to any band pass filter. The oscillation frequency of the new obtained oscillator is identical to the center frequency of the original band pass filter, and the useful properties of the selected band pass filter can be retained. Two examples are illustrated to confirm the feasibility of the proposed approach. The workability of the obtained oscillators is verified with PSPICE simulations.

How linear response shaped models of neural circuits and the quest for alternatives.

Science.gov (United States)

Herfurth, Tim; Tchumatchenko, Tatjana

2017-10-01

In the past decades, many mathematical approaches to solve complex nonlinear systems in physics have been successfully applied to neuroscience. One of these tools is the concept of linear response functions. However, phenomena observed in the brain emerge from fundamentally nonlinear interactions and feedback loops rather than from a composition of linear filters. Here, we review the successes achieved by applying the linear response formalism to topics, such as rhythm generation and synchrony and by incorporating it into models that combine linear and nonlinear transformations. We also discuss the challenges encountered in the linear response applications and argue that new theoretical concepts are needed to tackle feedback loops and non-equilibrium dynamics which are experimentally observed in neural networks but are outside of the validity regime of the linear response formalism. Copyright © 2017 Elsevier Ltd. All rights reserved.

Oscillation and non-oscillation criterion for Riemann–Weber type half-linear differential equations

Directory of Open Access Journals (Sweden)

Petr Hasil

2016-08-01

Full Text Available By the combination of the modified half-linear Prüfer method and the Riccati technique, we study oscillatory properties of half-linear differential equations. Taking into account the transformation theory of half-linear equations and using some known results, we show that the analysed equations in the Riemann–Weber form with perturbations in both terms are conditionally oscillatory. Within the process, we identify the critical oscillation values of their coefficients and, consequently, we decide when the considered equations are oscillatory and when they are non-oscillatory. As a direct corollary of our main result, we solve the so-called critical case for a certain type of half-linear non-perturbed equations.

Self-Organization, Urban Transformation, and Spatial Planning in Greater Jakarta, Indonesia

Directory of Open Access Journals (Sweden)

Yovi Dzulhijjah Rahmawati

2015-09-01

Full Text Available Penelitian ini bertujuan untuk mengidentifikasi peran sistem perencanaan tata ruang dalam menghadapi proses perorganisasian diri, sebagaimana dibuktikan oleh transformasi perkotaan yang kompleks di wilayah Jakarta. Wilayah Jakarta adalah salah satu wilayah megapolitan di Asia Tenggara yang mengalami proses transformasi yang cepat. Sangat disayangkan bahwa sistem perencanaan tata ruang yang ada sekarang di wilayah Jakarta belum mampu merespon transformasi kota secara non-linier. Kekurangan ini terbukti dari ketidaksinkronan antara dokumen-dokumen perencanaan tata ruang dan perubahan tata guna lahan perkotaan yang diperkuat dengan proses pengorganisasian diri. Perbedaan antara situasi empiris dan dokumen-dokumen perencanaan tata ruang yang ada telah menghasilkan ketidakcocokan antara sistem perencanaan tata ruang dengan sistem tata ruang di wilayah Jakarta. Ketidakcocokan ini terjadi karena sistem perencanaan tata ruang saat ini tidak mempertimbangkan ketidakpastian di masa depan. Situasi ini mengindikasikan adanya ‘fuzziness’ dalam implementasi sistem dan proses perencanaan tata ruang, sementara transformasi perkotaan telah berkembang sedemikian kompleksnya dan membutuhkan respon yang cepat dan tepat. Untuk dapat merespon ketidakcocokan ini, sistem perencanaan tata ruang di wilayah Jakarta harus lebih memperhatikan sistem perkotaan yang berkembang dalam proses yang tidak linear.Kata kunci. Pengorganisasian diri, transformasi perkotaan, ketidaklinieran, sistem perencanaan, Megapolitan Jakarta. This study aimed to identify the role of spatial planning in facing self-organizing processes as evidenced by a complex urban transformation in Greater Jakarta. Greater Jakarta is one of the mega urban-regions in Southeast Asia that are undergoing a rapid urban transformation process. This urban transformation has been developing through a non-linear transition. Unfortunately, the current spatial planning system in Greater Jakarta is not yet adequately

A canonical form of the equation of motion of linear dynamical systems

Science.gov (United States)

Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

2018-03-01

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

Dual-polarization nonlinear Fourier transform-based optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

2018-01-01

communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

CPS Transformation of Flow Information, Part II: Administrative Reductions

DEFF Research Database (Denmark)

Damian, Daniel; Danvy, Olivier

2001-01-01

the least solution. Preservation of least solutions solves a problem that was left open in Palsberg and Wand's article ‘CPS Transformation of Flow Information.’ Together, Palsberg and Wand's article and the present article show how to map in linear time the least solution of the flow constraints...

