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Approximate solution for solving fractional Riccati differential equations via trigonometric basic functions

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE 2018年第3期172卷 299-308页

作者： Agheli, Bahram Islamic Azad Univ Dept Math Qaemshahr Branch Qaemshahr Iran

In this paper, a method has been proposed to finding a numerical function for the Riccati differential equations of non integer order (FRDEs), in which trigonometric basic functions are used. First, by defining trigonometric basic functions, we define the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the numerical function is defined as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get a numerical solution function with discrete derivatives of the solution function, we have determined the numerical solution function which satisfies the FRDEs. In the end, the algorithm of the method is elaborated with several examples. Numerical results obtained show that the proposed algorithm gives very good numerical solutions. In one example, we have presented an absolute error comparison of some numerical methods. (C) 2018 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.

关键词： Trigonometric transform Riccati differential equations basic functions Caputo derivative

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Classification Scheme of Methods, Principles and Models of Construction of Hardware for Implementation of Function-specific Drivers of Primitive basic functions Based on System Analysis 13

Classification Scheme of Methods, Principles and Models of C...

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13th International Conference on Experience of Designing and Application of CAD Systems in Microelectronics (CADSM)

作者： Vladimir, Lukashenko Viktor, Spivak Andrii, Lukashenko NAS Ukraine EO Paton Elect Welding Inst 11 Bozhenko Str Kiev Ukraine Natl Tech Univ Ukraine KPI Kiev Ukraine

developed a Classification scheme of methods, principles and models of construction of hardware for implementation of function-specific drivers of primitive basic functions based on system analysis.

ISBN: (纸本)9786176077169

developed a Classification scheme of methods, principles and models of construction of hardware for implementation of function-specific drivers of primitive basic functions based on system analysis.

关键词： Classification scheme methods models principles basic functions

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Compression of the technological data in terms of Galois basic functions 2

Compression of the technological data in terms of Galois bas...

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2nd IEEE International Workshop on Intelligent Data Acquisition and Advanced Computing Systems

作者： Yatskiv, N Ternopil Acad Natl Econ UA-46004 Ternopol Ukraine

In this article data compression method on the basis of Galois basic functions of zero and first rank is proposed, efficiency of coding with the, usage of this method is investigated.

ISBN: (纸本)0780381386

In this article data compression method on the basis of Galois basic functions of zero and first rank is proposed, efficiency of coding with the, usage of this method is investigated.

关键词： basic functions data compression coding

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basic functions for Computational Implementation of the Box-Cox Symmetric Class of Distributions

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Open Journal of Statistics 2021年第6期11卷 1010-1016页

作者： Giovana Fumes-Ghantous José Eduardo Corrente Basic Science Department Faculty of Animal Science and Food Engineering University of S&atilde o Paulo S&atilde o Paulo Brazil Research Support Office Botucatu Medical School University of S&atilde o Paulo State Botucatu Brazil

A class of distributions called Box-Cox symmetric was proposed for random variables with asymmetric distributions. This class allows through its structure an interpretation of the parameters in terms of quantiles (in particular, the median), relative dispersion and skewness. This study presents the initial results of the computational development of basic functions of each of the distributions that make up the Box-Cox symmetric class. Four functions have been developed to compose a routine in software R up to now. These functions are related to random numbers generation, probability density function, cumulative distribution function, and quantile function associated to a given probability. Examples of implemented functions were presented. The gamlss routine was used to check the performance of developed functions.

关键词： Asymmetric Distributions basic functions Box-Cox Symmetric Class

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Extension of the Quadratic Bezier curves Based on the Linear Combination of basic functions

Extension of the Quadratic Bezier curves Based on the Linear...

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2011 IEEE International Conference on Computer Science and Automation Engineering(CSAE 2011)

作者： Zou Jing Hangzhou Institute of Service Engineering Hangzhou Normal University Hangzhou China Liang Xikun

＜正＞Based on the idea of the linear combination of basic functions,the quadratic Bezier curves is extended,and the nature of the expansion curve is also discussed in this *** extension of the quadratic Bezier curves expresses simple and contains the basic form of the original *** only enhances the shape-control capability of the quadratic Bezier curves,but also keeps the same degree of original *** is easy to find that the curve can be reshaped by adjusting the shape factor.

关键词： basic functions Linear Combination Bezier curves Shape factor Extension

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Nth-order fuzzy linear differential equations

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INFORMATION SCIENCES 2008年第5期178卷 1309-1324页

作者： Allahviranloo, T. Ahmady, E. Ahmady, N. Islamic Azad Univ Dept Math Sci & Res Branch Tehran Iran

In this paper a numerical method for solving nth-order linear differential equations with fuzzy initial conditions is considered. The idea is based on the collocation method. The existence theorem of the fuzzy solution is considered. This method is illustrated by solving several examples. (C) 2007 Elsevier Inc. All rights reserved.

