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Journal articles on the topic 'Orthogonal function'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Carballosa, W., J. C. Hernandez-Gomez, L. R. Pineiro, and Jose M. Sigarreta. "Generating function: multiple orthogonal polynomials." Applied Mathematical Sciences 10 (2016): 761–72. http://dx.doi.org/10.12988/ams.2016.510669.

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2

Jin, Chong, Hong Wang, and Xiao Zhou Xia. "A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data." Advanced Materials Research 291-294 (July 2011): 1015–20. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.1015.

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Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can b

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3

Hameed, Vazeerudeen Abdul. "Orthogonal Moment Invariant Function for Image Processing." Journal of Computational and Theoretical Nanoscience 16, no. 8 (2019): 3400–3403. http://dx.doi.org/10.1166/jctn.2019.8299.

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Orthogonal moments are of great importance in image processing due to their high discriminatory capability. Orthogonal moment invariant functions like Legendre moments and Complex Zernike moments are known for high computational complexity and/or they are complex valued. This paper presents a new orthogonal moment function that is real valued. The formulation is appraised to prove that it is computationally less complex when compared to the existing moment functions. The proposed orthogonal moment functions are appraised over their reversible nature to obtain the original data. The new moment

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4

YANG, SHOUZHI, and CHANGZHEN XIE. "A CLASS OF ORTHOGONAL TWO-DIRECTION REFINABLE FUNCTIONS AND TWO-DIRECTION WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 06 (2008): 883–94. http://dx.doi.org/10.1142/s0219691308002653.

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In this paper, an algorithm for constructing a class of orthogonal two-direction refinable functions and the corresponding orthogonal two-direction wavelets is obtained. In addition, the relation of both two-direction refinable functions and multiwavelets is discussed. We discover that Chui–Lian's orthogonal symmetric/antisymmetric multiscaling functions and the corresponding multiwavelets can be recovered by using an orthogonal two-direction refinable function and the corresponding two-direction wavelets, respectively. Finally, some construction examples are given.

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5

Peng, Kai. "The Application of Sets of Orthogonal Function to Signal Analyses." Applied Mechanics and Materials 380-384 (August 2013): 3613–17. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.3613.

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Generally speaking, the method of signal analysis is built on the basis that signal decomposition is an orthogonal component. There are different selection ways for the sets of orthogonal functions after transformation and the transformation of orthogonal functions does not affect expressed functions themselves. Aiming at different requirements for application, different sets of orthogonal functions need to be used. This thesis not only studies classical and modern sets of orthogonal functions Fourier and wavelet sequence but also proposes prospects for the new application of the sets of ortho

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6

Bakulin, Vladimir, and Victor Revenko. "Computational method for solving boundary value problems of mechanics deformable body using non-orthogonal functions." MATEC Web of Conferences 362 (2022): 01002. http://dx.doi.org/10.1051/matecconf/202236201002.

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In this paper a complete system of non-orthogonal functions was built on the basis of orthogonal sines and cosines. It is shown that the known orthogonal systems of functions are a degenerate case of non-orthogonal systems of functions. It has been proven that the continuous function can be approximated non-orthogonal functions in such a way that one selected nonorthogonal function will not included in this amount. The boundary value problem of the elasticity theory has been considered for an inhomogeneous plate. A new method for solving the boundary value problem is developed for the fourth-o

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7

Revenko, V. P. "Computational method for solving boundary problems of the theory of elasticity using non-orthogonal systems of functions." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2021): 101–6. http://dx.doi.org/10.17721/1812-5409.2021/3.19.

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A complete system of functions based on non-orthogonal sinuses and cosine was constructed. It has been proven that the continuous function can be approximated by a finite number of non-orthogonal functions in such a way that this amount does not enter the selected function of the non-orthogonal base. The numerical experiment confirmed the high accuracy of approximations of continuous functions by a small number of non-orthogonal functions. The flat problem of the theory of elasticity for the plate with variable elastic characteristics is considered. This equation is simplified when the charact

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8

Wanegar, Daniel F., and Ofodike A. Ezekoye. "Orthogonal function extension to enclosure theory." Journal of Quantitative Spectroscopy and Radiative Transfer 224 (February 2019): 272–78. http://dx.doi.org/10.1016/j.jqsrt.2018.11.005.

