A recursive formula expressing N-dimensional convolutions/correlations via(N-1)-dimensional ones is proposed. Its applications in pattern recognition (especially in optical pattern recognition) are discussed. (C) 1998...
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A recursive formula expressing N-dimensional convolutions/correlations via(N-1)-dimensional ones is proposed. Its applications in pattern recognition (especially in optical pattern recognition) are discussed. (C) 1998 Elsevier Science B.V.
This letter presents the recursive formulas of the moments of queue length for the M/M/1 queue and M/M/1/B queue, respectively. The higher moments of queue length are important for optimization problem. Our method pro...
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This letter presents the recursive formulas of the moments of queue length for the M/M/1 queue and M/M/1/B queue, respectively. The higher moments of queue length are important for optimization problem. Our method provides an alternative approach to derive the moments of queue length, instead of taking the derivatives of the moment generating function.
The simplex integration is a convenient method for the integration over complex domains. It automatically represents the ordinary integral over an arbitrary polyhedron as the algebraic sum of integrals over the orient...
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The simplex integration is a convenient method for the integration over complex domains. It automatically represents the ordinary integral over an arbitrary polyhedron as the algebraic sum of integrals over the oriented simplexes. An existing recursive formula for the integration of monomials over simplex, which was deduced based on special operations of matrices and was presented by the first author of this paper, has significant advantages: not only the computation amount is small, but also the integrals of all the lower order monomials are obtained while computing the integral of the highest order monomial. The extension to a polynomial can be obtained by the linearity of integrals. In this paper, the derivation of the existing recursive formula is detailed. A new recursive formula is emphatically proposed to simplify the existing recursive formula and further increase the speed of computation. The code for computer implementation is also presented. Examples show that the accuracy and efficiency of the recursive formula are higher than numerical integration. (C) 2020 Elsevier Inc. All rights reserved.
A useful recursive formula for obtaining the infinite sums of even order harmonic series Σ ∞ n =1 (1/ n 2 k ), k = 1, 2, …, is derived by an application of Fourier series expansion of some periodic functions. Since...
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A useful recursive formula for obtaining the infinite sums of even order harmonic series Σ ∞ n =1 (1/ n 2 k ), k = 1, 2, …, is derived by an application of Fourier series expansion of some periodic functions. Since the formula does not contain the Bernoulli numbers, infinite sums of even order harmonic series may be calculated by the formula without the Bernoulli numbers. Infinite sums of a few even order harmonic series, which are calculated using the recursive formula, are tabulated for easy reference.
This study proposes a recursive formula to value a surrenderable participating contract To capture the dynamics of stock returns over expansion-recession cycles and the occurrence of catastrophic events, we assume the...
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This study proposes a recursive formula to value a surrenderable participating contract To capture the dynamics of stock returns over expansion-recession cycles and the occurrence of catastrophic events, we assume the rate of return of the reference portfolio would follow a regime-switching model with jump risks. Our empirical results show that compared to the Black-Scholes model and the regime-switching model, the regime-switching model with jump risks can better explain the dynamics of the S&P 500 stock index. In addition, we give a recursive formula of a participating contract embedding a surrender option under a regime-switching model with jump risks. Sensitivity analysis shows that the changes of parameters of the regime-switching model with jump risks did influence participating contract premiums. The differences between valuations under the Black-Scholes model, the regime-switching model and the regime-switching model with jump risks suggest that it is critical to apply an appropriate model to value precisely a participating contract. (C) 2014 Elsevier B.V. All rights reserved.
The group determinant of a finite abelian group of cardinality n is a homogeneous polynomial in n variables of degree n. There is no known simple way to compute its coefficients. We derive a recursive formula for them.
The group determinant of a finite abelian group of cardinality n is a homogeneous polynomial in n variables of degree n. There is no known simple way to compute its coefficients. We derive a recursive formula for them.
In this paper, we construct a binary linear code connected with the Kloosterman sum for GL(2, q). Here q is a power of two. Then we obtain a recursive formula generating the power moments 2-dimensional Kloosterman sum...
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In this paper, we construct a binary linear code connected with the Kloosterman sum for GL(2, q). Here q is a power of two. Then we obtain a recursive formula generating the power moments 2-dimensional Kloosterman sum, equivalently that generating the even power moments of Kloosterman sum in terms of the frequencies of weights in the code. This is done via Pless power moment identity and by utilizing the explicit expression of the Kloosterman sum for GL(2, q).
In this paper, we provide an algorithm for evaluating the system state distribution for any multi-state consecutive-k-out-of-n:G system including the decreasing multi-state G system, the increasing multi-state G syste...
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In this paper, we provide an algorithm for evaluating the system state distribution for any multi-state consecutive-k-out-of-n:G system including the decreasing multi-state G system, the increasing multi-state G system, and other G systems. We evaluated our proposed algorithms in terms of the orders of computation time, and memory requirement. Furthermore, we conducted a numerical experiment to determine the actual computation time. Our proposed algorithm is more effective for systems with a large n.
Let A(epsilon) be an analytic square matrix and lambda(0) an eigenvalue of A(0) of algebraic multiplicity m >= 1. Then under the condition partial derivative/partial derivative epsilon det(lambda I - A(epsilon))|((...
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Let A(epsilon) be an analytic square matrix and lambda(0) an eigenvalue of A(0) of algebraic multiplicity m >= 1. Then under the condition partial derivative/partial derivative epsilon det(lambda I - A(epsilon))|((epsilon,lambda)=(0,lambda 0)) not equal 0, we prove that the Jordan normal form of A(0) corresponding to the eigenvalue lambda(0) consists of a single m x m Jordan block, the perturbed eigenvalues near lambda(0) and their corresponding eigenvectors can be represented by a single convergent Puiseux series containing only powers of epsilon(1/m), and there are explicit recursive formulas to compute all the Puiseux series coefficients from just the derivatives of A(epsilon) at the origin. Using these recursive formulas we calculate the series coefficients up to the second order and list them for quick reference. This paper gives, under a generic condition, explicit recursive formulas to compute the perturbed eigenvalues and eigenvectors for non-self-adjoint analytic perturbations of matrices with nonderogatory eigenvalues.
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