STABILITY SYSTEMS VIA HURWITZ POLYNOMIALS
Directory of Open Access Journals (Sweden)
BALTAZAR AGUIRRE HERNÁNDEZ
2017-01-01
Full Text Available To analyze the stability of a linear system of differential equations ẋ = Ax we can study the location of the roots of the characteristic polynomial pA(t associated with the matrix A. We present various criteria - algebraic and geometric - that help us to determine where the roots are located without calculating them directly.
Many-body orthogonal polynomial systems
International Nuclear Information System (INIS)
Witte, N.S.
1997-03-01
The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)
Algebraic polynomial system solving and applications
Bleylevens, I.W.M.
2010-01-01
The problem of computing the solutions of a system of multivariate polynomial equations can be approached by the Stetter-Möller matrix method which casts the problem into a large eigenvalue problem. This Stetter-Möller matrix method forms the starting point for the development of computational
Automatic Control Systems Modeling by Volterra Polynomials
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S. V. Solodusha
2012-01-01
Full Text Available The problem of the existence of the solutions of polynomial Volterra integral equations of the first kind of the second degree is considered. An algorithm of the numerical solution of one class of Volterra nonlinear systems of the first kind is developed. Numerical results for test examples are presented.
Algebraic limit cycles in polynomial systems of differential equations
International Nuclear Information System (INIS)
Llibre, Jaume; Zhao Yulin
2007-01-01
Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4
Holman, Matthew J.; Lindstrom, David (Technical Monitor)
2005-01-01
Our ongoing research program combines extensive deep and wide-field observations using a variety of observational platforms with numerical studies of the dynamics of small bodies in the outer solar system in order to advance the main scientific goals of the community studying the Kuiper belt and the outer solar system. These include: (1) determining the relative populations of the known classes of KBOs as well as other possible classes; ( 2 ) determining the size distributions or luminosity function of the individual populations or the Kuiper belt as a whole; (3) determining the inclinations distributions of these populations; (4) establishing the radial extent of the Kuiper belt; ( 5 ) measuring and relating the physical properties of different types of KBOs to those of other solar system bodies; and, (6) completing our systematic inventory of the satellites of the outer planets.
Discrete-time state estimation for stochastic polynomial systems over polynomial observations
Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.
2018-07-01
This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.
Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach
Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer
2018-02-01
This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.
Karlita, Tita; Yuniarno, Eko Mulyanto; Purnama, I. Ketut Eddy; Purnomo, Mauridhi Hery
2017-06-01
Analyzing ultrasound (US) images to get the shapes and structures of particular anatomical regions is an interesting field of study since US imaging is a non-invasive method to capture internal structures of a human body. However, bone segmentation of US images is still challenging because it is strongly influenced by speckle noises and it has poor image quality. This paper proposes a combination of local phase symmetry and quadratic polynomial fitting methods to extract bone outer contour (BOC) from two dimensional (2D) B-modes US image as initial steps of three-dimensional (3D) bone surface reconstruction. By using local phase symmetry, the bone is initially extracted from US images. BOC is then extracted by scanning one pixel on the bone boundary in each column of the US images using first phase features searching method. Quadratic polynomial fitting is utilized to refine and estimate the pixel location that fails to be detected during the extraction process. Hole filling method is then applied by utilize the polynomial coefficients to fill the gaps with new pixel. The proposed method is able to estimate the new pixel position and ensures smoothness and continuity of the contour path. Evaluations are done using cow and goat bones by comparing the resulted BOCs with the contours produced by manual segmentation and contours produced by canny edge detection. The evaluation shows that our proposed methods produces an excellent result with average MSE before and after hole filling at the value of 0.65.
Polynomial stabilization of some dissipative hyperbolic systems
Czech Academy of Sciences Publication Activity Database
Ammari, K.; Feireisl, Eduard; Nicaise, S.
2014-01-01
Roč. 34, č. 11 (2014), s. 4371-4388 ISSN 1078-0947 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : exponential stability * polynomial stability * observability inequality Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9924
Solving polynomial systems using no-root elimination blending schemes
Barton, Michael
2011-01-01
Searching for the roots of (piecewise) polynomial systems of equations is a crucial problem in computer-aided design (CAD), and an efficient solution is in strong demand. Subdivision solvers are frequently used to achieve this goal; however
Ratio asymptotics of Hermite-Pade polynomials for Nikishin systems
International Nuclear Information System (INIS)
Aptekarev, A I; Lopez, Guillermo L; Rocha, I A
2005-01-01
The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.
Polynomial algebra of discrete models in systems biology.
Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2010-07-01
An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.
Skew-orthogonal polynomials, differential systems and random matrix theory
International Nuclear Information System (INIS)
Ghosh, S.
2007-01-01
We study skew-orthogonal polynomials with respect to the weight function exp[-2V (x)], with V (x) = Σ K=1 2d (u K /K)x K , u 2d > 0, d > 0. A finite subsequence of such skew-orthogonal polynomials arising in the study of Orthogonal and Symplectic ensembles of random matrices, satisfy a system of differential-difference-deformation equation. The vectors formed by such subsequence has the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions. (author)
Polynomials associated with equilibria of affine Toda-Sutherland systems
International Nuclear Information System (INIS)
Odake, S; Sasaki, R
2004-01-01
An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle dynamics based on an affine simple root system. It is a 'cross' between two well-known integrable multi-particle dynamics, an affine Toda molecule (exponential potential, periodic nearest-neighbour interaction) and a Sutherland system (inverse sine-square interaction). Polynomials describing the equilibrium positions of affine Toda-Sutherland systems are determined for all affine simple root systems
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Global structure of a polynomial autonomous system on the plane
International Nuclear Information System (INIS)
Nguyen Van Chau.
1991-10-01
This note is to study the global behaviour of a polynomial autonomous system on the plane with divergence non-positive outside a bounded set. It is shown that in some certain conditions the global structure of such system can be simple. The main result here can be seen as an improvement of the result of Olech and Meister concerning with the global asymptotical stable conjecture of Markur and Yamable and the Jacobian Conjecture. (author). 13 refs
Freud, Géza
1971-01-01
Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as referenc
Cryovolcanism in the outer solar system
Geissler, Paul E.
2015-01-01
Cryovolcanism is defined as the extrusion of liquids and vapors of materials that would be frozen solid at the planetary surface temperatures of the icy bodies of the outer solar system. Active cryovolcanism is now known to occur on Saturn's moon Enceladus and on Neptune's moon Triton and is suspected on Jupiter's moon Europa, while evidence for past cryovolcanic activity is widespread throughout the outer solar system. This chapter examines the mechanisms and manifestations of cryovolcanism, beginning with a review of the materials that make up these unusual ‘‘magmas’’ and the means by which they might erupt and concluding with a volcanologist's tour of the farthest reaches of the solar system.
Poincare map for some polynomial systems of differential equations
International Nuclear Information System (INIS)
Varin, V P
2004-01-01
One approach to the classical problem of distinguishing between a centre and a focus for a system of differential equations with polynomial right-hand sides in the plane is discussed. For a broad class of such systems necessary and sufficient conditions for a centre are expressed in terms of equations in variations of higher order. By contrast with the existing methods of investigation, attention is concentrated on the explicit calculation of the asymptotic behaviour of the Poincare map rather than on finding sufficient centre conditions as such; this also enables one to study bifurcations of birth of arbitrarily strongly degenerate cycles.
Application of ANNs approach for solving fully fuzzy polynomials system
Directory of Open Access Journals (Sweden)
R. Novin
2017-11-01
Full Text Available In processing indecisive or unclear information, the advantages of fuzzy logic and neurocomputing disciplines should be taken into account and combined by fuzzy neural networks. The current research intends to present a fuzzy modeling method using multi-layer fuzzy neural networks for solving a fully fuzzy polynomials system. To clarify the point, it is necessary to inform that a supervised gradient descent-based learning law is employed. The feasibility of the method is examined using computer simulations on a numerical example. The experimental results obtained from the investigation of the proposed method are valid and delivers very good approximation results.
Solving polynomial systems using no-root elimination blending schemes
Barton, Michael
2011-12-01
Searching for the roots of (piecewise) polynomial systems of equations is a crucial problem in computer-aided design (CAD), and an efficient solution is in strong demand. Subdivision solvers are frequently used to achieve this goal; however, the subdivision process is expensive, and a vast number of subdivisions is to be expected, especially for higher-dimensional systems. Two blending schemes that efficiently reveal domains that cannot contribute by any root, and therefore significantly reduce the number of subdivisions, are proposed. Using a simple linear blend of functions of the given polynomial system, a function is sought after to be no-root contributing, with all control points of its BernsteinBézier representation of the same sign. If such a function exists, the domain is purged away from the subdivision process. The applicability is demonstrated on several CAD benchmark problems, namely surfacesurfacesurface intersection (SSSI) and surfacecurve intersection (SCI) problems, computation of the Hausdorff distance of two planar curves, or some kinematic-inspired tasks. © 2011 Elsevier Ltd. All rights reserved.
Dark matter in the outer solar system
Owen, T.; Cruikshank, D.; De Bergh, C.; Geballe, T.
1994-01-01
There are now a large number of small bodies in the outer solar system that are known to be covered with dark material. Attempts to identify that material have been thwarted by the absence of discrete absorption features in the reflection spectra of these planetesimals. An absorption at 2.2 micrometers that appeared to be present in several objects has not been confirmed by new observations. Three absorptions in the spectrum of the unusually red planetesimal 5145 Pholus are well-established, but their identity remains a mystery.
Liu, Chuang; Lam, H. K.
2015-01-01
In this paper, we propose a polynomial fuzzy observer controller for nonlinear systems, where the design is achieved through the stability analysis of polynomial-fuzzy-model-based (PFMB) observer-control system. The polynomial fuzzy observer estimates the system states using estimated premise variables. The estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model. The system stability of the P...
H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach
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Bomo W. Sanjaya
2014-07-01
Full Text Available This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simulation study is presented to show the effectiveness of the SOS-based H∞ control designfor nonlinear polynomial fuzzy systems.
Hamed Kharrati; Sohrab Khanmohammadi; Witold Pedrycz; Ghasem Alizadeh
2012-01-01
This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy m...
H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach
Bomo W. Sanjaya; Bambang Riyanto Trilaksono; Arief Syaichu-Rohman
2014-01-01
This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simul...
Sum-of-squares based observer design for polynomial systems with a known fixed time delay
Czech Academy of Sciences Publication Activity Database
Rehák, Branislav
2015-01-01
Roč. 51, č. 5 (2015), s. 858-873 ISSN 0023-5954 R&D Projects: GA ČR GA13-02149S Institutional support: RVO:67985556 Keywords : sum-of-squares polynomial * observer * polynomial system Subject RIV: BC - Control Systems Theory Impact factor: 0.628, year: 2015 http://www.kybernetika.cz/content/2015/5/856
International Nuclear Information System (INIS)
van Diejen, J.F.
1997-01-01
Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl. (orig.)
Li, Xiaomiao; Lam, Hak Keung; Song, Ge; Liu, Fucai
2017-01-01
This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based ({PFMB}) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares (SOS)-based stability ana...
International Nuclear Information System (INIS)
Aguirre-Hernández, B.; Campos-Cantón, E.; López-Renteria, J.A.; Díaz González, E.C.
2015-01-01
In this paper, we consider characteristic polynomials of n-dimensional systems that determine a segment of polynomials. One parameter is used to characterize this segment of polynomials in order to determine the maximal interval of dissipativity and unstability. Then we apply this result to the generation of a family of attractors based on a class of unstable dissipative systems (UDS) of type affine linear systems. This class of systems is comprised of switched linear systems yielding strange attractors. A family of these chaotic switched systems is determined by the maximal interval of perturbation of the matrix that governs the dynamics for still having scroll attractors
Directory of Open Access Journals (Sweden)
Hamed Kharrati
2012-01-01
Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.
Planar real polynomial differential systems of degree n > 3 having a weak focus of high order
International Nuclear Information System (INIS)
Llibre, J.; Rabanal, R.
2008-06-01
We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of the form linear plus a nonlinear homogeneous part of degree n having a weak focus of order n 2 -1 (respectively (n 2 -1)/2 ) at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n. (author)
Algebraic invariant curves of plane polynomial differential systems
Tsygvintsev, Alexei
2001-01-01
We consider a plane polynomial vector field P(x,y) dx + Q(x,y) dy of degree m>1. With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential ω = dx/P = dy/Q. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate has already been found by Cerveau and Lins Neto in a different way.
Recurrence approach and higher order polynomial algebras for superintegrable monopole systems
Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong
2018-05-01
We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.
Developments for the outer tracking system of the LHCb experiment
Bachmann, S; Haas, T; Uwer, U; Walter, M; Wiedner, D
2004-01-01
The outer tracking system of the LHCb experiment is discussed. The outer tracking system (OT) is made of three stations and every station is made up of four detecting planes with a double layer of straw tubes. The straw tubes are mounted in detector module boxes made up of sandwich panels. The use of a counting gas with a high drift velocity is suggested to cope with high bunch crossing rate at the LHCb experiment. (Edited abstract) 3 Refs.
Solar system astrophysics planetary atmospheres and the outer solar system
Milone, Eugene F
2014-01-01
The second edition of Solar System Astrophysics: Planetary Atmospheres and the Outer Solar System provides a timely update of our knowledge of planetary atmospheres and the bodies of the outer solar system and their analogs in other planetary systems. This volume begins with an expanded treatment of the physics, chemistry, and meteorology of the atmospheres of the Earth, Venus, and Mars, moving on to their magnetospheres and then to a full discussion of the gas and ice giants and their properties. From here, attention switches to the small bodies of the solar system, beginning with the natural satellites. Then comets, meteors, meteorites, and asteroids are discussed in order, and the volume concludes with the origin and evolution of our solar system. Finally, a fully revised section on extrasolar planetary systems puts the development of our system in a wider and increasingly well understood galactic context. All of the material is presented within a framework of historical importance. This book and its sist...
A general U-block model-based design procedure for nonlinear polynomial control systems
Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua
2016-10-01
The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.
Solar system astrophysics planetary atmospheres and the outer solar system
Milone, Eugene F
2008-01-01
Solar System Astrophysics opens with coverage of the atmospheres, ionospheres and magnetospheres of the Earth, Venus and Mars and the magnetosphere of Mercury. The book then provides an introduction to meteorology and treating the physics and chemistry of these areas in considerable detail. What follows are the structure, composition, particle environments, satellites, and rings of Jupiter, Saturn, Uranus and Neptune, making abundant use of results from space probes. Solar System Astrophysics follows the history, orbits, structure, origin and demise of comets and the physics of meteors and provides a thorough treatment of meteorites, the asteroids and, in the outer solar system, the Kuiper Belt objects. The methods and results of extrasolar planet searches, the distinctions between stars, brown dwarfs, and planets, and the origins of planetary systems are examined. Historical introductions precede the development and discussion in most chapters. A series of challenges, useful as homework assignments or as foc...
Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems
Directory of Open Access Journals (Sweden)
Xiaoxing Chen
2017-01-01
Full Text Available Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS- based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.
Colors of Outer Solar System Objects Measured with VATT
Romanishin, William; Tegler, S. C.; Consolmagno, G. J.
2010-10-01
Over the past 7 years, we have measured optical B-V and V-R colors for about 40 minor outer solar system objects using the 1.8-m Vatican Advanced Technology Telescope (VATT) located on Mt. Graham in southeast Arizona. We will present these colors and use them to update the discussion of colors of minor bodies in the outer solar system. We gratefully acknowledge funding from the NASA Planetary Astronomy Program to Northern Arizona University and the U. of Oklahoma which helped support this work.
Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
Directory of Open Access Journals (Sweden)
Ahmed Bendjeddou
2017-03-01
Full Text Available In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomial differential systems.
Testing reachability and stabilizability of systems over polynomial rings using Gröbner bases
Habets, L.C.G.J.M.
1993-01-01
Conditions for the reachability and stabilizability of systems over polynomial rings are well-known in the literature. For a system $ \\Sigma = (A,B)$ they can be expressed as right-invertibility cconditions on the matrix $(zI - A \\mid B)$. Therefore there is quite a strong algebraic relationship
Energy Technology Data Exchange (ETDEWEB)
Myers, N.J. [Univ. of Durham (United Kingdom)
1994-12-31
The author gives a hybrid method for the iterative solution of linear systems of equations Ax = b, where the matrix (A) is nonsingular, sparse and nonsymmetric. As in a method developed by Starke and Varga the method begins with a number of steps of the Arnoldi method to produce some information on the location of the spectrum of A. This method then switches to an iterative method based on the Faber polynomials for an annular sector placed around these eigenvalue estimates. The Faber polynomials for an annular sector are used because, firstly an annular sector can easily be placed around any eigenvalue estimates bounded away from zero, and secondly the Faber polynomials are known analytically for an annular sector. Finally the author gives three numerical examples, two of which allow comparison with Starke and Varga`s results. The third is an example of a matrix for which many iterative methods would fall, but this method converges.
Multimission nuclear electric propulsion system for outer planet exploration missions
International Nuclear Information System (INIS)
Mondt, J.F.
1981-01-01
A 100-kW reactor power system with a specific mass of 15 to 30 kg/kW/sub e/ and an electric thrust system with a specific mass of 5 to 10 kg/kW/sub e/ can be combined into a nuclear electric propulsion system. The system can be used for outer planet missions as well as earth orbital transfer vehicle missions. 5 refs
Ethane Ices in the Outer Solar System: Spectroscopy and Chemistry
Hudson, R. L.; Moore, M. H.; Raines, L. L.
2009-01-01
We report recent experiments on ethane ices made at temperatures applicable to the outer Solar System. New near- and mid-infrared data for crystalline and amorphous ethane, including new spectra for a seldom-studied solid phase that exists at 35-55 K, are presented along with radiation-chemical experiments showing the formation of more-complex hydrocarbons
General Reducibility and Solvability of Polynomial Equations ...
African Journals Online (AJOL)
General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...
A reachability test for systems over polynomial rings using Gröbner bases
Habets, L.C.G.J.M.
1992-01-01
Conditions for the reachability of a system over a polynomial ring are well known in the literature. However, the verification of these conditions remained a difficult problem in general. Application of the Gröbner Basis method from constructive commutative algebra makes it possible to carry out
Atmospheric Mining in the Outer Solar System: Outer Planet Orbital Transfer and Lander Analyses
Palaszewski, Bryan
2016-01-01
Atmospheric mining in the outer solar system has been investigated as a means of fuel production for high energy propulsion and power. Fusion fuels such as Helium 3 (3He) and deuterium can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. Helium 3 and deuterium were the primary gases of interest with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses were undertaken to investigate resource capturing aspects of atmospheric mining in the outer solar system. This included the gas capturing rate, storage options, and different methods of direct use of the captured gases. While capturing 3He, large amounts of hydrogen and 4He are produced. Analyses of orbital transfer vehicles (OTVs), landers, and the issues with in-situ resource utilization (ISRU) mining factories are included. Preliminary observations are presented on near-optimal selections of moon base orbital locations, OTV power levels, and OTV and lander rendezvous points. For analyses of round trip OTV flights from Uranus to Miranda or Titania, a 10- Megawatt electric (MWe) OTV power level and a 200 metricton (MT) lander payload were selected based on a relative short OTV trip time and minimization of the number of lander flights. A similar optimum power level is suggested for OTVs flying from low orbit around Neptune to Thalassa or Triton. Several moon base sites at Uranus and Neptune and the OTV requirements to support them are also addressed.
Control design and robustness analysis of a ball and plate system by using polynomial chaos
Energy Technology Data Exchange (ETDEWEB)
Colón, Diego [University of São Paulo, Polytechnic School, LAC -PTC, São Paulo (Brazil); Balthazar, José M. [São Paulo State University - Rio Claro Campus, Rio Claro (Brazil); Reis, Célia A. dos [São Paulo State University - Bauru Campus, Bauru (Brazil); Bueno, Átila M.; Diniz, Ivando S. [São Paulo State University - Sorocaba Campus, Sorocaba (Brazil); Rosa, Suelia de S. R. F. [University of Brasilia, Brasilia (Brazil)
2014-12-10
In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.
Tsai, Shun Hung; Chen, Yu-An; Chen, Yu-Wen; Lo, Ji-Chang; Lam, Hak-Keung
2017-01-01
A novel stabilization problem for T-S polynomial fuzzy system with time-delay is investigated in this paper. Firstly, a polynomial fuzzy controller for T-S polynomial fuzzy system with time-delay is proposed. In addition, based on polynomial Lyapunov-Krasovskii function and the developed polynomial slack variable matrices, a novel stabilization condition for T-S polynomial fuzzy system with time-delay is presented in terms of sum-of-square (SOS) form. Lastly, nonlinear system with time-delay ...
Polynomial f (R ) Palatini cosmology: Dynamical system approach
Szydłowski, Marek; Stachowski, Aleksander
2018-05-01
We investigate cosmological dynamics based on f (R ) gravity in the Palatini formulation. In this study, we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piecewise smooth dynamical system. This system is reduced to a 2D dynamical system of the Newtonian type. We demonstrate how the trajectories can be sewn to guarantee C0 extendibility of the metric similarly as "Milne-like" Friedmann-Lemaître-Robertson-Walker spacetimes are C0-extendible. We point out that importance of the dynamical system of the Newtonian type with nonsmooth right-hand sides in the context of Palatini cosmology. In this framework, we can investigate singularities which appear in the past and future of the cosmic evolution. We consider cosmological systems in both Einstein and Jordan frames. We show that at each frame the topological structures of phase space are different.
Localization of periodic orbits of polynomial systems by ellipsoidal estimates
International Nuclear Information System (INIS)
Starkov, Konstantin E.; Krishchenko, Alexander P.
2005-01-01
In this paper we study the localization problem of periodic orbits of multidimensional continuous-time systems in the global setting. Our results are based on the solution of the conditional extremum problem and using sign-definite quadratic and quartic forms. As examples, the Rikitake system and the Lamb's equations for a three-mode operating cavity in a laser are considered
Distributed stabilisation of spatially invariant systems: positive polynomial approach
Czech Academy of Sciences Publication Activity Database
Augusta, Petr; Hurák, Z.
2013-01-01
Roč. 24, Č. 1 (2013), s. 3-21 ISSN 1573-0824 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Multidimensional systems * Algebraic approach * Control design * Positiveness Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2013/TR/augusta-0382623.pdf
Localization of periodic orbits of polynomial systems by ellipsoidal estimates
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Avenue del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)]. E-mail: konst@citedi.mx; Krishchenko, Alexander P. [Bauman Moscow State Technical University, 2nd Baumanskaya Street, 5, Moscow 105005 (Russian Federation)]. E-mail: apkri@999.ru
2005-02-01
In this paper we study the localization problem of periodic orbits of multidimensional continuous-time systems in the global setting. Our results are based on the solution of the conditional extremum problem and using sign-definite quadratic and quartic forms. As examples, the Rikitake system and the Lamb's equations for a three-mode operating cavity in a laser are considered.
Demina, Maria V.
2018-05-01
The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing-van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing-van der Pol system are constructed.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Energy Technology Data Exchange (ETDEWEB)
Szederkenyi, Gabor; Hangos, Katalin M
2004-04-26
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Szederkényi, Gábor; Hangos, Katalin M.
2004-04-01
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
International Nuclear Information System (INIS)
Szederkenyi, Gabor; Hangos, Katalin M.
2004-01-01
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities
Fast exhaustive search for polynomial systems in F2
Bouillaguet, C.; Chen, H.-C.; Cheng, C.M.; Chou, T.; Niederhagen, R.F.; Shamir, A.; Yang, B.Y.
2010-01-01
Abstract. We analyze how fast we can solve general systems of multivariate equations of various low degrees over F2; this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive-search technique, our
Fast exhaustive search for polynomial systems in F2
Bouillaguet, C.; Chen, H.-C.; Cheng, C.M.; Chou, T.; Niederhagen, R.F.; Shamir, A.; Yang, B.Y.; Mangard, S.; Standaert, F.X.
2010-01-01
Abstract: We analyze how fast we can solve general systems of multivariate equations of various low degrees over $F_2$; this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive search technique, our
Living among giants exploring and settling the outer solar system
Carroll, Michael
2015-01-01
The outer Solar System is rich in resources and may be the best region in which to search for life beyond Earth. In fact, it may ultimately be the best place for Earthlings to set up permanent abodes. This book surveys the feasibility of that prospect, covering the fascinating history of exploration that kicks off our adventure into the outer Solar System. Although other books provide surveys of the outer planets, Carroll approaches it from the perspective of potential future human exploration, exploitation and settlement, using insights from today’s leading scientists in the field. These experts take us to targets such as the moons Titan, Triton, Enceladus, Iapetus and Europa, and within the atmospheres of the gas and ice giants. In these pages you will experience the thrill of discovery awaiting those who journey through the giant worlds and their moons. All the latest research is included, as are numerous illustrations, among them original paintings by the author, a renowned prize-winning space art...
Water and Volatiles in the Outer Solar System
Grasset, O.; Castillo-Rogez, J.; Guillot, T.; Fletcher, L. N.; Tosi, F.
2017-10-01
Space exploration and ground-based observations have provided outstanding evidence of the diversity and the complexity of the outer solar system. This work presents our current understanding of the nature and distribution of water and water-rich materials from the water snow line to the Kuiper Belt. This synthesis is timely, since a thorough exploration of at least one object in each region of the outer solar system has now been achieved. Next steps, starting with the Juno mission now in orbit around Jupiter, will be more focused on understanding the processes at work than on describing the general characteristics of each giant planet systems. This review is organized in three parts. First, the nature and the distribution of water and volatiles in giant and intermediary planets are described from their inner core to their outer envelopes. A special focus is given to Jupiter and Saturn, which are much better understood than the two ice giants (Uranus and Neptune) thanks to the Galileo and Cassini missions. Second, the icy moons will be discussed. Space missions and ground-based observations have revealed the variety of icy surfaces in the outer system. While Europa, Enceladus, and maybe Titan present past or even active tectonic and volcanic activities, many other moons have been dead worlds for more than 3 billion years. Ice compositions found at these bodies are also complex and it is now commonly admitted that icy surfaces are never composed of pure ices. A detailed review of the distribution of non-ice materials on the surfaces and in the tenuous atmospheres of the moons is proposed, followed by a more focused discussion on the nature and the characteristics of the liquid layers trapped below the cold icy crusts that have been suggested in the icy Galilean moons, and in Enceladus, Dione, and Titan at Saturn. Finally, the recent observations collected by Dawn at Ceres and New Horizons at Pluto, as well as the state of knowledge of other transneptunian objects
Energy Technology Data Exchange (ETDEWEB)
Li, Jun; Jiang, Bin; Guo, Hua, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States)
2013-11-28
A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.
Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems.
Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng
2011-10-01
This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.
Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong
2018-04-01
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.
Directory of Open Access Journals (Sweden)
Wang Mingjie
2017-01-01
Full Text Available A framework of non-intrusive polynomial chaos expansion method (PC was proposed to investigate the statistic characteristics of the response of structural-acoustic system containing random uncertainty. The PC method does not need to reformulate model equations, and the statistics of the response can be evaluated directly. The results show that compared to the direct Monte Carlo method (MCM based on the original numerical model, the PC method is effective and more efficient.
Efficient linear precoding for massive MIMO systems using truncated polynomial expansion
Müller, Axel
2014-06-01
Massive multiple-input multiple-output (MIMO) techniques have been proposed as a solution to satisfy many requirements of next generation cellular systems. One downside of massive MIMO is the increased complexity of computing the precoding, especially since the relatively \\'antenna-efficient\\' regularized zero-forcing (RZF) is preferred to simple maximum ratio transmission. We develop in this paper a new class of precoders for single-cell massive MIMO systems. It is based on truncated polynomial expansion (TPE) and mimics the advantages of RZF, while offering reduced and scalable computational complexity that can be implemented in a convenient parallel fashion. Using random matrix theory we provide a closed-form expression of the signal-to-interference-and-noise ratio under TPE precoding and compare it to previous works on RZF. Furthermore, the sum rate maximizing polynomial coefficients in TPE precoding are calculated. By simulation, we find that to maintain a fixed peruser rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and signal-to-noise ratio. © 2014 IEEE.
Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach.
Tanaka, Kazuo; Ohtake, Hiroshi; Wang, Hua O
2009-04-01
This paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi-Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach.
A Fast lattice-based polynomial digital signature system for m-commerce
Wei, Xinzhou; Leung, Lin; Anshel, Michael
2003-01-01
The privacy and data integrity are not guaranteed in current wireless communications due to the security hole inside the Wireless Application Protocol (WAP) version 1.2 gateway. One of the remedies is to provide an end-to-end security in m-commerce by applying application level security on top of current WAP1.2. The traditional security technologies like RSA and ECC applied on enterprise's server are not practical for wireless devices because wireless devices have relatively weak computation power and limited memory compared with server. In this paper, we developed a lattice based polynomial digital signature system based on NTRU's Polynomial Authentication and Signature Scheme (PASS), which enabled the feasibility of applying high-level security on both server and wireless device sides.
Hybrid rocket propulsion systems for outer planet exploration missions
Jens, Elizabeth T.; Cantwell, Brian J.; Hubbard, G. Scott
2016-11-01
Outer planet exploration missions require significant propulsive capability, particularly to achieve orbit insertion. Missions to explore the moons of outer planets place even more demanding requirements on propulsion systems, since they involve multiple large ΔV maneuvers. Hybrid rockets present a favorable alternative to conventional propulsion systems for many of these missions. They typically enjoy higher specific impulse than solids, can be throttled, stopped/restarted, and have more flexibility in their packaging configuration. Hybrids are more compact and easier to throttle than liquids and have similar performance levels. In order to investigate the suitability of these propulsion systems for exploration missions, this paper presents novel hybrid motor designs for two interplanetary missions. Hybrid propulsion systems for missions to Europa and Uranus are presented and compared to conventional in-space propulsion systems. The hybrid motor design for each of these missions is optimized across a range of parameters, including propellant selection, O/F ratio, nozzle area ratio, and chamber pressure. Details of the design process are described in order to provide guidance for researchers wishing to evaluate hybrid rocket motor designs for other missions and applications.
Colours of the Outer Solar System Origins Survey: An Update
Schwamb, Megan E.; Fraser, Wesley C.; Pike, Rosemary E.; Bannister, Michele T.; Marsset, Michaël; Kavelaars, J. J.; Benecchi, Susan; Delsanti, Audrey C.; Lehner, Matthew J.; Wang, Shiang-Yu; Thirouin, Audrey; Nesvorný, David
2018-01-01
The vast majority of the known dwarf-planet sized bodies are bright enough to be studied through optical and infrared spectroscopy. As a result, we have an understanding of the surface properties for the largest Kuiper belt objects (KBOs) which retain their primordial inventory of volatile ices. For the typically smaller > 22 mag KBO, we must rely instead on what colors reveal by proxy; yet this picture remains incomplete. Most KBO physical property studies examine the hodgepodge set of objects discovered by various surveys with different and varying detection biases that make it difficult if not impossible to reliably estimate the sizes of the different surface color groupings (compositional classes) residing in the modern-day Kuiper belt.The Colours of the Outer Solar System Origins Survey (Col-OSSOS) probes the surface properties within the Kuiper belt primarily through near simultaneous g,r and J colors with the Gemini North Telescope and u-band with Canada-France-Hawaii Telescope. The project aims to target ~100 KBOs brighter than 23.6 r‧ mag found by the Outer Solar System Origins Survey (OSSOS), a survey with a well-measured detection efficiency. Thus, Col-OSSOS provides the first brightness-complete, compositional-dynamical map of the Outer Solar System, probing in a new light the radial color distribution in the primordial planetesimal disk from which KBOs originated. We will provide an update on the current status of the program highlighting results from the first two years of the survey; including size estimates of the two color KBO subgroups (the red and neutral surfaces) within the dynamically excited Kuiper belt and implications for the early planetesimal disk composition based on neutral-colored binaries found in the cold classical Kuiper belt.
