Gotowe bibliografie tematyczne / Generalised weight polynomials

Gotowa bibliografia na temat „Generalised weight polynomials”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 10 lutego 2022

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Artykuły w czasopismach na temat "Generalised weight polynomials"

Blower, Gordon, i Yang Chen. "On Determinant Expansions for Hankel Operators". Concrete Operators 7, nr 1 (4.02.2020): 13–44. http://dx.doi.org/10.1515/conop-2020-0002.

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AbstractLet w be a semiclassical weight that is generic in Magnus’s sense, and ({p_n})_{n = 0}^\infty the corresponding sequence of orthogonal polynomials. We express the Christoffel–Darboux kernel as a sum of products of Hankel integral operators. For ψ ∈ L∞ (iℝ), let W(ψ) be the Wiener-Hopf operator with symbol ψ. We give sufficient conditions on ψ such that 1/ det W(ψ) W(ψ−1) = det(I − Γϕ1Γϕ2) where Γϕ1 and Γϕ2 are Hankel operators that are Hilbert–Schmidt. For certain, ψ Barnes’s integral leads to an expansion of this determinant in terms of the generalised hypergeometric 2mF2m-1. These results extend those of Basor and Chen [2], who obtained 4F3 likewise. We include examples where the Wiener–Hopf factors are found explicitly.

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Ftorek, Branislav, i Mariana Marˇcokov´A. "Markov type polynomial inequality for some generalized Hermite weight". Tatra Mountains Mathematical Publications 49, nr 1 (1.12.2011): 111–18. http://dx.doi.org/10.2478/v10127-011-0030-4.

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ABSTRACT In this paper we study some weighted polynomial inequalities of Markov type in L2-norm. We use the properties of the system of generalized Hermite polynomials . The polynomials H(α)n (x) are orthogonal in ℝ = (−∞,∞) with respect to the weight function . The classical Hermite polynomials Hn(x) present the special case for α = 0.

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Czyżycki, Tomasz, Jiří Hrivnák i Jiří Patera. "Generating Functions for Orthogonal Polynomials of A2, C2 and G2". Symmetry 10, nr 8 (20.08.2018): 354. http://dx.doi.org/10.3390/sym10080354.

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The generating functions of fourteen families of generalized Chebyshev polynomials related to rank two Lie algebras A 2 , C 2 and G 2 are explicitly developed. There exist two classes of the orthogonal polynomials corresponding to the symmetric and antisymmetric orbit functions of each rank two algebra. The Lie algebras G 2 and C 2 admit two additional polynomial collections arising from their hybrid character functions. The admissible shift of the weight lattice permits the construction of a further four shifted polynomial classes of C 2 and directly generalizes formation of the classical univariate Chebyshev polynomials of the third and fourth kinds. Explicit evaluating formulas for each polynomial family are derived and linked to the incomplete exponential Bell polynomials.

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Kang, J. Y. "Some Properties of Multiple Generalizedq-Genocchi Polynomials with Weight and Weak Weight". International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/179385.

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The present paper deals with the variousq-Genocchi numbers and polynomials. We define a new type of multiple generalizedq-Genocchi numbers and polynomials with weightαand weak weightβby applying the method ofp-adicq-integral. We will find a link between their numbers and polynomials with weightαand weak weightβ. Also we will obtain the interesting properties of their numbers and polynomials with weightαand weak weightβ. Moreover, we construct a Hurwitz-type zeta function which interpolates multiple generalizedq-Genocchi polynomials with weightαand weak weightβand find some combinatorial relations.

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Della Vecchia, B., G. Mastroianni i J. Szabados. "Generalized Bernstein polynomials with Pollaczek weight". Journal of Approximation Theory 159, nr 2 (sierpień 2009): 180–96. http://dx.doi.org/10.1016/j.jat.2009.02.008.

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Hrivnák, Jiří, Jiří Patera i Marzena Szajewska. "Discrete Orthogonality of Bivariate Polynomials of A2, C2 and G2". Symmetry 11, nr 6 (3.06.2019): 751. http://dx.doi.org/10.3390/sym11060751.