Exploring linear algebra labs and projects with Mathematica

CERN Document Server

Arangala, Crista

2014-01-01

Matrix Operations Lab 0: An Introduction to Mathematica Lab 1: Matrix Basics and Operations Lab 2: A Matrix Representation of Linear Systems Lab 3: Powers, Inverses, and Special Matrices Lab 4: Graph Theory and Adjacency Matrices Lab 5: Permutations and Determinants Lab 6: 4 x 4 Determinants and Beyond Project Set 1 Invertibility Lab 7: Singular or Nonsingular? Why Singularity Matters Lab 8: Mod It Out, Matrices with Entries in ZpLab 9: It's a Complex World Lab 10: Declaring Independence: Is It Linear? Project Set 2 Vector Spaces Lab 11: Vector Spaces and SubspacesLab 12: Basing It All on Just a Few Vectors Lab 13: Linear Transformations Lab 14: Eigenvalues and Eigenspaces Lab 15: Markov Chains, An Application of Eigenvalues Project Set 3 Orthogonality Lab 16: Inner Product Spaces Lab 17: The Geometry of Vector and Inner Product SpacesLab 18: Orthogonal Matrices, QR Decomposition, and Least Squares Regression Lab 19: Symmetric Matrices and Quadratic Forms Project Set 4 Matrix Decomposition with Applications L...

3D scattering transforms for disease classification in neuroimaging

Directory of Open Access Journals (Sweden)

Tameem Adel

2017-01-01

Full Text Available Classifying neurodegenerative brain diseases in MRI aims at correctly assigning discrete labels to MRI scans. Such labels usually refer to a diagnostic decision a learner infers based on what it has learned from a training sample of MRI scans. Classification from MRI voxels separately typically does not provide independent evidence towards or against a class; the information relevant for classification is only present in the form of complicated multivariate patterns (or “features”. Deep learning solves this problem by learning a sequence of non-linear transformations that result in feature representations that are better suited to classification. Such learned features have been shown to drastically outperform hand-engineered features in computer vision and audio analysis domains. However, applying the deep learning approach to the task of MRI classification is extremely challenging, because it requires a very large amount of data which is currently not available. We propose to instead use a three dimensional scattering transform, which resembles a deep convolutional neural network but has no learnable parameters. Furthermore, the scattering transform linearizes diffeomorphisms (due to e.g. residual anatomical variability in MRI scans, making the different disease states more easily separable using a linear classifier. In experiments on brain morphometry in Alzheimer's disease, and on white matter microstructural damage in HIV, scattering representations are shown to be highly effective for the task of disease classification. For instance, in semi-supervised learning of progressive versus stable MCI, we reach an accuracy of 82.7%. We also present a visualization method to highlight areas that provide evidence for or against a certain class, both on an individual and group level.

One lung ventilation using double‑lumen tubes: Initial experience ...

African Journals Online (AJOL)

2014-05-09

May 9, 2014 ... The use of DLT for OLV to enhance thoracic anesthetic practice should be .... Prior to our purchase of a pediatric flexible bronchoscope, verification of DLT ... The short duration of action of local anesthetic agents solely ...

A parametric FE modeling of brake for non-linear analysis

Energy Technology Data Exchange (ETDEWEB)

Ahmed,Ibrahim; Fatouh, Yasser [Automotive and Tractors Technology Department, Faculty of Industrial Education, Helwan University, Cairo (Egypt); Aly, Wael [Refrigeration and Air-Conditioning Technology Department, Faculty of Industrial Education, Helwan University, Cairo (Egypt)

2013-07-01

A parametric modeling of a drum brake based on 3-D Finite Element Methods (FEM) for non-contact analysis is presented. Many parameters are examined during this study such as the effect of drum-lining interface stiffness, coefficient of friction, and line pressure on the interface contact. Firstly, the modal analysis of the drum brake is also studied to get the natural frequency and instability of the drum to facilitate transforming the modal elements to non-contact elements. It is shown that the Unsymmetric solver of the modal analysis is efficient enough to solve this linear problem after transforming the non-linear behavior of the contact between the drum and the lining to a linear behavior. A SOLID45 which is a linear element is used in the modal analysis and then transferred to non-linear elements which are Targe170 and Conta173 that represent the drum and lining for contact analysis study. The contact analysis problems are highly non-linear and require significant computer resources to solve it, however, the contact problem give two significant difficulties. Firstly, the region of contact is not known based on the boundary conditions such as line pressure, and drum and friction material specs. Secondly, these contact problems need to take the friction into consideration. Finally, it showed a good distribution of the nodal reaction forces on the slotted lining contact surface and existing of the slot in the middle of the lining can help in wear removal due to the friction between the lining and the drum. Accurate contact stiffness can give a good representation for the pressure distribution between the lining and the drum. However, a full contact of the front part of the slotted lining could occur in case of 20, 40, 60 and 80 bar of piston pressure and a partially contact between the drum and lining can occur in the rear part of the slotted lining.

Application of differential transformation method for solving dengue transmission mathematical model

Science.gov (United States)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

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

Science.gov (United States)

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.

Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Directory of Open Access Journals (Sweden)

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.

Non-linear effects in transition edge sensors for X-ray detection

International Nuclear Information System (INIS)

Bandler, S.R.; Figueroa-Feliciano, E.; Iyomoto, N.; Kelley, R.L.; Kilbourne, C.A.; Murphy, K.D.; Porter, F.S.; Saab, T.; Sadleir, J.