The straw tube technology for the LHCb outer tracking system
Bachmann, S; Bagaturia, I; Deppe, H; Eisele, F; Haas, T; Hajduk, L; Langenegger, U; Michalowski, J; Nawrot, A; Polok, G; Pellegrino, A; Schuijlenburg, H; Schwierz, R; Sluijk, T; Spelt, J
2004-01-01
For the outer tracking system of the LHCb spectrometer 53.760 straws of 2.5 m length will be used. They are arranged in detector modules of 5 m length and 0.34 m width. The envisaged spatial resolution over the entire active area is 200$mu$m resulting in stringent requirements on the accuracy for the module construction. In this paper we discuss the optimisation of the straws, design and construction of detector modules. The long term operation properties of straws in two different counting g...
Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2008-01-01
In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set
Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)], E-mail: konst@citedi.mx
2008-10-06
In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set.
Fields and plasmas in the outer solar system. [Review
Energy Technology Data Exchange (ETDEWEB)
Smith, E J [Jet Propulsion Lab., Pasadena, CA (USA); Wolfe, J H [National Aeronautics and Space Administration, Moffett Field, CA (USA). Ames Research Center
1979-04-01
The most significant information about fields and plasmas in the outer solar system, based on observations by Pioneer 10 and 11 investigations, is reviewed. The characteristic evolution of solar wind streams beyond 1 AU has been observed. The region within which the velocity increases continuously near 1 AU is replaced at larger distances by a thick interaction region with abrupt jumps in the solar wind speed at the leading and trailing edges. These abrupt increases, accompanied by corresponding jumps in the field magnitude and in the solar wind density and temperature, consist typically of a forward and a reverse shock. The existance of two distinct corotating regions, separated by sharp boundaries, is a characteristic feature of the interplanetary medium in the outer solar system. Within the interaction regions, compression effects are dominant and the field strength, plasma density, plasma temperature and the level of fluctuations are enhanced. Within the intervening quiet regions, rarefaction effects dominante and the field magnitude, solar wind density and fluctuation level are very low. These changes in the structure of interplanetary space have significant consequences for the many energetic particles propagating through the medium.
Gassara, H.; El Hajjaji, A.; Chaabane, M.
2017-07-01
This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.
Dynamical limits on dark mass in the outer solar system
International Nuclear Information System (INIS)
Hogg, D.W.; Quinlan, G.D.; Tremaine, S.
1991-01-01
Simplified model solar systems with known observational errors are considered in conducting a dynamical search for dark mass and its minimum detectable amount, and in determining the significance of observed anomalies. The numerical analysis of the dynamical influence of dark mass on the orbits of outer planets and comets is presented in detail. Most conclusions presented are based on observations of the four giant planets where the observational errors in latitude and longitude are independent Gaussian variables with a standard deviation. Neptune's long orbital period cannot be predicted by modern ephemerides, and no evidence of dark mass is found in considering this planet. Studying the improvement in fit when observations are fitted to models that consider dark mass is found to be an efficient way to detect dark mass. Planet X must have a mass of more than about 10 times the minimum detectable mass to locate the hypothetical planet. It is suggested that the IRAS survey would have already located the Planet X if it is so massive and close that it dynamically influences the outer planets. Orbital residuals from comets are found to be more effective than those from planets in detecting the Kuiper belt. 35 refs
Robust ∞ Filtering of 2D Roesser Discrete Systems: A Polynomial Approach
Directory of Open Access Journals (Sweden)
Chakir El-Kasri
2012-01-01
procedure for generating conditions for the existence of a 2D discrete filter such that, for all admissible uncertainties, the error system is asymptotically stable, and the ∞ norm of the transfer function from the noise signal to the estimation error is below a prespecified level. These conditions are expressed as parameter-dependent linear matrix inequalities. Using homogeneous polynomially parameter-dependent filters of arbitrary degree on the uncertain parameters, the proposed method extends previous results in the quadratic framework and the linearly parameter-dependent framework, thus reducing its conservatism. Performance of the proposed method, in comparison with that of existing methods, is illustrated by two examples.
Nonnegativity of uncertain polynomials
Directory of Open Access Journals (Sweden)
iljak Dragoslav D.
1998-01-01
Full Text Available The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.
Miller, W., Jr.; Li, Q.
2015-04-01
The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.
International Nuclear Information System (INIS)
Miller, W Jr; Li, Q
2015-01-01
The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L 2 of H in terms of an eigenbasis of another symmetry operator L 1 , but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions. (paper)
Wang, S.; Huang, G. H.; Baetz, B. W.; Huang, W.
2015-11-01
This paper presents a polynomial chaos ensemble hydrologic prediction system (PCEHPS) for an efficient and robust uncertainty assessment of model parameters and predictions, in which possibilistic reasoning is infused into probabilistic parameter inference with simultaneous consideration of randomness and fuzziness. The PCEHPS is developed through a two-stage factorial polynomial chaos expansion (PCE) framework, which consists of an ensemble of PCEs to approximate the behavior of the hydrologic model, significantly speeding up the exhaustive sampling of the parameter space. Multiple hypothesis testing is then conducted to construct an ensemble of reduced-dimensionality PCEs with only the most influential terms, which is meaningful for achieving uncertainty reduction and further acceleration of parameter inference. The PCEHPS is applied to the Xiangxi River watershed in China to demonstrate its validity and applicability. A detailed comparison between the HYMOD hydrologic model, the ensemble of PCEs, and the ensemble of reduced PCEs is performed in terms of accuracy and efficiency. Results reveal temporal and spatial variations in parameter sensitivities due to the dynamic behavior of hydrologic systems, and the effects (magnitude and direction) of parametric interactions depending on different hydrological metrics. The case study demonstrates that the PCEHPS is capable not only of capturing both expert knowledge and probabilistic information in the calibration process, but also of implementing an acceleration of more than 10 times faster than the hydrologic model without compromising the predictive accuracy.
Julia Sets of Orthogonal Polynomials
DEFF Research Database (Denmark)
Christiansen, Jacob Stordal; Henriksen, Christian; Petersen, Henrik Laurberg
2018-01-01
For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials fPng to properties of the support. More precisely we relate the Julia set of Pn to the outer boundary of the support, the lled Julia...... set to the polynomial convex hull K of the support, and the Green's function associated with Pn to the Green's function for the complement of K....
About several classes of bi-orthogonal polynomials and discrete integrable systems
International Nuclear Information System (INIS)
Chang, Xiang-Ke; Chen, Xiao-Min; Hu, Xing-Biao; Tam, Hon-Wah
2015-01-01
By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry Lotka–Volterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotient–quotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided. (paper)
Exploring the Outer Solar System with the ESSENCE Supernova Survey
Energy Technology Data Exchange (ETDEWEB)
Becker, A.C.; /Washington U., Seattle, Astron. Dept.; Arraki, K.; /Washington U., Seattle, Astron. Dept.; Kaib, N.A.; /Washington U., Seattle, Astron. Dept.; Wood-Vasey, W.M.; /Harvard-Smithsonian Ctr. Astrophys.; Aguilera, C.; /Cerro-Tololo InterAmerican Obs.; Blackman, J.W.; /Australian Natl. U., Canberra; Blondin, S.; /Harvard-Smithsonian Ctr. Astrophys.; Challis, P.; /Harvard-Smithsonian Ctr. Astrophys.; Clocchiatti, A.; /Rio de Janeiro, Pont. U. Catol.; Covarrubias, R.; /Kyushu Sangyo U.; Damke, G.; /Cerro-Tololo InterAmerican Obs.; Davis, T.M.; /Bohr Inst. /Queensland U.; Filippenko, A.V.; /UC, Berkeley; Foley, R.J.; /UC, Berkeley; Garg, A.; /Harvard-Smithsonian Ctr. Astrophys. /Harvard U.; Garnavich, P.M.; /Notre Dame U.; Hicken, M.; /Harvard-Smithsonian Ctr. Astrophys. /Harvard U.; Jha, S.; /Harvard U. /SLAC; Kirshner, R.P.; /Harvard-Smithsonian Ctr. Astrophys.; Krisciunas, K.; /Notre Dame U. /Texas A-M; Leibundgut, B.; /Munich, Tech. U. /UC, Berkeley /NOAO, Tucson /Washington U., Seattle, Astron. Dept. /Fermilab /Harvard-Smithsonian Ctr. Astrophys. /Harvard U. /Chile U., Santiago /Ohio State U. /Cerro-Tololo InterAmerican Obs. /Harvard U. /Baltimore, Space Telescope Sci. /Johns Hopkins U. /Australian Natl. U., Canberra /Australian Natl. U., Canberra /Cerro-Tololo InterAmerican Obs. /Munich, Tech. U. /Harvard-Smithsonian Ctr. Astrophys. /Harvard U. /Cerro-Tololo InterAmerican Obs. /Texas A-M /Cerro-Tololo InterAmerican Obs.
2011-11-10
We report the discovery and orbital determination of 14 trans-Neptunian objects (TNOs) from the ESSENCE Supernova Survey difference imaging data set. Two additional objects discovered in a similar search of the SDSS-II Supernova Survey database were recovered in this effort. ESSENCE repeatedly observed fields far from the solar system ecliptic (-21{sup o} < {beta} < -5{sup o}), reaching limiting magnitudes per observation of I {approx} 23.1 and R {approx} 23.7. We examine several of the newly detected objects in detail, including 2003 UC{sub 414}, which orbits entirely between Uranus and Neptune and lies very close to a dynamical region that would make it stable for the lifetime of the solar system. 2003 SS{sub 422} and 2007 TA{sub 418} have high eccentricities and large perihelia, making them candidate members of an outer class of TNOs. We also report a new member of the 'extended' or 'detached' scattered disk, 2004 VN{sub 112}, and verify the stability of its orbit using numerical simulations. This object would have been visible to ESSENCE for only {approx}2% of its orbit, suggesting a vast number of similar objects across the sky. We emphasize that off-ecliptic surveys are optimal for uncovering the diversity of such objects, which in turn will constrain the history of gravitational influences that shaped our early solar system.
International Nuclear Information System (INIS)
Marquette, Ian
2015-01-01
Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works. (paper)
Alshamary, Haider Ali Jasim
2016-01-04
© 2015 IEEE. This paper considers the joint maximum likelihood (ML) channel estimation and data detection problem for massive SIMO (single input multiple output) wireless systems. We propose efficient algorithms achieving the exact ML non-coherent data detection, for both constant-modulus constellations and nonconstant-modulus constellations. Despite a large number of unknown channel coefficients in massive SIMO systems, we show that the expected computational complexity is linear in the number of receive antennas and polynomial in channel coherence time. To the best of our knowledge, our algorithms are the first efficient algorithms to achieve the exact joint ML channel estimation and data detection performance for massive SIMO systems with general constellations. Simulation results show our algorithms achieve considerable performance gains at a low computational complexity.
Alshamary, Haider Ali Jasim; Al-Naffouri, Tareq Y.; Zaib, Alam; Xu, Weiyu
2016-01-01
© 2015 IEEE. This paper considers the joint maximum likelihood (ML) channel estimation and data detection problem for massive SIMO (single input multiple output) wireless systems. We propose efficient algorithms achieving the exact ML non-coherent data detection, for both constant-modulus constellations and nonconstant-modulus constellations. Despite a large number of unknown channel coefficients in massive SIMO systems, we show that the expected computational complexity is linear in the number of receive antennas and polynomial in channel coherence time. To the best of our knowledge, our algorithms are the first efficient algorithms to achieve the exact joint ML channel estimation and data detection performance for massive SIMO systems with general constellations. Simulation results show our algorithms achieve considerable performance gains at a low computational complexity.
A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Zhong Cao
2014-01-01
Full Text Available This paper considers controller parameterization method of H∞ control for polynomial Hamiltonian systems (PHSs, which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems are H∞ stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimize H∞ control by adjusting parameters. All these results are expected to be of use in the study of H∞ control for nonlinear systems with perturbations.
Polynomial Heisenberg algebras
International Nuclear Information System (INIS)
Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M
2004-01-01
Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively
Lam, Hak-Keung
2016-01-01
This book presents recent research on the stability analysis of polynomial-fuzzy-model-based control systems where the concept of partially/imperfectly matched premises and membership-function dependent analysis are considered. The membership-function-dependent analysis offers a new research direction for fuzzy-model-based control systems by taking into account the characteristic and information of the membership functions in the stability analysis. The book presents on a research level the most recent and advanced research results, promotes the research of polynomial-fuzzy-model-based control systems, and provides theoretical support and point a research direction to postgraduate students and fellow researchers. Each chapter provides numerical examples to verify the analysis results, demonstrate the effectiveness of the proposed polynomial fuzzy control schemes, and explain the design procedure. The book is comprehensively written enclosing detailed derivation steps and mathematical derivations also for read...
Human Outer Solar System Exploration via Q-Thruster Technology
Joosten, B. Kent; White, Harold G.
2014-01-01
Propulsion technology development efforts at the NASA Johnson Space Center continue to advance the understanding of the quantum vacuum plasma thruster (QThruster), a form of electric propulsion. Through the use of electric and magnetic fields, a Q-thruster pushes quantum particles (electrons/positrons) in one direction, while the Qthruster recoils to conserve momentum. This principle is similar to how a submarine uses its propeller to push water in one direction, while the submarine recoils to conserve momentum. Based on laboratory results, it appears that continuous specific thrust levels of 0.4 - 4.0 N/kWe are achievable with essentially no onboard propellant consumption. To evaluate the potential of this technology, a mission analysis tool was developed utilizing the Generalized Reduced Gradient non-linear parameter optimization engine contained in the Microsoft Excel® platform. This tool allowed very rapid assessments of "Q-Ship" minimum time transfers from earth to the outer planets and back utilizing parametric variations in thrust acceleration while enforcing constraints on planetary phase angles and minimum heliocentric distances. A conservative Q-Thruster specific thrust assumption (0.4 N/kWe) combined with "moderate" levels of space nuclear power (1 - 2 MWe) and vehicle specific mass (45 - 55 kg/kWe) results in continuous milli-g thrust acceleration, opening up realms of human spaceflight performance completely unattainable by any current systems or near-term proposed technologies. Minimum flight times to Mars are predicted to be as low as 75 days, but perhaps more importantly new "retro-phase" and "gravity-augmented" trajectory shaping techniques were revealed which overcome adverse planetary phasing and allow virtually unrestricted departure and return opportunities. Even more impressively, the Jovian and Saturnian systems would be opened up to human exploration with round-trip times of 21 and 32 months respectively including 6 to 12 months of
Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles
2011-06-01
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
International Nuclear Information System (INIS)
Nishino, Akinori; Ujino, Hideaki; Komori, Yasushi; Wadati, Miki
2000-01-01
The non-symmetric Macdonald-Koornwinder polynomials are joint eigenfunctions of the commuting Cherednik operators which are constructed from the representation theory for the affine Hecke algebra corresponding to the BC N -type root system. We present the Rodrigues formula for the non-symmetric Macdonald-Koornwinder polynomials. The raising operators are derived from the realizations of the corresponding double affine Hecke algebra. In the quasi-classical limit, the above theory reduces to that of the BC N -type Sutherland model which describes many particles with inverse-square long-range interactions on a circle with one impurity. We also present the Rodrigues formula for the non-symmetric Jacobi polynomials of type BC N which are eigenstates of the BC N -type Sutherland model
Closed-form estimates of the domain of attraction for nonlinear systems via fuzzy-polynomial models.
Pitarch, José Luis; Sala, Antonio; Ariño, Carlos Vicente
2014-04-01
In this paper, the domain of attraction of the origin of a nonlinear system is estimated in closed form via level sets with polynomial boundaries, iteratively computed. In particular, the domain of attraction is expanded from a previous estimate, such as a classical Lyapunov level set. With the use of fuzzy-polynomial models, the domain of attraction analysis can be carried out via sum of squares optimization and an iterative algorithm. The result is a function that bounds the domain of attraction, free from the usual restriction of being positive and decrescent in all the interior of its level sets.
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
International Nuclear Information System (INIS)
Tsuchida, Takayuki; Wolf, Thomas
2005-01-01
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
Energy Technology Data Exchange (ETDEWEB)
Tsuchida, Takayuki [Department of Physics, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337 (Japan); Wolf, Thomas [Department of Mathematics, Brock University, St Catharines, ON L2S 3A1 (Canada)
2005-09-02
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.
US Decadal Survey Outer Solar System Missions: Trajectory Options
Spilker, T. R.; Atkinson, D. H.; Strange, N. J.; Landau, D.
2012-04-01
The report of the US Planetary Science Decadal Survey (PSDS), released in draft form March 7, 2011, identifies several mission concepts involving travel to high-priority outer solar system (OSS) destinations. These include missions to Europa and Jupiter, Saturn and two of its satellites, and Uranus. Because travel to the OSS involves much larger distances and larger excursions out of the sun's gravitational potential well than inner solar system (ISS) missions, transfer trajectories for OSS missions are stronger drivers of mission schedule and resource requirements than for ISS missions. Various characteristics of each planet system, such as obliquity, radiation belts, rings, deep gravity wells, etc., carry ramifications for approach trajectories or trajectories within the systems. The maturity of trajectory studies for each of these destinations varies significantly. Europa has been the focus of studies for well over a decade. Transfer trajectory options from Earth to Jupiter are well understood. Current studies focus on trajectories within the Jovian system that could reduce the total mission cost of a Europa orbiter mission. Three missions to the Saturn system received high priority ratings in the PSDS report: two flagship orbital missions, one to Titan and one to Enceladus, and a Saturn atmospheric entry probe mission for NASA's New Frontiers Program. The Titan Saturn System Mission (TSSM) studies of 2007-2009 advanced our understanding of trajectory options for transfers to Saturn, including solar electric propulsion (SEP) trajectories. But SEP trajectories depend more on details of spacecraft and propulsion system characteristics than chemical trajectories, and the maturity of SEP trajectory search tools has not yet caught up with chemical trajectory tools, so there is still more useful research to be done on Saturn transfers. The TSSM studies revealed much about Saturn-orbiting trajectories that yield efficient and timely delivery to Titan or Enceladus
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2009-10-02
Integrable couplings of relativistic Toda lattice systems in polynomial form and rational form, and their hierarchies, are derived from a four-by-four discrete matrix eigenvalue problem. The bi-Hamiltonian structure for every integrable coupling in the two hierarchies obtained is established by means of the discrete variational identity. Ultimately, Liouvolle integrability of the obtained integrable couplings is demonstrated.
DEFF Research Database (Denmark)
Rakhshan, Mohsen; Vafamand, Navid; Khooban, Mohammad Hassan
2018-01-01
This paper introduces a polynomial fuzzy model (PFM)-based maximum power point tracking (MPPT) control approach to increase the performance and efficiency of the solar photovoltaic (PV) electricity generation. The proposed method relies on a polynomial fuzzy modeling, a polynomial parallel......, a direct maximum power (DMP)-based control structure is considered for MPPT. Using the PFM representation, the DMP-based control structure is formulated in terms of SOS conditions. Unlike the conventional approaches, the proposed approach does not require exploring the maximum power operational point...
Zhang, Tie-Yan; Zhao, Yan; Xie, Xiang-Peng
2012-12-01
This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.
International Nuclear Information System (INIS)
Zhang Tie-Yan; Zhao Yan; Xie Xiang-Peng
2012-01-01
This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach. (general)
Palaszewski, Bryan
2017-01-01
Atmospheric mining in the outer solar system has been investigated as a means of fuel production for high energy propulsion and power. Fusion fuels such as Helium 3 (3He) and deuterium can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. Helium 3 and deuterium were the primary gases of interest with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses were undertaken to investigate resource capturing aspects of atmospheric mining in the outer solar system. This included the gas capturing rate, storage options, and different methods of direct use of the captured gases. While capturing 3He, large amounts of hydrogen and 4He are produced. The propulsion and transportation requirements for all of the major moons of Uranus and Neptune are presented. Analyses of orbital transfer vehicles (OTVs), landers, factories, and the issues with in-situ resource utilization (ISRU) low gravity processing factories are included. Preliminary observations are presented on near-optimal selections of moon base orbital locations, OTV power levels, and OTV and lander rendezvous points. Several artificial gravity in-space base designs and orbital sites at Uranus and Neptune and the OTV requirements to support them are also addressed.
Energy Technology Data Exchange (ETDEWEB)
Campigotto, C
1993-12-01
The first part is concerned with the introduction of quantum groups as an extension of Lie groups. In particular, we study the case of unitary enveloping algebras in dimension 2. We then connect the quantum group formalism to the construction of g CGC recurrent relations. In addition, we construct g-deformed Krawtchouck and Meixner orthogonal polynomials and list their respective main characteristics. The second part deals with some dynamical systems from a classical, a quantum and a gp-analogue point of view. We investigate the Coulomb Kepler system by using the canonical namical systems which contain as special cases some interesting systems for nuclear of atomic physics and for quantum chemistry, such as the Hartmann system, the ring-shaped oscillator, the Smarodinsky-Winternitz system, the Aharonov-Bohen system and the dyania of Dirac and Schroedinger. (author). 291 refs.
Uranus, Neptune, Pluto, and the outer solar system
Elkins-Tanton, Linda T
2010-01-01
Unlike all the planets closer to the Sun, known since antiquity, the farthest reaches are the discoveries of the modern world. Uranus was discovered in 1781, Neptune in 1846, Pluto in 1930, the Kuiper belt group of objects in 1992, and though the Oort cloud has been theorized since 1950, its first member was found in 2004. The discovery of the outer planets made such an impression on the minds of mankind that they were immortalized in the names of the newly discovered elements: uranium, neptunium, and plutonium, an astonishingly deadly constituent of atomic bombs. Uranus, Neptune, Pluto, and t
Polynomial expansion of the precoder for power minimization in large-scale MIMO systems
Sifaou, Houssem
2016-07-26
This work focuses on the downlink of a single-cell large-scale MIMO system in which the base station equipped with M antennas serves K single-antenna users. In particular, we are interested in reducing the implementation complexity of the optimal linear precoder (OLP) that minimizes the total power consumption while ensuring target user rates. As most precoding schemes, a major difficulty towards the implementation of OLP is that it requires fast inversions of large matrices at every new channel realizations. To overcome this issue, we aim at designing a linear precoding scheme providing the same performance of OLP but with lower complexity. This is achieved by applying the truncated polynomial expansion (TPE) concept on a per-user basis. To get a further leap in complexity reduction and allow for closed-form expressions of the per-user weighting coefficients, we resort to the asymptotic regime in which M and K grow large with a bounded ratio. Numerical results are used to show that the proposed TPE precoding scheme achieves the same performance of OLP with a significantly lower implementation complexity. © 2016 IEEE.
Effect of outer wing separation on lift and thrust generation in a flapping wing system
International Nuclear Information System (INIS)
Mahardika, Nanang; Viet, Nguyen Quoc; Park, Hoon Cheol
2011-01-01
We explore the implementation of wing feather separation and lead-lagging motion to a flapping wing. A biomimetic flapping wing system with separated outer wings is designed and demonstrated. The artificial wing feather separation is implemented in the biomimetic wing by dividing the wing into inner and outer wings. The features of flapping, lead-lagging, and outer wing separation of the flapping wing system are captured by a high-speed camera for evaluation. The performance of the flapping wing system with separated outer wings is compared to that of a flapping wing system with closed outer wings in terms of forward force and downward force production. For a low flapping frequency ranging from 2.47 to 3.90 Hz, the proposed biomimetic flapping wing system shows a higher thrust and lift generation capability as demonstrated by a series of experiments. For 1.6 V application (lower frequency operation), the flapping wing system with separated wings could generate about 56% higher forward force and about 61% less downward force compared to that with closed wings, which is enough to demonstrate larger thrust and lift production capability of the separated outer wings. The experiments show that the outer parts of the separated wings are able to deform, resulting in a smaller amount of drag production during the upstroke, while still producing relatively greater lift and thrust during the downstroke.
Itoh, Shoji; Sugihara, Masaaki
2016-01-01
We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithms. We show that the direction of a preconditioned system is switched by construction and by the settings of the initial shadow residual vector. We analyze and compare the polynomial structures of four preconditioned BiCG algorithms.
Directory of Open Access Journals (Sweden)
Ernest G. Kalnins
2013-10-01
Full Text Available We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2 and so(3. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.
Mahmood, Zahid; Ning, Huansheng; Ghafoor, AtaUllah
2017-03-24
Wireless Sensor Networks (WSNs) consist of lightweight devices to measure sensitive data that are highly vulnerable to security attacks due to their constrained resources. In a similar manner, the internet-based lightweight devices used in the Internet of Things (IoT) are facing severe security and privacy issues because of the direct accessibility of devices due to their connection to the internet. Complex and resource-intensive security schemes are infeasible and reduce the network lifetime. In this regard, we have explored the polynomial distribution-based key establishment schemes and identified an issue that the resultant polynomial value is either storage intensive or infeasible when large values are multiplied. It becomes more costly when these polynomials are regenerated dynamically after each node join or leave operation and whenever key is refreshed. To reduce the computation, we have proposed an Efficient Key Management (EKM) scheme for multiparty communication-based scenarios. The proposed session key management protocol is established by applying a symmetric polynomial for group members, and the group head acts as a responsible node. The polynomial generation method uses security credentials and secure hash function. Symmetric cryptographic parameters are efficient in computation, communication, and the storage required. The security justification of the proposed scheme has been completed by using Rubin logic, which guarantees that the protocol attains mutual validation and session key agreement property strongly among the participating entities. Simulation scenarios are performed using NS 2.35 to validate the results for storage, communication, latency, energy, and polynomial calculation costs during authentication, session key generation, node migration, secure joining, and leaving phases. EKM is efficient regarding storage, computation, and communication overhead and can protect WSN-based IoT infrastructure.
Coherent states for a polynomial su(1, 1) algebra and a conditionally solvable system
International Nuclear Information System (INIS)
Sadiq, Muhammad; Inomata, Akira; Junker, Georg
2009-01-01
In a previous paper (2007 J. Phys. A: Math. Theor. 40 11105), we constructed a class of coherent states for a polynomially deformed su(2) algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed su(1, 1) algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1, 1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1, 1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.
Shyu, H. C.; Reed, I. S.; Truong, T. K.; Hsu, I. S.; Chang, J. J.
1987-01-01
A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.
Directory of Open Access Journals (Sweden)
A.K. Parida
2016-09-01
Full Text Available In this paper Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system is presented for the prediction and analysis of financial and electrical energy market data. The normally used TSK-type feedforward fuzzy neural network is unable to take the full advantage of the use of the linear fuzzy rule base in accurate input–output mapping and hence the consequent part of the rule base is made nonlinear using polynomial or arithmetic basis functions. Further the Chebyshev polynomial functions provide an expanded nonlinear transformation to the input space thereby increasing its dimension for capturing the nonlinearities and chaotic variations in financial or energy market data streams. Also the locally recurrent neuro-fuzzy information system (LRNFIS includes feedback loops both at the firing strength layer and the output layer to allow signal flow both in forward and backward directions, thereby making the LRNFIS mimic a dynamic system that provides fast convergence and accuracy in predicting time series fluctuations. Instead of using forward and backward least mean square (FBLMS learning algorithm, an improved Firefly-Harmony search (IFFHS learning algorithm is used to estimate the parameters of the consequent part and feedback loop parameters for better stability and convergence. Several real world financial and energy market time series databases are used for performance validation of the proposed LRNFIS model.
Sorting of bacterial lipoproteins to the outer membrane by the Lol system.
Narita, Shin-ichiro; Tokuda, Hajime
2010-01-01
Bacterial lipoproteins comprise a subset of membrane proteins with a lipid-modified cysteine residue at their amino termini through which they are anchored to the membrane. In Gram-negative bacteria, lipoproteins are localized on either the inner or the outer membrane. The Lol system is responsible for the transport of lipoproteins to the outer membrane.The Lol system comprises an inner-membrane ABC transporter LolCDE complex, a periplasmic carrier protein, LolA, and an outer membrane receptor protein, LolB. Lipoproteins are synthesized as precursors in the cytosol and then translocated across the inner membrane by the Sec translocon to the outer leaflet of the inner membrane, where lipoprotein precursors are processed to mature lipoproteins. The LolCDE complex then mediates the release of outer membrane-specific lipoproteins from the inner membrane while the inner membrane-specific lipoproteins possessing Asp at position 2 are not released by LolCDE because it functions as a LolCDE avoidance signal, causing the retention of these lipoproteins in the inner membrane. A water-soluble lipoprotein-LolA complex is formed as a result of the release reaction mediated by LolCDE. This complex traverses the hydrophilic periplasm to reach the outer membrane, where LolB accepts a lipoprotein from LolA and then catalyzes its incorporation into the inner leaflet of the outer membrane.
Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Xue, Yusheng
2016-03-01
This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.
Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao
2018-02-01
Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.
Atmospheric chemistry and transport modeling in the outer solar system
Lee, Yuan-Tai (Anthony)
2001-11-01
This thesis consists of 1-D and 2-D photochemical- dynamical modeling in the upper atmospheres of outer planets. For 1-D modeling, a unified hydrocarbon photochemical model has been studied in Jupiter, Saturn, Uranus, Neptune, and Titan, by comparing with the Voyager observations, and the recent measurements of methyl radicals by ISO in Saturn and Neptune. The CH3 observation implies a kinetically sensitive test to the measured and estimated hydrocarbon rate constants at low temperatures. We identify the key reactions that control the concentrations of CH3 in the model, such as the three-body recombination reaction, CH3 + CH3 + M --> C 2H6 + M, and the recycling reaction H + CH3 + M --> CH4 + M. The results show reasonable agreement with ISO values. In Chapter 4, the detection of PH3 in the lower stratosphere and upper troposphere of Jupiter has provided a photochemical- dynamical coupling model to derive the eddy diffusion coefficient in the upper troposphere of Jupiter. Using a two-layers photochemical model with updated photodissociation cross-sections and chemical rate constants for NH3 and PH 3, we find that the upper tropospheric eddy diffusion coefficient 106 cm2 sec-1, are required to match the derived PH3 vertical profile by the observation. The best-fit functional form derivation of eddy diffusion coefficient in the upper troposphere of Jupiter above 400 mbar is K = 2.0 × 104 (n/2.2 × 1019)-0.5 cm 2 sec-1. On the other hand, Chapter 5 demonstrates a dynamical-only 2-D model of C2H6 providing a complete test for the current 2-D transport models in Jovian lower stratosphere and upper troposphere (270 to 0.1 mbar pressure levels). Different combinations of residual advection, horizontal eddy dispersion, and vertical eddy mixing are examined at different latitudes.
Implementation of an Outer Can Welding System for Savannah River Site FB-Line
International Nuclear Information System (INIS)
Howard, S.R.
2003-01-01
This paper details three phases of testing to confirm use of a Gas Tungsten Arc (GTA) system for closure welding the 3013 outer container used for stabilization/storage of plutonium metals and oxides. The outer container/lid closure joint was originally designed for laser welding, but for this application, the gas tungsten arc (GTA) welding process has been adapted. The testing progressed in three phases: (1) system checkout to evaluate system components for operational readiness, (2) troubleshooting to evaluate high weld failure rates and develop corrective techniques, and (3) pre-installation acceptance testing
Outer skin protection of columbium Thermal Protection System (TPS) panels
Culp, J. D.