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We develop discrete orthogonality relations on the finite sets of the generalized Chebyshev nodes related to the root systems A 2 , C 2 and G 2 . The orthogonality relations are consequences of orthogonality of four types of Weyl orbit functions on the fragments of the dual weight lattices. A uniform recursive construction of the polynomials as well as explicit presentation of all data needed for the discrete orthogonality relations allow practical implementation of the related Fourier methods. The polynomial interpolation method is developed and exemplified.

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Zaheer, Neyamat, i Aijaz A. Khan. "Some theorems on generalized polars with arbitrary weight". International Journal of Mathematics and Mathematical Sciences 10, nr 4 (1987): 757–76. http://dx.doi.org/10.1155/s0161171287000851.

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The present paper, which is a continuation of our earlier work in Annali di Mathematica [1] and Journal Math. Seminar [2] (EγEUθPIA), University of Athens, Greece, deals with the problem of determining sufficiency conditions for the nonvanishing of generalized polars (with a vanishing or nonvanishing weight) of the product of abstract homogeneous polynomials in the general case when the factor polynomials have been preassigned independent locations for their respective null-sets. Our main theorems here fully answer this general problem and include in them, as special cases, all the results on the topic known to date and established by Khan, Marden and Zaheer (see Pacific J. Math. 74 (1978), 2, pp. 535-557, and the papers cited above). Besides, one of the main theorems leads to an improved version of Marden's general theorem on critical points of rational functions of the formf1f2…fp/fp+1…fq,fibeing complex-valued polynomials of degreeni.

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Gao, Rugao, Keping Zhou i Yun Lin. "A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters". Complexity 2018 (3.12.2018): 1–14. http://dx.doi.org/10.1155/2018/7471460.

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The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. But in gPCEM, a nonlinear transformation of random variables should always be used to adapt the generalized Polynomial Chaos theory for the analysis of random problems with complicated probability distributions, which may introduce nonlinearity in the procedure of random uncertainty propagation as well as leading to approximation errors on the probability distribution function (PDF) of random variables. This paper aims to develop a flexible polynomial expansion method for response analysis of the finite element system with bounded random variables following arbitrary probability distributions. Based on the large family of Jacobi polynomials, an Improved Jacobi Chaos Expansion Method (IJCEM) is proposed. In IJCEM, the response of random system is approximated by the Jacobi expansion with the Jacobi polynomial basis whose weight function is the closest to the probability density distribution (PDF) of the random variable. Subsequently, the moments of the response can be efficiently calculated though the Jacobi expansion. As the IJCEM avoids the necessity that the PDF should be represented in terms of the weight function of polynomial basis by using the variant transformation, neither the nonlinearity nor the errors on random models will be introduced in IJCEM. Numerical examples on two random problems show that compared with gPCEM, the IJCEM can achieve better efficiency and accuracy for random problems with complex probability distributions.

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Kasuga, T., i R. Sakai. "Orthonormal polynomials with generalized Freud-type weights". Journal of Approximation Theory 121, nr 1 (marzec 2003): 13–53. http://dx.doi.org/10.1016/s0021-9045(02)00041-2.

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Brackx, Fred, Nele De Schepper i Frank Sommen. "Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space". International Journal of Mathematics and Mathematical Sciences 2004, nr 52 (2004): 2761–72. http://dx.doi.org/10.1155/s0161171204401045.

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A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into an orthogonality relation on the real axis by means of the so-called Clifford-Heaviside functions. Consequently, appropriate orthogonal polynomials on the real axis give rise to Clifford algebra-valued orthogonal polynomials in the unit ball. Three specific examples of such orthogonal polynomials in the unit ball are discussed, namely, the generalized Clifford-Jacobi polynomials, the generalized Clifford-Gegenbauer polynomials, and the shifted Clifford-Jacobi polynomials.

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Rozprawy doktorskie na temat "Generalised weight polynomials"

Griffiths, Wayne Bradley. "On a posteriori probability decoding of linear block codes over discrete channels". University of Western Australia. School of Electrical, Electronic and Computer Engineering, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0156.