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9

Liu, Wang Sheng, Yan Sun, Guo Dong Shi, and Xing Long Liu. "Research on Pneumatic Performance of Aero-Engine Blades through Function Method." Advanced Materials Research 605-607 (December 2012): 1326–29. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.1326.

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When we research on pneumatic performance of aero-engine blades,some functions are not solved directly in physical domain because blade coordinates are unknown,but they can be solved after being transformed to computational domain.For potential function and stream function have the orthogonality themselves,mesh of computational domain is orthogonal after orthogonal transformation and the functions are solved easily.The existence conditions are two-dimensional flow continuity equations.If fluid is irrotational and powerful flow,potential function and stream function are both usesd to describe f

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10

Nikolic, Sasa S., Miroslav B. Milovanovic, Nikola B. Dankovic, et al. "Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions." Elektronika ir Elektrotechnika 29, no. 2 (2023): 4–11. http://dx.doi.org/10.5755/j02.eie.33838.

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Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, an

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11

Akhlaghi, S., M. Tavassoli Kajani, and M. Allame. "Application of Müntz Orthogonal Functions on the Solution of the Fractional Bagley–Torvik Equation Using Collocation Method with Error Stimate." Advances in Mathematical Physics 2023 (August 26, 2023): 1–11. http://dx.doi.org/10.1155/2023/5520787.

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This paper uses Müntz orthogonal functions to numerically solve the fractional Bagley–Torvik equation with initial and boundary conditions. Müntz orthogonal functions are defined on the interval 0 , 1 and have simple and distinct real roots on this interval. For the function f ∈ L 2 0 , 1 , we obtain the best unique approximation using Müntz orthogonal functions. We obtain the Riemann–Liouville fractional integral operator for Müntz orthogonal functions so that we can reduce the complexity of calculations and increase the speed of solving the problem, which can be seen in the process of runnin

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12

Saini, Manish Kumar, Rajiv Kapoor, Ajai Kumar Singh, and Manisha. "Performance Comparison between Orthogonal, Bi-Orthogonal and Semi- Orthogonal Wavelets." Advanced Materials Research 433-440 (January 2012): 6521–26. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.6521.

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The main work in the wavelet analysis is to find a good wavelet basis to perform an optimal decomposition. The goal of the proposed study is to obtain a basis function that can give optimal information from PQ signal. The study presents the wavelet basis to obtain the reconstruction and decomposition filter coefficients for orthogonal, bi-orthogonal and semi-orthogonal wavelet basis. In this study, the task is to choose better wavelet basis which has been used for PQ signal compression or decomposition among orthogonal, bi-orthogonal and semi-orthogonal wavelet basis. Certain criterion have be

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13

Abdelkawy, M. A. "A Collocation Method Based on Jacobi and Fractional Order Jacobi Basis Functions for Multi-Dimensional Distributed-Order Diffusion Equations." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 7-8 (2018): 781–92. http://dx.doi.org/10.1515/ijnsns-2018-0111.

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AbstractIn this work, shifted fractional-order Jacobi orthogonal function in the interval $[0,\mathcal{T}]$ is outputted of the classical Jacobi polynomial (see Definition 2.3). Also, we list and derive some facts related to the shifted fractional-order Jacobi orthogonal function. Spectral collocation techniques are addressed to solve the multidimensional distributed-order diffusion equations (MDODEs). A mixed of shifted Jacobi polynomials and shifted fractional order Jacobi orthogonal functions are used as basis functions to adapt the spatial and temporal discretizations, respectively. Based

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14

Abedrahaman, Bashir. "INVERSE SPECTRAL PROPARTIES FOR SYMMETRIC OPERATORS WITH WEYL FUNCTIONS." Journal of Statistics and Actuarial Research 6, no. 1 (2022): 20–42. http://dx.doi.org/10.47604/jsar.1607.