1973-01-01
A coated columbium alloy material system 0.04 centimeter thick was developed which provides for increased reliability to the load bearing character of the system in the event of physical damage to and loss of the exterior protective coating. The increased reliability to the load bearing columbium alloy (FS-85) was achieved by interposing an oxidation resistant columbium alloy (B-1) between the FS-85 alloy and a fused slurry silicide coating. The B-1 alloy was applied as a cladding to the FS-85 and the composite was fused slurry silicide coated. Results of material evaluation testing included cyclic oxidation testing of specimens with intentional coating defects, tensile testing of several material combinations exposed to reentry profile conditions, and emittance testing after cycling of up to 100 simulated reentries. The clad material, which was shown to provide greater reliability than unclad materials, holds significant promise for use in the thermal protection system of hypersonic reentry vehicles.
Laboratory Studies of Ethane Ice Relevant to Outer Solar System Surfaces
Moore, Marla H.; Hudson, Reggie; Raines, Lily
2009-01-01
Oort Cloud comets, as well as TNOs Makemake (2045 FYg), Quaoar, and Pluto, are known to contain ethane. However, even though this molecule is found on several outer Solar System objects relatively little information is available about its amorphous and crystalline phases. In new experiments, we have prepared ethane ices at temperatures applicable to the outer Solar System, and have heated and ion-irradiated these ices to study phase changes and ethane's radiation chemistry using mid-IR spectroscopy (2.2 - 16.6 microns). Included in our work is the meta-stable phase that exists at 35 - 55 K. These results, including newly obtained optical constants, are relevant to ground-based observational campaigns, the New Horizons mission, and supporting laboratory work. An improved understanding of solid-phase ethane may contribute to future searches for this and other hydrocarbons in the outer Solar System.
Directory of Open Access Journals (Sweden)
Chih-Hong Lin
2015-01-01
Full Text Available Because the V-belt continuously variable transmission (CVT system driven by permanent magnet synchronous motor (PMSM has much unknown nonlinear and time-varying characteristics, the better control performance design for the linear control design is a time consuming procedure. In order to overcome difficulties for design of the linear controllers, the hybrid recurrent Laguerre-orthogonal-polynomial neural network (NN control system which has online learning ability to respond to the system’s nonlinear and time-varying behaviors is proposed to control PMSM servo-driven V-belt CVT system under the occurrence of the lumped nonlinear load disturbances. The hybrid recurrent Laguerre-orthogonal-polynomial NN control system consists of an inspector control, a recurrent Laguerre-orthogonal-polynomial NN control with adaptive law, and a recouped control with estimated law. Moreover, the adaptive law of online parameters in the recurrent Laguerre-orthogonal-polynomial NN is derived using the Lyapunov stability theorem. Furthermore, the optimal learning rate of the parameters by means of modified particle swarm optimization (PSO is proposed to achieve fast convergence. Finally, to show the effectiveness of the proposed control scheme, comparative studies are demonstrated by experimental results.
Performance of the RASNIK Optical Alignment Monitoring System for the LHCb Outer Tracker Detector
Szczekowski, Marek; Ukleja, Artur; Pellegrino, Antonio; Hart, Robert; Syryczynski, Krzysztof
2017-01-01
We present the results collected by an optical system for position control of the Outer Tracker detector stations in the LHCb experiment. This system has been constructed using the RASNIK three-point alignment monitors. The measurements are based on data taken in Run 2 of LHC.
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...
Palaszewski, Bryan A.
2014-01-01
Atmospheric mining in the outer solar system has been investigated as a means of fuel production for high energy propulsion and power. Fusion fuels such as Helium 3 (3He) and hydrogen can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. Helium 3 and hydrogen (deuterium, etc.) were the primary gases of interest with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses were undertaken to investigate resource capturing aspects of atmospheric mining in the outer solar system. This included the gas capturing rate, storage options, and different methods of direct use of the captured gases. Additional supporting analyses were conducted to illuminate vehicle sizing and orbital transportation issues. While capturing 3He, large amounts of hydrogen and 4He are produced. With these two additional gases, the potential for fueling small and large fleets of additional exploration and exploitation vehicles exists. Additional aerospacecraft or other aerial vehicles (UAVs, balloons, rockets, etc.) could fly through the outer planet atmospheres, for global weather observations, localized storm or other disturbance investigations, wind speed measurements, polar observations, etc. Deep-diving aircraft (built with the strength to withstand many atmospheres of pressure) powered by the excess hydrogen or helium 4 may be designed to probe the higher density regions of the gas giants. Outer planet atmospheric properties, atmospheric storm data, and mission planning for future outer planet UAVs are presented.
International Nuclear Information System (INIS)
Viswanathan, V.K.
1981-01-01
This paper describes the need for non-raytracing schemes in the optical design and analysis of large carbon-dioxide lasers like the Gigawatt, Gemini, and Helios lasers currently operational at Los Alamos, and the Antares laser fusion system under construction. The scheme currently used at Los Alamos involves characterizing the various optical components with a Zernike polynomial set obtained by the digitization of experimentally produced interferograms of the components. A Fast Fourier Transform code then propagates the complex amplitude and phase of the beam through the whole system and computes the optical parameters of interest. The analysis scheme is illustrated through examples of the Gigawatt, Gemini, and Helios systems. A possible way of using the Zernike polynomials in optical design problems of this type is discussed. Comparisons between the computed values and experimentally obtained results are made and it is concluded that this appears to be a valid approach. As this is a review article, some previously published results are also used where relevant
Using Real and Simulated TNOs to Constrain the Outer Solar System
Kaib, Nathan
2018-04-01
Over the past 2-3 decades our understanding of the outer solar system’s history and current state has evolved dramatically. An explosion in the number of detected trans-Neptunian objects (TNOs) coupled with simultaneous advances in numerical models of orbital dynamics has driven this rapid evolution. However, successfully constraining the orbital architecture and evolution of the outer solar system requires accurately comparing simulation results with observational datasets. This process is challenging because observed datasets are influenced by orbital discovery biases as well as TNO size and albedo distributions. Meanwhile, such influences are generally absent from numerical results. Here I will review recent work I and others have undertaken using numerical simulations in concert with catalogs of observed TNOs to constrain the outer solar system’s current orbital architecture and past evolution.
Exploring small bodies in the outer solar system with stellar occultations
Elliot, Jim L.; Dunham, Edward W.; Olkin, C. B.
1995-01-01
Stellar occultation observations probe the atmospheric structure and extinction of outer solar system bodies with a spatial resolution of a few kilometers, and an airborne platform allows the observation of occultations by small bodies that are not visible from fixed telescopes. Results from occultations by Triton, Pluto, and Chiron observed with KAO are discussed, and future directions for this program are presented.
Krishnamoorthi, R; Anna Poorani, G
2016-01-01
Iris normalization is an important stage in any iris biometric, as it has a propensity to trim down the consequences of iris distortion. To indemnify the variation in size of the iris owing to the action of stretching or enlarging the pupil in iris acquisition process and camera to eyeball distance, two normalization schemes has been proposed in this work. In the first method, the iris region of interest is normalized by converting the iris into the variable size rectangular model in order to avoid the under samples near the limbus border. In the second method, the iris region of interest is normalized by converting the iris region into a fixed size rectangular model in order to avoid the dimensional discrepancies between the eye images. The performance of the proposed normalization methods is evaluated with orthogonal polynomials based iris recognition in terms of FAR, FRR, GAR, CRR and EER.
International Nuclear Information System (INIS)
Guppy, C.B.
1962-03-01
In the methods adopted in this report transfer functions in the form of the ratio of two polynomials of the complex variable s are derived from sets of laplace transformed simultaneous differential equations. The set of algebraic simultaneous equations are solved using Cramer's Rule and this gives rise to determinants having polynomial elements. It is shown how the determinants are formed when transfer functions are specified. The procedure for finding the polynomial coefficients from a given determinant is fully described. The first method adopted is a direct one and reduces a determinant with first degree polynomial elements to secular form and follows this by an application of the similarity transformation to reduce the determinant to a form from which the polynomial coefficients can be read out directly. The programme is able to solve a single determinant with polynomial elements and this can be used to reduce an eigenvalue problem in the form of a secular determinant to polynomial form if the need arises. A description is given of the way in which the data is to be set out for solution by the programme. A description is also given of a method used in an earlier programme for solving polynomial determinants by curve fitting techniques using Chebyshev Polynomials. In this method determinants with polynomial elements of any degree can be solved. (author)
Diouf, C.; Younes, M.; Noaja, A.; Azou, S.; Telescu, M.; Morel, P.; Tanguy, N.
2017-11-01
The linearization performance of various digital baseband pre-distortion schemes is evaluated in this paper for a coherent optical OFDM (CO-OFDM) transmitter employing a semiconductor optical amplifier (SOA). In particular, the benefits of using a parallel two-box (PTB) behavioral model, combining a static nonlinear function with a memory polynomial (MP) model, is investigated for mitigating the system nonlinearities and compared to the memoryless and MP models. Moreover, the robustness of the predistorters under different operating conditions and system uncertainties is assessed based on a precise SOA physical model. The PTB scheme proves to be the most effective linearization technique for the considered setup, with an excellent performance-complexity tradeoff over a wide range of conditions.
Irreducible multivariate polynomials obtained from polynomials in ...
Indian Academy of Sciences (India)
Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: Nicolae. ... Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ..... This shows us that deg ai = (n − i) deg f2 for each i = 0,..., n, so min k>0.
Encrenaz, T; Owen, T. C; Sotin, C
2005-01-01
This volume gives an integrated summary of the science related to the four giant planets in our solar system. It is the result of an ISSI workshop on «A comparative study of the outer planets before the exploration of Saturn by Cassini-Huygens» which was held at ISSI in Bern on January 12-16, 2004. Representatives of several scientific communities, such as planetary scientists, astronomers, space physicists, chemists and astrobiologists have met with the aim to review the knowledge on four major themes: (1) the study of the formation and evolution processes of the outer planets and their satellites, beginning with the formation of compounds and planetesimals in the solar nebula, and the subsequent evolution of the interiors of the outer planets, (2) a comparative study of the atmospheres of the outer planets and Titan, (3) the study of the planetary magnetospheres and their interactions with the solar wind, and (4) the formation and properties of satellites and rings, including their interiors, surfaces, an...
DS-CDMA system outer loop power control and improvement for multi-service
Institute of Scientific and Technical Information of China (English)
Guan Mingxiang; Guo Qing; Li Xing
2008-01-01
When a new user accesses the CDMA system, the load will change drastically, and therefore, the advanced outer loop power control (OLPC) technology has to be adopted to enrich the target signal interference ratio (SIR) and improve the system performance. The existing problems about DS-CDMA outer loop power control for multi-service are introduced and the power control theoretical model is analyzed. System simulation is adopted on how to obtain the theoretical performance and parameter optimization of the power control algorithm. The OLPC algorithm is improved and the performance comparisons between the old algorithm and the improved algorithm are given. The results show good performance of the improved OLPC algorithm and prove the validity of the improved method for multi-service.
Radiolysis of Amino Acids in Outer Solar-System Ice Analogs
Gerakines, Perry A.; Hudson, Reggie L.
2011-01-01
Amino acids have been found in cometary dust particles and in the organic component of meteorites. These molecules, important for pre-biotic chemistry and for active biological systems, might be formed in cold planetary or interstellar environments and then delivered to H20-rich surfaces in the outer solar system. Many models for the availability of organic species on Earth and elsewhere depend on the ability of these molecules to survive in radiation-rich space environments. This poster presents results of O.8-MeV proton radiolysis of ice films at lS-140K. using infrared spectroscopy, the destruction rates of glycine, alanine, and phenylalanine have been determined for both pure films and those containing amino acids diluted in H2o. our results are discussed in terms of the survivability of these molecules in the icy surfaces present in the outer solar system and the possibility of their detection by instruments on board the New Horizons spacecraft
A companion matrix for 2-D polynomials
International Nuclear Information System (INIS)
Boudellioua, M.S.
1995-08-01
In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs
Branched polynomial covering maps
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
1999-01-01
A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere....
Bai , Shi; Bouvier , Cyril; Kruppa , Alexander; Zimmermann , Paul
2016-01-01
International audience; The general number field sieve (GNFS) is the most efficient algo-rithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial tha...
Directory of Open Access Journals (Sweden)
Đorđević Bojan D.
2013-01-01
Full Text Available The description and prediction of the thermophysical and transport properties of ternary organic non-electrolyte systems including water by the polynomial equations are reviewed. Empirical equations of Radojković et al. (also known as Redlich-Kister, Kohler, Jacob-Fitzner, Colinet, Tsao-Smith, Toop, Scatchard et al. and Rastogi et al. are compared with experimental data of available papers appeared in well know international journals (Fluid Phase Equilibria, Journal of Chemical and Engineering Data, Journal of Chemical Thermodynamics, Journal of Solution Chemistry, Journal of the Serbian Chemical Society, The Canadian Journal of Chemical Engineering, Journal of Molecular Liquids, Thermochimica Acta, etc.. The applicability of empirical models to estimate excess molar volumes, VE, excess viscosities, ηE, excess free energies of activation of a viscous flow,
Atmospheric Mining in the Outer Solar System: Resource Capturing, Storage, and Utilization
Palaszewski, Bryan
2014-01-01
Atmospheric mining in the outer solar system has been investigated as a means of fuel production for high energy propulsion and power. Fusion fuels such as helium 3 and hydrogen can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. Helium 3 and hydrogen (deuterium, etc.) were the primary gases of interest with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses were undertaken to investigate resource capturing aspects of atmospheric mining in the outer solar system. This included the gas capturing rate for hydrogen helium 4 and helium 3, storage options, and different methods of direct use of the captured gases. Additional supporting analyses were conducted to illuminate vehicle sizing and orbital transportation issues.
Palaszewski, Bryan
2014-01-01
Establishing a lunar presence and creating an industrial capability on the Moon may lead to important new discoveries for all of human kind. Historical studies of lunar exploration, in-situ resource utilization (ISRU) and industrialization all point to the vast resources on the Moon and its links to future human and robotic exploration. In the historical work, a broad range of technological innovations are described and analyzed. These studies depict program planning for future human missions throughout the solar system, lunar launched nuclear rockets, and future human settlements on the Moon, respectively. Updated analyses based on the visions presented are presented. While advanced propulsion systems were proposed in these historical studies, further investigation of nuclear options using high power nuclear thermal propulsion, nuclear surface power, as well as advanced chemical propulsion can significantly enhance these scenarios. Robotic and human outer planet exploration options are described in many detailed and extensive studies. Nuclear propulsion options for fast trips to the outer planets are discussed. To refuel such vehicles, atmospheric mining in the outer solar system has also been investigated as a means of fuel production for high energy propulsion and power. Fusion fuels such as helium 3 (3He) and hydrogen (H2) can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. Helium 3 and H2 (deuterium, etc.) were the primary gases of interest with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses have investigated resource capturing aspects of atmospheric mining in the outer solar system. These analyses included the gas capturing rate, storage options, and different methods of direct use of the captured gases. While capturing 3He, large amounts of hydrogen and 4He are produced. With these two additional
On the Existence of Regular and Irregular Outer Moons Orbiting the Pluto–Charon System
Energy Technology Data Exchange (ETDEWEB)
Michaely, Erez; Perets, Hagai B.; Grishin, Evgeni [Physics Department, Technion—Israel Institute of Technology, Haifa 3200004 (Israel)
2017-02-10
The dwarf planet Pluto is known to host an extended system of five co-planar satellites. Previous studies have explored the formation and evolution of the system in isolation, neglecting perturbative effects by the Sun. Here we show that secular evolution due to the Sun can strongly affect the evolution of outer satellites and rings in the system, if such exist. Although precession due to extended gravitational potential from the inner Pluto–Charon binary quench such secular evolution up to a {sub crit} ∼ 0.0035 au (∼0.09 R {sub Hill} the Hill radius; including all of the currently known satellites), outer orbits can be significantly altered. In particular, we find that co-planar rings and satellites should not exist beyond a {sub crit}; rather, satellites and dust particles in these regions secularly evolve on timescales ranging between 10{sup 4} and 10{sup 6} years, and quasi-periodically change their inclinations and eccentricities through secular evolution (Lidov–Kozai oscillations). Such oscillations can lead to high inclinations and eccentricities, constraining the range where such satellites (and dust particles) can exist without crossing the orbits of the inner satellites or crossing the outer Hill stability range. Outer satellites, if such exist are therefore likely to be irregular satellites, with orbits limited to be non-circular and/or highly inclined. Current observations, including the recent data from the New-Horizons mission explored only inner regions (<0.0012 au) and excluded the existence of additional satellites; however, the irregular satellites discussed here should reside farther, in the yet uncharted regions around Pluto.
On the Existence of Regular and Irregular Outer Moons Orbiting the Pluto–Charon System
International Nuclear Information System (INIS)
Michaely, Erez; Perets, Hagai B.; Grishin, Evgeni
2017-01-01
The dwarf planet Pluto is known to host an extended system of five co-planar satellites. Previous studies have explored the formation and evolution of the system in isolation, neglecting perturbative effects by the Sun. Here we show that secular evolution due to the Sun can strongly affect the evolution of outer satellites and rings in the system, if such exist. Although precession due to extended gravitational potential from the inner Pluto–Charon binary quench such secular evolution up to a crit ∼ 0.0035 au (∼0.09 R Hill the Hill radius; including all of the currently known satellites), outer orbits can be significantly altered. In particular, we find that co-planar rings and satellites should not exist beyond a crit ; rather, satellites and dust particles in these regions secularly evolve on timescales ranging between 10 4 and 10 6 years, and quasi-periodically change their inclinations and eccentricities through secular evolution (Lidov–Kozai oscillations). Such oscillations can lead to high inclinations and eccentricities, constraining the range where such satellites (and dust particles) can exist without crossing the orbits of the inner satellites or crossing the outer Hill stability range. Outer satellites, if such exist are therefore likely to be irregular satellites, with orbits limited to be non-circular and/or highly inclined. Current observations, including the recent data from the New-Horizons mission explored only inner regions (<0.0012 au) and excluded the existence of additional satellites; however, the irregular satellites discussed here should reside farther, in the yet uncharted regions around Pluto.
Branched polynomial covering maps
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
2002-01-01
A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch ...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved.......A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...
Atmospheric Mining in the Outer Solar System: Aerial Vehicle Mission and Design Issues
Palaszewski, Bryan
2015-01-01
Atmospheric mining in the outer solar system has been investigated as a means of fuel production for high energy propulsion and power. Fusion fuels such as Helium 3 (3He) and deuterium can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. Helium 3 and deuterium were the primary gases of interest with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses were undertaken to investigate resource capturing aspects of atmospheric mining in the outer solar system. This included the gas capturing rate, storage options, and different methods of direct use of the captured gases. While capturing 3He, large amounts of hydrogen and 4He are produced. With these two additional gases, the potential for fueling small and large fleets of additional exploration and exploitation vehicles exists. The mining aerospacecraft (ASC) could fly through the outer planet atmospheres, for global weather observations, localized storm or other disturbance investigations, wind speed measurements, polar observations, etc. Analyses of orbital transfer vehicles (OTVs), landers, and in-situ resource utilization (ISRU) mining factories are included. Preliminary observations are presented on near-optimal selections of moon base orbital locations, OTV power levels, and OTV and lander rendezvous points.
Chromatic polynomials of random graphs
International Nuclear Information System (INIS)
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
International Nuclear Information System (INIS)
Noble, R.J.
1998-08-01
Recent results are presented in the study of radioisotope electric propulsion as a near-term technology for sending small robotic sciencecraft to the outer Solar System and near-interstellar space. Radioisotope electric propulsion (REP) systems are low-thrust, ion propulsion units based on radioisotope electric generators and ion thrusters. Powerplant specific masses are expected to be in the range of 100 to 200 kg/kW of thrust power. Planetary rendezvous missions to Pluto, fast missions to the heliopause (100 AU) with the capability to decelerate an orbiter for an extended science program and prestellar missions to the first gravitational lens focus of the Sun (550 AU) are investigated
International Nuclear Information System (INIS)
Raymond, Sean N.; Armitage, Philip J.; Gorelick, Noel
2010-01-01
We develop an idealized dynamical model to predict the typical properties of outer extrasolar planetary systems, at radii comparable to the Jupiter-to-Neptune region of the solar system. The model is based upon the hypothesis that dynamical evolution in outer planetary systems is controlled by a combination of planet-planet scattering and planetary interactions with an exterior disk of small bodies ('planetesimals'). Our results are based on 5000 long duration N-body simulations that follow the evolution of three planets from a few to 10 AU, together with a planetesimal disk containing 50 M + from 10 to 20 AU. For large planet masses (M ∼> M Sat ), the model recovers the observed eccentricity distribution of extrasolar planets. For lower-mass planets, the range of outcomes in models with disks is far greater than that which is seen in isolated planet-planet scattering. Common outcomes include strong scattering among massive planets, sudden jumps in eccentricity due to resonance crossings driven by divergent migration, and re-circularization of scattered low-mass planets in the outer disk. We present the distributions of the eccentricity and inclination that result, and discuss how they vary with planet mass and initial system architecture. In agreement with other studies, we find that the currently observed eccentricity distribution (derived primarily from planets at a ∼ -1 and periods in excess of 10 years will provide constraints on this regime. Finally, we present an analysis of the predicted separation of planets in two-planet systems, and of the population of planets in mean-motion resonances (MMRs). We show that, if there are systems with ∼ Jupiter-mass planets that avoid close encounters, the planetesimal disk acts as a damping mechanism and populates MMRs at a very high rate (50%-80%). In many cases, resonant chains (in particular the 4:2:1 Laplace resonance) are set up among all three planets. We expect such resonant chains to be common among massive
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...
Contributions to fuzzy polynomial techniques for stability analysis and control
Pitarch Pérez, José Luis
2014-01-01
The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees...
New Opportunities for Outer Solar System Science using Radioisotope Electric Propulsion
Energy Technology Data Exchange (ETDEWEB)
Noble, Robert J.; /SLAC; Amini, Rashied; Beauchamp, Patricia M.; /Caltech, JPL; Bennett, Gary L.; /Metaspace Enterprises; Brophy, John R.; Buratti, Bonnie J.; Ervin, Joan; /Caltech, JPL; Fernandez, Yan R.; /Central Florida U.; Grundy, Will; /Lowell Observ.; Khan, Mohammed Omair; /Caltech, JPL; King, David Q.; /Aerojet; Lang, Jared; /Caltech, JPL; Meech, Karen J.; /Hawaii U.; Newhouse, Alan; Oleson, Steven R.; Schmidt, George R.; /GRC; Spilker, Thomas; West, John L.; /Caltech, JPL
2010-05-26
Today, our questions and hypotheses about the Solar System's origin have surpassed our ability to deliver scientific instruments to deep space. The moons of the outer planets, the Trojan and Centaur minor planets, the trans-Neptunian objects (TNO), and distant Kuiper Belt objects (KBO) hold a wealth of information about the primordial conditions that led to the formation of our Solar System. Robotic missions to these objects are needed to make the discoveries, but the lack of deep-space propulsion is impeding this science. Radioisotope electric propulsion (REP) will revolutionize the way we do deep-space planetary science with robotic vehicles, giving them unprecedented mobility. Radioisotope electric generators and lightweight ion thrusters are being developed today which will make possible REP systems with specific power in the range of 5 to 10 W/kg. Studies have shown that this specific power range is sufficient to perform fast rendezvous missions from Earth to the outer Solar System and fast sample return missions. This whitepaper discusses how mobility provided by REP opens up entirely new science opportunities for robotic missions to distant primitive bodies. We also give an overview of REP technology developments and the required next steps to realize REP.
Application of polynomial preconditioners to conservation laws
Geurts, Bernardus J.; van Buuren, R.; Lu, H.
2000-01-01
Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of
MAKING PLANET NINE: A SCATTERED GIANT IN THE OUTER SOLAR SYSTEM
International Nuclear Information System (INIS)
Bromley, Benjamin C.; Kenyon, Scott J.
2016-01-01
Correlations in the orbits of several minor planets in the outer solar system suggest the presence of a remote, massive Planet Nine. With at least 10 times the mass of the Earth and a perihelion well beyond 100 au, Planet Nine poses a challenge to planet formation theory. Here we expand on a scenario in which the planet formed closer to the Sun and was gravitationally scattered by Jupiter or Saturn onto a very eccentric orbit in an extended gaseous disk. Dynamical friction with the gas then allowed the planet to settle in the outer solar system. We explore this possibility with a set of numerical simulations. Depending on how the gas disk evolves, scattered super-Earths or small gas giants settle on a range of orbits, with perihelion distances as large as 300 au. Massive disks that clear from the inside out on million-year timescales yield orbits that allow a super-Earth or gas giant to shepherd the minor planets as observed. A massive planet can achieve a similar orbit in a persistent, low-mass disk over the lifetime of the solar system.
MAKING PLANET NINE: A SCATTERED GIANT IN THE OUTER SOLAR SYSTEM
Energy Technology Data Exchange (ETDEWEB)
Bromley, Benjamin C. [Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Room 201, Salt Lake City, UT 84112 (United States); Kenyon, Scott J., E-mail: bromley@physics.utah.edu, E-mail: skenyon@cfa.harvard.edu [Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138 (United States)
2016-07-20
Correlations in the orbits of several minor planets in the outer solar system suggest the presence of a remote, massive Planet Nine. With at least 10 times the mass of the Earth and a perihelion well beyond 100 au, Planet Nine poses a challenge to planet formation theory. Here we expand on a scenario in which the planet formed closer to the Sun and was gravitationally scattered by Jupiter or Saturn onto a very eccentric orbit in an extended gaseous disk. Dynamical friction with the gas then allowed the planet to settle in the outer solar system. We explore this possibility with a set of numerical simulations. Depending on how the gas disk evolves, scattered super-Earths or small gas giants settle on a range of orbits, with perihelion distances as large as 300 au. Massive disks that clear from the inside out on million-year timescales yield orbits that allow a super-Earth or gas giant to shepherd the minor planets as observed. A massive planet can achieve a similar orbit in a persistent, low-mass disk over the lifetime of the solar system.
Making Planet Nine: A Scattered Giant in the Outer Solar System
Bromley, Benjamin C.; Kenyon, Scott J.
2016-07-01
Correlations in the orbits of several minor planets in the outer solar system suggest the presence of a remote, massive Planet Nine. With at least 10 times the mass of the Earth and a perihelion well beyond 100 au, Planet Nine poses a challenge to planet formation theory. Here we expand on a scenario in which the planet formed closer to the Sun and was gravitationally scattered by Jupiter or Saturn onto a very eccentric orbit in an extended gaseous disk. Dynamical friction with the gas then allowed the planet to settle in the outer solar system. We explore this possibility with a set of numerical simulations. Depending on how the gas disk evolves, scattered super-Earths or small gas giants settle on a range of orbits, with perihelion distances as large as 300 au. Massive disks that clear from the inside out on million-year timescales yield orbits that allow a super-Earth or gas giant to shepherd the minor planets as observed. A massive planet can achieve a similar orbit in a persistent, low-mass disk over the lifetime of the solar system.
International Nuclear Information System (INIS)
Ohtani, H; Ito, A M; Hagita, K; Kato, T; Saitoh, T; Takeda, T
2013-01-01
We propose in this paper a data compression scheme for large-scale particle simulations, which has favorable prospects for scientific visualization of particle systems. Our data compression concepts deal with the data of particle orbits obtained by simulation directly and have the following features: (i) Through control over the compression scheme, the difference between the simulation variables and the reconstructed values for the visualization from the compressed data becomes smaller than a given constant. (ii) The particles in the simulation are regarded as independent particles and the time-series data for each particle is compressed with an independent time-step for the particle. (iii) A particle trajectory is approximated by a polynomial function based on the characteristic motion of the particle. It is reconstructed as a continuous curve through interpolation from the values of the function for intermediate values of the sample data. We name this concept ''TOKI (Time-Order Kinetic Irreversible compression)''. In this paper, we present an example of an implementation of a data-compression scheme with the above features. Several application results are shown for plasma and galaxy formation simulation data
Verdin, Andrew; Funk, Christopher C.; Rajagopalan, Balaji; Kleiber, William
2016-01-01
Robust estimates of precipitation in space and time are important for efficient natural resource management and for mitigating natural hazards. This is particularly true in regions with developing infrastructure and regions that are frequently exposed to extreme events. Gauge observations of rainfall are sparse but capture the precipitation process with high fidelity. Due to its high resolution and complete spatial coverage, satellite-derived rainfall data are an attractive alternative in data-sparse regions and are often used to support hydrometeorological early warning systems. Satellite-derived precipitation data, however, tend to underrepresent extreme precipitation events. Thus, it is often desirable to blend spatially extensive satellite-derived rainfall estimates with high-fidelity rain gauge observations to obtain more accurate precipitation estimates. In this research, we use two different methods, namely, ordinary kriging and κ-nearest neighbor local polynomials, to blend rain gauge observations with the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates in data-sparse Central America and Colombia. The utility of these methods in producing blended precipitation estimates at pentadal (five-day) and monthly time scales is demonstrated. We find that these blending methods significantly improve the satellite-derived estimates and are competitive in their ability to capture extreme precipitation.
Efficient linear precoding for massive MIMO systems using truncated polynomial expansion
Mü ller, Axel; Kammoun, Abla; Bjö rnson, Emil; Debbah, Mé roú ane
2014-01-01
Massive multiple-input multiple-output (MIMO) techniques have been proposed as a solution to satisfy many requirements of next generation cellular systems. One downside of massive MIMO is the increased complexity of computing the precoding
International Nuclear Information System (INIS)
Kalmykov, Mikhail Yu.; Kniehl, Bernd A.
2012-05-01
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.
On the fates of minor bodies in the outer solar system
International Nuclear Information System (INIS)
Gladman, B.; Duncan, M.
1990-01-01
The equations of motion of roughly one thousand test particles in the outer solar system for up to 22.5 million years have been integrated. The test particles are placed on initially circular orbits about the sun and feel the gravitational influence of the sun and four (or in some cases two) of the giant planets. The initial conditions of the planets are obtained from their current orbital elements, and their mutual gravitational interactions are fully included. Test particles that undergo a close approach to a planet are removed from the integration. Interior to Jupiter the creation of gaps in the test-particle semimajor-axis distribution appears to be associated with resonances in the outer asteroid belt. Exterior to Neptune there is a dynamical erosion of the region just beyond the giant planets (i.e., at the inner edge of the Kuiper belt). The majority of the test particles between the giant planets are perturbed to a close approach to a planet on timescales of millions of years. These results suggest that there are very few initially circular orbits between the giant planets that are stable against a close approach to a planet over the lifetime of the solar system. 45 refs
A Miniaturized Seismometer for Surface Measurements in the Outer Solar System
Banerdt, W. B.; Pike, W. T.
2001-01-01
Seismology is a powerful tool for investigating the inner structure and dynamic processes of a planetary body. The interior structure information derived from seismic measurements is complementary to other methods of probing the subsurface (such as gravity and electromagnetics), both in terms of spatial and depth resolution and the relevant types of material properties being sensed. The propagation of seismic waves is sensitive to composition (via density and elastic parameters), temperature (via attenuation) and physical state (solid vs. liquid). In addition, the seismicity (level and distribution in space and time of seismic activity) provides information on the impact flux and tectonic forces currently active within the body. The major satellites of the outer solar system provide obvious targets for seismic investigations. In addition, small bodies, such as asteroids and comets, can also benefit from seismic measurements. We have developed an extremely small, lightweight, low-power seismometer for planetary applications which is ideally suited for use in the outer solar system. This instrument has previously been proposed and selected for use on a comet (on the Rosetta Lander, subsequently deselected for programmatic reasons) and Mars (on the NetLander mission). Additional information is contained in the original extended abstract.
Dynamics of one-dimensional self-gravitating systems using Hermite-Legendre polynomials
Barnes, Eric I.; Ragan, Robert J.