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One of the facets of the mobile or wireless environment is that errors quite often occur in bursts. Thus, strong codes are required to provide protection against such errors. This in turn motivates the employment of decoding algorithms which are simple to implement, yet are still able to attempt to take the dependence or memory of the channel model into account in order to give optimal decoding estimates. Furthermore, such algorithms should be able to be applied for a variety of channel models and signalling alphabets. The research presented within this thesis describes a number of algorithms which can be used with linear block codes. Given the received word, these algorithms determine the symbol which was most likely transmitted, on a symbol-by-symbol basis. Due to their relative simplicity, a collection of algorithms for memoryless channels is reported first. This is done to establish the general style and principles of the overall collection. The concept of matrix diagonalisation may or may not be applied, resulting in two different types of procedure. Ultimately, it is shown that the choice between them should be motivated by whether storage space or computational complexity has the higher priority. As with all other procedures explained herein, the derivation is first performed for a binary signalling alphabet and then extended to fields of prime order. These procedures form the paradigm for algorithms used in conjunction with finite state channel models, where errors generally occur in bursts. In such cases, the necessary information is stored in matrices rather than as scalars. Finally, by analogy with the weight polynomials of a code and its dual as characterised by the MacWilliams identities, new procedures are developed for particular types of Gilbert-Elliott channel models. Here, the calculations are derived from three parameters which profile the occurrence of errors in those models. The decoding is then carried out using polynomial evaluation rather than matrix multiplication. Complementing this theory are several examples detailing the steps required to perform the decoding, as well as a collection of simulation results demonstrating the practical value of these algorithms.

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Chung, Jaewook. "Issues in Implementation of Public Key Cryptosystems". Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2853.

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A new class of moduli called the low-weight polynomial form integers (LWPFIs) is introduced. LWPFIs are expressed in a low-weight, monic polynomial form, p = f(t). While the generalized Mersenne numbers (GMNs) proposed by Solinas allow only powers of two for t, LWPFIs allow any positive integers. In our first proposal of LWPFIs, we limit the coefficients of f(t) to be 0 and ±1, but later we extend LWPFIs to allow any integer of less than t for the coefficients of f(t). Modular multiplication using LWPFIs is performed in two phases: 1) polynomial multiplication in Z[t]/f(t) and 2) coefficient reduction. We present an efficient coefficient reduction algorithm based on a division algorithm derived from the Barrett reduction algorithm. We also show a coefficient reduction algorithm based on the Montgomery reduction algorithm. We give analysis and experimental results on modular multiplication using LWPFIs.

New three, four and five-way squaring formulae based on the Toom-Cook multiplication algorithm are presented. All previously known squaring algorithms are symmetric in the sense that the point-wise multiplication step involves only squarings. However, our squaring algorithms are asymmetric and use at least one multiplication in the point-wise multiplication step. Since squaring can be performed faster than multiplication, our asymmetric squaring algorithms are not expected to be faster than other symmetric squaring algorithms for large operand sizes. However, our algorithms have much less overhead and do not require any nontrivial divisions. Hence, for moderately small and medium size operands, our algorithms can potentially be faster than other squaring algorithms. Experimental results confirm that one of our three-way squaring algorithms outperforms the squaring function in GNU multiprecision library (GMP) v4. 2. 1 for certain range of input size. Moreover, for degree-two squaring in Z[x], our algorithms are much faster than any other squaring algorithms for small operands.

We present a side channel attack on XTR cryptosystems. We analyze the statistical behavior of simultaneous XTR double exponentiation algorithm and determine what information to gather to reconstruct the two input exponents. Our analysis and experimental results show that it takes U^{1. 25} tries, where U = max(a,b) on average to find the correct exponent pair (a,b). Using this result, we conclude that an adversary is expected to make U^{0. 625} tries on average until he/she finds the correct secret key used in XTR single exponentiation algorithm, which is based on the simultaneous XTR double exponentiation algorithm.

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Ackermann, Maria Helena. "Mixture models based on power means and generalised Q-fractions". Diss., 2011. http://hdl.handle.net/2263/27481.

