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991.
Gerber and Li (1981) formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent repeated experiments when the initial outcomes of the process are known. We show how this system of equations can be obtained by using the classical gambling team technique. We also present a form of solution of the system and give an example showing how first results of trials influence the probabilities that a chosen pattern precedes the remaining ones in a realization of the process. 相似文献
992.
993.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(3):442-447
This paper considers the impulsive functional differential equations with infinite delays or finite delays. Some new sufficient conditions are obtained to guarantee the global exponential stability by employing the improved Razumikhin technique and Lyapunov functions. The result extends and improves some recent works. Moreover, the obtained Razumikhin condition is very simple and effective to implement in real problems and it is helpful to investigate the stability of delayed neural networks and synchronization problems of chaotic systems under impulsive perturbation. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained result in this paper. 相似文献
994.
995.
《Applied and Computational Harmonic Analysis》2014,36(2):348-353
In this letter, a new set of orthogonal band-limited basis functions is introduced. This set of basis functions is derived from the inverse Fourier transform of the frequency domain Walsh functions. The Fourier transforms of the Walsh functions were calculated by Siemens and Kitai in 1973 but they have been overlooked in the literature. Some of the properties of these functions are studied in this paper. Moreover, the orthogonal discrete version of these functions is obtained by truncation, sampling and orthogonalization utilizing the orthogonal Procrustes problem. 相似文献
997.
《Journal of the Egyptian Mathematical Society》2014,22(1):14-18
This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications. 相似文献
998.
《Journal of the Egyptian Mathematical Society》2014,22(1):36-44
By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived. 相似文献
999.
《Journal of the Egyptian Mathematical Society》2014,22(3):511-516
In this article, we present a new numerical method to solve the integro-differential equations (IDEs). The proposed method uses the Legendre cardinal functions to express the approximate solution as a finite series. In our method the operational matrix of derivatives is used to reduce IDEs to a system of algebraic equations. To demonstrate the validity and applicability of the proposed method, we present some numerical examples. We compare the obtained numerical results from the proposed method with some other methods. The results show that the proposed algorithm is of high accuracy, more simple and effective. 相似文献
1000.