2014-01-01
The current paradigm for understanding galaxy formation in the Universe depends on the existence of self-gravitating collisionless dark matter. Modelling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective non-linear dynamics of many particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyse the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase-space distribution functions f(x, v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.
Weierstrass polynomials for links
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
1997-01-01
There is a natural way of identifying links in3-space with polynomial covering spaces over thecircle. Thereby any link in 3-space can be definedby a Weierstrass polynomial over the circle. Theequivalence relation for covering spaces over thecircle is, however, completely different from...
Polynomial-time Algorithms for Computing Distances of Fuzzy Transition Systems
Chen, Taolue; Han, Tingting; Cao, Yongzhi
2017-01-01
Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature. Such a distance, defined as a pseudo-ultrametric over the state space of the model, provides a quantitative analogue of bisimilarity. In this paper, we focus on the problem of computing these distances. We first extend the definition of the pseudo-ultrametric by introducing discount such that the discounting factor being equal to 1 capture...
Atmospheric Mining in the Outer Solar System: Resource Capturing, Exploration, and Exploitation
Palaszewski, Bryan
2015-01-01
Atmospheric mining in the outer solar system (AMOSS) has been investigated as a means of fuel production for high-energy propulsion and power. Fusion fuels such as helium 3 (He-3) and hydrogen can be wrested from the atmospheres of Uranus and Neptune and either returned to Earth or used in-situ for energy production. 3He and hydrogen (deuterium, etc.) were the primary gases of interest, with hydrogen being the primary propellant for nuclear thermal solid core and gas core rocket-based atmospheric flight. A series of analyses were undertaken to investigate resource capturing aspects of AMOSS. These analyses included the gas capturing rate, storage options, and different methods of direct use of the captured gases. Additional supporting analyses were conducted to illuminate vehicle sizing and orbital transportation issues. While capturing 3He, large amounts of hydrogen and helium 4 (He-4) are produced. With these two additional gases, the potential exists for fueling small and large fleets of additional exploration and exploitation vehicles. Additional aerospacecraft or other aerial vehicles (UAVs, balloons, rockets, etc.) could fly through the outer-planet atmosphere to investigate cloud formation dynamics, global weather, localized storms or other disturbances, wind speeds, the poles, and so forth. Deep-diving aircraft (built with the strength to withstand many atmospheres of pressure) powered by the excess hydrogen or 4He may be designed to probe the higher density regions of the gas giants.
EVIDENCE FOR AN ACCRETION ORIGIN FOR THE OUTER HALO GLOBULAR CLUSTER SYSTEM OF M31
International Nuclear Information System (INIS)
Mackey, A. D.; Huxor, A. P.; Ferguson, A. M. N.; Irwin, M. J.; Chapman, S. C.; Tanvir, N. R.; McConnachie, A. W.; Ibata, R. A.; Lewis, G. F.
2010-01-01
We use a sample of newly discovered globular clusters from the Pan-Andromeda Archaeological Survey (PAndAS) in combination with previously cataloged objects to map the spatial distribution of globular clusters in the M31 halo. At projected radii beyond ∼30 kpc, where large coherent stellar streams are readily distinguished in the field, there is a striking correlation between these features and the positions of the globular clusters. Adopting a simple Monte Carlo approach, we test the significance of this association by computing the probability that it could be due to the chance alignment of globular clusters smoothly distributed in the M31 halo. We find that the likelihood of this possibility is low, below 1%, and conclude that the observed spatial coincidence between globular clusters and multiple tidal debris streams in the outer halo of M31 reflects a genuine physical association. Our results imply that the majority of the remote globular cluster system of M31 has been assembled as a consequence of the accretion of cluster-bearing satellite galaxies. This constitutes the most direct evidence to date that the outer halo globular cluster populations in some galaxies are largely accreted.
Arabic text classification using Polynomial Networks
Directory of Open Access Journals (Sweden)
Mayy M. Al-Tahrawi
2015-10-01
Full Text Available In this paper, an Arabic statistical learning-based text classification system has been developed using Polynomial Neural Networks. Polynomial Networks have been recently applied to English text classification, but they were never used for Arabic text classification. In this research, we investigate the performance of Polynomial Networks in classifying Arabic texts. Experiments are conducted on a widely used Arabic dataset in text classification: Al-Jazeera News dataset. We chose this dataset to enable direct comparisons of the performance of Polynomial Networks classifier versus other well-known classifiers on this dataset in the literature of Arabic text classification. Results of experiments show that Polynomial Networks classifier is a competitive algorithm to the state-of-the-art ones in the field of Arabic text classification.
Generalizations of orthogonal polynomials
Bultheel, A.; Cuyt, A.; van Assche, W.; van Barel, M.; Verdonk, B.
2005-07-01
We give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of these applications, which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, and random matrices.
STELLAR ACTIVITY AND EXCLUSION OF THE OUTER PLANET IN THE HD 99492 SYSTEM
Energy Technology Data Exchange (ETDEWEB)
Kane, Stephen R.; Thirumalachari, Badrinath; Hinkel, Natalie R. [Department of Physics and Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132 (United States); Henry, Gregory W. [Center of Excellence in Information Systems, Tennessee State University, 3500 John A. Merritt Blvd., Box 9501, Nashville, TN 37209 (United States); Jensen, Eric L. N. [Dept of Physics and Astronomy, Swarthmore College, Swarthmore, PA 19081 (United States); Boyajian, Tabetha S.; Fischer, Debra A. [Department of Astronomy, Yale University, New Haven, CT 06511 (United States); Howard, Andrew W. [Institute for Astronomy, University of Hawaii, Honolulu, HI 96822 (United States); Isaacson, Howard T. [Astronomy Department, University of California, Berkeley, CA 94720 (United States); Wright, Jason T., E-mail: skane@sfsu.edu [Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802 (United States)
2016-03-20
A historical problem for indirect exoplanet detection has been contending with the intrinsic variability of the host star. If the variability is periodic, it can easily mimic various exoplanet signatures, such as radial velocity (RV) variations that originate with the stellar surface rather than the presence of a planet. Here we present an update for the HD 99492 planetary system, using new RV and photometric measurements from the Transit Ephemeris Refinement and Monitoring Survey. Our extended time series and subsequent analyses of the Ca ii H and K emission lines show that the host star has an activity cycle of ∼13 years. The activity cycle correlates with the purported orbital period of the outer planet, the signature of which is thus likely due to the host star activity. We further include a revised Keplerian orbital solution for the remaining planet, along with a new transit ephemeris. Our transit-search observations were inconclusive.
Suess, S. T.; Thomas, B. T.; Nerney, S. F.
1985-01-01
Observations of the azimuthal component of the IMF are evaluated through the use of an MHD model which shows the effect of magnetic flux tubes opening in the outer solar system. It is demonstrated that the inferred meridional transport of magnetic flux is consistent with predictions by the MHD model. The computed azimuthal and radial magnetic flux deficits are almost identical to the observations. It is suggested that the simplest interpretation of the observations is that meridional flows are created by a direct body force on the plasma. This is consistent with the analytic model of Nerney and Suess (1975), in which such flux deficits in the IMF arise naturally from the meridional gradient in the spiralling field.
Time travel and chemical evolution - a look at the outer solar system
International Nuclear Information System (INIS)
Owen, T.
1987-01-01
It has been hypothesized that the chemical conditions today on the planets and moons of the outer solar system are similar to conditions on earth soon after it formed. If this is so, much can be learned about the chemistry that led to life on earth. While Jupiter is a poor terrestrial analog, its satellite Europa has a smooth icy surface that may cover a layer of liquid water tens of kilometers deep. It is possible that sunlight could filter through cracks in the ice, providing energy to drive chemical reactions in the water below the ice. It is noted that the surface of Titan may include lakes or oceans of ethane and that Triton may also have liquids on its surface. Studies of cometary nuclei will be undertaken during the Comet Rendezvous-Asteroid Flyby mission
Space weathering and the color indexes of minor bodies in the outer Solar System
Kaňuchová, Zuzana; Brunetto, Rosario; Melita, Mario; Strazzulla, Giovanni
2012-09-01
The surfaces of small bodies in the outer Solar System are rich in organic compounds and carbonaceous refractories mixed with ices and silicates. As made clear by dedicated laboratory experiments space weathering (e.g. energetic ion bombardment) can produce red colored materials starting from bright and spectrally flat ices. In a classical scenario, the space weathering processes “nurture” alter the small bodies surface spectra but are in competition with resurfacing agents that restore the original colors, and the result of these competing processes continuously modifying the surfaces is supposed to be responsible for the observed spectral variety of those small bodies. However an alternative point of view is that the different colors are due to “nature” i.e. to the different primordial composition of different objects. In this paper we present a model, based on laboratory results, that gives an original contribution to the “nature” vs. “nurture” debate by addressing the case of surfaces showing different fractions of rejuvenated vs. space weathered surface, and calculating the corresponding color variations. We will show how a combination of increasing dose coupled to different resurfacing can reproduce the whole range of observations of small outer Solar System bodies. Here we demonstrate, for the first time that objects having a fully weathered material turn back in the color-color diagrams. At the same time, object with the different ratio of pristine and weathered surface areas lay on specific lines in color-color diagrams, if exposed to the same amount of irradiation.
Superiority of legendre polynomials to Chebyshev polynomial in ...
African Journals Online (AJOL)
In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev ...
International Nuclear Information System (INIS)
Hansen, E.J.; Frisch, C.F.; McDade, R.L. Jr.; Johnston, K.H.
1981-01-01
Outer membrane proteins of Haemophilus influenzae type b which are immunogenic in infant rats were identified by a radioimmunoprecipitation method. Intact cells of H. influenzae type b were radioiodinated by a lactoperoxidase-catalyzed procedure, and an outer membrane-containing fraction was prepared from these cells. These radioiodinated outer membranes were mixed with sera obtained from rats convalescing from systemic H. influenzae type b disease induced at 6 days of age, and the resultant (antibody-outer membrane protein antigen) complexes were extracted from these membranes by treatment with nonionic detergent and ethylenediaminetetraacetic acid. These soluble antibody-antigen complexes were isolated by means of adsorption to protein A-bearing staphylococci, and the radioiodinated protein antigens were identified by gel electrophoresis followed by autoradiography. Infant rats were shown to mount a readily detectable antibody response to several different proteins present in the outer membrane of H. influenzae type b. Individual infant rats were found to vary both qualitatively and quantitatively in their immune response to these immunogenic outer membrane proteins
Extended biorthogonal matrix polynomials
Directory of Open Access Journals (Sweden)
Ayman Shehata
2017-01-01
Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.
Golden, Ryan; Cho, Ilwoo
2015-01-01
In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...
Quantum entanglement via nilpotent polynomials
International Nuclear Information System (INIS)
Mandilara, Aikaterini; Akulin, Vladimir M.; Smilga, Andrei V.; Viola, Lorenza
2006-01-01
We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed
Chromatic polynomials for simplicial complexes
DEFF Research Database (Denmark)
Møller, Jesper Michael; Nord, Gesche
2016-01-01
In this note we consider s s -chromatic polynomials for finite simplicial complexes. When s=1 s=1 , the 1 1 -chromatic polynomial is just the usual graph chromatic polynomial of the 1 1 -skeleton. In general, the s s -chromatic polynomial depends on the s s -skeleton and its value at r...
The Outer Solar System Origins Survey. I. ; Design and First-Quarter Discoveries
Bannister, Michele T.; Kavelaars, J. J.; Petit, Jean-Marc; Gladman, Brett J.; Gwyn, Stephen D. J.; Chen, Ying-Tung; Volk, Kathryn; Alexandersen, Mike; Benecchi, Susan D.; Delsanti, Audrey;
2016-01-01
We report the discovery, tracking, and detection circumstances for 85 trans-Neptunian objects (TNOs) from the first 42 square degrees of the Outer Solar System Origins Survey. This ongoing r-band solar system survey uses the 0.9 square degree field of view MegaPrime camera on the 3.6 meter Canada-France-Hawaii Telescope. Our orbital elements for these TNOs are precise to a fractional semimajor axis uncertainty of less than 0.1 percent. We achieve this precision in just two oppositions, as compared to the normal three to five oppositions, via a dense observing cadence and innovative astrometric technique. These discoveries are free of ephemeris bias, a first for large trans-Neptunian surveys. We also provide the necessary information to enable models of TNO orbital distributions to be tested against our TNO sample. We confirm the existence of a cold "kernel" of objects within the main cold classical Kuiper Belt and infer the existence of an extension of the "stirred" cold classical Kuiper Belt to at least several au beyond the 2:1 mean motion resonance with Neptune. We find that the population model of Petit et al. remains a plausible representation of the Kuiper Belt. The full survey, to be completed in 2017, will provide an exquisitely characterized sample of important resonant TNO populations, ideal for testing models of giant planet migration during the early history of the solar system.
The theory of contractions of 2D 2nd order quantum superintegrable systems and its relation to the Askey scheme for hypergeometric orthogonal polynomials
International Nuclear Information System (INIS)
Miller, Willard Jr
2014-01-01
We describe a contraction theory for 2nd order superintegrable systems, showing that all such systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. Analogously, all of the quadratic symmetry algebras of these systems can be obtained by a sequence of contractions starting from S9. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.This relates the scheme directly to explicitly solvable quantum mechanical systems. Amazingly, all of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2, C). The present paper concentrates on describing this intimate link between Lie algebra and superintegrable system contractions, with the detailed calculations presented elsewhere. Joint work with E. Kalnins, S. Post, E. Subag and R. Heinonen.
Looking for Life in the Ocean Worlds of the Outer Solar System
Lunine, Jonathan I.; Waite, J. Hunter
2016-04-01
Interest in searching for life in the outer solar system has intensified recently with the new start of the Europa Multiple Flyby Mission and the insertion through a NASA community announcement of an Ocean Worlds (Titan and Enceladus) theme in the list of possible New Frontiers Missions. As part of a Discovery proposal called "Enceladus Life Finder", or ELF, a multidisciplinary team of scientists led by the authors developed a set of measurements for determining the habitability of Enceladus' internal ocean and the presence of biological activity therein, obtained by flying through Enceladus' plume. We call this set of measurements "Life's intrinsic forensic evidence", or LIFE. The LIFE protocol is implemented by flying two mass spectrometers through the plume -one optimized for gas and the other for ice. The measurements and information derived therefrom cut to the heart of what biological activity does that distinguishes it from abiotic processes. They also tightly constrain the essential parameters of ocean habitability including pH, redox state, available free energy and temperature of any active hydrothermal systems on the floor of the Enceladus ocean. In addition to Enceladus, such a protocol is applicable to Europa should deep-seated plumes be present there, Further, with appropriate modifications from terrestrial-type biochemistry, LIFE is potentially applicable to testing for exotic biochemistries in the seas of Titan. In this talk we will focus on the basic concept of the LIFE protocol and explain its application to each of these bodies.
Progressive outer retinal necrosis syndrome in the course of systemic lupus erythematosus.
Turno-Kręcicka, A; Tomczyk-Socha, M; Zimny, A
2016-12-01
Progressive outer retinal necrosis syndrome (PORN) is a severe clinical variant of necrotizing herpetic chorioretinitis, which occurs almost exclusively in patients with advanced acquired immunodeficiency syndrome (AIDS). To date, only a few cases of PORN have been reported in patients, mostly among those who were immunocompromised. To our knowledge, only one case of PORN in a patient with systemic lupus erythematosus (SLE) has been described. We report the case of a 44-year old HIV-negative patient with lupus nephritis, whom was being treated by mycophenolate mophetil (MMF), arechin and prednisone. After 14 months of MMF therapy, the patient revealed PORN symptoms; and several months later, the patient developed Type B primary central nervous system lymphoma (PCNSL). PORN is usually compared to acute retinal necrosis (ARN) syndrome, because of having the same causative agent: varicella zoster virus (VZV). There are also some similarities in clinical findings. Our observation supports the hypothesis that PORN symptoms in HIV-negative patients can be an intermediate form between ARN and PORN, and can vary according to the patient's immune status. © The Author(s) 2016.
Lam, H K
2012-02-01
This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.
THE M33 GLOBULAR CLUSTER SYSTEM WITH PAndAS DATA: THE LAST OUTER HALO CLUSTER?
International Nuclear Information System (INIS)
Cockcroft, Robert; Harris, William E.; Ferguson, Annette M. N.
2011-01-01
We use CFHT/MegaCam data to search for outer halo star clusters in M33 as part of the Pan-Andromeda Archaeological Survey. This work extends previous studies out to a projected radius of 50 kpc and covers over 40 deg 2 . We find only one new unambiguous star cluster in addition to the five previously known in the M33 outer halo (10 kpc ≤ r ≤ 50 kpc). Although we identify 2440 cluster candidates of various degrees of confidence from our objective image search procedure, almost all of these are likely background contaminants, mostly faint unresolved galaxies. We measure the luminosity, color, and structural parameters of the new cluster in addition to the five previously known outer halo clusters. At a projected radius of 22 kpc, the new cluster is slightly smaller, fainter, and redder than all but one of the other outer halo clusters, and has g' ∼ 19.9, (g' - i') ∼ 0.6, concentration parameter c ∼ 1.0, a core radius r c ∼ 3.5 pc, and a half-light radius r h ∼ 5.5 pc. For M33 to have so few outer halo clusters compared to M31 suggests either tidal stripping of M33's outer halo clusters by M31, or a very different, much calmer accretion history of M33.
Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation
International Nuclear Information System (INIS)
Demina, Maria V; Kudryashov, Nikolai A
2012-01-01
Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of any system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is also obtained that translating relative equilibria of point vortices with arbitrary circulations can be constructed using a generalization of the Tkachenko equation. Roots of any pair of polynomials solving the Tkachenko equation and the generalized Tkachenko equation are proved to give positions of point vortices in stationary and translating relative equilibria accordingly. These results are valid even if the polynomials in a pair have multiple or common roots. It is obtained that the Adler–Moser polynomial provides non-unique polynomial solutions of the Tkachenko equation. It is shown that the generalized Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers. (paper)
Lunine, J. I.; Stevenson, D. J.
1985-01-01
The thermodynamic stability of clathrate hydrate is calculated to predict the formation conditions corresponding to a range of solar system parameters. The calculations were performed using the statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data concerning clathrate hydrate and its components. Dissociation pressures and partition functions (Langmuir constants) are predicted at low pressure for CO clathrate (hydrate) using the properties of chemicals similar to CO. It is argued that nonsolar but well constrained noble gas abundances may be measurable by the Galileo spacecraft in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances of the Jovian satellite Titan are predicted, assuming that most of the methane in Titan is accreted as clathrate. It is suggested that under thermodynamically appropriate conditions, complete clathration of water ice could have occurred in high-pressure nebulas around giant planets, but probably not in the outer solar nebula. The stability of clathrate in other pressure ranges is also discussed.
Production of Oxidants by Ion Bombardment of Icy Moons in the Outer Solar System
Directory of Open Access Journals (Sweden)
Philippe Boduch
2011-01-01
Full Text Available Our groups in Brazil, France and Italy have been active, among others in the world, in performing experiments on physical-chemical effects induced by fast ions colliding with solids (frozen gases, carbonaceous and organic materials, silicates, etc. of astrophysical interest. The used ions span a very large range of energies, from a few keV to hundreds MeV. Here we present a summary of the results obtained so far on the formation of oxidants (hydrogen peroxide and ozone after ion irradiation of frozen water, carbon dioxide and their mixtures. Irradiation of pure water ice produces hydrogen peroxide whatever is the used ion and at different temperatures. Irradiation of carbon dioxide and water frozen mixtures result in the production of molecules among which hydrogen peroxide and ozone. The experimental results are discussed in the light of the relevance they have to support the presence of an energy source for biosphere on Europa and other icy moons in the outer Solar System.
Okounkov's BC-Type Interpolation Macdonald Polynomials and Their q=1 Limit
Koornwinder, T.H.
2015-01-01
This paper surveys eight classes of polynomials associated with A-type and BC-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or shifted) Jack and Macdonald polynomials and their BC-type extensions. Among these the BC-type interpolation Jack polynomials were
International Nuclear Information System (INIS)
Schardt, A.W.; Behannon, K.W.; Lepping, R.P.; Carbary, J.F.; Eviatar, A.; Siscoe, G.L.
1984-01-01
Similarities between the Saturnian and terrestrial outer magnetosphere are examined. Saturn, like earth, has a fully developed magnetic tail, 80 to 100 RS in diameter. One major difference between the two outer magnetospheres is the hydrogen and nitrogen torus produced by Titan. This plasma is, in general, convected in the corotation direction at nearly the rigid corotation speed. Energies of magnetospheric particles extend to above 500 keV. In contrast, interplanetary protons and ions above 2 MeV have free access to the outer magnetosphere to distances well below the Stormer cutoff. This access presumably occurs through the magnetotail. In addition to the H+, H2+, and H3+ ions primarily of local origin, energetic He, C, N, and O ions are found with solar composition. Their flux can be substantially enhanced over that of interplanetary ions at energies of 0.2 to 0.4 MeV/nuc
Colouring and knot polynomials
International Nuclear Information System (INIS)
Welsh, D.J.A.
1991-01-01
These lectures will attempt to explain a connection between the recent advances in knot theory using the Jones and related knot polynomials with classical problems in combinatorics and statistical mechanics. The difficulty of some of these problems will be analysed in the context of their computational complexity. In particular we shall discuss colourings and groups valued flows in graphs, knots and the Jones and Kauffman polynomials, the Ising, Potts and percolation problems of statistical physics, computational complexity of the above problems. (author). 20 refs, 9 figs
Additive and polynomial representations
Krantz, David H; Suppes, Patrick
1971-01-01
Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz
Modeling Surface Processes Occurring on Moons of the Outer Solar System
Umurhan, O. M.; White, O. L.; Moore, J. M.; Howard, A. D.; Schenk, P.
2016-12-01
A variety of processes, some with familiar terrestrial analogs, are known to take place on moon surfaces in the outer solar system. In this talk, we discuss the observed features of mass wasting and surface transport seen on both Jupiter's moon Calisto and one of Saturn's Trojan moons Helene. We provide a number of numerical models using upgraded version of MARSSIM in support of several hypotheses suggested on behalf of the observations made regarding these objects. Calisto exhibits rolling plains of low albedo materials surrounding relatively high jutting peaks harboring high albedo deposits. Our modeling supports the interpretation that Calisto's surface is a record of erosion driven by the sublimation of CO2 and H2O contained in the bedrock. Both solar insolation and surface re-radiation drives the sublimation leaving behind debris which we interpret to be the observed darkened regolith and, further, the high albedo peaks are water ice deposits on surface cold traps. On the other hand, the 45 km scale Helene, being a milligravity environment, exhibits mysterious looking streaks and grooves of very high albedo materials extending for several kilometers with a down-sloping grade of 7o-9o. Helene's cratered terrain also shows evidence of narrowed septa. The observed surface features suggest some type of advective processes are at play in this system. Our modeling lends support to the suggestion that Helene's surface materials behave as a Bingham plastic material - our flow modeling with such rheologies can reproduce the observed pattern of streakiness depending upon the smoothness of the underlying bedrock; the overall gradients observed; and the narrowed septa of inter-crater regions.
Extreme Worlds of the Outer Solar System: Dynamic Processes on Uranus & Io
Kleer, Katherine Rebecca de
A central goal of planetary science is the creation of a framework within which the properties of each solar system body can be understood as the product of initial conditions acted on by fundamental physical processes. The solar system's extreme worlds -- those objects that lie at the far ends of the spectrum in terms of planetary environment -- bring to light our misconceptions and present us with opportunities to expand and generalize this framework. Unraveling the processes at work in diverse planetary environments contextualizes our understanding of Earth, and provides a basis for interpreting specific signatures from planets beyond our own solar system. Uranus and Io, with their unusual planetary environments, present two examples of such worlds in the outer solar system. Uranus, one of the outer solar system's ice giants, produces an anomalously low heat flow and orbits the sun on its side. Its relative lack of bright storm features and its bizarre multi-decadal seasons provide insight into the relative effects of internal heat flow and time- varying solar insolation on atmospheric dynamics, while its narrow rings composed of dark, macroscopic particles encode the history of bombardment and satellite disruption within the system. Jupiter's moon Io hosts the most extreme volcanic activity anywhere in the solar system. Its tidally-powered geological activity provides a window into this satellite's interior, permitting rare and valuable investigations into the exchange of heat and materials between interiors and surfaces. In particular, Io provides a laboratory for studying the process of tidal heating, which shapes planets and satellites in our solar system and beyond. A comparison between Earth and Io contextualizes the volcanism at work on our home planet, revealing the effects of planetary size, atmospheric density, and plate tectonics on the style and mechanisms of geological activity. This dissertation investigates the processes at work on these solar
Zubarev, Anatoliy; Kozlova, Natalia; Kokhanov, Alexander; Oberst, Jürgen; Nadezhdina, Irina; Patraty, Vyacheslav; Karachevtseva, Irina
Introduction. While Galilean satellites have been observed by different spacecrafts, including Pioneer, Voyager-1 and -2, Galileo, New Horizons, and Enceladus by Cassini and Voyager-2, only data from Galileo, Cassini and the two Voyagers are useful for precise mapping [1, 2]. For purposes of future missions to the system of outer planets we have re-computed the control point network of the Io, Ganymede and Enceladus to support spacecraft navigation and coordinate knowledge. Based on the control networks, we have produced global image mosaics and maps. Geodesy approach. For future mission Laplace-P we mainly focused on Ganymede which coverage is nearly complete except for polar areas (which includes multispectral data). However, large differences exist in data resolutions (minimum global resolution: 30 km/pixel). Only few areas enjoy coverage by highest resolution images, so we suggest to obtain regional Digital Elevation Models (DEMs) from stereo images for selected areas. Also using our special software, we provide calculation of illumination conditions of Ganymede surface in various representations [3]. Finally, we propose a careful evaluation of all available data from the previous Voyager and Galileo missions to re-determine geodetic control and rotation model for other Galilean satellites - Callisto and Europe. Mapping. Based on re-calculated control point networks and global mosaics we have prepared new maps for Io, Ganymede and Enceladus [4]. Due to the difference in resolution between the images, which were also taken from different angles relative to the surface, we can prepare only regional high resolution shape models, so for demonstrating of topography and mapping of the satellites we used orthographic projection with different parameters. Our maps, which include roughness calculations based on our GIS technologies [5], will also be an important tool for studies of surface morphology. Conclusions. Updated data collection, including new calculation of
On the Laurent polynomial rings
International Nuclear Information System (INIS)
Stefanescu, D.
1985-02-01
We describe some properties of the Laurent polynomial rings in a finite number of indeterminates over a commutative unitary ring. We study some subrings of the Laurent polynomial rings. We finally obtain two cancellation properties. (author)
Computing the Alexander Polynomial Numerically
DEFF Research Database (Denmark)
Hansen, Mikael Sonne
2006-01-01
Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically.......Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically....
Ates, Louis S.
2015-05-04
Mycobacteria possess different type VII secretion (T7S) systems to secrete proteins across their unusual cell envelope. One of these systems, ESX-5, is only present in slow-growing mycobacteria and responsible for the secretion of multiple substrates. However, the role of ESX-5 substrates in growth and/or virulence is largely unknown. In this study, we show that esx-5 is essential for growth of both Mycobacterium marinum and Mycobacterium bovis. Remarkably, this essentiality can be rescued by increasing the permeability of the outer membrane, either by altering its lipid composition or by the introduction of the heterologous porin MspA. Mutagenesis of the first nucleotide-binding domain of the membrane ATPase EccC5 prevented both ESX-5-dependent secretion and bacterial growth, but did not affect ESX-5 complex assembly. This suggests that the rescuing effect is not due to pores formed by the ESX-5 membrane complex, but caused by ESX-5 activity. Subsequent proteomic analysis to identify crucial ESX-5 substrates confirmed that all detectable PE and PPE proteins in the cell surface and cell envelope fractions were routed through ESX-5. Additionally, saturated transposon-directed insertion-site sequencing (TraDIS) was applied to both wild-type M. marinum cells and cells expressing mspA to identify genes that are not essential anymore in the presence of MspA. This analysis confirmed the importance of esx-5, but we could not identify essential ESX-5 substrates, indicating that multiple of these substrates are together responsible for the essentiality. Finally, examination of phenotypes on defined carbon sources revealed that an esx-5 mutant is strongly impaired in the uptake and utilization of hydrophobic carbon sources. Based on these data, we propose a model in which the ESX-5 system is responsible for the transport of cell envelope proteins that are required for nutrient uptake. These proteins might in this way compensate for the lack of MspA-like porins in slow
Directory of Open Access Journals (Sweden)
Louis S Ates
2015-05-01
Full Text Available Mycobacteria possess different type VII secretion (T7S systems to secrete proteins across their unusual cell envelope. One of these systems, ESX-5, is only present in slow-growing mycobacteria and responsible for the secretion of multiple substrates. However, the role of ESX-5 substrates in growth and/or virulence is largely unknown. In this study, we show that esx-5 is essential for growth of both Mycobacterium marinum and Mycobacterium bovis. Remarkably, this essentiality can be rescued by increasing the permeability of the outer membrane, either by altering its lipid composition or by the introduction of the heterologous porin MspA. Mutagenesis of the first nucleotide-binding domain of the membrane ATPase EccC5 prevented both ESX-5-dependent secretion and bacterial growth, but did not affect ESX-5 complex assembly. This suggests that the rescuing effect is not due to pores formed by the ESX-5 membrane complex, but caused by ESX-5 activity. Subsequent proteomic analysis to identify crucial ESX-5 substrates confirmed that all detectable PE and PPE proteins in the cell surface and cell envelope fractions were routed through ESX-5. Additionally, saturated transposon-directed insertion-site sequencing (TraDIS was applied to both wild-type M. marinum cells and cells expressing mspA to identify genes that are not essential anymore in the presence of MspA. This analysis confirmed the importance of esx-5, but we could not identify essential ESX-5 substrates, indicating that multiple of these substrates are together responsible for the essentiality. Finally, examination of phenotypes on defined carbon sources revealed that an esx-5 mutant is strongly impaired in the uptake and utilization of hydrophobic carbon sources. Based on these data, we propose a model in which the ESX-5 system is responsible for the transport of cell envelope proteins that are required for nutrient uptake. These proteins might in this way compensate for the lack of Msp
Ates, Louis S.; Ummels, Roy; Commandeur, Susanna; van der Weerd, Robert; Sparrius, Marion; Weerdenburg, Eveline; Alber, Marina; Kalscheuer, Rainer; Piersma, Sander R.; Abdallah, Abdallah; Abd El Ghany, Moataz; Abdel-Haleem, Alyaa M.; Pain, Arnab; Jimé nez, Connie R.; Bitter, Wilbert; Houben, Edith N.G.