2006-01-01

In a microcalorimeter that uses a transition-edge sensor to detect energy depositions, the small signal energy resolution improves with decreasing heat capacity. This improvement remains true up to the point where non-linear and saturation effects become significant. This happens when the energy deposition causes a significant change in the sensor resistance. Not only does the signal size become a non-linear function of the energy deposited, but also the noise becomes non-stationary over the duration of the pulse. Algorithms have been developed that can calculate the optimal performance given this non-linear behavior that typically requires significant processing and calibration work-both of which are impractical for space missions. We have investigated the relative importance of the various non-linear effects, with the hope that a computationally simple transformation can overcome the largest of the non-linear and non-stationary effects, producing a highly linear 'gain' for pulse-height versus energy, and close to the best energy resolution at all energies when using a Wiener filter

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

Directory of Open Access Journals (Sweden)

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.

Second order oscillations of a Vlasov-Poisson plasma in the Fourier transformed space

International Nuclear Information System (INIS)

Sedlacek, Z.; Nocera, L.

1991-05-01

The Vlasov-Poisson system of equations in the Fourier-transformed velocity space is studied. At first some results of the linear theory are reformulated: in the new representation the Van Kampen eigenmodes and their adjoint are found to be ordinary functions with convenient piece-wise continuity properties. A transparent derivation is given of the free-streaming temporal echo in terms of the kinematics of wave packets in the Fourier-transformed velocity space. This analysis is further extended to include Coulomb interactions which allows to establish a connection between the echo theory, the second order oscillations of Best and the phenomenon of linear sidebands. The calculation of the time evolution of the global second order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. It is concluded that the phenomenon of linear sidebands may be properly explained in terms of the intrinsic features of the equilibrium distribution function. (author) 5 figs., 32 refs

Linear GPR Imaging Based on Electromagnetic Plane-Wave Spectra and Diffraction Tomography

DEFF Research Database (Denmark)

Meincke, Peter

2004-01-01

Two linear diffraction-tomography based inversion schemes, referred to as the Fourier transform method (FTM) and the far-field method (FFM), are derived for 3-dimensional fixed-offset GPR imaging of buried objects. The FTM and FFM are obtained by using different asymptotic approximations...

Invariant relationships deriving from classical scaling transformations

International Nuclear Information System (INIS)

Bludman, Sidney; Kennedy, Dallas C.

2011-01-01

Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are not symmetries of the equations of motion. In the case of scaling, symmetry leads to a scaling evolutionary law, a first-order equation in terms of scale invariants, linearly relating kinematic and dynamic degrees of freedom. This scaling evolutionary law appears in dynamical and in static systems. Applied to dynamical central-force systems, the scaling evolutionary equation leads to generalized virial laws, which linearly connect the kinetic and potential energies. Applied to barotropic hydrostatic spheres, the scaling evolutionary equation linearly connects the gravitational and internal energy densities. This implies well-known properties of polytropes, describing degenerate stars and chemically homogeneous nondegenerate stellar cores.

Linearization Method and Linear Complexity

Science.gov (United States)

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.

An introduction to linear ordinary differential equations using the impulsive response method and factorization

CERN Document Server

Camporesi, Roberto

2016-01-01

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

Non-Linear State Estimation Using Pre-Trained Neural Networks

DEFF Research Database (Denmark)

Bayramoglu, Enis; Andersen, Nils Axel; Ravn, Ole

2010-01-01

effecting the transformation. This function is approximated by a neural network using offline training. The training is based on monte carlo sampling. A way to obtain parametric distributions of flexible shape to be used easily with these networks is also presented. The method can also be used to improve...... other parametric methods around regions with strong non-linearities by including them inside the network....

Performance Improvement of Sensorless Vector Control for Matrix Converter Drives Using PQR Transformation

DEFF Research Database (Denmark)

Lee, Kyo-Beum; Blaabjerg, Frede

2005-01-01

This paper presents a new method to improve sensorless performance of matrix converter drives using PQR power transformation. The non-linearity of matrix converter drives such as commutation delay, turn-on and turn-off time of switching device, and on-state switching device voltage drop is modelled...... using PQR transformation and compensated using a reference current control scheme. To eliminate the input current distortion due to the input voltage unbalance, a simple method using PQR transformation is also proposed. The proposed compensation method is applied for high performance induction motor...

Linearized supergravity with a dynamical preferred frame

CERN Document Server

Marakulin, Arthur

2016-01-01

We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field. By restricting to the level of linear perturbations around Lorentz-violating vacuum and using the superfield formalism we construct the most general action invariant under the linearized supergravity transformations. We show that, unlike its non-supersymmetric counterpart, the model contains only a single free dimensionless parameter, besides the usual dimensionful gravitational coupling. This makes the model highly predictive. An analysis of the spectrum of physical excitations reveal superluminal velocity of gravitons. The latter property leads to the extension of the gravitational multiplet by additional fermonic and bosonic states with helicities $\\pm 3/2$ and $\\pm 1$. We outline the observational constraints on the model following from its low-energy phenomenology.

Higher-order schemes for the Laplace transformation method for parabolic problems

KAUST Repository

Douglas, C.; Kim, I.; Lee, H.; Sheen, D.