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We prove that an operator measure in general is non-orthogonal and unbounded and two orthogonal spectral measures are unitarily equivalent. In accordance with the stieltjes inversion formula the spectral measure admits an analytic continuation .We discuss and prove a sharp estimate that a strictly monotone function on each component interval of the inverse function is analytic and also strictly monotone with Weyl functions.

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15

Liu, Han Min, Guang Ming Dai, and Xue Song Yan. "Orthogonal Genetic Algorithm and its Application in Function Optimization." Applied Mechanics and Materials 121-126 (October 2011): 4528–31. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.4528.

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Traditional genetic algorithm trapped into the local minimum easily. Therefore, based on a simple genetic algorithm and combine the base ideology of orthogonal test then applied it to the population initialization, crossover operator, as well as the introduction of adaptive orthogonal local search to prevent local convergence to form a new orthogonal evolutionary algorithm. Through the series of numerical experiments, proved the efficiency of the new algorithm.

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16

Wang, Hong, Chong Jin, Hong Yuan, and Xiao Zhou Xia. "Study on Useful Concrete Elastic-Plastic Constitutive Model." Applied Mechanics and Materials 117-119 (October 2011): 351–55. http://dx.doi.org/10.4028/www.scientific.net/amm.117-119.351.

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In order to simulate the elastic-plastic behavior of concrete better, an effective curve fitting method is employed to find the constitutive function based on Legendre orthogonal polynomial and least square method. And a new numerical analysis program using arch-length method to deal with nonlinear problem is designed. The most important consequence is that not only the fitting function, but also its derivative function and its definite integral are recursive. The fitting curve given by new method is applied in numerical analyzing. Cube model is examined under uniaxial compressing with complet

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17

Riyadi. "Weakly Orthogonally Additive Functionals on Mcshane-Bochner Integral Function Spaces Defined in Euclidean Spaces Rn." JST (Jurnal Sains dan Teknologi) 13, no. 1 (2024): 118–26. http://dx.doi.org/10.23887/jstundiksha.v13i1.80947.

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The study of weakly orthogonal additive functions impacts the structural properties of a function space and allows further investigation into the solution of broader mathematical problems. The aim of this research is to analyze the properties and application of weak orthogonal additive functions on the McShane-Bochner integral function space defined in Euclidean space. . The research method used is Research and Development (R&D). This type of research is descriptive qualitative. Population in this study is Vectors in Euclidean Space RN\mathbb{R}^NRN: This research begins by conducting a pr

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18

Ismail, Mourad E. H., and Dennis Stanton. "q-Integral and Moment Representations for q-Orthogonal Polynomials." Canadian Journal of Mathematics 54, no. 4 (2002): 709–35. http://dx.doi.org/10.4153/cjm-2002-027-2.

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AbstractWe develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.

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19

Mukha, V. S. "Orthogonal Polynomials and Fourier Series for Functions of Vector Variable: Multidimensional-Matrix Approach." Asian Journal of Probability and Statistics 25, no. 3 (2023): 84–98. http://dx.doi.org/10.9734/ajpas/2023/v25i3565.

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In the article, the theory of the Fourier series on the orthogonal multidimensional-matrix polynomials is developed. The known results from the theory of the orthogonal polynomials of the vector variable and the Fourier series are given and the new results are presented. In particular, the known results of the Fourier series are extended to the case of the multidimensional-matrix functions, what allows us to solve more general approximation problems. The general case of the approximation of the multidimensional-matrix function of the vector argument by the Fourier series on the orthogonal mult

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20

Mukha, V. S. "Fourier series for the multidimensional-matrix functions of the vector variable." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 60, no. 1 (2024): 15–28. http://dx.doi.org/10.29235/1561-2430-2024-60-1-15-28.