2015-01-01
Mycobacteria possess different type VII secretion (T7S) systems to secrete proteins across their unusual cell envelope. One of these systems, ESX-5, is only present in slow-growing mycobacteria and responsible for the secretion of multiple substrates. However, the role of ESX-5 substrates in growth and/or virulence is largely unknown. In this study, we show that esx-5 is essential for growth of both Mycobacterium marinum and Mycobacterium bovis. Remarkably, this essentiality can be rescued by increasing the permeability of the outer membrane, either by altering its lipid composition or by the introduction of the heterologous porin MspA. Mutagenesis of the first nucleotide-binding domain of the membrane ATPase EccC5 prevented both ESX-5-dependent secretion and bacterial growth, but did not affect ESX-5 complex assembly. This suggests that the rescuing effect is not due to pores formed by the ESX-5 membrane complex, but caused by ESX-5 activity. Subsequent proteomic analysis to identify crucial ESX-5 substrates confirmed that all detectable PE and PPE proteins in the cell surface and cell envelope fractions were routed through ESX-5. Additionally, saturated transposon-directed insertion-site sequencing (TraDIS) was applied to both wild-type M. marinum cells and cells expressing mspA to identify genes that are not essential anymore in the presence of MspA. This analysis confirmed the importance of esx-5, but we could not identify essential ESX-5 substrates, indicating that multiple of these substrates are together responsible for the essentiality. Finally, examination of phenotypes on defined carbon sources revealed that an esx-5 mutant is strongly impaired in the uptake and utilization of hydrophobic carbon sources. Based on these data, we propose a model in which the ESX-5 system is responsible for the transport of cell envelope proteins that are required for nutrient uptake. These proteins might in this way compensate for the lack of MspA-like porins in slow
Stochastic Estimation via Polynomial Chaos
2015-10-01
AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2016-05-15
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
Polynomial optimization : Error analysis and applications
Sun, Zhao
2015-01-01
Polynomial optimization is the problem of minimizing a polynomial function subject to polynomial inequality constraints. In this thesis we investigate several hierarchies of relaxations for polynomial optimization problems. Our main interest lies in understanding their performance, in particular how
Roots of the Chromatic Polynomial
DEFF Research Database (Denmark)
Perrett, Thomas
The chromatic polynomial of a graph G is a univariate polynomial whose evaluation at any positive integer q enumerates the proper q-colourings of G. It was introduced in connection with the famous four colour theorem but has recently found other applications in the field of statistical physics...... extend Thomassen’s technique to the Tutte polynomial and as a consequence, deduce a density result for roots of the Tutte polynomial. This partially answers a conjecture of Jackson and Sokal. Finally, we refocus our attention on the chromatic polynomial and investigate the density of chromatic roots...
Polynomials in algebraic analysis
Multarzyński, Piotr
2012-01-01
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \\cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear ...
Colours of minor bodies in the outer solar system. II. A statistical analysis revisited
Hainaut, O. R.; Boehnhardt, H.; Protopapa, S.
2012-10-01
We present an update of the visible and near-infrared colour database of Minor Bodies in the Outer Solar System (MBOSSes), which now includes over 2000 measurement epochs of 555 objects, extracted from over 100 articles. The list is fairly complete as of December 2011. The database is now large enough to enable any dataset with a large dispersion to be safely identified and rejected from the analysis. The selection method used is quite insensitive to individual outliers. Most of the rejected datasets were observed during the early days of MBOSS photometry. The individual measurements are combined in a way that avoids possible rotational artifacts. The spectral gradient over the visible range is derived from the colours, as well as the R absolute magnitude M(1,1). The average colours, absolute magnitude, and spectral gradient are listed for each object, as well as the physico-dynamical classes using a classification adapted from Gladman and collaborators. Colour-colour diagrams, histograms, and various other plots are presented to illustrate and investigate class characteristics and trends with other parameters, whose significances are evaluated using standard statistical tests. Except for a small discrepancy for the J-H colour, the largest objects, with M(1,1) < 5, are indistinguishable from the smaller ones. The larger ones are slightly bluer than the smaller ones in J-H. Short-period comets, Plutinos and other resonant objects, hot classical disk objects, scattered disk objects and detached disk objects have similar properties in the visible, while the cold classical disk objects and the Jupiter Trojans form two separate groups of their spectral properties in the visible wavelength range. The well-known colour bimodality of Centaurs is confirmed. The hot classical disk objects with large inclinations, or large orbital excitations are found to be bluer than the others, confirming a previously known result. Additionally, the hot classical disk objects with a
Sagan, Carl; Thompson, W. Reid; Chyba, Christopher F.; Khare, B. N.
1991-01-01
A review and partial summary of projects within several areas of research generally involving the origin, distribution, chemistry, and spectral/dielectric properties of volatiles and organic materials in the outer solar system and early terrestrial environments are presented. The major topics covered include: (1) impact delivery of volatiles and organic compounds to the early terrestrial planets; (2) optical constants measurements; (3) spectral classification, chemical processes, and distribution of materials; and (4) radar properties of ice, hydrocarbons, and organic heteropolymers.
Open Problems Related to the Hurwitz Stability of Polynomials Segments
Directory of Open Access Journals (Sweden)
Baltazar Aguirre-Hernández
2018-01-01
Full Text Available In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
International Nuclear Information System (INIS)
Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray
2003-01-01
Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray
2003-07-01
Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.
Global sensitivity analysis by polynomial dimensional decomposition
Energy Technology Data Exchange (ETDEWEB)
Rahman, Sharif, E-mail: rahman@engineering.uiowa.ed [College of Engineering, The University of Iowa, Iowa City, IA 52242 (United States)
2011-07-15
This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.
Kurz, W.; Ferre, E. C.; Robertson, A. H. F.; Avery, A. J.; Kutterolf, S.
2015-12-01
During International Ocean Discovery Program (IODP) Expedition 352, a section through the volcanic stratigraphy of the outer fore arc of the Izu-Bonin-Mariana (IBM) system was drilled to trace magmatism, tectonics, and crustal accretion associated with subduction initiation. Structures within drill cores, borehole and site survey seismic data indicate that tectonic deformation in the outer IBM fore arc is mainly post-magmatic. Extension generated asymmetric sediment basins such as half-grabens at sites 352-U1439 and 352-U1442 on the upper trench slope. Along their eastern margins the basins are bounded by west-dipping normal faults. Deformation was localized along multiple sets of faults, accompanied by syn-tectonic pelagic and volcaniclastic sedimentation. The lowermost sedimentary units were tilted eastward by ~20°. Tilted beds were covered by sub-horizontal beds. Biostratigraphic constraints reveal a minimum age of the oldest sediments at ~ 35 Ma; timing of the sedimentary unconformities is between ~ 27 and 32 Ma. At sites 352-U1440 and 352-U1441 on the outer fore arc strike-slip faults are bounding sediment basins. Sediments were not significantly affected by tectonic tilting. Biostratigraphy gives a minimum age of the basement-cover contact between ~29.5 and 32 Ma. The post-magmatic structures reveal a multiphase tectonic evolution of the outer IBM fore arc. At sites 352-U1439 and 352-U1442, shear with dominant reverse to oblique reverse displacement was localized along subhorizontal fault zones, steep slickensides and shear fractures. These were either re-activated as or cut by normal-faults and strike-slip faults. Extension was also accommodated by steep to subvertical mineralized veins and extensional fractures. Faults at sites 352-U1440 and 352-U1441 show mainly strike-slip kinematics. Sediments overlying the igneous basement(maximum Late Eocene to Recent age), document ash and aeolian input, together with mass wasting of the fault-bounded sediment ponds.
Polynomial approximation on polytopes
Totik, Vilmos
2014-01-01
Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
International Nuclear Information System (INIS)
Milks, Matthew M; Guise, Hubert de
2005-01-01
The construction of su(2) intelligent states is simplified using a polynomial representation of su(2). The cornerstone of the new construction is the diagonalization of a 2 x 2 matrix. The method is sufficiently simple to be easily extended to su(3), where one is required to diagonalize a single 3 x 3 matrix. For two perfectly general su(3) operators, this diagonalization is technically possible but the procedure loses much of its simplicity owing to the algebraic form of the roots of a cubic equation. Simplified expressions can be obtained by specializing the choice of su(3) operators. This simpler construction will be discussed in detail
Minimal residual method stronger than polynomial preconditioning
Energy Technology Data Exchange (ETDEWEB)
Faber, V.; Joubert, W.; Knill, E. [Los Alamos National Lab., NM (United States)] [and others
1994-12-31
Two popular methods for solving symmetric and nonsymmetric systems of equations are the minimal residual method, implemented by algorithms such as GMRES, and polynomial preconditioning methods. In this study results are given on the convergence rates of these methods for various classes of matrices. It is shown that for some matrices, such as normal matrices, the convergence rates for GMRES and for the optimal polynomial preconditioning are the same, and for other matrices such as the upper triangular Toeplitz matrices, it is at least assured that if one method converges then the other must converge. On the other hand, it is shown that matrices exist for which restarted GMRES always converges but any polynomial preconditioning of corresponding degree makes no progress toward the solution for some initial error. The implications of these results for these and other iterative methods are discussed.
Fast beampattern evaluation by polynomial rooting
Häcker, P.; Uhlich, S.; Yang, B.
2011-07-01
Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.
Moore, Jeffrey Morgan; Howard, Alan D.; Schenk, Paul M.
2013-01-01
Mass movement and landform degradation reduces topographic relief by moving surface materials to a lower gravitational potential. In addition to the obvious role of gravity, abrasive mechanical erosion plays a role, often in combination with the lowering of cohesion, which allows disaggregation of the relief-forming material. The identification of specific landform types associated with mass movement and landform degradation provides information about local sediment particle size and abundance and transportation processes. Generally, mass movements can be classified in terms of the particle sizes of the transported material and the speed the material moved during transport. Most degradation on outer planet satellites appears consistent with sliding or slumping, impact erosion, and regolith evolution. Some satellites, such as Callisto and perhaps Hyperion and Iapetus, have an appearance that implies that some additional process is at work, most likely sublimation-driven landform modification and mass wasting. A variant on this process is thermally driven frost segregation as seen on all three icy Galilean satellites and perhaps elsewhere. Titan is unique among outer planet satellites in that Aeolian and fluvial processes also operate to erode, transport, and deposit material. We will evaluate the sequence and extent of various landform-modifying erosional and volatile redistribution processes that have shaped these icy satellites using a 3-D model that simulates the following surface and subsurface processes: 1) sublimation and re-condensation of volatiles; 2) development of refractory lag deposits; 3) disaggregation and downward sloughing of surficial material; 4) radiative heating/cooling of the surface (including reflection, emission, and shadowing by other surface elements); 5) thermal diffusion; and 6) vapor diffusion. The model will provide explicit simulations of landform development and thusly predicts the topographic and volatile evolution of the surface
Vasconcelos, F A; Pilling, S; Rocha, W R M; Rothard, H; Boduch, P
2017-09-13
In order to investigate the role of medium mass cosmic rays and energetic solar particles in the processing of N 2 -rich ice on frozen moons and cold objects in the outer solar system, the bombardment of an N 2 : H 2 O : NH 3 : CO 2 (98.2 : 1.5 : 0.2 : 0.1) ice mixture at 16 K employing 15.7 MeV 16 O 5+ was performed. The changes in the ice chemistry were monitored and quantified by Fourier transformed infrared spectroscopy (FTIR). The results indicate the formation of azide radicals (N 3 ), and nitrogen oxides, such as NO, NO 2 , and N 2 O, as well as the production of CO, HNCO, and OCN - . The effective formation and destruction cross-sections are roughly on the order of 10 -12 cm 2 and 10 -13 cm 2 , respectively. From laboratory molecular analyses, we estimated the destruction yields for the parent species and the formation yields for the daughter species. For N 2 , this value was 9.8 × 10 5 molecules per impact of ions, and for the most abundant new species (N 3 ), it was 1.1 × 10 5 molecules per impact of ions. From these yields, an estimation of how many species are destroyed or formed in a given timescale (10 8 years) in icy bodies in the outer solar system was calculated. This work reinforces the idea that such physicochemical processes triggered by cosmic rays, solar wind, and magnetospheric particles (medium-mass ions) in nitrogen-rich ices may play an important role in the formation of molecules (including pre-biotic species precursors such as amino acids and other "CHON" molecules) in very cold astrophysical environments, such as those in the outer region of the solar system (e.g. Titan, Triton, Pluto, and other KBOs).
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Orthogonal polynomials derived from the tridiagonal representation approach
Alhaidari, A. D.
2018-01-01
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose properties give the structure and dynamics of the corresponding physical system. For a certain range of parameters, one of these polynomials has a mix of continuous and discrete spectra making it suitable for describing physical systems with both scattering and bound states. In this work, we define these polynomials by their recursion relations and highlight some of their properties using numerical means. Due to the prime significance of these polynomials in physics, we hope that our short expose will encourage experts in the field of orthogonal polynomials to study them and derive their properties (weight functions, generating functions, asymptotics, orthogonality relations, zeros, etc.) analytically.
Polynomial methods in combinatorics
Guth, Larry
2016-01-01
This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book. Some of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accompl...
Polynomial representations of GLn
Green, James A; Erdmann, Karin
2007-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Polynomial representations of GLN
Green, James A
1980-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Polynomials formalism of quantum numbers
International Nuclear Information System (INIS)
Kazakov, K.V.
2005-01-01
Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru
Efficient computation of Laguerre polynomials
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2017-01-01
textabstractAn efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials . Ln(α)(z) are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for . n large and . α small, are used
Optimization over polynomials : Selected topics
Laurent, M.; Jang, Sun Young; Kim, Young Rock; Lee, Dae-Woong; Yie, Ikkwon
2014-01-01
Minimizing a polynomial function over a region defined by polynomial inequalities models broad classes of hard problems from combinatorics, geometry and optimization. New algorithmic approaches have emerged recently for computing the global minimum, by combining tools from real algebra (sums of
Wong-Loya, J. A.; Santoyo, E.; Andaverde, J. A.; Quiroz-Ruiz, A.
2015-12-01
A Web-Based Computer System (RPM-WEBBSYS) has been developed for the application of the Rational Polynomial Method (RPM) to estimate static formation temperatures (SFT) of geothermal and petroleum wells. The system is also capable to reproduce the full thermal recovery processes occurred during the well completion. RPM-WEBBSYS has been programmed using advances of the information technology to perform more efficiently computations of SFT. RPM-WEBBSYS may be friendly and rapidly executed by using any computing device (e.g., personal computers and portable computing devices such as tablets or smartphones) with Internet access and a web browser. The computer system was validated using bottomhole temperature (BHT) measurements logged in a synthetic heat transfer experiment, where a good matching between predicted and true SFT was achieved. RPM-WEBBSYS was finally applied to BHT logs collected from well drilling and shut-in operations, where the typical problems of the under- and over-estimation of the SFT (exhibited by most of the existing analytical methods) were effectively corrected.
Stam, Frank; Kuisma, Heikki; Gao, Feng; Saarilahti, Jaakko; Gomes Martins, David; Kärkkäinen, Anu; Marrinan, Brendan; Pintal, Sebastian
2017-05-01
The deadliest disease in the world is coronary artery disease (CAD), which is related to a narrowing (stenosis) of blood vessels due to fatty deposits, plaque, on the arterial walls. The level of stenosis in the coronary arteries can be assessed by Fractional Flow Reserve (FFR) measurements. This involves determining the ratio between the maximum achievable blood flow in a diseased coronary artery and the theoretical maximum flow in a normal coronary artery. The blood flow is represented by a pressure drop, thus a pressure wire or pressure sensor integrated in a catheter can be used to calculate the ratio between the coronary pressure distal to the stenosis and the normal coronary pressure. A 2 Fr (0.67mm) outer diameter catheter was used, which required a high level of microelectronics miniaturisation to fit a pressure sensing system into the outer wall. The catheter has an eccentric guidewire lumen with a diameter of 0.43mm, which implies that the thickest catheter wall section provides less than 210 microns height for flex assembly integration consisting of two dies, a capacitive MEMS pressure sensor and an ASIC. In order to achieve this a very thin circuit flex was used, and the two chips were thinned down to 75 microns and flip chip mounted face down on the flex. Many challenges were involved in obtaining a flex layout that could wrap into a small tube without getting the dies damaged, while still maintaining enough flexibility for the catheter to navigate the arterial system.
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-12-08
This report presents the results of an analysis of the capability of nuclear bimodal systems to perform outer solar system exploration missions. Missions of interest include orbiter mission s to Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. An initial technology baseline consisting of a NEBA 10 kWe, 1000 N thrust, 850 s, 1500 kg bimodal system was selected, and its performance examined against a data base for trajectories to outer solar system planetary destinations to select optimal direct and gravity assisted trajectories for study. A conceptual design for a common bimodal spacecraft capable of performing missions to all the planetary destinations was developed and made the basis of end to end mission designs for orbiter missions to Jupiter, Saturn, and Neptune. Concepts for microspacecraft capable of probing Jupiter`s atmosphere and exploring Titan were also developed. All mission designs considered use the Atlas 2AS for launch. It is shown that the bimodal nuclear power and propulsion system offers many attractive option for planetary missions, including both conventional planetary missions in which all instruments are carried by a single primary orbiting spacecraft, and unconventional missions in which the primary spacecraft acts as a carrier, relay, and mother ship for a fleet of micro spacecraft deployed at the planetary destination.
Polynomial fuzzy model-based approach for underactuated surface vessels
DEFF Research Database (Denmark)
Khooban, Mohammad Hassan; Vafamand, Navid; Dragicevic, Tomislav
2018-01-01
The main goal of this study is to introduce a new polynomial fuzzy model-based structure for a class of marine systems with non-linear and polynomial dynamics. The suggested technique relies on a polynomial Takagi–Sugeno (T–S) fuzzy modelling, a polynomial dynamic parallel distributed compensation...... surface vessel (USV). Additionally, in order to overcome the USV control challenges, including the USV un-modelled dynamics, complex nonlinear dynamics, external disturbances and parameter uncertainties, the polynomial fuzzy model representation is adopted. Moreover, the USV-based control structure...... and a sum-of-squares (SOS) decomposition. The new proposed approach is a generalisation of the standard T–S fuzzy models and linear matrix inequality which indicated its effectiveness in decreasing the tracking time and increasing the efficiency of the robust tracking control problem for an underactuated...
Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
Horozov, Emil
2016-05-01
We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.
Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers
Directory of Open Access Journals (Sweden)
Jaume Llibre
2015-10-01
Full Text Available We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of any cubic homogeneous polynomial center when it is perturbed inside the class of all polynomial differential systems of degree n.
On generalized Fibonacci and Lucas polynomials
Energy Technology Data Exchange (ETDEWEB)
Nalli, Ayse [Department of Mathematics, Faculty of Sciences, Selcuk University, 42075 Campus-Konya (Turkey)], E-mail: aysenalli@yahoo.com; Haukkanen, Pentti [Department of Mathematics, Statistics and Philosophy, 33014 University of Tampere (Finland)], E-mail: mapehau@uta.fi
2009-12-15
Let h(x) be a polynomial with real coefficients. We introduce h(x)-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these h(x)-Fibonacci polynomials. We also introduce h(x)-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q{sub h}(x) that generalizes the Q-matrix whose powers generate the Fibonacci numbers.
Parallel Construction of Irreducible Polynomials
DEFF Research Database (Denmark)
Frandsen, Gudmund Skovbjerg
Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....
Orthogonal polynomials in transport theories
International Nuclear Information System (INIS)
Dehesa, J.S.
1981-01-01
The asymptotical (k→infinity) behaviour of zeros of the polynomials gsub(k)sup((m)(ν)) encountered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude antiwsub(k) of the kth Legendre polynomial needed in the expansion of the scattering function. The parameters antiwsub(k) describe the anisotropy of scattering of the medium considered. In particular, it is shown that the asymptotical density of zeros of the polynomials gsub(k)sup(m)(ν) is an inverted semicircle for the anisotropic non-multiplying scattering medium
International Nuclear Information System (INIS)
Blake, R.L.
1979-06-01
This report presents an objective discussion of the importance of the atmospheric/solar-terrestrial system to national energy programs. A brief sketch is given of the solar-terrestrial environment, extending from the earth's surface to the sun. Processes in this natural system influence several energy activities directly or indirectly, and some present and potential energy activities can influence the natural system. It is not yet possible to assess the two-way interactions quantitatively or to evaluate the economic impact. An investment by the Department of Energy (DOE) in a long-range basic research program would be an important part of the department's mission. Existing programs by other agencies in this area of research are reviewed, and a compatible DOE program is outlined. 18 figures, 5 tables
An introduction to orthogonal polynomials
Chihara, Theodore S
1978-01-01
Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some
Scattering theory and orthogonal polynomials
International Nuclear Information System (INIS)
Geronimo, J.S.
1977-01-01
The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms
Reliability considerations in long-life outer planet spacecraft system design
Casani, E. K.
1975-01-01
A Mariner Jupiter/Saturn mission has been planned for 1977. System reliability questions are discussed, taking into account the actual and design lifetime, causes of mission termination, in-flight failures and their consequences for the mission, and the use of redundancy to avoid failures. The design process employed optimizes the use of proven subsystem and system designs and then makes the necessary improvements to increase the lifetime as required.
Hasanvand, Hamed; Mozafari, Babak; Arvan, Mohammad R; Amraee, Turaj
2015-11-01
This paper addresses the application of a static Var compensator (SVC) to improve the damping of interarea oscillations. Optimal location and size of SVC are defined using bifurcation and modal analysis to satisfy its primary application. Furthermore, the best-input signal for damping controller is selected using Hankel singular values and right half plane-zeros. The proposed approach is aimed to design a robust PI controller based on interval plants and Kharitonov's theorem. The objective here is to determine the stability region to attain robust stability, the desired phase margin, gain margin, and bandwidth. The intersection of the resulting stability regions yields the set of kp-ki parameters. In addition, optimal multiobjective design of PI controller using particle swarm optimization (PSO) algorithm is presented. The effectiveness of the suggested controllers in damping of local and interarea oscillation modes of a multimachine power system, over a wide range of loading conditions and system configurations, is confirmed through eigenvalue analysis and nonlinear time domain simulation. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Non-existence criteria for Laurent polynomial first integrals
Directory of Open Access Journals (Sweden)
Shaoyun Shi
2003-01-01
Full Text Available In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations $\\dot x = f(x$, $x \\in \\mathbb{R}^n$ with $f(0 = 0$. We show that if the eigenvalues of the Jacobi matrix of the vector field $f(x$ are $\\mathbb{Z}$-independent, then the system has no nontrivial Laurent polynomial integrals.
Families of superintegrable Hamiltonians constructed from exceptional polynomials
International Nuclear Information System (INIS)
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc
2012-01-01
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)
Organics and Ices in the Outer Solar System: Connections to the Interstellar Medium
Pendleton, Y. J.; Cruikshank, D. P.
2017-01-01
The solar nebula, that aggregate of gas and dust that formed the birthplace of the Sun, planets and plethora of small bodies comprising the Solar System, originated in a molecular cloud that is thought to have spawned numerous additional stars, some with their own planets and attendant small bodies. The question of the chemical and physical reprocessing of the original interstellar materials in the solar nebula has challenged both theory and observations. The acquisition and analysis of samples of comet and asteroid solids, and a growing suite of in-situ and close-up analyses of relatively unaltered small Solar System bodies now adds critical new dimensions to the study of the origin and evolution of the early solar nebula. Better understanding the original composition of the material from which our solar nebula formed, and the processing that material experienced, will aid in formulations of chemistry that might occur in other solar systems. While we seek to understand the compositional history of planetary bodies in our own Solar System, we will inevitably learn more about the materials that comprise exoplanets and their surrounding systems.
Bannai-Ito polynomials and dressing chains
Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
2012-01-01
Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by quadratic algebras. The Bannai-Ito polynomials and their kernel polynomials -- the complementary Bannai-Ito polynomials -- are shown to arise in the framework of the SDG maps.
Birth-death processes and associated polynomials
van Doorn, Erik A.
2003-01-01
We consider birth-death processes on the nonnegative integers and the corresponding sequences of orthogonal polynomials called birth-death polynomials. The sequence of associated polynomials linked with a sequence of birth-death polynomials and its orthogonalizing measure can be used in the analysis
Turbine airfoil with a compliant outer wall
Campbell, Christian X [Oviedo, FL; Morrison, Jay A [Oviedo, FL
2012-04-03
A turbine airfoil usable in a turbine engine with a cooling system and a compliant dual wall configuration configured to enable thermal expansion between inner and outer layers while eliminating stress formation in the outer layer is disclosed. The compliant dual wall configuration may be formed a dual wall formed from inner and outer layers separated by a support structure. The outer layer may be a compliant layer configured such that the outer layer may thermally expand and thereby reduce the stress within the outer layer. The outer layer may be formed from a nonplanar surface configured to thermally expand. In another embodiment, the outer layer may be planar and include a plurality of slots enabling unrestricted thermal expansion in a direction aligned with the outer layer.
Completeness of the ring of polynomials
DEFF Research Database (Denmark)
Thorup, Anders
2015-01-01
Consider the polynomial ring R:=k[X1,…,Xn]R:=k[X1,…,Xn] in n≥2n≥2 variables over an uncountable field k. We prove that R is complete in its adic topology, that is, the translation invariant topology in which the non-zero ideals form a fundamental system of neighborhoods of 0. In addition we pro...
Design of RTPV generators integrated with new millennium spacecraft for outer solar system
International Nuclear Information System (INIS)
Schock, A.; Or, C.; Kumar, V.
1996-01-01
The National Aeronautics and Space Administration's recently inaugurated New Millennium program, with its emphasis on miniaturized spacecraft, has generated interest in a low-power (10- to 30-watt), low-mass, high-efficiency RTPV (Radioisotope Thermophotovoltaic) power system. This led to a Department of Energy (DOE)-sponsored design study of such a system. A 75-watt design employed two 250-watt General Purpose Heat Source (GPHS) modules that DOE had previously developed and safety-qualified for various space missions. These modules were too large for the small RTPVs described in this paper. To minimize the need for new development and safety verification studies, derivative designs for 125-watt and 62.5-watt heat source modules containing identical fuel pellets, clads, impact shell, and thermal insulation were generated along with a novel heat source support scheme to reduce the heat losses through the structural supports, and a new and much simpler radiator structure, employing no honeycombs or heat pipes. Previous RTPV study had been based on the use of GaSb PV cells and spectrally selective IR filters. Because of the very encouraging results of system design studies, in the fall of 1994 an experimental program was initiated to develop improved filters and cells, to demonstrate how much improvement can actually be achieved. First priority was given to filter improvements, because our system studies indicated that improved filters would have a much greater effect on system performance than cell improvements. By September 1995 about 94% of the filter performance improvement projected in 1993 had been achieved. (Abstract Truncated)
On Multiple Polynomials of Capelli Type
Directory of Open Access Journals (Sweden)
S.Y. Antonov
2016-03-01
Full Text Available This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.
The MagOrion - A propulsion system for human exploration of the outer planets
International Nuclear Information System (INIS)
Andrews, Jason; Andrews, Dana
2000-01-01
Manned exploration beyond Mars requires very high specific energy. The only potential solution under discussion is fusion propulsion. However, fusion has been ten years away for forty years. We have an available solution that combines new technology with an old concept-'Project Orion'. The proposed 'MagOrion' Propulsion System combines a magnetic sail (MagSail) with conventional small yield (0.5 to 1.0 kiloton) shaped nuclear fission devices. At denonation, roughly eighty percent of the yield appears as a highly-ionized plasma, and when detonated two kilometers behind a robust MagSail, approximately half of this plasma can be stopped and turned into thrust. A MagOrion can provide a system acceleration of one or more gravities with effective specific impulses ranging from 15,000 to 45,000 seconds. Dana Andrews and Robert Zubrin published a paper in 1997 that described the operating principles of the MagOrion. We have taken that concept through conceptual design to identify the major operational features and risks. The risks are considerable, but the potential payoff is staggering. Our proposed MagOrion will enable affordable exploration of the solar system
Polynomial fuzzy observer designs: a sum-of-squares approach.
Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O
2012-10-01
This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.
Energy Technology Data Exchange (ETDEWEB)
Dr. Steven Howe; Nathan Jerred; Troy Howe; Adarsh Rajguru
2014-05-01
Exploration to the outer planets is an ongoing endeavor but in the current economical environment, cost reduction is the forefront of all concern. The success of small satellites such as CubeSats launched to Near-Earth Orbit has lead to examine their potential use to achieve cheaper science for deep space applications. However, to achieve lower cost missions; hardware, launch and operations costs must be minimized. Additionally, as we push towards smaller exploration beds with relative limited power sources, allowing for adequate communication back to Earth is imperative. Researchers at the Center for Space Nuclear Research are developing the potential of utilizing an advanced, radioisotope-based system. This system will be capable of providing both the propulsion power needed to reach the destination and the additional requirements needed to maintain communication while at location. Presented here are a basic trajectory analysis, communication link budget and concept of operations of a dual-mode (thermal and electric) radioisotope-based propulsion system, for a proposed mission to Enceladus (Saturnian icy moon) using a 6U CubeSat payload. The radioisotope system being proposed will be the integration of three sub-systems working together to achieve the overall mission. At the core of the system, stored thermal energy from radioisotope decay is transferred to a passing propellant to achieve high thrust – useful for quick orbital maneuvering. An auxiliary closed-loop Brayton cycle can be operated in parallel to the thrusting mode to provide short bursts of high power for high data-rate communications back to Earth. Additionally, a thermal photovoltaic (TPV) energy conversion system will use radiation heat losses from the core. This in turn can provide the electrical energy needed to utilize the efficiency of ion propulsion to achieve quick interplanetary transit times. The intelligent operation to handle all functions of this system under optimized conditions adds
COMPOSITIONS AND ORIGINS OF OUTER PLANET SYSTEMS: INSIGHTS FROM THE ROCHE CRITICAL DENSITY
International Nuclear Information System (INIS)
Tiscareno, Matthew S.; Hedman, Matthew M.; Burns, Joseph A.; Castillo-Rogez, Julie
2013-01-01
We consider the Roche critical density (ρ Roche ), the minimum density of an orbiting object that, at a given distance from its planet, is able to hold itself together by self-gravity. It is directly related to the more familiar ''Roche limit,'' the distance from a planet at which a strengthless orbiting object of given density is pulled apart by tides. The presence of a substantial ring requires that transient clumps have an internal density less than ρ Roche . Conversely, in the presence of abundant material for accretion, an orbiting object with density greater than ρ Roche will grow. Comparing the ρ Roche values at which the Saturn and Uranus systems transition rapidly from disruption-dominated (rings) to accretion-dominated (moons), we infer that the material composing Uranus' rings is likely more rocky, as well as less porous, than that composing Saturn's rings. From the high values of ρ Roche at the innermost ring moons of Jupiter and Neptune, we infer that those moons may be composed of denser material than expected, or more likely that they are interlopers that formed farther from their planets and have since migrated inward, now being held together by internal material strength. Finally, the ''Portia group'' of eight closely packed Uranian moons has an overall surface density similar to that of Saturn's A ring. Thus, it can be seen as an accretion-dominated ring system, of similar character to the standard ring systems except that its material has a characteristic density greater than the local ρ Roche .
International Nuclear Information System (INIS)
Noble, R.J.
1999-01-01
Radioisotopes have been used successfully for more than 25 years to supply the heat for thermoelectric generators on various deep-space probes. Radioisotope electric propulsion (REP) systems have been proposed as low-thrust ion propulsion units based on radioisotope electric generators and ion thrusters. The perceived liability of radioisotope electric generators for ion propulsion is their high mass. Conventional radioisotope thermoelectric generators have a specific mass of about 200 kg/kW of electric power. Many development efforts have been undertaken with the aim of reducing the specific mass of radioisotope electric systems. Recent performance estimates suggest that specific masses of 50 kg/kW may be achievable with thermophotovoltaic and alkali metal thermal-to-electric conversion generators. Powerplants constructed from these near-term radioisotope electric generators and long-life ion thrusters will likely have specific masses in the range of 100 to 200 kg/kW of thrust power if development continues over the next decade. In earlier studies, it was concluded that flight times within the Solar System are indeed insensitive to reductions in the powerplant specific mass, and that a timely scientific program of robotic planetary rendezvous and near-interstellar space missions is enabled by primary electric propulsion once the powerplant specific mass is in the range of 100 to 200 kg/kW. Flight times can be substantially reduced by using hybrid propulsion schemes that combine chemical propulsion, gravity assist, and electric propulsion. Hybrid schemes are further explored in this article to illustrate how the performance of REP is enhanced for Pluto rendezvous, heliopause orbiter, and gravitational lens missions
Formation of the satellites of the outer solar system - Sources of their atmospheres
International Nuclear Information System (INIS)
Coradini, A.; Cerroni, P.; Magni, G.; Federico, C.