2011-01-01

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely

Matrix model and time-like linear dila ton matter

International Nuclear Information System (INIS)

Takayanagi, Tadashi

2004-01-01

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

On-chip power-combining techniques for watt-level linear power amplifiers in 0.18 μm CMOS

International Nuclear Information System (INIS)

Ren Zhixiong; Zhang Kefeng; Liu Lanqi; Li Cong; Chen Xiaofei; Liu Dongsheng; Liu Zhenglin; Zou Xuecheng

2015-01-01

Three linear CMOS power amplifiers (PAs) with high output power (more than watt-level output power) for high data-rate mobile applications are introduced. To realize watt-level output power, there are two 2.4 GHz PAs using an on-chip parallel combining transformer (PCT) and one 1.95 GHz PA using an on-chip series combining transformer (SCT) to combine output signals of multiple power stages. Furthermore, some linearization techniques including adaptive bias, diode linearizer, multi-gated transistors (MGTR) and the second harmonic control are applied in these PAs. Using the proposed power combiner, these three PAs are designed and fabricated in TSMC 0.18 μm RFCMOS process. According to the measurement results, the proposed two linear 2.4 GHz PAs achieve a gain of 33.2 dB and 34.3 dB, a maximum output power of 30.7 dBm and 29.4 dBm, with 29% and 31.3% of peak PAE, respectively. According to the simulation results, the presented linear 1.95 GHz PA achieves a gain of 37.5 dB, a maximum output power of 34.3 dBm with 36.3% of peak PAE. (paper)

Linear and nonlinear optical signals in probability and phase-space representations

International Nuclear Information System (INIS)

Man'ko, Margarita A

2006-01-01

Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed

Three-dimensional technology for linear morphological studies: a re-examination of cranial variation in four southern African indigenous populations.

Science.gov (United States)

Franklin, D; Freedman, L; Milne, N

2005-01-01

In order to compare linear dimensions made by traditional anthropometric techniques, and those obtained from three-dimensional coordinates, samples of four indigenous southern African populations were analysed. Linear measurements were obtained using mathematically transformed, three-dimensional landmark data on 207 male crania of Cape Nguni, Natal Nguni, Sotho and Shangaan. Univariate comparisons for accuracy of the transformed linear data were made with those in a traditional linear study by de Villiers (The Skull of the South African Negro: A Biometrical and Morphological Study. Witwatersrand University Press, Johannesburg) on similar samples and equivalent landmarks. Comparisons were not made with her Penrose (Ann Eugenics 18 (1954) 337) analysis as an apparently anomalous 'shape'-'size' statistic was found. The univariate comparisons demonstrated that accurate linear measurements could be derived from three-dimensional data, showing that it is possible to simultaneously obtain data for three-dimensional geometric 'shape' and linear interlandmark analyses. Using Penrose and canonical variates analyses of the transformed three-dimensional interlandmark measurements, similar population distances were found for the four indigenous southern African populations. The inter-population distance relationships took the form of three separated pairs of distances, with the within-pair distances very similar in size. The cranial features of the four populations were found to be overall very similar morphometrically. However the populations were each shown by CVA to have population specific features, and using discriminant analyses 50% or more of the individual crania (with the exception of the Sotho) could be referred to their correct populations.

Spatial transformation for deep penetration of one-speed neutrons in slabs

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1999-01-01

An exponential transformation has been introduced to facilitate the calculation of the neutron flux in deep penetration problems. One-speed neutrons were considered with isotropic or linearly anisotropic scattering. The S n -method was used, but some problems were solved with the integral equation method, too. Comparisons have been made with older and newer results obtained by others. It turns out that an exponential transformation may lead to more accurate results in S n -calculations but not when using the integral equation method

Moment-based method for computing the two-dimensional discrete Hartley transform

Science.gov (United States)

Dong, Zhifang; Wu, Jiasong; Shu, Huazhong

2009-10-01

In this paper, we present a fast algorithm for computing the two-dimensional (2-D) discrete Hartley transform (DHT). By using kernel transform and Taylor expansion, the 2-D DHT is approximated by a linear sum of 2-D geometric moments. This enables us to use the fast algorithms developed for computing the 2-D moments to efficiently calculate the 2-D DHT. The proposed method achieves a simple computational structure and is suitable to deal with any sequence lengths.

Dynamic load testing on the bearing capacity of prestressed tubular concrete piles in soft ground

Science.gov (United States)

Yu, Chuang; Liu, Songyu

2008-11-01

Dynamic load testing (DLT) is a high strain test method for assessing pile performance. The shaft capacity of a driven PTC (prestressed tubular concrete) pile in marine soft ground will vary with time after installation. The DLT method has been successfully transferred to the testing of prestressed pipe piles in marine soft clay of Lianyungang area in China. DLT is investigated to determine the ultimate bearing capacity of single pile at different period after pile installation. The ultimate bearing capacity of single pile was founded to increase more than 70% during the inventing 3 months, which demonstrate the time effect of rigid pile bearing capacity in marine soft ground. Furthermore, the skin friction and axial force along the pile shaft are presented as well, which present the load transfer mechanism of pipe pile in soft clay. It shows the economy and efficiency of DLT method compared to static load testing method.

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

International Nuclear Information System (INIS)

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

Weighted least squares phase unwrapping based on the wavelet transform

Science.gov (United States)

Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia

2007-01-01

The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.

An introduction to Laplace transforms and Fourier series

CERN Document Server

Dyke, Phil

2014-01-01

Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...

On analyticity of linear waves scattered by a layered medium

Science.gov (United States)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Modular transformations of conformal blocks in WZW models on Riemann surfaces of higher genus

International Nuclear Information System (INIS)

Miao Li; Ming Yu.