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In the article, the theory of the Fourier series on the orthogonal multidimensional-matrix (mdm) polynomials is developed. The known results from the theory of the orthogonal polynomials of the vector variable and the Fourier series are given and the new results are presented. In particular, the known results of the Fourier series theory are extended to the case of the mdm functions, what allows us to solve more general approximation problems. The general case of the approximation of the mdm function of the vector argument by the Fourier series on the orthogonal mdm polynomials is realized pro

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21

Rajkovic, Predrag, Sladjana Marinkovic, and Miomir Stankovic. "Orthogonal polynomials with varying weight of Laguerre type." Filomat 29, no. 5 (2015): 1053–62. http://dx.doi.org/10.2298/fil1505053r.

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In this paper, we define and examine a new functional product in the space of real polynomials. This product includes the weight function which depends on degrees of the participants. In spite of it does not have all properties of an inner product, we construct the sequence of orthogonal polynomials. These polynomials can be eigenfunctions of a differential equation what was used in some considerations in the theoretical physics. In special, we consider Laguerre type weight function and prove that the corresponding orthogonal polynomial sequence is connected with Laguerre polynomials. We study

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22

Pottosin, Yu V. "Minimization of Boolean functions in the class of orthogonal disjunctive normal forms." Informatics 18, no. 2 (2021): 33–47. http://dx.doi.org/10.37661/1816-0301-2021-18-2-33-47.

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The orthogonal disjunctive normal forms (DNFs) of Boolean functions have wide applications in the logical design of discrete devices. The problem of DNF orthogonalization is to get for a given function such a DNF that any two its terms would be orthogonal, i. e. the conjunction of them would be equal identically to zero. An approach to solve the problem using the means of graph theory is suggested. The approach is proposed by representation of the function as perfect DNF. Obtaining all the intervals of the Boolean space where the given function has value 1 is supposed, and the intersection gra

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23

Morier-Genoud, Sophie, and Valentin Ovsienko. "Orthogonal Designs and a Cubic Binary Function." IEEE Transactions on Information Theory 59, no. 3 (2013): 1583–89. http://dx.doi.org/10.1109/tit.2012.2229335.

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24

Ferreira, Chelo, José L. López, Rafael Navarro, and Ester Pérez Sinusa. "Orthogonal basis for the optical transfer function." Applied Optics 55, no. 34 (2016): 9688. http://dx.doi.org/10.1364/ao.55.009688.

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25

Dresse, Zoé, and Walter Van Assche. "Orthogonal polynomials for Minkowski’s question mark function." Journal of Computational and Applied Mathematics 284 (August 2015): 171–83. http://dx.doi.org/10.1016/j.cam.2014.07.013.

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26

Durairajan, T. M. "Optimal estimating function for non-orthogonal model." Journal of Statistical Planning and Inference 33, no. 3 (1992): 381–84. http://dx.doi.org/10.1016/0378-3758(92)90006-e.

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27

Peherstorfer, F., V. P. Spiridonov, and A. S. Zhedanov. "Toda chain, Stieltjes function, and orthogonal polynomials." Theoretical and Mathematical Physics 151, no. 1 (2007): 505–28. http://dx.doi.org/10.1007/s11232-007-0038-8.

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28

Ghosh, Aniruddha, Anindya Ghosh, Anindita Ganguly, and Saumya Deep Chatterjee. "Unidentified Input Observer using orthogonal Hybrid function." IFAC-PapersOnLine 51, no. 1 (2018): 255–60. http://dx.doi.org/10.1016/j.ifacol.2018.05.064.

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29

Shiow-Shung Yang and Ching-Shiow Tseng. "An orthogonal neural network for function approximation." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 26, no. 5 (1996): 779–85. http://dx.doi.org/10.1109/3477.537319.

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30

Mahadevaswamy.B.S. "INEQUALITIES FOR ORTHOGONAL POLYNOMIALS AND BESSEL FUNCTION." international journal of engineering technology and management sciences 6, no. 6 (2022): 641–49. http://dx.doi.org/10.46647/ijetms.2022.v06i06.108.

