排序方式: 共有19条查询结果,搜索用时 11 毫秒
1.
Francesca Aicardi 《Functional Analysis and Other Mathematics》2008,2(1):1-13
We prove the propositions stated in Part I [Funct Anal Other Math 1(2):93–109 ([2006])] and give the explicit formulas for X
p
(a,b).
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Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
In this paper, we state and prove a new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shifted Chebyshev polynomials themselves. We develop also a direct solution technique for solving the linear multi-order fractional differential equations (FDEs) with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives (described in the Caputo sense) are based on shifted Chebyshev polynomials TL,n(x) with x ∈ (0, L), L > 0 and n is the polynomial degree. We presented a shifted Chebyshev collocation method with shifted Chebyshev–Gauss points used as collocation nodes for solving nonlinear multi-order fractional initial value problems. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results. 相似文献
4.
Francis N. Castro Robin Chapman Luis A. Medina L. Brehsner Sepúlveda 《Discrete Mathematics》2018,341(7):1915-1931
Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of , an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field . Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences. 相似文献
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We briefly review series solutions of differential equations problems of the second order that lead to coefficients expressed in terms of determinants. Derivative type formulas involving a generating function with several parameters are developed for these determinant coefficients in first order problems. These permit constructing determinant forms for the heat polynomials and their Appell transforms. Hadamard's theorem for bounding determinants and conical regions are used to deduce simplified versions of expansion theorems involving these polynomials and associated Appell transforms. Extended versions of the heat equation are also considered. 相似文献
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A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a given differential equation, in particular symmetries and integrability (see Tempesta, 2010 [40]). Our approach is based on the properties of a suitable Galois differential algebra, that we shall call a Rota algebra. A formulation of the procedure in terms of category theory is proposed. In order to render the lattice dynamics confined, a Borel regularization is also adopted. As a byproduct of the theory, a connection between number sequences and integrability is discussed. 相似文献
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In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives which is applied together with spectral tau method for numerical solution of general linear multi-term fractional differential equations (FDEs). A new approach implementing shifted Jacobi operational matrix in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of nonlinear multi-term FDEs. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The proposed methods are applied for solving linear and nonlinear multi-term FDEs subject to initial or boundary conditions, and the exact solutions are obtained for some tested problems. Special attention is given to the comparison of the numerical results obtained by the new algorithm with those found by other known methods. 相似文献
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Ivana Kovacic Zvonko Rakaric Livija Cveticanin 《Applied mathematics and computation》2010,217(8):3944-3954
This paper is concerned with a class of conservative oscillators the restitution force of which is of a power form which includes positive non-integer exponents. It is shown how an approximate Lagrangian and Hamilton’s variational principle can be used to obtain a second-order approximate solution for their free vibrations. Due to the fact that, in a general case, when the restoring force is multi-term, the period cannot be obtained from the energy conservation law in a closed form, the problem is formulated as a one-point boundary-value problem, and a non-simultaneous variation is introduced. The explicit expressions for the amplitudes and frequency of oscillations are derived, in which there are no restrictions on the values of the non-integer powers. The analytically obtained results are compared with numerical results as well as with some approximate analytical results from the literature. 相似文献
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Varsha Daftardar-Gejji Sachin Bhalekar 《Journal of Mathematical Analysis and Applications》2008,345(2):754-765
Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind. 相似文献
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《Indagationes Mathematicae》2021,32(4):847-860
Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue–Morse measure. 相似文献