1989-05-01

We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilson line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g > 0 Riemann surfaces depend only on those for g ≤ 3. (author). 13 refs, 15 figs

A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula

KAUST Repository

Hale, Nicholas; Townsend, Alex

2014-01-01

-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency

Unconditional quantum cloning of coherent states with linear optics

International Nuclear Information System (INIS)

Leuchs, G.; Andersen, U.L.; Josse, V.

2005-01-01

Intense light pulses with non-classical properties are used to implement protocols for quantum communication. Most of the elements in the tool box needed to assemble the experimental set-ups for these protocols are readily described by Bogoliubov transformations corresponding to Gaussian transformations that map Gaussian states onto Gaussian states. One particularly interesting application is quantum cloning of a coherent state. A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is only limited by detection inefficiencies. Experimentally we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/3. (author)

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

NARCIS (Netherlands)

Baak, M.; Gadatsch, S.; Harrington, R.; Verkerke, W.

2015-01-01

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model׳s parameters and transformed according to a specific

Relativistic energy eigenvalues for the Dirac equation in the presence of vector and scalar potentials via the simple similarity transformation

International Nuclear Information System (INIS)

Barakat, T

2012-01-01

Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = -A/r + B 1 r and scalar S(r) = B 2 r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of the asymptotic iteration method. Moreover, within the same framework we were able to obtain the relativistic energy eigenvalues for the Dirac equation with vector Coulomb plus scalar linear, and with pure scalar linear potentials; V (r) = -A/r, S(r) = B 2 r, and V (r) = 0, S(r) = B 2 r, respectively.

Multi-band Image Registration Method Based on Fourier Transform

Institute of Scientific and Technical Information of China (English)

庹红娅; 刘允才

2004-01-01

This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.

Structural and Interfacial Properties of Hyperbranched-Linear Polymer Surfactant

OpenAIRE

Qiang, Taotao; Bu, Qiaoqiao; Huang, Zhaofeng; Wang, Xuechuan

2014-01-01

With oleic acid grafting modification, a series of hyperbranched-linear polymer surfactants (HLPS) were prepared by hydroxyl-terminated hyperbranched polymer (HBP), which was gained through a step synthesis method using trimethylolpropane and AB2 monomer. The AB2 monomers were obtained through the Michael addition reaction of methyl acrylate and diethanol amine. The structures of HLPS were characterised by Fourier transform infrared spectrophotometer and nuclear magnetic resonance (NMR), whic...

Violations of local equilibrium and linear response in classical lattice systems

International Nuclear Information System (INIS)

Aoki, Kenichiro; Kusnezov, Dimitri

2003-01-01

We quantitatively and systematically analyze how local equilibrium, and linear response in transport are violated as systems move far from equilibrium. This is done by studying heat flow in classical lattice models with and without bulk transport behavior, in 1-3 dimensions, at various temperatures. Equations of motion for the system are integrated numerically to construct the non-equilibrium steady states. Linear response and local equilibrium assumptions are seen to break down in a similar manner. We quantify the breakdown through the analysis of both microscopic and macroscopic observables and examine its transformation properties under general redefinitions of the non-equilibrium temperature

"Detachment of the carinal hook following endobronchial intubation with a double lumen tube"

Directory of Open Access Journals (Sweden)

Rocha Ana C

2011-10-01

Full Text Available Abstract Background Carinal hooks increases difficulty at endotracheal intubation. Amputation of the carinal hook during passage and malpositioning of the tube to the hook are some of the potential problems related with left-sided Carlens double lumen tube (DLT. This article reports an amputation of the hook during a difficult selective intubation and aimed at calling the attention to complications associated with DLTs and the importance of fiberoptic bronchoscopy. Case presentation A 68 year-old woman was scheduled for right-sided thoracotomy in whom blind DLT insertion was performed. Narrowed trachea causes difficulty in rotating the DLT 90° counter-clockwise. After carinal hook was noticed upon visual inspection of the DLT, fiberoptic bronchoscopy was used to remove the missing part (with the use of forceps from the right mainstem bronchus. Conclusion Insertion of DLTs with carinal hook is associated with technical problems and potentially life-threatening hazards have discouraged their use. Fiberoptic evaluation and repositioning solves most of the problems. Although amputation of the carinal hook has not been previously reported, clinicians should be alert. This case report emphasizes the utility of the fiberoptic bronchoscopy in the operating theatre for placement, positioning and inspection of the carinal hook DLT.

Torque decomposition and control in an iron core linear permanent magnet motor.

NARCIS (Netherlands)

Overboom, T.T.; Smeets, J.P.C.; Stassen, J.M.; Jansen, J.W.; Lomonova, E.

2012-01-01

Abstract—This paper concerns the decomposition and control of the torque produced by an iron core linear permanent magnet motor. The proposed method is based on the dq0-decomposition of the three-phase currents using Park’s transformation. The torque is decomposed into a reluctance component and two

Process identification method based on the Z transformation; Methode d'identification de processus par la transformation en Z

Energy Technology Data Exchange (ETDEWEB)

Zwingelstein, G [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1968-07-01

A simple method is described for identifying the transfer function of a linear retard-less system, based on the inversion of the Z transformation of the transmittance using a computer. It is assumed in this study that the signals at the entrance and at the exit of the circuit considered are of the deterministic type. The study includes: the theoretical principle of the inversion of the Z transformation, details about programming simulation, and identification of filters whose degrees vary from the first to the fifth order. (authors) [French] On decrit une methode simple d'identification de fonction de transfert d'un systeme lineaire sans retard, qui repose sur l'inversion de la transformee en Z de la transmittance a l'aide d'un calculateur. On suppose dans cette etude, que les signaux a l'entree et a la sortie du circuit considere sont de type deterministe. L'etude comporte: le principe theorique de l'inversion de la transformation en Z, les details de la programmation, la simulation et l'identification de filtres dont le degre varie du premier au cinquieme ordre. (auteurs)

Automatic Fourier transform and self-Fourier beams due to parabolic potential

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2015-12-15

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

Numerical proceessing of radioimmunoassay results using logit-log transformation method

International Nuclear Information System (INIS)

Textoris, R.