关键词： fuzzy number extension principle basic functions fuzzy distance fuzzy differential equations

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Non-linear approximation method by an approach in stages

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COMPUTATIONAL MECHANICS 2003年第3期32卷 177-184页

作者： Beda, T Chevalier, Y Univ Yaounde 1 ENS Polytech Yaounde Cameroon LISMMA ISMCM F-93407 Paris France

This work presents a new methodology of approximation of functions. The identification is done graphically, stage-by-stage, taking into account the form of the generating functions. The above method is developed in this article within the scope of an efficient tool for modeling physical systems and as a reliable curve-fitting method that can use any basic function. Thus, it represents a non-linear identification procedure. On the one hand, simulated cases that do not represent any physical model are studied, and on the other hand, real cases that model physical systems as rubber behavior law are illustrated. The Ogden hyperelastic and the extended Gent-Thomas models for rubber materials are shown to give an accurate prediction of Treloar's classical data with the help of mechanical parameters evaluated by the stage approach. Critical and comparative analyses of the stage approach are presented with the usual non-linear iterative procedures such as the non-linear least squares.

关键词： approximation nonlinearity basic functions behavior identification stage-by-stage

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Reconstruction of Gaussian processes with an arbitrary number of samples and discrete jitter

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IETE JOURNAL OF RESEARCH 2005年第5期51卷 361-370页

作者： Kazakov, VA Rodriguez, D Natl Polytech Inst Mexico Dept Telecommun Mexico City DF Mexico Natl Polytech Inst Mexico Sch Mech & Elect Engn Mexico City DF Mexico

The Sampling-Reconstruction Procedure (SRP) of the Gaussian processes with an arbitrary number of samples is considered when all or some of the samples have jitter. The investigation method is based on the conditional mean rule. The optimal error reconstruction function and the basic functions of each sample are calculated in the time domain for some non trivial examples when the type of covariance function and the discrete distribution law of the jitter are changed. The jitter of each sample is independent and has different discrete distribution law. In order to get all the results we apply the operation of the statistical average to the conditional mean and the conditional variance with regard to the random intervals.

关键词： discrete jitter error reconstruction function basic functions sampling and reconstruction of Gaussian processes 2000 AMS Mathematics subject classification-94A20 94A12

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AN ALTERNATIVE APPROACH TO THE LINEAR-THEORY OF VISCOELASTICITY AND SOME CHARACTERISTIC EFFECTS BEING DISTINCTIVE OF THE TYPE OF MATERIAL

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RHEOLOGICA ACTA 1995年第1期34卷 2-11页

作者： GIESEKUS, H Department of Chemical Engineering University of Dortmund Dortmund Germany

In the introduction some postulates on which the linear theory of viscoelasticity is based are recalled, and the postulate of passivity is substituted by a stronger postulate called detailed passivity. Next, a symmetric formulation of this theory is presented which is founded in a well-balanced way on the limiting properties of elasticity and viscosity. This leads to the introduction of the basic functions of creep compliance J+(t) and stressing viscosity eta+(t) associated to one another, whereas the basic functions retardation fluidity phi+(t) and relaxation modulus G+(t) emerge as their time derivatives. Correspondingly, four complex basic functions are defined as their Carson transforms. In addition to the proper retardation and relaxation terms, these basic functions contain the non-disappearing constants of either instantaneous compliance J0 or instantaneous viscosity eta0 and also of either ultimate fluidity phi(infinity) or ultimate modulus G(infinity). Therefrom ensues a classification of linear viscoelastic materials into four types: instantaneous elasticity or viscosity is allowed to combine with ultimate viscosity or elasticity. The latter alternative, signifying fluidlike or solidlike materials, leads, of course, to a quite different behavior in many situations;however, remarkable distinctive features are associated to the first one as well. A few respective examples are outlined: 1) propagation of shear waves in a half-space with periodic and step-shaped excitation, 2) dissipation of work in a torsional vibration damper, and 3) shear flow between two parallel porous plates with injection and suction. Finally, materials with viscous initial behavior are defended against the notion that they be of no or almost no real significance.

关键词： LINEAR VISCOELASTICITY DETAILED PASSIVITY basic functions INSTANTANEOUS PROPERTIES ULTIMATE PROPERTIES

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Trigonometric F^mn-transform of multi-variable functions and its application to the partial differential equations and image processing

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SOFT COMPUTING 2022年第24期26卷 13301-13331页

作者： Alikhani, R. Perfilieva, Irina Ganjeh-Alamdari, M. Univ Tabriz Dept Math Tabriz Iran Univ Ostrava Inst Res & Applicat Fuzzy Modeling 30 Dubna 22 Ostrava 70103 1 Czech Republic

In this study, we focus on the extension of the trigonometric F-transform for functions in one variable to: (i) a larger domain, (ii) a higher degree of the F-m-transform, and (iii) many-variable functions to improve its approximation properties over the entire domain and especially at its boundaries. In addition, the properties of approximation and convergence of direct and inverse extended and multidimensional trigonometric F-m-transforms are discussed. Then, direct formulas for partial derivatives of functions of several variables are obtained in terms of trigonometric F-m-transforms, which are used to solve the Cauchy problem for the transport equation. A new image compression method is proposed and compared with well-established compression methods such as JPEG, JPEG 2000 and their less complex variations JPEG(APDCBT), JPEG(APUBT3), APUBT3-NUP, and JPEG-FT. We have shown that this (t) (F) over bar (11)-transform image compression method has high accuracy and reasonably low (irreducible) complexity.

关键词： F-transform of multi-variable functions Trigonometric F-m-transform Fuzzy partitions basic functions Approximation Partial differential equations Transport equation Image processing

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