1989-01-01
The present account of the current understanding of regular satellite systems' origins gives attention to the essential processes leading to current satellite configurations, proceeding on the concept that the presence of atmospheres is connected with the final phases of satellite formation. Four major formation stages are envisioned: (1) the disk phase, linking the formation of the primary body to that of the satellites; (2) the formation phase of intermediate-sized bodies; (3) the collisional evolution of planatesimals; and (4) a series of evolutionary phases linking the primordial phases to currently observed states, in which the internal composition and thermal history of the satellites are key factors in satellite atmosphere formation
Ghosh, Shubhrangshu
2017-09-01
The correlated and coupled dynamics of accretion and outflow around black holes (BHs) are essentially governed by the fundamental laws of conservation as outflow extracts matter, momentum and energy from the accretion region. Here we analyze a robust form of 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in BH systems. We solve the complete set of coupled MHD conservation equations self-consistently, through invoking a generalized polynomial expansion in two dimensions. We perform a critical analysis of the accretion-outflow region and provide a complete quasi-analytical family of solutions for advective flows. We obtain the physically plausible outflow solutions at high turbulent viscosity parameter α (≳ 0.3), and at a reduced scale-height, as magnetic stresses compress or squeeze the flow region. We found that the value of the large-scale poloidal magnetic field B P is enhanced with the increase of the geometrical thickness of the accretion flow. On the other hand, differential magnetic torque (-{r}2{\\bar{B}}\\varphi {\\bar{B}}z) increases with the increase in \\dot{M}. {\\bar{B}}{{P}}, -{r}2{\\bar{B}}\\varphi {\\bar{B}}z as well as the plasma beta β P get strongly augmented with the increase in the value of α, enhancing the transport of vertical flux outwards. Our solutions indicate that magnetocentrifugal acceleration plausibly plays a dominant role in effusing out plasma from the radial accretion flow in a moderately advective paradigm which is more centrifugally dominated. However in a strongly advective paradigm it is likely that the thermal pressure gradient would play a more contributory role in the vertical transport of plasma.
Cosmographic analysis with Chebyshev polynomials
Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando
2018-05-01
The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.
PLANETS AROUND LOW-MASS STARS (PALMS). IV. THE OUTER ARCHITECTURE OF M DWARF PLANETARY SYSTEMS
Energy Technology Data Exchange (ETDEWEB)
Bowler, Brendan P. [California Institute of Technology, Division of Geological and Planetary Sciences, 1200 East California Boulevard, Pasadena, CA 91101 (United States); Liu, Michael C. [Institute for Astronomy, University of Hawai' i, 2680 Woodlawn Drive, Honolulu, HI 96822 (United States); Shkolnik, Evgenya L. [Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, AZ 86001 (United States); Tamura, Motohide, E-mail: bpbowler@caltech.edu [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan)
2015-01-01
to single M dwarfs between 10-100 AU is 2.8{sub −1.5}{sup +2.4}%. Altogether we find that giant planets, especially massive ones, are rare in the outskirts of M dwarf planetary systems. Although the first directly imaged planets were found around massive stars, there is currently no statistical evidence for a trend of giant planet frequency with stellar host mass at large separations as predicted by the disk instability model of giant planet formation.
Imaging characteristics of Zernike and annular polynomial aberrations.
Mahajan, Virendra N; Díaz, José Antonio
2013-04-01
The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.
Polynomial weights and code constructions
DEFF Research Database (Denmark)
Massey, J; Costello, D; Justesen, Jørn
1973-01-01
polynomial included. This fundamental property is then used as the key to a variety of code constructions including 1) a simplified derivation of the binary Reed-Muller codes and, for any primepgreater than 2, a new extensive class ofp-ary "Reed-Muller codes," 2) a new class of "repeated-root" cyclic codes...... of long constraint length binary convolutional codes derived from2^r-ary Reed-Solomon codes, and 6) a new class ofq-ary "repeated-root" constacyclic codes with an algebraic decoding algorithm.......For any nonzero elementcof a general finite fieldGF(q), it is shown that the polynomials(x - c)^i, i = 0,1,2,cdots, have the "weight-retaining" property that any linear combination of these polynomials with coefficients inGF(q)has Hamming weight at least as great as that of the minimum degree...
Orthogonal Polynomials and Special Functions
Assche, Walter
2003-01-01
The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.
Symmetric functions and orthogonal polynomials
Macdonald, I G
1997-01-01
One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.
Outer Solar System Nomenclature
National Research Council Canada - National Science Library
Owen, Tobias C
2000-01-01
The work to be carried out on the subject grant during the next funding period will center on names needed for surface features on the Galilean satellites of Jupiter, names for the newly discovered...
Rummel, J. D.; Race, M. S.
2016-12-01
Enceladus and Europa are bodies with icy/watery environments and potential habitable conditions for life, making both of great interest in astrobiological studies of chemical evolution and /or origin of life. They are also of significant planetary protection concern for spacecraft missions because of the potential for harmful contamination during exploration. At a 2015 COSPAR colloquium in Bern Switzerland, international scientists identified an urgent need to establish planetary protection requirements for missions proposing to return samples to Earth from Saturn's moon Enceladus. Deliberations at the meeting resulted in recommended policy updates for both forward and back contamination requirements for missions to Europa and Enceladus, including missions sampling plumes originating from those bodies. These recently recommended COSPAR policy revisions and biological contamination requirements will be applied to future missions to Europa and Encealadus, particularly noticeable in those with plans for in situ life detection and sample return capabilities. Included in the COSPAR policy are requirementsto `break the chain of contact' with Europa or Enceladus, to keep pristine returned materials contained, and to complete required biohazard analyses, testing and/or sterilization upon return to Earth. Subsequent to the Bern meeting, additional discussions of Planetary Protection of Outer Solar System bodies (PPOSS) are underway in a 3-year study coordinated by the European Science Foundation and involving multiple international partners, including Japan, China and Russia, along with a US observer. This presentation will provide science and policy updates for those whose research or activities will involve icy moon missions and exploration.
Thompson, W. Reid; Murray, B. G. J. P. T.; Khare, B. N.; Sagan, Carl
1987-01-01
The results of laboratory experiments simulating the irradiation of hydrocarbon-H2O or hydrocarbon-H2O/NH3 clathrates by charged particles in the outer solar system are reported. Ices produced by condensing and boiling liquid CH4 on an H2O frost surface at 100 K or by cocondensing frosts from gaseous mixtures were exposed to coronal-discharge electron irradiation at 77 K, and the spectral properties of the irradiated surfaces were determined. Significant darkening of the initially white ices was observed at doses of 1 Gerg/sq cm, corresponding to 8-500 yrs of irradiation by Uranian magnetospheric electrons on the surfaces of the principal Uranian satellites, or to total destruction of CH4 in the upper 1 mm of the satellite surfaces after 0.05-3.0 Myr. It is estimated that 10 m or more of icy satellite or comet surfaces would be radiation-hardened to a CH4-free ice-tholin mixture over 4 Gyr.
Synchronization of generalized Henon map using polynomial controller
International Nuclear Information System (INIS)
Lam, H.K.
2010-01-01
This Letter presents the chaos synchronization of two discrete-time generalized Henon map, namely the drive and response systems. A polynomial controller is proposed to drive the system states of the response system to follow those of the drive system. The system stability of the error system formed by the drive and response systems and the synthesis of the polynomial controller are investigated using the sum-of-squares (SOS) technique. Based on the Lyapunov stability theory, stability conditions in terms of SOS are derived to guarantee the system stability and facilitate the controller synthesis. By satisfying the SOS-based stability conditions, chaotic synchronization is achieved. The solution of the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. A simulation example is given to illustrate the merits of the proposed polynomial control approach.
On Modular Counting with Polynomials
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt
2006-01-01
For any integers m and l, where m has r sufficiently large (depending on l) factors, that are powers of r distinct primes, we give a construction of a (symmetric) polynomial over Z_m of degree O(\\sqrt n) that is a generalized representation (commonly also called weak representation) of the MODl f...
Global Polynomial Kernel Hazard Estimation
DEFF Research Database (Denmark)
Hiabu, Munir; Miranda, Maria Dolores Martínez; Nielsen, Jens Perch
2015-01-01
This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically redu...
Congruences concerning Legendre polynomials III
Sun, Zhi-Hong
2010-01-01
Let $p>3$ be a prime, and let $R_p$ be the set of rational numbers whose denominator is coprime to $p$. Let $\\{P_n(x)\\}$ be the Legendre polynomials. In this paper we mainly show that for $m,n,t\\in R_p$ with $m\
Two polynomial division inequalities in
Directory of Open Access Journals (Sweden)
Goetgheluck P
1998-01-01
Full Text Available This paper is a first attempt to give numerical values for constants and , in classical estimates and where is an algebraic polynomial of degree at most and denotes the -metric on . The basic tools are Markov and Bernstein inequalities.
Dirichlet polynomials, majorization, and trumping
International Nuclear Information System (INIS)
Pereira, Rajesh; Plosker, Sarah
2013-01-01
Majorization and trumping are two partial orders which have proved useful in quantum information theory. We show some relations between these two partial orders and generalized Dirichlet polynomials, Mellin transforms, and completely monotone functions. These relations are used to prove a succinct generalization of Turgut’s characterization of trumping. (paper)
Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano
2012-05-10
The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.
The modified Gauss diagonalization of polynomial matrices
International Nuclear Information System (INIS)
Saeed, K.
1982-10-01
The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)
Sheffer and Non-Sheffer Polynomial Families
Directory of Open Access Journals (Sweden)
G. Dattoli
2012-01-01
Full Text Available By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
A Summation Formula for Macdonald Polynomials
de Gier, Jan; Wheeler, Michael
2016-03-01
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.
A New Generalisation of Macdonald Polynomials
Garbali, Alexandr; de Gier, Jan; Wheeler, Michael
2017-06-01
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters ( q, t) and polynomial in a further two parameters ( u, v). We evaluate these polynomials explicitly as a matrix product. At u = v = 0 they reduce to Macdonald polynomials, while at q = 0, u = v = s they recover a family of inhomogeneous symmetric functions originally introduced by Borodin.
International Nuclear Information System (INIS)
Fraser, Wesley C.; Brown, Michael E.; Glass, Florian
2015-01-01
Here, we present additional photometry of targets observed as part of the Hubble Wide Field Camera 3 (WFC3) Test of Surfaces in the Outer Solar System. Twelve targets were re-observed with the WFC3 in the optical and NIR wavebands designed to complement those used during the first visit. Additionally, all of the observations originally presented by Fraser and Brown were reanalyzed through the same updated photometry pipeline. A re-analysis of the optical and NIR color distribution reveals a bifurcated optical color distribution and only two identifiable spectral classes, each of which occupies a broad range of colors and has correlated optical and NIR colors, in agreement with our previous findings. We report the detection of significant spectral variations on five targets which cannot be attributed to photometry errors, cosmic rays, point-spread function or sensitivity variations, or other image artifacts capable of explaining the magnitude of the variation. The spectrally variable objects are found to have a broad range of dynamical classes and absolute magnitudes, exhibit a broad range of apparent magnitude variations, and are found in both compositional classes. The spectrally variable objects with sufficiently accurate colors for spectral classification maintain their membership, belonging to the same class at both epochs. 2005 TV189 exhibits a sufficiently broad difference in color at the two epochs that span the full range of colors of the neutral class. This strongly argues that the neutral class is one single class with a broad range of colors, rather than the combination of multiple overlapping classes
Associated polynomials and birth-death processes
van Doorn, Erik A.
2001-01-01
We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to
Perek, Lubos
1993-10-01
Various aspects of space-environment management are discussed. Attention is called to the fact that, while space radio communications are already under an adequate management by the International Communications Union, the use of nuclear power sources is regulated by the recently adopted set of principles, and space debris will be discussed in the near future at the UN COPUOS, other aspects of management of outer space received little or no attention of the international community. These include the competency of crews and technical equipment of spacecraft launched by newcomers to space exploration; monitoring of locations and motions of space objects (now in national hands), with relevant data made accessible through a computer network; and the requirement to use space only for beneficial purposes and not for promoting narrow and debatable interests damaging the outer space environment and impeding on astronomical observations. It is suggested that some of these tasks would be best performed by an international space agency within the UN system of organizations.
BSDEs with polynomial growth generators
Directory of Open Access Journals (Sweden)
Philippe Briand
2000-01-01
Full Text Available In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.
Special polynomials associated with some hierarchies
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2008-01-01
Special polynomials associated with rational solutions of a hierarchy of equations of Painleve type are introduced. The hierarchy arises by similarity reduction from the Fordy-Gibbons hierarchy of partial differential equations. Some relations for these special polynomials are given. Differential-difference hierarchies for finding special polynomials are presented. These formulae allow us to obtain special polynomials associated with the hierarchy studied. It is shown that rational solutions of members of the Schwarz-Sawada-Kotera, the Schwarz-Kaup-Kupershmidt, the Fordy-Gibbons, the Sawada-Kotera and the Kaup-Kupershmidt hierarchies can be expressed through special polynomials of the hierarchy studied
Space complexity in polynomial calculus
Czech Academy of Sciences Publication Activity Database
Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil
2015-01-01
Roč. 44, č. 4 (2015), s. 1119-1153 ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/10.1137/120895950
Codimensions of generalized polynomial identities
International Nuclear Information System (INIS)
Gordienko, Aleksei S
2010-01-01
It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q + and t element of Z + such that gc n (A)∼Cn t d n as n→∞, where d=PI exp(A) element of Z + . Thus, Amitsur's and Regev's conjectures hold for the codimensions gc n (A) of the generalized polynomial identities. Bibliography: 6 titles.
A fast numerical test of multivariate polynomial positiveness with applications
Czech Academy of Sciences Publication Activity Database
Augusta, Petr; Augustová, Petra
2018-01-01
Roč. 54, č. 2 (2018), s. 289-303 ISSN 0023-5954 Institutional support: RVO:67985556 Keywords : stability * multidimensional systems * positive polynomials * fast Fourier transforms * numerical algorithm Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 0.379, year: 2016 https://www.kybernetika.cz/content/2018/2/289/paper.pdf
Stable piecewise polynomial vector fields
Directory of Open Access Journals (Sweden)
Claudio Pessoa
2012-09-01
Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.
Simulation of aspheric tolerance with polynomial fitting
Li, Jing; Cen, Zhaofeng; Li, Xiaotong
2018-01-01
The shape of the aspheric lens changes caused by machining errors, resulting in a change in the optical transfer function, which affects the image quality. At present, there is no universally recognized tolerance criterion standard for aspheric surface. To study the influence of aspheric tolerances on the optical transfer function, the tolerances of polynomial fitting are allocated on the aspheric surface, and the imaging simulation is carried out by optical imaging software. Analysis is based on a set of aspheric imaging system. The error is generated in the range of a certain PV value, and expressed as a form of Zernike polynomial, which is added to the aspheric surface as a tolerance term. Through optical software analysis, the MTF of optical system can be obtained and used as the main evaluation index. Evaluate whether the effect of the added error on the MTF of the system meets the requirements of the current PV value. Change the PV value and repeat the operation until the acceptable maximum allowable PV value is obtained. According to the actual processing technology, consider the error of various shapes, such as M type, W type, random type error. The new method will provide a certain development for the actual free surface processing technology the reference value.
Solving the interval type-2 fuzzy polynomial equation using the ranking method
Rahman, Nurhakimah Ab.; Abdullah, Lazim
2014-07-01
Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.
International Nuclear Information System (INIS)
Anderson, J.L.
1988-01-01
The region above the earth from about 90 km to 150 km is a major part of the upper or outer atmosphere. It is relatively unexplored, being too high for balloons or aircraft and too low for persistent orbiting spacecraft. However, the concept of a tethered subsatellite, deployed downward from an orbiting, more massive craft such as the Space Shuttle, opens the possibility of a research capability that could provide global mapping of this region. The need for research in this thick spherical shell above the earth falls into two major categories: (1) scientific data for understanding and modeling the global atmosphere and thereby determining its role in the earth system, and (2) engineering data for the design of future aerospace vehicles that will operate there. This paper presents an overview and synthesis of the currently perceived research needs and the state-of-the-art of the proposed tethered research capability. 16 references
Solutions of interval type-2 fuzzy polynomials using a new ranking method
Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani
2015-10-01
A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.
Algebraic polynomials with random coefficients
Directory of Open Access Journals (Sweden)
K. Farahmand
2002-01-01
Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.
Improved multivariate polynomial factoring algorithm
International Nuclear Information System (INIS)
Wang, P.S.
1978-01-01
A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known problems of the original algorithm, namely, the leading coefficient problem, the bad-zero problem and the occurrence of extraneous factors. It has an algorithm for correctly predetermining leading coefficients of the factors. A new and efficient p-adic algorithm named EEZ is described. Bascially it is a linearly convergent variable-by-variable parallel construction. The improved algorithm is generally faster and requires less store then the original algorithm. Machine examples with comparative timing are included
Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
Killings, duality and characteristic polynomials
Álvarez, Enrique; Borlaf, Javier; León, José H.
1998-03-01
In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Introduction to Real Orthogonal Polynomials
1992-06-01
uses Green’s functions. As motivation , consider the Dirichlet problem for the unit circle in the plane, which involves finding a harmonic function u(r...xv ; a, b ; q) - TO [q-N ab+’q ; q, xq b. Orthogoy RMotion O0 (bq :q)x p.(q* ; a, b ; q) pg(q’ ; a, b ; q) (q "q), (aq)x (q ; q), (I -abq) (bq ; q... motivation and justi- fication for continued study of the intrinsic structure of orthogonal polynomials. 99 LIST OF REFERENCES 1. Deyer, W. M., ed., CRC
Kurz, Walter; Ferré, Eric C.; Robertson, Alastair; Avery, Aaron; Christeson, Gail L.; Morgan, Sally; Kutterorf, Steffen; Sager, William W.; Carvallo, Claire; Shervais, John; Party IODP Expedition 352, Scientific
2015-04-01
IODP Expedition 352 was designed to drill through the entire volcanic sequence of the Bonin forearc. Four sites were drilled, two on the outer fore arc and two on the upper trench slope. Site survey seismic data, combined with borehole data, indicate that tectonic deformation in the outer IBM fore arc is mainly post-magmatic. Post-magmatic extension resulted in the formation of asymmetric sedimentary basins such as, for example, the half-grabens at sites 352-U1439 and 352-U1442 located on the upper trench slope. Along their eastern margins these basins are bounded by west-dipping normal faults. Sedimentation was mainly syn-tectonic. The lowermost sequence of the sedimentary units was tilted eastward by ~20°. These tilted bedding planes were subsequently covered by sub-horizontally deposited sedimentary beds. Based on biostratigraphic constraints, the minimum age of the oldest sediments is ~ 35 Ma; the timing of the sedimentary unconformities lies between ~ 27 and 32 Ma. At sites 352-U1440 and 352-U1441, located on the outer forearc, post-magmatic deformation resulted mainly in strike-slip faults possibly bounding the sedimentary basins. The sedimentary units within these basins were not significantly affected by post-sedimentary tectonic tilting. Biostratigraphic ages indicate that the minimum age of the basement-cover contact lies between ~29.5 and 32 Ma. Overall, the post-magmatic tectonic structures observed during Expedition 352 reveal a multiphase tectonic evolution of the outer IBM fore arc. At sites 352-U1439 and 352-U1442, shear with dominant reverse to oblique reverse displacement was localized along distinct subhorizontal cataclastic shear zones as well as steeply dipping slickensides and shear fractures. These structures, forming within a contractional tectonic regime, were either re-activated as or cross-cut by normal-faults as well as strike-slip faults. Extension was also accommodated by steeply dipping to subvertical mineralized veins and
Polynomial chaos expansion with random and fuzzy variables
Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.
2016-06-01
A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.
Euler polynomials and identities for non-commutative operators
De Angelis, Valerio; Vignat, Christophe
2015-12-01
Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.
Mampel, Jörg; Maier, Elke; Tralau, Tewes; Ruff, Jürgen; Benz, Roland; Cook, Alasdair M.
2004-01-01
Inducible mineralization of TSA (4-toluenesulphonate) by Comamonas testosteroni T-2 is initiated by a secondary transport system, followed by oxygenation and oxidation by TsaMBCD to 4-sulphobenzoate under the regulation of TsaR and TsaQ. Evidence is presented for a novel, presumably two-component transport system (TsaST). It is proposed that TsaT, an outer-membrane porin, formed an anion-selective channel that works in co-operation with the putative secondary transporter, TsaS, located in the...
On polynomial solutions of the Heun equation
International Nuclear Information System (INIS)
Gurappa, N; Panigrahi, Prasanta K
2004-01-01
By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)
A new Arnoldi approach for polynomial eigenproblems
Energy Technology Data Exchange (ETDEWEB)
Raeven, F.A.
1996-12-31
In this paper we introduce a new generalization of the method of Arnoldi for matrix polynomials. The new approach is compared with the approach of rewriting the polynomial problem into a linear eigenproblem and applying the standard method of Arnoldi to the linearised problem. The algorithm that can be applied directly to the polynomial eigenproblem turns out to be more efficient, both in storage and in computation.
Bayer Demosaicking with Polynomial Interpolation.
Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil
2016-08-30
Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.
International Nuclear Information System (INIS)
Benasser Algehawi, Mohammed; Samsudin, Azman
2010-01-01
We present a method to extract key pairs needed for the Identity Based Encryption (IBE) scheme from extended Chebyshev polynomial over finite fields Z p . Our proposed scheme relies on the hard problem and the bilinear property of the extended Chebyshev polynomial over Z p . The proposed system is applicable, secure, and reliable.
Fermionic formula for double Kostka polynomials
Liu, Shiyuan
2016-01-01
The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\\Bla,\\Bmu}(t),$ indexed by two double partitions $\\Bla,\\Bmu,$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{\\Bla,\\Bmu}(t)$ in the special case where $\\Bmu=(-,\\mu'').$ We formula...
Polynomial sequences generated by infinite Hessenberg matrices
Directory of Open Access Journals (Sweden)
Verde-Star Luis
2017-01-01
Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.
Current advances on polynomial resultant formulations
Sulaiman, Surajo; Aris, Nor'aini; Ahmad, Shamsatun Nahar
2017-08-01
Availability of computer algebra systems (CAS) lead to the resurrection of the resultant method for eliminating one or more variables from the polynomials system. The resultant matrix method has advantages over the Groebner basis and Ritt-Wu method due to their high complexity and storage requirement. This paper focuses on the current resultant matrix formulations and investigates their ability or otherwise towards producing optimal resultant matrices. A determinantal formula that gives exact resultant or a formulation that can minimize the presence of extraneous factors in the resultant formulation is often sought for when certain conditions that it exists can be determined. We present some applications of elimination theory via resultant formulations and examples are given to explain each of the presented settings.
Computational Technique for Teaching Mathematics (CTTM): Visualizing the Polynomial's Resultant
Alves, Francisco Regis Vieira
2015-01-01
We find several applications of the Dynamic System Geogebra--DSG related predominantly to the basic mathematical concepts at the context of the learning and teaching in Brasil. However, all these works were developed in the basic level of Mathematics. On the other hand, we discuss and explore, with DSG's help, some applications of the polynomial's…
A Genetic algorithm for evaluating the zeros (roots) of polynomial ...
African Journals Online (AJOL)
This paper presents a Genetic Algorithm software (which is a computational, search technique) for finding the zeros (roots) of any given polynomial function, and optimizing and solving N-dimensional systems of equations. The software is particularly useful since most of the classic schemes are not all embracing.
Aging Studies for the Large Honeycomb Drift Tube System of the Outer Tracker of HERA-B
Albrecht, H; Beck, M; Belkov, A; Berkhan, K; Bohm, G; Bruinsma, M; Buran, T; Capeans, M; Chamanina, J; Chen, BX; Deckers, H; Dehmelt, K; Dong, X; Eckmann, R; Emelianov, D; Fourletov, S; Golutvin, I; Hohlmann, M; Hoepfner, Kerstin; Hulsbergen, W; Jia, Y; Jiang, C; Kapitza, H; Karabekyan, S; Ke, Z; Kiryushin, Y; Kolanoski, H; Korpar, S; Krizan, P; Krucker, D; Lanyov, A; Liu, Y Q; Lohse, T; Loke, R; Mankel, R; Medin, G; Michel, E; Moshkin, A; Ni, J; Nowak, S; Ouchrif, M; Padilla, C; Pose, D; Ressing, D; Saveliev, V; Schmidt, B; Schmidt-Parzefall, W; Schreiner, A; Schwanke, U; Schwarz, Andreas S; Siccama, I; Solunin, S; Somov, S; Souvorov, V; Spiridonov, A; Staric, M; Stegmann, C; Steinkamp, O; Tesch, N; Tsakov, I; Uwer, U; Vassiliev, S; Vukotic, I; Walter, M; Wang, J J; Wang, Y M; Wurth, R; Yang, J; Zheng, Z; Zhu, Z; Zimmerman, R
2003-01-01
The HERA-B Outer Tracker consists of drift tubes folded from polycarbonate foil and is operated with Ar/CF4/CO2 as drift gas. The detector has to stand radiation levels which are similar to LHC conditions. The first prototypes exposed to radiation in HERA-B suffered severe radiation damage due to the development of self-sustaining currents (Malter effect). In a subsequent extended R&D program major changes to the original concept for the drift tubes (surface conductivity, drift gas, production materials) have been developed and validated for use in harsh radiation environments. In the test program various aging effects (like Malter currents, gain loss due to anode aging and etching of the anode gold surface) have been observed and cures by tuning of operation parameters have been developed.
Coustenis, A.; Atreya, S.; Castillo-Rogez, J.; Mueller-Wodarg, I.; Spilker, L.; Strazzulla, G.
2018-06-01
This issue contains six articles on original research and review papers presented in the past year in sessions organized during several international meetings and congresses including the European Geosciences Union (EGU), European Planetary Science Congress (EPSC) and others. The manuscripts cover recent observations and models of the atmospheres, magnetospheres and surfaces of the giant planets and their satellites based on ongoing and recent planetary missions. Concepts of architecture and payload for future space missions are also presented. The six articles in this special issue cover a variety of objects in the outer solar system ranging from Jupiter to Neptune and the possibilities for their exploration. A brief introductory summary of their findings follows.
Polynomial solutions of nonlinear integral equations
International Nuclear Information System (INIS)
Dominici, Diego
2009-01-01
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials
Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...
African Journals Online (AJOL)
Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...
Topological string partition functions as polynomials
International Nuclear Information System (INIS)
Yamaguchi, Satoshi; Yau Shingtung
2004-01-01
We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus. (author)
Polynomial solutions of nonlinear integral equations
Energy Technology Data Exchange (ETDEWEB)
Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu
2009-05-22
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.
A generalization of the Bernoulli polynomials
Directory of Open Access Journals (Sweden)
Pierpaolo Natalini
2003-01-01
Full Text Available A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the factorization method introduced by Infeld and Hull (1951.
The Bessel polynomials and their differential operators
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1987-10-01
Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
Exceptional polynomials and SUSY quantum mechanics
Indian Academy of Sciences (India)
Abstract. We show that for the quantum mechanical problem which admit classical Laguerre/. Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional. Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the ...
Connections between the matching and chromatic polynomials
Directory of Open Access Journals (Sweden)
E. J. Farrell
1992-01-01
Full Text Available The main results established are (i a connection between the matching and chromatic polynomials and (ii a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.
Laguerre polynomials by a harmonic oscillator
Baykal, Melek; Baykal, Ahmet
2014-09-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.
Laguerre polynomials by a harmonic oscillator
International Nuclear Information System (INIS)
Baykal, Melek; Baykal, Ahmet
2014-01-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)
On Generalisation of Polynomials in Complex Plane
Directory of Open Access Journals (Sweden)
Maslina Darus
2010-01-01
Full Text Available The generalised Bell and Laguerre polynomials of fractional-order in complex z-plane are defined. Some properties are studied. Moreover, we proved that these polynomials are univalent solutions for second order differential equations. Also, the Laguerre-type of some special functions are introduced.
Dual exponential polynomials and linear differential equations
Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne
2018-01-01
We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.
Technique for image interpolation using polynomial transforms
Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.
1993-01-01
We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is
Factoring polynomials over arbitrary finite fields
Lange, T.; Winterhof, A.
2000-01-01
We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of
Directory of Open Access Journals (Sweden)
Ofir Bahar
2014-01-01
Full Text Available Pattern recognition receptors (PRRs play an important role in detecting invading pathogens and mounting a robust defense response to restrict infection. In rice, one of the best characterized PRRs is XA21, a leucine rich repeat receptor-like kinase that confers broad-spectrum resistance to multiple strains of the bacterial pathogen Xanthomonas oryzae pv. oryzae (Xoo. In 2009 we reported that an Xoo protein, called Ax21, is secreted by a type I-secretion system and that it serves to activate XA21-mediated immunity. This report has recently been retracted. Here we present data that corrects our previous model. We first show that Ax21 secretion does not depend on the predicted type I secretion system and that it is processed by the general secretion (Sec system. We further show that Ax21 is an outer membrane protein, secreted in association with outer membrane vesicles. Finally, we provide data showing that ax21 knockout strains do not overcome XA21-mediated immunity.
Kilic, Veli Tayfun; Unal, Emre; Demir, Hilmi Volkan
2017-05-01
In this work, we investigate a method proposed for vessel detection and coil powering in an all-surface inductive heating system composed of outer squircle coils. Besides conventional circular coils, coils with different shapes such as outer squircle coils are used for and enable efficient all-surface inductive heating. Validity of the method, which relies on measuring inductance and resistance values of a loaded coil at different frequencies, is experimentally demonstrated for a coil with shape different from conventional circular coil. Simple setup was constructed with a small coil to model an all-surface inductive heating system. Inductance and resistance maps were generated by measuring coil's inductance and resistance values at different frequencies loaded by a plate made of different materials and located at various positions. Results show that in an induction hob for various coil geometries it is possible to detect a vessel's presence, to identify its material type and to specify its position on the hob surface by considering inductance and resistance of the coil measured on at least two different frequencies. The studied method is important in terms of enabling safe, efficient and user flexible heating in an all-surface inductive heating system by automatically detecting the vessel's presence and powering on only the coils that are loaded by the vessel with predetermined current levels.
On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations
Cima, A.; Gasull, A.; Mañosas, F.
2017-12-01
In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions. We show that the addressed problems can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then we approach to these equations either applying several tools developed to study extended Fermat problems for polynomial equations, or reducing the question to the computation of the genus of some associated planar algebraic curves.
Matrix product formula for Macdonald polynomials
Cantini, Luigi; de Gier, Jan; Wheeler, Michael
2015-09-01
We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik-Zamolodchikov equations, which arise by considering representations of the Zamolodchikov-Faddeev and Yang-Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1.