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In this paper, we have given several proofs inequality discovered by Turban for Legendre polynomials. A single derivation and some their results were given. We also established in equality for bassel function. We illustrate and rederive the left hand inequality further more to establish the estimate for 0(x).

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31

Wu, Guochang, Dengfeng Li, Huimin Xiao, and Zhanwei Liu. "The M-band cardinal orthogonal scaling function." Applied Mathematics and Computation 215, no. 9 (2010): 3271–79. http://dx.doi.org/10.1016/j.amc.2009.10.015.

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32

Hamlington, B. D., R. R. Leben, M. W. Strassburg, and K. ‐Y Kim. "Cyclostationary empirical orthogonal function sea‐level reconstruction." Geoscience Data Journal 1, no. 1 (2014): 13–19. http://dx.doi.org/10.1002/gdj3.6.

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33

Yu, Lean, Zebin Yang, and Ling Tang. "Quantile estimators with orthogonal pinball loss function." Journal of Forecasting 37, no. 3 (2018): 401–17. http://dx.doi.org/10.1002/for.2510.

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34

Güldoğan Lekesiz, Esra, and Iván Area. "Some New Families of Finite Orthogonal Polynomials in Two Variables." Axioms 12, no. 10 (2023): 932. http://dx.doi.org/10.3390/axioms12100932.

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In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an infinite family of univariate orthogonal polynomials. For these new classes of bivariate finite orthogonal polynomials, we present a bivariate weight function, the domain of orthogonality, the orthogonality relation, the recurrence relations, the second-order partial differential equations, the generating functions, as well as the parameter deri

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35

Jaballah, Ali, and Fathi B. Saidi. "Orthogonal Symmetries and Reflections in Banach Spaces." Journal of Mathematics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/1073589.

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Let X be a Banach space. We introduce a concept of orthogonal symmetry and reflection in X. We then establish its relation with the concept of best approximation and investigate its implication on the shape of the unit ball of the Banach space X by considering sections over subspaces. The results are then applied to the space C(I) of continuous functions on a compact set I. We obtain some nontrivial symmetries of the unit ball of C(I). We also show that, under natural symmetry conditions, every odd function is orthogonal to every even function in X. We conclude with some suggestions for furthe

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36

Blazquez-Martín, Agustín, Ester Verde-Sesto, Angel J. Moreno, Arantxa Arbe, Juan Colmenero, and José A. Pomposo. "Advances in the Multi-Orthogonal Folding of Single Polymer Chains into Single-Chain Nanoparticles." Polymers 13, no. 2 (2021): 293. http://dx.doi.org/10.3390/polym13020293.

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The folding of certain proteins (e.g., enzymes) into perfectly defined 3D conformations via multi-orthogonal interactions is critical to their function. Concerning synthetic polymers chains, the “folding” of individual polymer chains at high dilution via intra-chain interactions leads to so-called single-chain nanoparticles (SCNPs). This review article describes the advances carried out in recent years in the folding of single polymer chains into discrete SCNPs via multi-orthogonal interactions using different reactive chemical species where intra-chain bonding only occurs between groups of th

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37

Belim, Svetlana, and Sergei Belim. "The chaotic masking message model using orthogonal functions." Transaction of Scientific Papers of the Novosibirsk State Technical University, no. 1-2 (August 26, 2020): 67–76. http://dx.doi.org/10.17212/2307-6879-2020-1-2-67-76.

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The model for chaotic signal masking is proposed in the article. The digital signal in the bit representation is encoded using a family of orthogonal functions. Random white noise is superimposed on the resulting analog signal. The white noise amplitude is significantly greater than the amplitude of the signal. The functions orthogonal property is used to retrieve a useful signal. The advantage proposed this model is that it is not necessary to match the noise generators in the source and in the receiver of the message. The integration operation is required to retrieve the message. The using a

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38

Berg, Christian, and Mourad E. H. Ismail. "q-Hermite Polynomials and Classical Orthogonal Polynomials." Canadian Journal of Mathematics 48, no. 1 (1996): 43–63. http://dx.doi.org/10.4153/cjm-1996-002-4.