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Mixture experiments are widely applied. The Scheffé quadratic polynomial is the most popular mixture model in industry due to its simplicity, but it fails to accurately describe the behaviour of response variables that deviate greatly from linear blending. Higherorder Scheffé polynomials do possess the ability to predict such behaviour but become increasingly more complex to use and the number of estimable parameters grow exponentially [15]. A parameter-parsimonious mixture model, developed from the linear blending rule with weighted power means and Wohl's Q-fractions, is introduced. Bootstrap is employed to analyse the model statistically. The model is proved to be flexible enough to model non-linear deviations from linear blending without losing the simplicity of the linear blending rule.
Dissertation (MSc)--University of Pretoria, 2011.
Chemical Engineering
unrestricted

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Części książek na temat "Generalised weight polynomials"

Johnsen, Trygve, i Hugues Verdure. "Relative Generalized Hamming Weights and Extended Weight Polynomials of Almost Affine Codes". W Coding Theory and Applications, 207–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66278-7_17.

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de Graaf, J. "Riesz Bases of Special Polynomials in Weighted Sobolev Spaces of Analytic Functions". W Generalized Functions and Their Applications, 61–85. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-1591-7_7.

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Vértesi, P. "Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights. Some new theorems and applications". W New Developments in Approximation Theory, 329–39. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8696-3_20.

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Marks II, Robert J. "Generalizations of the Sampling Theorem". W Handbook of Fourier Analysis & Its Applications. Oxford University Press, 2009. http://dx.doi.org/10.1093/oso/9780195335927.003.0011.

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There have been numerous interesting and useful generalizations of the sampling theorem. Some are straightforward variations on the fundamental cardinal series. Oversampling, for example, results in dependent samples and allows much greater flexibility in the choice of interpolation functions. In Chapter 7, we will see that it can also result in better performance in the presence of sample data noise. Bandlimited signal restoration from samples of various filtered versions of the signal is the topic addressed in Papoulis’ generalization [1086, 1087] of the sampling theorem. Included as special cases are recurrent nonuniform sampling and simultaneously sampling a signal and one or more of its derivatives. Kramer [772] generalized the sampling theorem to signals that were bandlimited in other than the Fourier sense. We also demonstrate that the cardinal series is a special case of Lagrangian polynomial interpolation. Sampling in two or more dimensions is the topic of Section 8.9. There are a number of functions other than the sinc which can be used to weight a signal’s samples in such a manner as to uniquely characterize the signal. Use of these generalized interpolation functions allows greater flexibility in dealing with sampling theorem type characterizations. If a bandlimited signal has bandwidth B, then it can also be considered to have bandwidthW ≥ B.

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Streszczenia konferencji na temat "Generalised weight polynomials"

Francès, Guillem, Augusto B. Corrêa, Cedric Geissmann i Florian Pommerening. "Generalized Potential Heuristics for Classical Planning". W Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/771.

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Generalized planning aims at computing solutions that work for all instances of the same domain. In this paper, we show that several interesting planning domains possess compact generalized heuristics that can guide a greedy search in guaranteed polynomial time to the goal, and which work for any instance of the domain. These heuristics are weighted sums of state features that capture the number of objects satisfying a certain first-order logic property in any given state. These features have a meaningful interpretation and generalize naturally to the whole domain. Additionally, we present an approach based on mixed integer linear programming to compute such heuristics automatically from the observation of small training instances. We develop two variations of the approach that progressively refine the heuristic as new states are encountered. We illustrate the approach empirically on a number of standard domains, where we show that the generated heuristics will correctly generalize to all possible instances.

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"Output end-point weighted generalized predictive control-a polynomial approach". W Proceedings of the 1999 American Control Conference. IEEE, 1999. http://dx.doi.org/10.1109/acc.1999.783179.

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Griffiths, Wayne, Hans-Jurgen Zepernick i Manora Caldera. "APP decoding of non-binary block codes on Gilbert-Elliott channels using generalized weight polynomials". W 2008 International Symposium on Information Theory and Its Applications (ISITA). IEEE, 2008. http://dx.doi.org/10.1109/isita.2008.4895567.

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Deguchi, Tetsuo. "Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the sl2 Loop Algebra". W Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772527_0011.

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Chalfoun, Joe, Catherine Bidard, Delphine Keller i Yann Perrot. "Long Reach Articulated Carrier: Geometric and Elastic Error Calibration of the Flexible Model Followed by Nonlinear Generalized Error Calibration With Ordinary Polynomials". W ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35221.