Matrix product formula for Macdonald polynomials
International Nuclear Information System (INIS)
Cantini, Luigi; Gier, Jan de; Michael Wheeler
2015-01-01
We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik–Zamolodchikov equations, which arise by considering representations of the Zamolodchikov–Faddeev and Yang–Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1. (paper)
Johnson, Christopher Daniel
2018-01-01
Negotiated at the United Nations and in force since 1967, the Outer Space Treaty has been ratified by over 100 countries and is the most important and foundational source of space law. The treaty, whose full title is "Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, Including the Moon and Other Celestial Bodies," governs all of humankind's activities in outer space, including activities on other celestial bodies and many activities on Earth related to outer space. All space exploration and human spaceflight, planetary sciences, and commercial uses of space—such as the global telecommunications industry and the use of space technologies such as position, navigation, and timing (PNT), take place against the backdrop of the general regulatory framework established in the Outer Space Treaty. A treaty is an international legal instrument which balances rights and obligations between states, and exists as a kind of mutual contract of shared understandings, rights, and responsibilities between them. Negotiated and drafted during the Cold War era of heightened political tensions, the Outer Space Treaty is largely the product of efforts by the United States and the USSR to agree on certain minimum standards and obligations to govern their competition in "conquering" space. Additionally, the Outer Space Treaty is similar to other treaties, including treaties governing the high seas, international airspace, and the Antarctic, all of which govern the behavior of states outside of their national borders. The treaty is brief in nature and only contains 17 articles, and is not comprehensive in addressing and regulating every possible scenario. The negotiating states knew that the Outer Space Treaty could only establish certain foundational concepts such as freedom of access, state responsibility and liability, non-weaponization of space, the treatment of astronauts in distress, and the prohibition of non-appropriation of
Mirror symmetry, toric branes and topological string amplitudes as polynomials
Energy Technology Data Exchange (ETDEWEB)
Alim, Murad
2009-07-13
The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)
Mirror symmetry, toric branes and topological string amplitudes as polynomials
International Nuclear Information System (INIS)
Alim, Murad
2009-01-01
The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)
on the performance of Autoregressive Moving Average Polynomial
African Journals Online (AJOL)
Timothy Ademakinwa
Distributed Lag (PDL) model, Autoregressive Polynomial Distributed Lag ... Moving Average Polynomial Distributed Lag (ARMAPDL) model. ..... Global Journal of Mathematics and Statistics. Vol. 1. ... Business and Economic Research Center.
Schardt, A. W.; Behannon, K. W.; Carbary, J. F.; Eviatar, A.; Lepping, R. P.; Siscoe, G. L.
1983-01-01
Similarities between the Saturnian and terrestrial outer magnetosphere are examined. Saturn, like Earth, has a fully developed magnetic tail, 80 to 100 RS in diameter. One major difference between the two outer magnetospheres is the hydrogen and nitrogen torus produced by Titan. This plasma is, in general, convected in the corotation direction at nearly the rigid corotation speed. Energies of magnetospheric particles extend to above 500 keV. In contrast, interplanetary protons and ions above 2 MeV have free access to the outer magnetosphere to distances well below the Stormer cutoff. This access presumably occurs through the magnetotail. In addition to the H+, H2+, and H3+ ions primarily of local origin, energetic He, C, N, and O ions are found with solar composition. Their flux can be substantially enhanced over that of interplanetary ions at energies of 0.2 to 0.4 MeV/nuc.
Neck curve polynomials in neck rupture model
International Nuclear Information System (INIS)
Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul
2012-01-01
The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of 280 X 90 with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.
Polynomial model inversion control: numerical tests and applications
Novara, Carlo
2015-01-01
A novel control design approach for general nonlinear systems is described in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. Extensive simulations are carried out to test the numerical efficiency of the approach. Numerical examples of applicative interest are presented, concerned with control of the Duffing oscillator, control of a robot manipulator and insulin regulation in a type 1 diabetic p...
International Nuclear Information System (INIS)
Gerdt, Vladimir P.; Severyanov, Vasily M.
2006-01-01
A C package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z 2 whose total number of solutions in Z 2 determines the output of the quantum computation defined by the circuit. The generated polynomial system can further be converted to the canonical Grobner basis form which provides a universal algorithmic tool for counting the number of common roots of the polynomials
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren
2017-01-01
, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose
Polynomials in finite geometries and combinatorics
Blokhuis, A.; Walker, K.
1993-01-01
It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.
Polynomial analysis of ambulatory blood pressure measurements
Zwinderman, A. H.; Cleophas, T. A.; Cleophas, T. J.; van der Wall, E. E.
2001-01-01
In normotensive subjects blood pressures follow a circadian rhythm. A circadian rhythm in hypertensive patients is less well established, and may be clinically important, particularly with rigorous treatments of daytime blood pressures. Polynomial analysis of ambulatory blood pressure monitoring
Handbook on semidefinite, conic and polynomial optimization
Anjos, Miguel F
2012-01-01
This book offers the reader a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization and polynomial optimization. It covers theory, algorithms, software and applications.
Transversals of Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...
Generalized catalan numbers, sequences and polynomials
KOÇ, Cemal; GÜLOĞLU, İsmail; ESİN, Songül
2010-01-01
In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.
Schur Stability Regions for Complex Quadratic Polynomials
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Single-site Lennard-Jones models via polynomial chaos surrogates of Monte Carlo molecular simulation
Kadoura, Ahmad Salim; Siripatana, Adil; Sun, Shuyu; Knio, Omar; Hoteit, Ibrahim
2016-01-01
In this work, two Polynomial Chaos (PC) surrogates were generated to reproduce Monte Carlo (MC) molecular simulation results of the canonical (single-phase) and the NVT-Gibbs (two-phase) ensembles for a system of normalized structureless Lennard
An algorithmic approach to solving polynomial equations associated with quantum circuits
International Nuclear Information System (INIS)
Gerdt, V.P.; Zinin, M.V.
2009-01-01
In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Groebner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Groebner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Groebner bases over F 2
About the solvability of matrix polynomial equations
Netzer, Tim; Thom, Andreas
2016-01-01
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.
Two polynomial representations of experimental design
Notari, Roberto; Riccomagno, Eva; Rogantin, Maria-Piera
2007-01-01
In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Groebner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch between them. Examples include fractions of full factorial designs and designs for mixture experiments.
Rotation of 2D orthogonal polynomials
Czech Academy of Sciences Publication Activity Database
Yang, B.; Flusser, Jan; Kautský, J.
2018-01-01
Roč. 102, č. 1 (2018), s. 44-49 ISSN 0167-8655 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal polynomials * Recurrent relation * Hermite-like polynomials * Hermite moments Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.995, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0483250.pdf
Small RNAs controlling outer membrane porins
DEFF Research Database (Denmark)
Valentin-Hansen, Poul; Johansen, Jesper; Rasmussen, Anders A
2007-01-01
are key regulators of environmental stress. Recent work has revealed an intimate interplay between small RNA regulation of outer membrane proteins and the stress-induced sigmaE-signalling system, which has an essential role in the maintenance of the integrity of the outer membrane.......Gene regulation by small non-coding RNAs has been recognized as an important post-transcriptional regulatory mechanism for several years. In Gram-negative bacteria such as Escherichia coli and Salmonella, these RNAs control stress response and translation of outer membrane proteins and therefore...
Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions
Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie
2011-01-01
In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...
International Nuclear Information System (INIS)
Lutz, B.L.; de Bergh, C.; Maillard, J.P.
1983-01-01
The analysis of the near-infrared spectrum of monodeuterated methane (CH 3 D) near 6400 cm -1 and 5100 cm -1 is presented as the first of a series of papers dealing with laboratory studies of this molecule and with observational searches for it in outer solar system objects. Three new parallel bands which have locally perturbed upper states connecting with the ground state are identified, and approximate rotational constants are derived. The band centered near 6425 cm -1 and the 9613 A band previously analyzed by Lutz, Danehy, and Ramsay are found to form an apparent vibrational progression with the ν 2 fundamental at 2200 cm -1 , and vibrational assignments of 3ν 2 and 5ν 2 , respectively, are proposed. Detailed comparison of the rotational constants of the states involved is shown to support these assignments
Vertex models, TASEP and Grothendieck polynomials
International Nuclear Information System (INIS)
Motegi, Kohei; Sakai, Kazumitsu
2013-01-01
We examine the wavefunctions and their scalar products of a one-parameter family of integrable five-vertex models. At a special point of the parameter, the model investigated is related to an irreversible interacting stochastic particle system—the so-called totally asymmetric simple exclusion process (TASEP). By combining the quantum inverse scattering method with a matrix product representation of the wavefunctions, the on-/off-shell wavefunctions of the five-vertex models are represented as a certain determinant form. Up to some normalization factors, we find that the wavefunctions are given by Grothendieck polynomials, which are a one-parameter deformation of Schur polynomials. Introducing a dual version of the Grothendieck polynomials, and utilizing the determinant representation for the scalar products of the wavefunctions, we derive a generalized Cauchy identity satisfied by the Grothendieck polynomials and their duals. Several representation theoretical formulae for the Grothendieck polynomials are also presented. As a byproduct, the relaxation dynamics such as Green functions for the periodic TASEP are found to be described in terms of the Grothendieck polynomials. (paper)
2013-09-10
...\\ including the regulation of workplace safety and health.\\2\\ The Coast Guard's regulatory authority extends... 147 [Docket No. USCG-2012-0779] RIN 1625-AC05 Safety and Environmental Management System Requirements... a vessel-specific Safety and Environmental Management System (SEMS) that incorporates the management...
Bradbury, Hilary
2003-01-01
Provides a rationale for applying holistic systems thinking to sustainable development Suggests student activities for four topics: (1) exploration of external organizational environment; (2) inner-directed exploration of the natural world; (3) exploration of the individual's world; and (4) personal impact on the larger system. (Contains 29…
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)] e-mail: konst@citedi.mx
2005-08-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2005-01-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered
vs. a polynomial chaos-based MCMC
Siripatana, Adil
2014-08-01
Bayesian Inference of Manning\\'s n coefficient in a Storm Surge Model Framework: comparison between Kalman lter and polynomial based method Adil Siripatana Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms de ned through the formulation of Manning\\'s n coefficients. This thesis considers the Bayesian inference problem of the Manning\\'s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part of the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning\\'s n coefficient and a 2-D parameterized Manning\\'s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an in ation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK lter, 5 we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning\\'s n coe cient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to di erent OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the
Relations between Möbius and coboundary polynomials
Jurrius, R.P.M.J.
2012-01-01
It is known that, in general, the coboundary polynomial and the Möbius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will investigate if it is possible that the Möbius polynomial of a matroid, together with the Möbius polynomial of
Expansion of Sobolev functions in series in Laguerre polynomials
International Nuclear Information System (INIS)
Selyakov, K.I.
1985-01-01
The solution of the integral equation for the Sobolev functions is represented in the form of series in Laguerre polynomials. The coefficients of these series are simultaneously the coefficients of the power series for the Ambartsumyan-Chandrasekhar H functions. Infinite systems of linear algebraic equations with Toeplitz matrices are given for the coefficients of the series. Numerical results and approximate expressions are given for the case of isotropic scattering
First-Order Polynomial Heisenberg Algebras and Coherent States
International Nuclear Information System (INIS)
Castillo-Celeita, M; Fernández C, D J
2016-01-01
The polynomial Heisenberg algebras (PHA) are deformations of the Heisenberg- Weyl algebra characterizing the underlying symmetry of the supersymmetric partners of the Harmonic oscillator. When looking for the simplest system ruled by PHA, however, we end up with the harmonic oscillator. In this paper we are going to realize the first-order PHA through the harmonic oscillator. The associated coherent states will be also constructed, which turn out to be the well known even and odd coherent states. (paper)
Positive polynomials and robust stabilization with fixed-order controllers
Czech Academy of Sciences Publication Activity Database
Henrion, Didier; Šebek, M.; Kučera, V.
2003-01-01
Roč. 48, č. 7 (2003), s. 1178-1186 ISSN 0018-9286 R&D Projects: GA ČR GA102/02/0709; GA MŠk ME 496 Institutional research plan: CEZ:AV0Z1075907 Keywords : fixed-order control lers * linear matrix inequality * polynomials, robust control Subject RIV: BC - Control Systems Theory Impact factor: 1.896, year: 2003
Venkatapathy, Ethiraj; Ellerby, D.; Gage, P.; Gasch, M.; Hwang, H.; Prabhu, D.; Stackpoole, M.; Wercinski, Paul
2018-01-01
This invited talk will provide an assessment of the TPS needs for Outer Planet In-situ missions to destinations with atmosphere. The talk will outline the drivers for TPS from destination, science, mission architecture and entry environment. An assessment of the readiness of the TPS, both currently available and under development, for Saturn, Titan, Uranus and Neptune are provided. The challenges related to sustainability of the TPS for future missions are discussed.
Recognition of Arabic Sign Language Alphabet Using Polynomial Classifiers
Directory of Open Access Journals (Sweden)
M. Al-Rousan
2005-08-01
Full Text Available Building an accurate automatic sign language recognition system is of great importance in facilitating efficient communication with deaf people. In this paper, we propose the use of polynomial classifiers as a classification engine for the recognition of Arabic sign language (ArSL alphabet. Polynomial classifiers have several advantages over other classifiers in that they do not require iterative training, and that they are highly computationally scalable with the number of classes. Based on polynomial classifiers, we have built an ArSL system and measured its performance using real ArSL data collected from deaf people. We show that the proposed system provides superior recognition results when compared with previously published results using ANFIS-based classification on the same dataset and feature extraction methodology. The comparison is shown in terms of the number of misclassified test patterns. The reduction in the rate of misclassified patterns was very significant. In particular, we have achieved a 36% reduction of misclassifications on the training data and 57% on the test data.
Special polynomials associated with rational solutions of some hierarchies
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2009-01-01
New special polynomials associated with rational solutions of the Painleve hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials associated with the hierarchies. It is shown that rational solutions of the Caudrey-Dodd-Gibbon, the Kaup-Kupershmidt and the modified hierarchy for these ones can be obtained using new special polynomials.
On the Connection Coefficients of the Chebyshev-Boubaker Polynomials
Directory of Open Access Journals (Sweden)
Paul Barry
2013-01-01
Full Text Available The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.
New polynomial-based molecular descriptors with low degeneracy.
Directory of Open Access Journals (Sweden)
Matthias Dehmer
Full Text Available In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power.
Broussard, J. R.; Halyo, N.
1984-01-01
This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.
Outer scale of atmospheric turbulence
Lukin, Vladimir P.
2005-10-01
In the early 70's, the scientists in Italy (A.Consortini, M.Bertolotti, L.Ronchi), USA (R.Buser, Ochs, S.Clifford) and USSR (V.Pokasov, V.Lukin) almost simultaneously discovered the phenomenon of deviation from the power law and the effect of saturation for the structure phase function. During a period of 35 years we have performed successively the investigations of the effect of low-frequency spectral range of atmospheric turbulence on the optical characteristics. The influence of the turbulence models as well as a outer scale of turbulence on the characteristics of telescopes and systems of laser beam formations has been determined too.
RADIOISOTOPE-DRIVEN DUAL-MODE PROPULSION SYSTEM FOR CUBESAT-SCALE PAYLOADS TO THE OUTER PLANETS
Energy Technology Data Exchange (ETDEWEB)
N. D. Jerred; T. M. Howe; S. D. Howe; A. Rajguru
2014-02-01
It is apparent the cost of planetary exploration is rising as mission budgets declining. Currently small scientific beds geared to performing limited tasks are being developed and launched into low earth orbit (LEO) in the form of small-scale satellite units, i.e., CubeSats. These micro- and nano-satellites are gaining popularity among the university and science communities due to their relatively low cost and design flexibility. To date these small units have been limited to performing tasks in LEO utilizing solar-based power. If a reasonable propulsion system could be developed, these CubeSat platforms could perform exploration of various extra-terrestrial bodies within the solar system engaging a broader range of researchers. Additionally, being mindful of mass, smaller cheaper launch vehicles (approximately 1,000 kgs to LEO) can be targeted. Thus, in effect, allows for beneficial exploration to be conducted within limited budgets. Researchers at the Center for Space Nuclear Research (CSNR) are proposing a low mass, radioisotope-based, dual-mode propulsion system capable of extending the exploration realm of these CubeSats out of LEO.
A new class of generalized polynomials associated with Hermite and Bernoulli polynomials
Directory of Open Access Journals (Sweden)
M. A. Pathan
2015-05-01
Full Text Available In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials Φ_{n}^{(α}(x,ν of degree n and order α introduced by Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials B_n(x, generalized Bernoulli numbers B_n(a,b, generalized Bernoulli polynomials B_n(x;a,b,c of Luo et al, Hermite-Bernoulli polynomials {_HB}_n(x,y of Dattoli et al and {_HB}_n^{(α} (x,y of Pathan are generalized to the one {_HB}_n^{(α}(x,y,a,b,c which is called the generalized polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x, B_n(a,b, B_n(x;a,b,c and {}_HB_n^{(α}(x,y;a,b,c are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomials
Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials
Ait-Haddou, Rachid; Goldman, Ron
2015-01-01
We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.
Certain non-linear differential polynomials sharing a non zero polynomial
Directory of Open Access Journals (Sweden)
Majumder Sujoy
2015-10-01
functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008, 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011, 23-32.].
Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials
Ait-Haddou, Rachid
2015-06-07
We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.
Introduction to the spectral theory of polynomial operator pencils
Markus, A S
1988-01-01
This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Kreibreven and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, resea...
Design of a polynomial ring based symmetric homomorphic encryption scheme
Directory of Open Access Journals (Sweden)
Smaranika Dasgupta
2016-09-01
Full Text Available Security of data, especially in clouds, has become immensely essential for present-day applications. Fully homomorphic encryption (FHE is a great way to secure data which is used and manipulated by untrusted applications or systems. In this paper, we propose a symmetric FHE scheme based on polynomial over ring of integers. This scheme is somewhat homomorphic due to accumulation of noise after few operations, which is made fully homomorphic using a refresh procedure. After certain amount of homomorphic computations, large ciphertexts are refreshed for proper decryption. The hardness of the scheme is based on the difficulty of factorizing large integers. Also, it requires polynomial addition which is computationally cost effective. Experimental results are shown to support our claim.
Image Compression Based On Wavelet, Polynomial and Quadtree
Directory of Open Access Journals (Sweden)
Bushra A. SULTAN
2011-01-01
Full Text Available In this paper a simple and fast image compression scheme is proposed, it is based on using wavelet transform to decompose the image signal and then using polynomial approximation to prune the smoothing component of the image band. The architect of proposed coding scheme is high synthetic where the error produced due to polynomial approximation in addition to the detail sub-band data are coded using both quantization and Quadtree spatial coding. As a last stage of the encoding process shift encoding is used as a simple and efficient entropy encoder to compress the outcomes of the previous stage.The test results indicate that the proposed system can produce a promising compression performance while preserving the image quality level.
Optimization of polynomials in non-commuting variables
Burgdorf, Sabine; Povh, Janez
2016-01-01
This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos
Directory of Open Access Journals (Sweden)
F. Santonja
2012-01-01
Full Text Available Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model.
Statistics of stationary points of random finite polynomial potentials
International Nuclear Information System (INIS)
Mehta, Dhagash; Niemerg, Matthew; Sun, Chuang
2015-01-01
The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology. However, there are few reliable methods available which can find all the SPs accurately. Hence, one has to rely on indirect methods such as Random Matrix theory. With a combination of the numerical polynomial homotopy continuation method and a certification method, we obtain all the certified SPs of the most general polynomial RP for each sample chosen from the Gaussian distribution with mean 0 and variance 1. While obtaining many novel results for the finite size case of the RP, we also discuss the implications of our results on mathematics of random systems and string theory landscapes. (paper)
Scattering amplitudes from multivariate polynomial division
Energy Technology Data Exchange (ETDEWEB)
Mastrolia, Pierpaolo, E-mail: pierpaolo.mastrolia@cern.ch [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Dipartimento di Fisica e Astronomia, Universita di Padova, Padova (Italy); INFN Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Mirabella, Edoardo, E-mail: mirabell@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Ossola, Giovanni, E-mail: GOssola@citytech.cuny.edu [New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Peraro, Tiziano, E-mail: peraro@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)
2012-11-15
We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Groebner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.
Outer Continental Shelf Lands Act
National Oceanic and Atmospheric Administration, Department of Commerce — This data represents geographic terms used within the Outer Continental Shelf Lands Act (OCSLA or Act). The Act defines the United States outer continental shelf...
Remarks on determinants and the classical polynomials
International Nuclear Information System (INIS)
Henning, J.J.; Kranold, H.U.; Louw, D.F.B.
1986-01-01
As motivation for this formal analysis the problem of Landau damping of Bernstein modes is discussed. It is shown that in the case of a weak but finite constant external magnetic field, the analytical structure of the dispersion relations is of such a nature that longitudinal waves propagating orthogonal to the external magnetic field are also damped, contrary to normal belief. In the treatment of the linearized Vlasov equation it is found convenient to generate certain polynomials by the problem at hand and to explicitly write down expressions for these polynomials. In the course of this study methods are used that relate to elementary but fairly unknown functional relationships between power sums and coefficients of polynomials. These relationships, also called Waring functions, are derived. They are then used in other applications to give explicit expressions for the generalized Laguerre polynomials in terms of determinant functions. The properties of polynomials generated by a wide class of generating functions are investigated. These relationships are also used to obtain explicit forms for the cumulants of a distribution in terms of its moments. It is pointed out that cumulants (or moments, for that matter) do not determine a distribution function
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef
2017-06-30
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.
Institute of Scientific and Technical Information of China (English)
XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian
2007-01-01
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.
Quantized vortices in the ideal bose gas: a physical realization of random polynomials.
Castin, Yvan; Hadzibabic, Zoran; Stock, Sabine; Dalibard, Jean; Stringari, Sandro
2006-02-03
We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.
Polynomial chaos functions and stochastic differential equations
International Nuclear Information System (INIS)
Williams, M.M.R.
2006-01-01
The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory
New realisation of Preisach model using adaptive polynomial approximation
Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young
2012-09-01
Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.
From Jack to Double Jack Polynomials via the Supersymmetric Bridge
Lapointe, Luc; Mathieu, Pierre
2015-07-01
The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine {widehat{sl}_2} algebra.
Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.
Temel, Burcin; Mills, Greg; Metiu, Horia
2008-03-27
We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.
Twisted Polynomials and Forgery Attacks on GCM
DEFF Research Database (Denmark)
Abdelraheem, Mohamed Ahmed A. M. A.; Beelen, Peter; Bogdanov, Andrey
2015-01-01
Polynomial hashing as an instantiation of universal hashing is a widely employed method for the construction of MACs and authenticated encryption (AE) schemes, the ubiquitous GCM being a prominent example. It is also used in recent AE proposals within the CAESAR competition which aim at providing...... in an improved key recovery algorithm. As cryptanalytic applications of our twisted polynomials, we develop the first universal forgery attacks on GCM in the weak-key model that do not require nonce reuse. Moreover, we present universal weak-key forgeries for the nonce-misuse resistant AE scheme POET, which...
Polynomial Vector Fields in One Complex Variable
DEFF Research Database (Denmark)
Branner, Bodil
In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....
The chromatic polynomial and list colorings
DEFF Research Database (Denmark)
Thomassen, Carsten
2009-01-01
We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph.......We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph....
Complex centers of polynomial differential equations
Directory of Open Access Journals (Sweden)
Mohamad Ali M. Alwash
2007-07-01
Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.
Differential recurrence formulae for orthogonal polynomials
Directory of Open Access Journals (Sweden)
Anton L. W. von Bachhaus
1995-11-01
Full Text Available Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(xY'n(x=fn(xYn(x+Yn-1(x. Part II - A recurrence formula of the form: rn(xY'n(x+sn(xY'n+1(x+tn(xY'n-1(x=0, is derived using the result of Part I.
Louisiana Geographic Information Center — This data set contains arcs representing the Environmental Sensitivity Index (ESI) classification of the outer coast of Louisiana. The ESI is a classification and...
Smoothing optimization of supporting quadratic surfaces with Zernike polynomials
Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu
2018-03-01
A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.
Polynomial regression analysis and significance test of the regression function
International Nuclear Information System (INIS)
Gao Zhengming; Zhao Juan; He Shengping
2012-01-01
In order to analyze the decay heating power of a certain radioactive isotope per kilogram with polynomial regression method, the paper firstly demonstrated the broad usage of polynomial function and deduced its parameters with ordinary least squares estimate. Then significance test method of polynomial regression function is derived considering the similarity between the polynomial regression model and the multivariable linear regression model. Finally, polynomial regression analysis and significance test of the polynomial function are done to the decay heating power of the iso tope per kilogram in accord with the authors' real work. (authors)
Energy Technology Data Exchange (ETDEWEB)
Konagaya, Masaaki; Iida, Mitsuo [Suzuka National Hospital, Mie (Japan); Konagaya, Yoko; Honda, Hitoshi
1993-06-01
We studied extrapyramidal symptoms and T2-weighted MRI findings of the putamen in 20 patients with multiple system atrophy (MSA) and 25 with idiopathic Parkinson's disease. Nine of the 20 MSA patients showed extrapyramidal symptoms. We could not observe cerebellar ataxia in two of the 9 patients because of severe rigidity and skinesia. Eight of the 9 MSA patients with extrapyramidal symptoms showed linear hyperintensity in the outer margin of the putamen. This abnormal intensity was bilateral and symmetric in most patients. However, in MSA patients without extrapyramidal symptoms, only one patient showed the linear hyperintensity. We could not find such abnormal intensity in any of the patients with Parkinson's disease. On proton density MRI, the signal intensity in the lesion was higher than that in the gray matter, which leads the speculation that the hyperintensity is gliosis of the putamen or increased extracellular fluid space caused by severe shrinkage of the putamen. These characteristic MRI findings may distinguish MSA with extrapyramidal symptoms from Parkinson's disease. (J.P.N.).
Nonclassical Orthogonal Polynomials and Corresponding Quadratures
Fukuda, H; Alt, E O; Matveenko, A V
2004-01-01
We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.
Intrinsic Diophantine approximation on general polynomial surfaces
DEFF Research Database (Denmark)
Tiljeset, Morten Hein
2017-01-01
We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...
Quantum Hilbert matrices and orthogonal polynomials
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...
Information-theoretic lengths of Jacobi polynomials
Energy Technology Data Exchange (ETDEWEB)
Guerrero, A; Dehesa, J S [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, Granada (Spain); Sanchez-Moreno, P, E-mail: agmartinez@ugr.e, E-mail: pablos@ugr.e, E-mail: dehesa@ugr.e [Instituto ' Carlos I' de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain)
2010-07-30
The information-theoretic lengths of the Jacobi polynomials P{sup ({alpha}, {beta})}{sub n}(x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are investigated. They quantify the spreading of the polynomials along the orthogonality interval [- 1, 1] in a complementary but different way as the root-mean-square or standard deviation because, contrary to this measure, they do not refer to any specific point of the interval. The explicit expressions of the Fisher length are given. The Renyi lengths are found by the use of the combinatorial multivariable Bell polynomials in terms of the polynomial degree n and the parameters ({alpha}, {beta}). The Shannon length, which cannot be exactly calculated because of its logarithmic functional form, is bounded from below by using sharp upper bounds to general densities on [- 1, +1] given in terms of various expectation values; moreover, its asymptotics is also pointed out. Finally, several computational issues relative to these three quantities are carefully analyzed.
Indecomposability of polynomials via Jacobian matrix
International Nuclear Information System (INIS)
Cheze, G.; Najib, S.
2007-12-01
Uni-multivariate decomposition of polynomials is a special case of absolute factorization. Recently, thanks to the Ruppert's matrix some effective results about absolute factorization have been improved. Here we show that with a jacobian matrix we can get sharper bounds for the special case of uni-multivariate decomposition. (author)
On selfadjoint functors satisfying polynomial relations
DEFF Research Database (Denmark)
Agerholm, Troels; Mazorchuk, Volodomyr
2011-01-01
We study selfadjoint functors acting on categories of finite dimen- sional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint func- tors satisfying several easy relations, in particular, idempotents and square roots of a sum...
Polynomial Variables and the Jacobian Problem
Indian Academy of Sciences (India)
algebra and algebraic geometry, and ... algebraically, to making the change of variables (X, Y) r--t. (X +p, Y ... aX + bY + p and eX + dY + q are linear polynomials in X, Y. ..... [5] T T Moh, On the Jacobian conjecture and the confipration of roots,.
Function approximation with polynomial regression slines
International Nuclear Information System (INIS)
Urbanski, P.
1996-01-01
Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author)
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Characteristic polynomials of linear polyacenes and their ...
Indian Academy of Sciences (India)
Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal's triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP's. Thus it ...
Coherent states for polynomial su(2) algebra
International Nuclear Information System (INIS)
Sadiq, Muhammad; Inomata, Akira
2007-01-01
A class of generalized coherent states is constructed for a polynomial su(2) algebra in a group-free manner. As a special case, the coherent states for the cubic su(2) algebra are discussed. The states so constructed reduce to the usual SU(2) coherent states in the linear limit
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Spectral properties of birth-death polynomials
van Doorn, Erik A.
2015-01-01
We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by
Spectral properties of birth-death polynomials
van Doorn, Erik A.
We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by
Optimization of Cubic Polynomial Functions without Calculus
Taylor, Ronald D., Jr.; Hansen, Ryan
2008-01-01
In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…
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 ...
Inequalities for a Polynomial and its Derivative
Indian Academy of Sciences (India)
Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 110; Issue 2. Inequalities for a Polynomial and its Derivative. V K Jain. Volume 110 Issue 2 May 2000 pp 137- ...
Integral Inequalities for Self-Reciprocal Polynomials
Indian Academy of Sciences (India)
Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. Integral Inequalities for Self-Reciprocal Polynomials. Horst Alzer. Volume 120 Issue 2 April 2010 ...
Directory of Open Access Journals (Sweden)
V. P. Gribkova
2014-01-01
Full Text Available The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points using a method of mechanical quadrature and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation, which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming.
Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality
Ayala, Mario; Carinci, Gioia; Redig, Frank
2018-06-01
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann-Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.
Density of Real Zeros of the Tutte Polynomial
DEFF Research Database (Denmark)
Ok, Seongmin; Perrett, Thomas
2018-01-01
The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...
Density of Real Zeros of the Tutte Polynomial
DEFF Research Database (Denmark)
Ok, Seongmin; Perrett, Thomas
2017-01-01
The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...
Some Polynomials Associated with the r-Whitney Numbers
Indian Academy of Sciences (India)
26
Abstract. In the present article we study three families of polynomials associated with ... [29, 39] for their relations with the Bernoulli and generalized Bernoulli polynomials and ... generating functions in a similar way as in the classical cases.
On an Inequality Concerning the Polar Derivative of a Polynomial
Indian Academy of Sciences (India)
Abstract. In this paper, we present a correct proof of an -inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.
Structural identifiability of polynomial and rational systems
J. Nemcová (Jana)
2010-01-01
htmlabstractSince analysis and simulation of biological phenomena require the availability of their fully specified models, one needs to be able to estimate unknown parameter values of the models. In this paper we deal with identifiability of parametrizations which is the property of one-to-one
2-variable Laguerre matrix polynomials and Lie-algebraic techniques
International Nuclear Information System (INIS)
Khan, Subuhi; Hassan, Nader Ali Makboul
2010-01-01
The authors introduce 2-variable forms of Laguerre and modified Laguerre matrix polynomials and derive their special properties. Further, the representations of the special linear Lie algebra sl(2) and the harmonic oscillator Lie algebra G(0,1) are used to derive certain results involving these polynomials. Furthermore, the generating relations for the ordinary as well as matrix polynomials related to these matrix polynomials are derived as applications.
The generalized Yablonskii-Vorob'ev polynomials and their properties
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2008-01-01
Rational solutions of the generalized second Painleve hierarchy are classified. Representation of the rational solutions in terms of special polynomials, the generalized Yablonskii-Vorob'ev polynomials, is introduced. Differential-difference relations satisfied by the polynomials are found. Hierarchies of differential equations related to the generalized second Painleve hierarchy are derived. One of these hierarchies is a sequence of differential equations satisfied by the generalized Yablonskii-Vorob'ev polynomials
Polynomial selection in number field sieve for integer factorization
Directory of Open Access Journals (Sweden)
Gireesh Pandey
2016-09-01
Full Text Available The general number field sieve (GNFS is the fastest algorithm for factoring large composite integers which is made up by two prime numbers. Polynomial selection is an important step of GNFS. The asymptotic runtime depends on choice of good polynomial pairs. In this paper, we present polynomial selection algorithm that will be modelled with size and root properties. The correlations between polynomial coefficient and number of relations have been explored with experimental findings.