1983-01-01

The mathematical model and algorithm are described of the numerical processing of the results of a radioimmunoassay by the logit-log transformation method and by linear regression with weight factors. The limiting value of the curve for zero concentration is optimized with regard to the residual sum by the iterative method by multiple repeats of the linear regression. Typical examples are presented of the approximation of calibration curves. The method proved suitable for all hitherto used RIA sets and is well suited for small computers with internal memory of min. 8 Kbyte. (author)

Contact symmetries of general linear second-order ordinary differential equations: letter to the editor

NARCIS (Netherlands)

Martini, Ruud; Kersten, P.H.M.

1983-01-01

Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

Science.gov (United States)

Falvo, Cyril

2018-02-01

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.

Transformation condition in a Fe-based shape memory alloy under thermomechanical loadings

International Nuclear Information System (INIS)

Nishimura, F.; Watanabe, T.; Tanaka, K.

2000-01-01

The martensitic transformation start conditions in an Fe-9%Cr-5%Ni-14%Mn-6%Si polycrystalline shape memory alloy (SMA) are studied in the stress-temperature space. The martensite start condition is represented by an oval cone, which is not governed by the von Mises type condition. The subsequent martensite start condition is also investigated. The martensite start stress increases both in the initial loading and in the subsequent loading, with the progress of prior martensitic transformation. The concept of linear hardening in plasticity explains well the experimental results. On the contrary, the subsequent martensite start stress returns to the initial value with the progress of the reverse transformation. (orig.)

Basic linear algebra subprograms for FORTRAN usage

Science.gov (United States)

Lawson, C. L.; Hanson, R. J.; Kincaid, D. R.; Krogh, F. T.

1977-01-01

A package of 38 low level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of components of largest magnitude. The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are also provided in assembly language for the IBM 360/67, the CDC 6600 and CDC 7600, and the Univac 1108.

A Direct Algorithm for Pole Placement by State-derivative Feedback for Single-input Linear Systems

Directory of Open Access Journals (Sweden)

Taha H. S. Abdelaziz

2003-01-01

Full Text Available This paper deals with the direct solution of the pole placement problem for single-input linear systems using state-derivative feedback. This pole placement problem is always solvable for any controllable systems if all eigenvalues of the original system are nonzero. Then any arbitrary closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results in a formula similar to the Ackermann formula. Its derivation is based on the transformation of a linear single-input system into Frobenius canonical form by a special coordinate transformation, then solving the pole placement problem by state derivative feedback. Finally the solution is extended also for single-input time-varying control systems. The simulation results are included to show the effectiveness of the proposed approach.

A temperature and mass dependence of the linear Boltzmann collision operator from group theory point of view

International Nuclear Information System (INIS)

Saveliev, V.

1996-01-01

The Lie group of the transformations affecting the parameters of the linear Boltzmann collision operator such as temperature of background gas and ratio of masses of colliding particles and molecules is discovered. The group also describes the conservation laws for collisions and main symmetries of the collision operator. New algebraic properties of the collision operator are derived. Transformations acting on the variables and parameters and leaving the linear Boltzmann kinetic equation invariant are found. For the constant collision frequency the integral representation of solutions for nonuniform case in terms of the distribution function of particles drifting in a gas with zero temperature is deduced. The new exact relaxation solutions are obtained too. copyright 1996 American Institute of Physics

Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

Directory of Open Access Journals (Sweden)

Hassan A. Zedan

2012-01-01

Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.

Simultaneous Helmert transformations among multiple frames considering all relevant measurements

Science.gov (United States)

Chang, Guobin; Lin, Peng; Bian, Hefang; Gao, Jingxiang

2018-03-01

Helmert or similarity models are widely employed to relate different coordinate frames. It is often encountered in practice to transform coordinates from more than one old frame into a new one. One may perform separate Helmert transformations for each old frame. However, although each transformation is locally optimal, this is not globally optimal. Transformations among three frames, namely one new and two old, are studied as an example. Simultaneous Helmert transformations among all frames are also studied. Least-squares estimation of the transformation parameters and the coordinates in the new frame of all stations involved is performed. A functional model for the transformations among multiple frames is developed. A realistic stochastic model is followed, in which not only non-common stations are taken into consideration, but also errors in all measurements are addressed. An algorithm of iterative linearizations and estimations is derived in detail. The proposed method is globally optimal, and, perhaps more importantly, it produces a unified network of the new frame providing coordinate estimates for all involved stations and the associated covariance matrix, with the latter being consistent with the true errors of the former. Simulations are conducted, and the results validate the superiority of the proposed combined method over separate approaches.

Chiropractic biophysics technique: a linear algebra approach to posture in chiropractic.