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The Interactive Robotics Unit of CEA LIST has developed a very challenging robotic carrier (called P.A.C.) which is able to perform high range intervention tasks inside blind hot cells. This long reach multi-link carrier has 11 degrees of freedom (DOF), an operational range over 6 meters of full extension and weighs less than 30 kg. The gravity effect in the manipulator is largely compensated by a special mechanical structure (the parallelogram) that helps to reduce the size of the actuators used to operate the robot. Due to its size and weight, this large robot manipulator holds lots of elastic and geometric deformations. Hence, it presents very low position accuracy. A flexible model is developed to take into account most of the structure deformations. A calibration method of the robot flexible parameters is used to reduce the positioning error of the end effector and the intermediate joints. Then, a second calibration method of the robot using generalized error matrices is applied to further reduce the residual positioning error of the system. These matrices are a polynomial function of the system geometry and joint variables. This method is first tested by simulation to ensure its viability on large manipulators. After encouraging simulation results, an experimental field is made for the calibration of the PAC manipulator. Results show that the adopted flexible model, with the new calibrated parameters, followed by the polynomial model is a good combination to correct and reduce the system errors.

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Shiau, Ting Nung, i Jer Rong Chang. "Multiobjective Optimization of Rotor-Bearing System With Critical Speeds Constraints". W ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-117.

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An efficient optimal design algorithm is developed to individually or simultaneously minimize the total weight of shaft and the transsmitted forces at the bearings which play very important roles in designing a rotor-bearing system under the constraints of critical speeds. The cross sectional area of shaft, the bearing stiffness, and the positions of bearings and disks are chosen as the design variables. The dynamic characteristics are determined by applying the generalized polynomial expansion method and the sensitivity analysis is also investigated. For multiobjective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are applied. The results show that the present multiobjective optimization algorithm can greatly reduce both the weight of shaft and the forces at the bearings with critical speeds constraints.

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Shiau, T. N., H. J. Lee i Y. J. Tsai. "Multilevel Optimization of Rotor Bearing System With Dynamic Behavior Constraints". W ASME Turbo Expo 2000: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/2000-gt-0392.

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The main purpose of this study is to investigate the multilevel optimization of rotor-bearing systems. The design variables include the shaft inner radius, the bearings stiffness, and the axial position of the bearings and disks. The design objectives are minimization of the shaft weight and transmitted force to the bearings. Constraints are placed on the critical speeds, the maximum shaft bending stress, and the maximum amplitude of the steady state response. In the multilevel optimization, three levels are considered and each level includes a single objective and/or multiobjective with various design variables and constraints. For each level, the method of feasible direction (MFD) is used. In addition, the weighting method (WM) is used for multiobjective optimization. The dynamic analysis is carried out using the generalized polynomial expansion method. The results show that the shaft weight and transmitted forces can be simultaneously reduced with the multilevel technique and are better than those obtained using the multiobjective optimization technique with only a single level.

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Shiau, Ting Nung, Chun Pao Kuo i Jiunn Rong Hwang. "Multiobjective Optimization of a Flexible Rotor in Magnetic Bearings With Critical Speeds and Control Current Constraints". W ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-297.

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This paper presents the single objective optimization and the multi-objective optimization for a flexible rotor system with magnetic bearings. The weight of rotor shaft and the transmitted forces at the magnetic bearings are minimized either individually or simultaneously under the constraints on the critical speeds and the control currents of magnetic bearings. The design variables are the cross-sectional area of the shaft, the bias currents of magnetic bearings, and the positions of the disk and the magnetic bearings. The dynamic characteristics are analyzed using the generalized polynomial expansion method and the sensitivity analysis is also studied. For single objective optimization, the method of feasible directions (MFD) is applied. For multi-objective optimization, the methods including the weighting method (WM), goal programming method (GPM), and the fuzzy method (FM) are employed. It is found that the system design can be significantly affected by the choices of the bias currents of magnetic bearings, the position of the disk with unbalance and the magnetic bearings. The results also show that a better compromized design can always be obtained for multi-objective optimization.

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