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AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegö and leads naturally to the Al-Salam-Chihara polynomials then to the Askey-Wilson polynomials, the big q-Jacobi polynomials and the biorthogonal rational functions of Al-Salam and Verma, and some recent biorthogonal functions of Al-Salam a

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39

Mossadegh, Vahid, and Mahmood Ghanbari. "Identification of a Non-Linear System Using Volterra Series Model with Calculated Kernels by Legendre Orthogonal Function." International Journal of Advances in Applied Sciences 6, no. 3 (2017): 185. http://dx.doi.org/10.11591/ijaas.v6.i3.pp185-192.

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Modeling and identification of non-linear systems have gained lots of attentions especially in industrial processes. Most of the actual systems have non-linear behavior and the first and simplest solution in modeling such systems is to linearize them which in most cases the result of linearization is not satisfactory. In this paper, modeling of non-linear systems is investigated using Volterra series model based on Legendre orthogonal function. Expansion of Volterra series kernels by Legendre orthogonal functions causes a reduction in the number of model parameters; hence, complexity of calcul

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40

Choque, Abdon, and Tatjana Vukasinac. "Korobov’s controllability function method via orthogonal polynomials on [0,∞)." V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, no. 100 (December 23, 2024): 61–78. https://doi.org/10.26565/2221-5646-2024-100-04.

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Given a controllable system described by ordinary or partial differential equations and an initial state, the problem of finding a set of bounded positional controls that transfer the initial state to another state, not necessarily an equilibrium point, in finite time is called the synthesis problem. In the present work, we consider a family of Brunovsky systems of dimension n. A family of bounded positional controls un(x) is developed to stabilize a given Brunovsky system in finite time. We employ orthogonal polynomials associated with a function distribution σ(τ, θ) defined for τ ∈ [0, +∞) a

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41

Wang, Lan Feng, Kai Jun Sun, and Jing Ben Yin. "Classifying Cardinal Orthogonal Scaling Function with Dilation Factor 3." Advanced Materials Research 282-283 (July 2011): 437–39. http://dx.doi.org/10.4028/www.scientific.net/amr.282-283.437.

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Sampling theorem plays an important role in many fields such as signal processing and image processing. In this paper, the cardinal orthogonal scaling function with dilation factor 3 is classified by the highpass filter coefficient, thus, the sampling theorem in the wavelet subspace is obtained. Then, the symmetry property of cardinal orthogonal scaling function is discussed.

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42

Wang, Jian-Ming, Zu-Jian Wang, Hong-Chun Yuan, and Xue-Xiang Xu. "Orthogonal state of coherent state based on Hermite-excited superposition operator: Production and Wigner function." Modern Physics Letters B 33, no. 26 (2019): 1950320. http://dx.doi.org/10.1142/s0217984919503202.

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An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator [Formula: see text]. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.

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43

Chan, Steve Wai, King Fai Lai, and Mansoor Syed. "Semi-Orthogonal Binary Spline Wavelets in Incompressible Fluid Dynamics." Applied Mechanics and Materials 249-250 (December 2012): 164–69. http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.164.

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Jia and coworkers [1] have shown that with =M_N and  ̃=M_1as a pair of locally supported refinable functions, one can construct a function, _N(N being an odd integer) given by _N≔∑_(j=0)^N▒〖((-1)^j)/2 [M_(N+1) (j)+M_N (j+1) ] M_N (2∙-j)〗. Here M_N is a binary spline function of degree N. For r =0, 1, 2, …, N-1, the set {2^(j/2) _N^((r) ) (2^j∙-j);j,k ϵ Z} is a Riesz basis for L_2 (R). This base involves the first N-1 derivatives of the generating function and therefore is useful for dynamical systems with derivative constraints.

