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31.
In this paper, we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime
powers, e.g.,
for any distinct odd primes p and q. Meanwhile, we discuss the connections with the prime recognitions.
Received November 5, 1998, Accepted December 7, 2000. 相似文献
32.
It is observed that the harmonic balance (HB) method of parametric identification of nonlinear system may not give right identification
results for a single test data. A multiple-trial HB scheme is suggested to obtain improved results in the identification,
compared with a single sample test. Several independent tests are conducted by subjecting the system to a range of harmonic
excitations. The individual data sets are combined to obtain the matrix for inversion. This leads to the mean square error
minimization of the entire set of periodic orbits. It is shown that the combination of independent test data gives correct
results even in the case where the individual data sets give wrong results. 相似文献
33.
In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method. 相似文献
34.
Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis 下载免费PDF全文
Z. Barikbin E. Keshavarz Hedayati 《Numerical Methods for Partial Differential Equations》2017,33(4):1143-1158
In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017 相似文献
35.
In this paper, the wind-induced, horizontal vibrations of a vertical Euler–Bernoulli beam will be considered. At the top of
the beam, a tuned mass damper (TMD) has been installed. The horizontal vibrations can be described by an initial-boundary
value problem. Perturbation methods will be applied to construct approximations of the solutions of the initial-boundary value
problem, and it will be shown that the TMD uniformly damps the oscillation modes of the beam. In the analysis, it will be
assumed that damping, wind-force, and gravity effects are small but not negligible. 相似文献
36.
The paper is devoted to a rigorous construction of a parabolic system of partial differential equations which displays space–time
chaotic behavior in its global attractor. The construction starts from a periodic array of identical copies of a temporally
chaotic reaction-diffusion system (RDS) on a bounded domain with Dirichlet boundary conditions. We start with the case without
coupling where space–time chaos, defined via embedding of multi- dimensional Bernoulli schemes, is easily obtained. We introduce
small coupling by replacing the Dirichlet boundary conditions by strong absorption between the active islands. Using hyperbolicity
and delicate PDE estimates we prove persistence of the embedded Bernoulli scheme. Furthermore we smoothen the nonlinearity
and obtain a RDS which has polynomial interaction terms with space and time-periodic coefficients and which has a hyperbolic
invariant set on which the dynamics displays spatio-temporal chaos. Finally we show that such a system can be embedded in
a bigger system which is autonomous and homogeneous and still contains space–time chaos. Obviously, hyperbolicity is lost
in this step.
Research partially supported by the INTAS project Attractors for Equations of Mathematical Physics, by CRDF and by the Alexander von Humboldt–Stiftung. 相似文献
37.
Jonathan M. Fraser 《Mathematische Nachrichten》2015,288(17-18):2028-2041
We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures. 相似文献
38.
Jian-Lin Li 《Journal of Functional Analysis》2011,260(4):1086-1095
In the present paper we will study the spectral property of a class of self-affine measures under the condition of compatible pair. We first answer a question of Dutkay and Jorgensen concerning the relationship between spectral self-affine measure and compatible pair. We then consider the spectra of Bernoulli convolutions and obtain a sharp result which extends the corresponding result of Jorgensen, Kornelson and Shuman. Finally, we provide a structural property for the integer spectrum of a spectral self-affine measure. 相似文献
39.
For testing “univariate” binomial proportions, it has been proven that, under mild conditions, there exist group sequential designs which satisfy the pre-specified Type I error and power of the single-stage design while the sample size is bounded above by that of the single-stage design (Kepner and Chang, 2003). In this article, we extend this result and prove the existence of such group sequential designs for various decision rules in the space of bivariate binomial variables. We also demonstrate how to obtain the actual group sequential designs for detecting changes in bivariate binomial variables. 相似文献
40.
利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式. 相似文献