Science.gov (United States)

Harrison, D D; Janik, T J; Harrison, G R; Troyanovich, S; Harrison, D E; Harrison, S O

1996-10-01

This paper discusses linear algebra as applied to human posture in chiropractic, specifically chiropractic biophysics technique (CBP). Rotations, reflections and translations are geometric functions studied in vector spaces in linear algebra. These mathematical functions are termed rigid body transformations and are applied to segmental spinal movement in the literature. Review of the literature indicates that these linear algebra concepts have been used to describe vertebral motion. However, these rigid body movers are presented here as applying to the global postural movements of the head, thoracic cage and pelvis. The unique inverse functions of rotations, reflections and translations provide a theoretical basis for making postural corrections in neutral static resting posture. Chiropractic biophysics technique (CBP) uses these concepts in examination procedures, manual spinal manipulation, instrument assisted spinal manipulation, postural exercises, extension traction and clinical outcome measures.

Preliminary Study of Linear Density, Tenacity, and Crystallinity of Cotton Fibers

Directory of Open Access Journals (Sweden)

Yongliang Liu

2014-07-01

Full Text Available An investigation of the relationships among fiber linear density, tenacity, and structure is important to help cotton breeders modify varieties for enhanced fiber end-use qualities. This study employed the Stelometer instrument, which is the traditional fiber tenacity reference method and might still be an option as a rapid screening tool because of its low cost and portable attributes. In addition to flat bundle break force and weight variables from a routine Stelometer test, the number of fibers in the bundle were counted manually and the fiber crystallinity (CIIR was characterized by the previously proposed attenuated total reflection-sampling device based Fourier transform infrared (ATR-FTIR protocol. Based on the plots of either tenacity vs. linear density or fiber count vs. mass, the fibers were subjectively divided into fine or coarse sets, respectively. Relative to the distinctive increase in fiber tenacity with linear density, there was an unclear trend between the linear density and CIIR for these fibers. Samples with similar linear density were found to increase in tenacity with fiber CIIR. In general, Advanced Fiber Information System (AFIS fineness increases with fiber linear density.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

New results on the mathematical problems in nonlinear physics; Nuevos resultados sobre problemas matematicos en fisica no-linear

Energy Technology Data Exchange (ETDEWEB)

NONE

1980-07-01

The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs.

Space–time transformation for the propagator in de Broglie–Bohm ...

Indian Academy of Sciences (India)

A linear space–time transformation proposed to calculate the propagator in the de Broglie–Bohm theory, is viewed as an expansion of the guiding wave function over the velocity space. It is shown that the quantum evolution is preserved in its semiclassical scheme through this change. The case of ...

su(1,2) Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame

International Nuclear Information System (INIS)

Jin Shuo; Xie Binghao; Yu Zhaoxian; Hou Jingmin

2008-01-01

The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure: the Hamiltonian can be written as a linear function of the su(1,2) algebra generators. Based on it, the energy eigenvalues are obtained by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics

Solar activity and transformer failures in the Greek national electric grid

Directory of Open Access Journals (Sweden)

Zois Ioannis Panayiotis

2013-11-01

Full Text Available Aims: We study both the short term and long term effects of solar activity on the large transformers (150 kV and 400 kV of the Greek national electric grid. Methods: We use data analysis and various statistical methods and models. Results: Contrary to common belief in PPC Greece, we see that there are considerable both short term (immediate and long term effects of solar activity onto large transformers in a mid-latitude country like Greece. Our results can be summarised as follows: For the short term effects: During 1989–2010 there were 43 “stormy days” (namely days with for example Ap ≥ 100 and we had 19 failures occurring during a stormy day plus or minus 3 days and 51 failures occurring during a stormy day plus or minus 7 days. All these failures can be directly related to Geomagnetically Induced Currents (GICs. Explicit cases are briefly presented. For the long term effects, again for the same period 1989–2010, we have two main results: The annual number of transformer failures seems to follow the solar activity pattern. Yet the maximum number of transformer failures occurs about half a solar cycle after the maximum of solar activity. There is statistical correlation between solar activity expressed using various newly defined long term solar activity indices and the annual number of transformer failures. These new long term solar activity indices were defined using both local (from the geomagnetic station in Greece and global (planetary averages geomagnetic data. Applying both linear and non-linear statistical regression we compute the regression equations and the corresponding coefficients of determination.

Lie algebras under constraints and nonbijective canonical transformations

International Nuclear Information System (INIS)

Kibler, M.; Winternitz, P.

1987-10-01

The concept of a Lie algebra under constraints is developed in connection with the theory of nonbijective canonical transformations. A finite dimensional vector space M, carrying a faithful linear representation of a Lie algebra L, is mapped into a lower dimensional space antiM in such a maner that a subalgebra L 0 of L is mapped into D(L 0 ) = 0. The Lie algebra L under the constraint D(L 0 ) = 0 is the largest subalgebra L 1 of L that can be represented faithfully on antiM. If L 0 is semi-simple, then L 1 is shown to be the centraliser cent L L 0 . If L is semi-simple and L 0 is an one-dimensional diagonal subalgebra of a Cartan subalgebra of L, then L 1 is shown to be the factor algebra cent L L 0 /L 0 . The latter two results are applied to nonbijective canonical transformations generalizing the Kustaanheimo-Stiefel transformation

Kinematic Analysis of Volleyball Attack in the Net Center with Various Types of Take-Off.