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Angelani, Luca. "Orthogonal run-and-tumble walks." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 12 (2022): 123207. http://dx.doi.org/10.1088/1742-5468/aca588.

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Abstract Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions of the probability distribution function (in the Laplace–Fourier domain), the mean-square displacement and the effective diffusion constant in terms of transition rate parameters. As case studies we treat and discuss two classes of motion, alternate/forward and isotropic/backward, obtaining, when possible, analytic expressions of probability distrib

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Kondakov, N. A. "Determination of the pulse transfer function of composite plants using orthogonal functions." Journal of Mathematical Sciences 69, no. 5 (1994): 1359–62. http://dx.doi.org/10.1007/bf01259282.

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Zhedanov, A. S. "Gauss Sums and Orthogonal Polynomials." International Journal of Modern Physics A 12, no. 01 (1997): 289–94. http://dx.doi.org/10.1142/s0217751x97000438.

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It is shown that q-Hermite polynomials for q a root of unity are orthogonal on finite numbers of points of the real axes. The (complex) weight function coincides with a special type of the Gauss sums in number theory. The same Gauss sum plays the role of the weight function for the Stiltjes–Wigert and Rogers–Szegö polynomials leading to the orthogonality on the regular N-gons.

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Chen, Qing Jiang, Chuan Li Cai, and Jian Tang Zhao. "The Research of Orthogonal Symmetric Matrix-Valued Wavelets Packets with Multiscale and Applications." Advanced Materials Research 915-916 (April 2014): 1300–1303. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.1300.

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Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we introduce orthogonal matrix-valued wavelets with poly-scale, which are wavelets for vector fields, based on the notion of full rank subdivision operators. It is demonstrated that, like in the scalar and multiwavelet case, the existence of an orthogonal matrix-valued scaling function guarantees the existence of orthogonal matrix-valued wavelet functions. Secondly, we propose a construction algorim for compactly supported orthog onal two-directional matri

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Zhang, Fang Jun. "The M-Band Symmetric Orthogonal Scaling Function in Higher Dimensions." Applied Mechanics and Materials 482 (December 2013): 322–25. http://dx.doi.org/10.4028/www.scientific.net/amm.482.322.

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Wavelet theory has a key role in signal processing and image processing. In this paper, the characterization of the M-band symmetric orthogonal scaling function is obtained in higher dimensions. Then, a symmetric cardinal orthogonal scaling function is classified. The existing some results in one dimension are generalized to the case of higher dimensions.

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Saka, J. A., and O. O. Oyadare. "A general construction of mutually orthogonal latin squares of prime order." International Journal of Algebra and Statistics 7, no. 1-2 (2018): 77–93. http://dx.doi.org/10.20454/ijas.2018.1451.

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This paper presents a general method of constructing a complete set of Mutually Orthogonal Latin Squares (MOLS) of the order of any prime, via the use of generating functions dened on the nite eld of this order. Apart from using the generating function to get a complete set of Mutually Orthogonal Latin Squares, the studies of the generating functions opens up the possibility of getting at the deep structural properties of MOLS. Copious examples were given for detailed illustrations.

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Nasrullah, Nasrullah, Mawardi Bahri, Muh Zakir, and Muhammad Afdal Bau. "The Ortogonal Property of Directional short-time quaternion Fourier transform." Daya Matematis: Jurnal Inovasi Pendidikan Matematika 10, no. 3 (2022): 223. http://dx.doi.org/10.26858/jdm.v10i3.40800.

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This study will examine the orthogonal properties of Directional Short-time quaternion Fourier transform (DSTQFT) which is a further study of DSTFT with an expansion in the form of a function that has a Quaternion value. The orthogonal properties of DSTQFT are obtained by combining the orthogonal properties of DSTFT and the Fourier quaternion transform (QFT). Based on the results of the study, it was found that the orthogonal nature of the Directional Short-Time quaternion Fourier Transform (DSTQFT) is different from the orthogonal nature of the Directional Short-Time Fourier Transform (DSTFT)

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