Interlacing of zeros of quasi-orthogonal meixner polynomials | Driver ...
African Journals Online (AJOL)
... interlacing of zeros of quasi-orthogonal Meixner polynomials Mn(x;β; c) with the zeros of their nearest orthogonal counterparts Mt(x;β + k; c), l; n ∈ ℕ, k ∈ {1; 2}; is also discussed. Mathematics Subject Classication (2010): 33C45, 42C05. Key words: Discrete orthogonal polynomials, quasi-orthogonal polynomials, Meixner
Strong result for real zeros of random algebraic polynomials
Directory of Open Access Journals (Sweden)
T. Uno
2001-01-01
Full Text Available An estimate is given for the lower bound of real zeros of random algebraic polynomials whose coefficients are non-identically distributed dependent Gaussian random variables. Moreover, our estimated measure of the exceptional set, which is independent of the degree of the polynomials, tends to zero as the degree of the polynomial tends to infinity.
On the Lorentz degree of a product of polynomials
Ait-Haddou, Rachid
2015-01-01
In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.
A Determinant Expression for the Generalized Bessel Polynomials
Directory of Open Access Journals (Sweden)
Sheng-liang Yang
2013-01-01
Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.
On the estimation of the degree of regression polynomial
International Nuclear Information System (INIS)
Toeroek, Cs.
1997-01-01
The mathematical functions most commonly used to model curvature in plots are polynomials. Generally, the higher the degree of the polynomial, the more complex is the trend that its graph can represent. We propose a new statistical-graphical approach based on the discrete projective transformation (DPT) to estimating the degree of polynomial that adequately describes the trend in the plot
Zeros and uniqueness of Q-difference polynomials of meromorphic ...
Indian Academy of Sciences (India)
Meromorphic functions; Nevanlinna theory; logarithmic order; uniqueness problem; difference-differential polynomial. Abstract. In this paper, we investigate the value distribution of -difference polynomials of meromorphic function of finite logarithmic order, and study the zero distribution of difference-differential polynomials ...
Uniqueness and zeros of q-shift difference polynomials
Indian Academy of Sciences (India)
In this paper, we consider the zero distributions of -shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical Hayman results on the zeros of differential polynomials to -shift difference polynomials. We also investigate the uniqueness problem of -shift ...
Polynomially Riesz elements | Živković-Zlatanović | Quaestiones ...
African Journals Online (AJOL)
A Banach algebra element ɑ ∈ A is said to be "polynomially Riesz", relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image Tp ∈ B is quasinilpotent. Keywords: Homomorphism of Banach algebras, polynomially Riesz element, Fredholm spectrum, Browder element, ...
Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials
International Nuclear Information System (INIS)
Tratnik, M.V.
1990-01-01
Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials
Commutators with idempotent values on multilinear polynomials in ...
Indian Academy of Sciences (India)
Multilinear polynomial; derivations; generalized polynomial identity; prime ring; right ideal. Abstract. Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R , f ( x 1 , … , x n ) a multilinear polynomial over C , ϱ a nonzero right ideal of R and m > 1 a fixed integer such that.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Degenerate r-Stirling Numbers and r-Bell Polynomials
Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.
2018-01-01
The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.
Vacuum Outer-Gap Structure in Pulsar Outer Magnetospheres
International Nuclear Information System (INIS)
Gui-Fang, Lin; Li, Zhang
2009-01-01
We study the vacuum outer-gap structure in the outer magnetosphere of rotation-powered pulsars by considering the limit of trans-field height through a pair production process. In this case, the trans-field height is limited by the photon-photon pair production process and the outer boundary of the outer gap can be extended outside the light cylinder. By solving self-consistently the Poisson equation for electrical potential and the Boltzmann equations of electrons/positrons and γ-rays in a vacuum outer gap for the parameters of Vela pulsar, we obtain an approximate geometry of the outer gap, i.e. the trans-field height is limited by the pair-production process and increases with the radial distance to the star and the width of the outer gap starts at the inner boundary (near the null charge surface) and ends at the outer boundary which locates inside or outside the light cylinder depending on the inclination angle. (geophysics, astronomy, and astrophysics)
Energy Technology Data Exchange (ETDEWEB)
Materese, Christopher K.; Cruikshank, Dale P.; Sandford, Scott A.; Imanaka, Hiroshi; Nuevo, Michel [NASA Ames Research Center, MS 245-6, Moffett Field, CA 94035-1000 (United States)
2015-10-20
Radiation processing of the surface ices of outer Solar System bodies may be an important process for the production of complex chemical species. The refractory materials resulting from radiation processing of known ices are thought to impart to them a red or brown color, as perceived in the visible spectral region. In this work, we analyzed the refractory materials produced from the 1.2-keV electron bombardment of low-temperature N{sub 2}-, CH{sub 4}-, and CO-containing ices (100:1:1), which simulates the radiation from the secondary electrons produced by cosmic ray bombardment of the surface ices of Pluto. Despite starting with extremely simple ices dominated by N{sub 2}, electron irradiation processing results in the production of refractory material with complex oxygen- and nitrogen-bearing organic molecules. These refractory materials were studied at room temperature using multiple analytical techniques including Fourier-transform infrared spectroscopy, X-ray absorption near-edge structure (XANES) spectroscopy, and gas chromatography coupled with mass spectrometry (GC-MS). Infrared spectra of the refractory material suggest the presence of alcohols, carboxylic acids, ketones, aldehydes, amines, and nitriles. XANES spectra of the material indicate the presence of carboxyl groups, amides, urea, and nitriles, and are thus consistent with the IR data. Atomic abundance ratios for the bulk composition of these residues from XANES analysis show that the organic residues are extremely N-rich, having ratios of N/C ∼ 0.9 and O/C ∼ 0.2. Finally, GC-MS data reveal that the residues contain urea as well as numerous carboxylic acids, some of which are of interest for prebiotic and biological chemistries.
Polynomial Digital Control of a Series Equal Liquid Tanks
Directory of Open Access Journals (Sweden)
Bobála Vladimír
2016-01-01
Full Text Available Time-delays are mainly caused by the time required to transport mass, energy or information, but they can also be caused by processing time or accumulation. Typical examples of such processes are e.g. pumps, liquid storing tanks, distillation columns or some types of chemical reactors. In many cases time-delay is caused by the effect produced by the accumulation of a large number of low-order systems. Several industrial processes have the time-delay effect produced by the accumulation of a great number of low-order systems with the identical dynamic. The dynamic behavior of series these low-order systems is expressed by high-order system. One of possibilities of control of such processes is their approximation by low-order model with time-delay. The paper is focused on the design of the digital polynomial control of a set of equal liquid cylinder atmospheric tanks. The designed control algorithms are realized using the digital Smith Predictor (SP based on polynomial approach – by minimization of the Linear Quadratic (LQ criterion. The LQ criterion was combined with pole assignment.
Large level crossings of a random polynomial
Directory of Open Access Journals (Sweden)
Kambiz Farahmand
1987-01-01
Full Text Available We know the expected number of times that a polynomial of degree n with independent random real coefficients asymptotically crosses the level K, when K is any real value such that (K2/nÃ¢Â†Â’0 as nÃ¢Â†Â’Ã¢ÂˆÂž. The present paper shows that, when K is allowed to be large, this expected number of crossings reduces to only one. The coefficients of the polynomial are assumed to be normally distributed. It is shown that it is sufficient to let KÃ¢Â‰Â¥exp(nf where f is any function of n such that fÃ¢Â†Â’Ã¢ÂˆÂž as nÃ¢Â†Â’Ã¢ÂˆÂž.
Sparse DOA estimation with polynomial rooting
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Fernandez Grande, Efren
2015-01-01
Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve highresol......Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve...... highresolution imaging. Utilizing the dual optimal variables of the CS optimization problem, it is shown with Monte Carlo simulations that the DOAs are accurately reconstructed through polynomial rooting (Root-CS). Polynomial rooting is known to improve the resolution in several other DOA estimation methods...
On factorization of generalized Macdonald polynomials
International Nuclear Information System (INIS)
Kononov, Ya.; Morozov, A.
2016-01-01
A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W ∞ - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U q (SL N ) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)
Quantum Hurwitz numbers and Macdonald polynomials
Harnad, J.
2016-11-01
Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Polynomial structures in one-loop amplitudes
International Nuclear Information System (INIS)
Britto, Ruth; Feng Bo; Yang Gang
2008-01-01
A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2ε)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2ε)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.
Global Monte Carlo Simulation with High Order Polynomial Expansions
International Nuclear Information System (INIS)
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-01-01
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, possibly increasing the communication across a loosely coupled system and thereby improving convergence over the conventional fission bank approach used in most production Monte Carlo codes. The project examined a number of basis functions, including global Legendre polynomials as well as 'local' piecewise polynomials such as finite element hat functions and higher order versions. The global FET showed an improvement in convergence over the conventional fission bank approach. The local FET methods showed some advantages versus global polynomials in handling geometries with discontinuous material properties. The conventional finite element hat functions had the disadvantage that the expansion coefficients could not be estimated directly but had to be obtained by solving a linear system whose matrix elements were estimated. An alternative fission matrix-based response matrix algorithm was formulated. Studies were made of two alternative applications of the FET, one based on the kernel density estimator and one based on Arnoldi's method of minimized iterations. Preliminary results for both methods indicate improvements in fission source convergence. These developments indicate that the FET has promise for speeding up Monte Carlo fission source convergence
Link polynomial, crossing multiplier and surgery formula
International Nuclear Information System (INIS)
Deguchi, Tetsuo; Yamada, Yasuhiko.
1989-01-01
Relations between link polynomials constructed from exactly solvable lattice models and topological field theory are reviewed. It is found that the surgery formula for a three-sphere S 3 with Wilson lines corresponds to the Markov trace constructed from the exactly solvable models. This indicates that knot theory intimately relates various important subjects such as exactly solvable models, conformal field theories and topological quantum field theories. (author)
Moments, positive polynomials and their applications
Lasserre, Jean Bernard
2009-01-01
Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones,
Polynomials and identities on real Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Kraus, M.
2012-01-01
Roč. 385, č. 2 (2012), s. 1015-1026 ISSN 0022-247X R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : Polynomials on Banach spaces Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11006743
Polynomial expansions and transition strengths
International Nuclear Information System (INIS)
Draayer, J.P.
1980-01-01
The subject is statistical spectroscopy applied to determining strengths and strength sums of excitation processes in nuclei. The focus will be on a ds-shell isoscalar E2 study with detailed shell-model results providing the standard for comparison; similar results are available for isovector E2 and M1 and E4 transitions as well as for single-particle transfer and ν +- decay. The present study is intended to serve as a tutorial for applications where shell-model calculations are not feasible. The problem is posed and a schematic theory for strengths and sums is presented. The theory is extended to include the effect of correlations between H, the system Hamiltonian, and theta, the excitation operator. Associated with correlation measures is a geometry that can be used to anticipate the goodness of a symmetry. This is illustrated for pseudo SU(3) in the fp-shell. Some conclusions about fluctuations and collectivity that one can deduce from the statistical results for strengths are presented
Eye aberration analysis with Zernike polynomials
Molebny, Vasyl V.; Chyzh, Igor H.; Sokurenko, Vyacheslav M.; Pallikaris, Ioannis G.; Naoumidis, Leonidas P.
1998-06-01
New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberration, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.
Predicting physical time series using dynamic ridge polynomial neural networks.
Directory of Open Access Journals (Sweden)
Dhiya Al-Jumeily
Full Text Available Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques.
Large N Penner matrix model and a novel asymptotic formula for the generalized Laguerre polynomials
International Nuclear Information System (INIS)
Deo, N
2003-01-01
The Gaussian Penner matrix model is re-examined in the light of the results which have been found in double-well matrix models. The orthogonal polynomials for the Gaussian Penner model are shown to be the generalized Laguerre polynomials L (α) n (x) with α and x depending on N, the size of the matrix. An asymptotic formula for the orthogonal polynomials is derived following closely the orthogonal polynomial method of Deo (1997 Nucl. Phys. B 504 609). The universality found in the double-well matrix model is extended to include non-polynomial potentials. An asymptotic formula is also found for the Laguerre polynomial using the saddle-point method by rescaling α and x with N. Combining these results a novel asymptotic formula is found for the generalized Laguerre polynomials (different from that given in Szego's book) in a different asymptotic regime. This may have applications in mathematical and physical problems in the future. The density-density correlators are derived and are the same as those found for the double-well matrix models. These correlators in the smoothed large N limit are sensitive to odd and even N where N is the size of the matrix. These results for the two-point density-density correlation function may be useful in finding eigenvalue effects in experiments in mesoscopic systems or small metallic grains. There may be applications to string theory as well as the tunnelling of an eigenvalue from one valley to the other being an important quantity there
Linear precoding based on polynomial expansion: reducing complexity in massive MIMO
Mueller, Axel; Kammoun, Abla; Bjö rnson, Emil; Debbah, Mé rouane
2016-01-01
By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
Turbine airfoil with outer wall thickness indicators
Marra, John J; James, Allister W; Merrill, Gary B
2013-08-06
A turbine airfoil usable in a turbine engine and including a depth indicator for determining outer wall blade thickness. The airfoil may include an outer wall having a plurality of grooves in the outer surface of the outer wall. The grooves may have a depth that represents a desired outer surface and wall thickness of the outer wall. The material forming an outer surface of the outer wall may be removed to be flush with an innermost point in each groove, thereby reducing the wall thickness and increasing efficiency. The plurality of grooves may be positioned in a radially outer region of the airfoil proximate to the tip.
A Polynomial Estimate of Railway Line Delay
DEFF Research Database (Denmark)
Cerreto, Fabrizio; Harrod, Steven; Nielsen, Otto Anker
2017-01-01
Railway service may be measured by the aggregate delay over a time horizon or due to an event. Timetables for railway service may dampen aggregate delay by addition of additional process time, either supplement time or buffer time. The evaluation of these variables has previously been performed...... by numerical analysis with simulation. This paper proposes an analytical estimate of aggregate delay with a polynomial form. The function returns the aggregate delay of a railway line resulting from an initial, primary, delay. Analysis of the function demonstrates that there should be a balance between the two...
Conditional Density Approximations with Mixtures of Polynomials
DEFF Research Database (Denmark)
Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre
2015-01-01
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
Butler, T.; Dawson, C.; Wildey, T.
2011-01-01
We develop computable a posteriori error estimates for linear functionals of a solution to a general nonlinear stochastic differential equation with random model/source parameters. These error estimates are based on a variational analysis applied to stochastic Galerkin methods for forward and adjoint problems. The result is a representation for the error estimate as a polynomial in the random model/source parameter. The advantage of this method is that we use polynomial chaos representations for the forward and adjoint systems to cheaply produce error estimates by simple evaluation of a polynomial. By comparison, the typical method of producing such estimates requires repeated forward/adjoint solves for each new choice of random parameter. We present numerical examples showing that there is excellent agreement between these methods. © 2011 Society for Industrial and Applied Mathematics.
Polynomial solutions of the Monge-Ampère equation
Energy Technology Data Exchange (ETDEWEB)
Aminov, Yu A [B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar' kov (Ukraine)
2014-11-30
The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.
Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials
International Nuclear Information System (INIS)
Gruenbaum, F A; Vinet, Luc; Zhedanov, Alexei
2004-01-01
We study operator pencils on generators of the Lie algebras sl 2 and the oscillator algebra. These pencils are linear in a spectral parameter λ. The corresponding generalized eigenvalue problem gives rise to some sets of orthogonal polynomials and Laurent biorthogonal polynomials (LBP) expressed in terms of the Gauss 2 F 1 and degenerate 1 F 1 hypergeometric functions. For special choices of the parameters of the pencils, we identify the resulting polynomials with the Hendriksen-van Rossum LBP which are widely believed to be the biorthogonal analogues of the classical orthogonal polynomials. This places these examples under the umbrella of the generalized bispectral problem which is considered here. Other (non-bispectral) cases give rise to some 'nonclassical' orthogonal polynomials including Tricomi-Carlitz and random-walk polynomials. An application to solutions of relativistic Toda chain is considered
Least squares orthogonal polynomial approximation in several independent variables
International Nuclear Information System (INIS)
Caprari, R.S.
1992-06-01
This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab
Need for higher order polynomial basis for polynomial nodal methods employed in LWR calculations
International Nuclear Information System (INIS)
Taiwo, T.A.; Palmiotti, G.
1997-01-01
The paper evaluates the accuracy and efficiency of sixth order polynomial solutions and the use of one radial node per core assembly for pressurized water reactor (PWR) core power distributions and reactivities. The computer code VARIANT was modified to calculate sixth order polynomial solutions for a hot zero power benchmark problem in which a control assembly along a core axis is assumed to be out of the core. Results are presented for the VARIANT, DIF3D-NODAL, and DIF3D-finite difference codes. The VARIANT results indicate that second order expansion of the within-node source and linear representation of the node surface currents are adequate for this problem. The results also demonstrate the improvement in the VARIANT solution when the order of the polynomial expansion of the within-node flux is increased from fourth to sixth order. There is a substantial saving in computational time for using one radial node per assembly with the sixth order expansion compared to using four or more nodes per assembly and fourth order polynomial solutions. 11 refs., 1 tab
Czech Academy of Sciences Publication Activity Database
Knížek, J.; Tichý, Petr; Beránek, L.; Šindelář, Jan; Vojtěšek, B.; Bouchal, P.; Nenutil, R.; Dedík, O.
2010-01-01
Roč. 7, č. 10 (2010), s. 48-60 ISSN 0974-5718 Grant - others:GA MZd(CZ) NS9812; GA ČR(CZ) GAP304/10/0868 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10750506 Keywords : polynomial regression * orthogonalization * numerical methods * markers * biomarkers Subject RIV: BA - General Mathematics
Khader, M M
2013-10-01
In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.
Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians
Ndayiragije, François; Van Assche, Walter
2013-01-01
Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to $r>1$ different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Followi...
On Roots of Polynomials and Algebraically Closed Fields
Directory of Open Access Journals (Sweden)
Schwarzweller Christoph
2017-10-01
Full Text Available In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].
General quantum polynomials: irreducible modules and Morita equivalence
International Nuclear Information System (INIS)
Artamonov, V A
1999-01-01
In this paper we continue the investigation of the structure of finitely generated modules over rings of general quantum (Laurent) polynomials. We obtain a description of the lattice of submodules of periodic finitely generated modules and describe the irreducible modules. We investigate the problem of Morita equivalence of rings of general quantum polynomials, consider properties of division rings of fractions, and solve Zariski's problem for quantum polynomials
Applications of polynomial optimization in financial risk investment
Zeng, Meilan; Fu, Hongwei
2017-09-01
Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.
Root and Critical Point Behaviors of Certain Sums of Polynomials
Indian Academy of Sciences (India)
13
There is an extensive literature concerning roots of sums of polynomials. Many papers and books([5], [6],. [7]) have written about these polynomials. Perhaps the most immediate question of sums of polynomials,. A + B = C, is “given bounds for the roots of A and B, what bounds can be given for the roots of C?” By. Fell [3], if ...
Quadratic polynomial interpolation on triangular domain
Li, Ying; Zhang, Congcong; Yu, Qian
2018-04-01
In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.
On factorization of generalized Macdonald polynomials
Energy Technology Data Exchange (ETDEWEB)
Kononov, Ya. [Landau Institute for Theoretical Physics, Chernogolovka (Russian Federation); HSE, Math Department, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation)
2016-08-15
A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W{sub ∞} - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U{sub q}(SL{sub N}) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)
Positive trigonometric polynomials and signal processing applications
Dumitrescu, Bogdan
2017-01-01
This revised edition is made up of two parts: theory and applications. Though many of the fundamental results are still valid and used, new and revised material is woven throughout the text. As with the original book, the theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The programming environment has also evolved, and the books examples are changed accordingly. The applications section is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semi-definite programming form, ready to be solved with algorithms freely available, like those from the libraries SeDuMi, CVX and Pos3Poly. A new chapter discusses applications in super-resolution theory, where Bounded Real Lemma for trigonometric polynomials is an important tool. This revision is written to be more appealing and easier to use for new readers. < Features updated information on LMI...
On factorization of generalized Macdonald polynomials
Kononov, Ya.; Morozov, A.
2016-08-01
A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from W_∞ —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U_q(SL_N) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.
From sequences to polynomials and back, via operator orderings
Energy Technology Data Exchange (ETDEWEB)
Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 (United States); De Angelis, Valerio, E-mail: vdeangel@xula.edu [Department of Mathematics, Xavier University of Louisiana, New Orleans, Louisiana 70125 (United States); Vignat, Christophe, E-mail: vignat@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d' Orsay (France)
2013-12-15
Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.
On Multiple Interpolation Functions of the -Genocchi Polynomials
Directory of Open Access Journals (Sweden)
Jin Jeong-Hee
2010-01-01
Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.
Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Directory of Open Access Journals (Sweden)
Oksana Bihun
2018-01-01
Full Text Available Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x=qν(xpν(x, where A is a linear differential operator and each qν(x is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.
International Nuclear Information System (INIS)
Riley, D; Dodson, K
2001-01-01
The Lawrence Livermore National Laboratory (LLNL) Plutonium Packaging System (PuPS) prepares packages to meet the DOE Standard 3013 (Reference 1). The PuPS equipment was supplied by the British Nuclear Fuels Limited (BNFL). The DOE Standard 3013 requires that the welding of the Outer Can meets ASME Section VIII Division 1 (Reference 2). ASME Section VIII references to ASME Section IX (Reference 3) for most of the welding requirements, but UW-13.2 (d) of Section VIII requires a certain depth and width of the weld. In this document the UW-13.2(d) requirement is described as the (a+b)/2t s ratio. This ratio has to be greater than or equal to one to meet the requirements of UW-13.2(d). The Outer Can welds had not been meeting this requirement. Three methods are being followed to resolve this issue: (1) Modify the welding parameters to achieve the requirement, (2) Submit a weld case to ASME that changes the UW-13.2(d) requirement for their review and approval, and (3) Change the requirements in the DOE-STD-3013. Each of these methods are being pursued. This report addresses how the first method was addressed for the LLNL PuPS. The experimental work involved adjusting the Outer Can rotational speed and the power applied to the can. These adjustments resulted in being able to achieve the ASME VIII, UW-13.2(d) requirement
International Nuclear Information System (INIS)
Jockers, K.
1981-01-01
In connection with the planned ESA space probe to Halley's Comet, a survey of our current knowledge of comets, and of open questions concerning them. The coma and the plasma and dust tail arise from the nucleus of the comet. Comets contain large amounts of water ice, and are surrounded by a gigantic cloud of hydrogen that is not visible to ground observation. The plasma tail arises by interaction with the solar wind. The cometary dust probably contains the most significant information on the origins of the solar system. Comets may contain prebiotic complex molecules. (orig.)
Can a polynomial interpolation improve on the Kaplan-Yorke dimension?
International Nuclear Information System (INIS)
Richter, Hendrik
2008-01-01
The Kaplan-Yorke dimension can be derived using a linear interpolation between an h-dimensional Lyapunov exponent λ (h) >0 and an h+1-dimensional Lyapunov exponent λ (h+1) <0. In this Letter, we use a polynomial interpolation to obtain generalized Lyapunov dimensions and study the relationships among them for higher-dimensional systems
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
Czech Academy of Sciences Publication Activity Database
Henrion, Didier; Lasserre, J.-B.
č. 2 (2003), s. 165-194 ISSN 0098-3500 R&D Projects: GA MŠk ME 496 Institutional research plan: CEZ:AV0Z1075907 Keywords : polynomial programming * semidefinite programming * linear matrix inequality Subject RIV: BC - Control Systems Theory Impact factor: 0.979, year: 2003
A polynomial expansion method and its application in the coupled Zakharov-Kuznetsov equations
International Nuclear Information System (INIS)
Huang Wenhua
2006-01-01
A polynomial expansion method is presented to solve nonlinear evolution equations. Applying this method, the coupled Zakharov-Kuznetsov equations in fluid system are studied and many exact travelling wave solutions are obtained. These solutions include solitary wave solutions, periodic solutions and rational type solutions
Khataybeh, S. N.; Hashim, I.
2018-04-01
In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.
International Nuclear Information System (INIS)
Cooling, C.M.; Williams, M.M.R.; Nygaard, E.T.; Eaton, M.D.
2013-01-01
Highlights: • A point kinetics model for the Medical Isotope Production Reactor is formulated. • Reactivity insertions are simulated using this model. • Polynomial chaos is used to simulate uncertainty in reactor parameters. • The computational efficiency of polynomial chaos is compared to that of Monte Carlo. -- Abstract: This paper models a conceptual Medical Isotope Production Reactor (MIPR) using a point kinetics model which is used to explore power excursions in the event of a reactivity insertion. The effect of uncertainty of key parameters is modelled using intrusive polynomial chaos. It is found that the system is stable against reactivity insertions and power excursions are all bounded and tend towards a new equilibrium state due to the negative feedbacks inherent in Aqueous Homogeneous Reactors (AHRs). The Polynomial Chaos Expansion (PCE) method is found to be much more computationally efficient than that of Monte Carlo simulation in this application
Relations between zeros of special polynomials associated with the Painleve equations
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding relations of roots of polynomials is presented. Our approach allows us to get a number of relations between the zeros of the classical polynomials as well as the roots of special polynomials associated with rational solutions of the Painleve equations. We apply the method to obtain the relations for the zeros of several polynomials. These are: the Hermite polynomials, the Laguerre polynomials, the Yablonskii-Vorob'ev polynomials, the generalized Okamoto polynomials, and the generalized Hermite polynomials. All the relations found can be considered as analogues of generalized Stieltjes relations
The CMS Outer Hadron Calorimeter
Acharya, Bannaje Sripathi; Banerjee, Sunanda; Banerjee, Sudeshna; Bawa, Harinder Singh; Beri, Suman Bala; Bhandari, Virender; Bhatnagar, Vipin; Chendvankar, Sanjay; Deshpande, Pandurang Vishnu; Dugad, Shashikant; Ganguli, Som N; Guchait, Monoranjan; Gurtu, Atul; Kalmani, Suresh Devendrappa; Kaur, Manjit; Kohli, Jatinder Mohan; Krishnaswamy, Marthi Ramaswamy; Kumar, Arun; Maity, Manas; Majumder, Gobinda; Mazumdar, Kajari; Mondal, Naba Kumar; Nagaraj, P; Narasimham, Vemuri Syamala; Patil, Mandakini Ravindra; Reddy, L V; Satyanarayana, B; Sharma, Seema; Singh, B; Singh, Jas Bir; Sudhakar, Katta; Tonwar, Suresh C; Verma, Piyush
2006-01-01
The CMS hadron calorimeter is a sampling calorimeter with brass absorber and plastic scintillator tiles with wavelength shifting fibres for carrying the light to the readout device. The barrel hadron calorimeter is complemented with a outer calorimeter to ensure high energy shower containment in CMS and thus working as a tail catcher. Fabrication, testing and calibrations of the outer hadron calorimeter are carried out keeping in mind its importance in the energy measurement of jets in view of linearity and resolution. It will provide a net improvement in missing $\\et$ measurements at LHC energies. The outer hadron calorimeter has a very good signal to background ratio even for a minimum ionising particle and can hence be used in coincidence with the Resistive Plate Chambers of the CMS detector for the muon trigger.
International Nuclear Information System (INIS)
Duncan, R.; Craver, J.E.
1989-01-01
This patent describes a nuclear reactor fuel assembly grid. It comprises a first outer grip strap segment end. The first end having a first tab arranged in substantially the same plane as the plane defined by the first end; a second outer grip strap end. The second end having a second slot arranged in substantially the same plane as the plane defined by the second end, with the tab being substantially disposed in the slot, defining a socket therebetween; and a fort tine interposed substantially perpendicularly in the socket
Differential operators associated with Hermite polynomials
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1989-09-01
This paper considers the boundary value problems for the Hermite differential equation -(e -x2 y'(x))'+e -x2 y(x)=λe -x2 y(x), (x is an element of (-∞, ∞)) in both the so-called right-definite and left-definite cases based partly on a classical approach due to E.C. Titchmarsh. We then link the Titchmarsh approach with operator theoretic results in the spaces L w 2 (-∞, ∞) and H p,q 2 (-∞, ∞). The results in the left-definite case provide an indirect proof of the completeness of the Hermite polynomials in L w 2 (-∞, ∞). (author). 17 refs
Micheuz, P.; Kurz, W.; Ferre, E. C.
2015-12-01
IODP Expedition 352 aimed to drill through the entire volcanic sequence of the Bonin fore arc. Four sites were drilled, two on the outer fore arc and two on the upper trench slope. Analysis of structures within drill cores, combined with borehole and site survey seismic data, indicates that tectonic deformation in the outer Izu-Bonin-Mariana fore arc is mainly post-magmatic, associated with the development of syn-tectonic sedimentary basins. Within the magmatic basement, deformation was accommodated by shear along cataclastic fault zones, and the formation of tension fractures, hybrid (tension and shear) fractures, and shear fractures. Veins commonly form by mineral filling of tension or hybrid fractures and, generally, show no or limited observable macroscale displacement along the fracture plane. The vein filling generally consists of (Low Mg-) calcite and/or various types of zeolite as well as clay. Vein frequency varies with depth but does not seem to correlate with the proximity of faults. This may indicate that these veins are genetically related to hydrothermal activity taking place shortly after magma cooling. Host-rock fragments are commonly embedded within precipitated vein material pointing to a high fluid pressure. Vein thickness varies from < 1 mm up to 15 mm. The wider veins appear to have formed in incremental steps of extension. Calcite veins tend to be purely dilational at shallow depths, but gradually evolve towards oblique tensional veins at depth, as shown by the growth of stretched calcite and/or zeolites (idiomorphic and/or stretched) with respect to vein margins. With increasing depth, the calcite grains exhibit deformation microstructures more frequently than at shallower core intervals. These microstructures include thin twinning (type I twins), increasing in width with depth (type I and type II twins), curved twins, and subgrain boundaries indicative of incipient plastic deformation.
Connection coefficients between Boas-Buck polynomial sets
Cheikh, Y. Ben; Chaggara, H.
2006-07-01
In this paper, a general method to express explicitly connection coefficients between two Boas-Buck polynomial sets is presented. As application, we consider some generalized hypergeometric polynomials, from which we derive some well-known results including duplication and inversion formulas.
Mathematical Use Of Polynomials Of Different End Periods Of ...
African Journals Online (AJOL)
This paper focused on how polynomials of different end period of random numbers can be used in the application of encryption and decryption of a message. Eight steps were used in generating information on how polynomials of different end periods of random numbers in the application of encryption and decryption of a ...
On the Lorentz degree of a product of polynomials
Ait-Haddou, Rachid
2015-01-01
In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence
Exponential time paradigms through the polynomial time lens
Drucker, A.; Nederlof, J.; Santhanam, R.; Sankowski, P.; Zaroliagis, C.
2016-01-01
We propose a general approach to modelling algorithmic paradigms for the exact solution of NP-hard problems. Our approach is based on polynomial time reductions to succinct versions of problems solvable in polynomial time. We use this viewpoint to explore and compare the power of paradigms such as
On polynomial selection for the general number field sieve
Kleinjung, Thorsten
2006-12-01
The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.
A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Directory of Open Access Journals (Sweden)
Laugier Alexandre
2016-09-01
Full Text Available We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.
Animating Nested Taylor Polynomials to Approximate a Function
Mazzone, Eric F.; Piper, Bruce R.
2010-01-01
The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…