Science.gov (United States)

Zahálka, František; Malý, Tomáš; Malá, Lucia; Ejem, Miloslav; Zawartka, Marek

2017-09-01

The aim of the study was to describe and compare kinematics in two types of execution of attack hit, the goofy approach and regular approach. The research group consisted of players from the Czech Republic's top league (n = 12, age 28.0 ± 4.3 years, body height 196.6 ± 5.6 cm, body mass 89.7 ± 6.7 kg) divided into two groups according to the individual type of approach in the attack. Analysis of movement was performed by 3D kinematics video analysis, space coordinates were calculated by the DLT (Direct Linear Transformation) method together with interpretation software TEMA Bio 2.3 (Image Systems AB, Sweden). The players started their run-up from a distance of about 4 - 4.5 m from the net with similar maximal vertical velocity (2.91 - 2.96 m⋅s -1 ). The trajectory of players with goofy approach seemed to be convenient for the rotation of shoulders and hips in the moment of ball contact. Differences between both groups were observed. Players with a goofy approach had a longer flight phase compared to regularly approaching players.

Deconvolution When Classifying Noisy Data Involving Transformations

KAUST Repository

Carroll, Raymond

2012-09-01

In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.

Deconvolution When Classifying Noisy Data Involving Transformations.

Science.gov (United States)

Carroll, Raymond; Delaigle, Aurore; Hall, Peter

2012-09-01

In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.

Deconvolution When Classifying Noisy Data Involving Transformations

KAUST Repository

Carroll, Raymond; Delaigle, Aurore; Hall, Peter

2012-01-01

In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.

Bifurcation of rupture path by linear and cubic damping force

Science.gov (United States)

Dennis L. C., C.; Chew X., Y.; Lee Y., C.

2014-06-01

Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.

Parameter optimization in the regularized kernel minimum noise fraction transformation

DEFF Research Database (Denmark)

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....

Fourier transforms in NMR, optical, and mass spectrometry

International Nuclear Information System (INIS)

Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH

1990-01-01

This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs

Multi-port network and 3D finite-element models for accurate transformer calculations: Single-phase load-loss test

Energy Technology Data Exchange (ETDEWEB)

Escarela-Perez, R. [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo 180, Col. Reynosa, C.P. 02200, Mexico D.F. (Mexico); Kulkarni, S.V. [Electrical Engineering Department, Indian Institute of Technology, Bombay (India); Melgoza, E. [Instituto Tecnologico de Morelia, Av. Tecnologico 1500, Morelia, Mich., C.P. 58120 (Mexico)

2008-11-15

A six-port impedance network for a three-phase transformer is obtained from a 3D time-harmonic finite-element (FE) model. The network model properly captures the eddy current effects of the transformer tank and frame. All theorems and tools of passive linear networks can be used with the multi-port model to simulate several important operating conditions without resorting anymore to computationally expensive 3D FE simulations. The results of the network model are of the same quality as those produced by the FE program. Although the passive network may seem limited by the assumption of linearity, many important transformer operating conditions imply unsaturated states. Single-phase load-loss measurements are employed to demonstrate the effectiveness of the network model and to understand phenomena that could not be explained with conventional equivalent circuits. In addition, formal deduction of novel closed-form formulae is presented for the calculation of the leakage impedance measured at the high and low voltage sides of the transformer. (author)

Loci of catabolism of beta-very low density lipoprotein in vivo delineated with a residualizing label, 125I-dilactitol tyramine

International Nuclear Information System (INIS)

Daugherty, A.; Thorpe, S.R.; Lange, L.G.; Sobel, B.E.; Schonfeld, G.

1985-01-01

beta-Very low density lipoprotein (beta-VLDL) may be a major atherogenic lipoprotein, and knowledge of the sites of its catabolism should facilitate elucidation of mechanisms important in the regulation of its plasma concentrations. In this study, catabolic sites of beta-VLDL have been delineated in normolipidemic rabbits with a novel, radioiodinated, residualizing label, 125 I-dilactitol tyramine ( 125 I-DLT). Comparative studies of beta-VLDL and low density lipoprotein catabolism were performed with 125 I-DLT conjugated to each lipoprotein and with lipoproteins iodine-labeled conventionally. Conjugation did not alter size distributions or charge characteristics of lipoprotein particles. The overall processing (binding and degradation) of lipoproteins by cultured rabbit skin fibroblasts was not influenced by 125 I-DLT derivatization, suggesting that attachment of the label did not influence cell receptor-lipoprotein interactions. Furthermore, although degradation products of 125 I-lipoproteins leaked out of the cells and into the medium, the degradation products of 125 I-DLT lipoproteins were retained by the cells. The principal catabolic site of beta-VLDL in normolipidemic rabbits was found to be the liver with 54 +/- 4% of injected 125 I retained in this organ 24 h after injection of 125 I-DLT-beta-VLDL. When catabolism was normalized to tissue weight, the liver and adrenals were found to be approximately equally active in the metabolism of beta-VLDL. In agreement with results of other studies with residualizing labels, the principal organ of catabolism of 125 I-DLT-LDL in vivo was the liver. The adrenals were the most highly catabolizing organ when results were normalized for tissue weight

A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

Science.gov (United States)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Linear decomposition approach for a class of nonconvex programming problems.