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排序方式: 共有206条查询结果,搜索用时 15 毫秒
21.
In this paper we solve the problem about optimal interval quadrature formula for the class WrF of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearrangements of averaged monosplines is proved. 相似文献
22.
In the present paper, we obtain three unified fractional derivative formulae (FDF). The first involves the product of a general
class of polynomials and the multivariableH-function. The second involves the product of a general class of polynomials and two multivariableH-functions and has been obtained with the help of the generalized Leibniz rule for fractional derivatives. The last FDF also
involves the product of a general class of polynomials and the multivariableH-function but it is obtained by the application of the first FDF twice and it involves two independent variables instead of
one. The polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which
are of the typex
ρ
Π
i=1
s
(x
t
i
+α
i
)
σ
i
are quite general in nature. These formulae, besides being of very general character have been put in a compact form avoiding
the occurrence of infinite series and thus making them useful in applications. Our findings provide interesting unifications
and extensions of a number of (new and known) results. For the sake of illustration, we give here exact references to the
results (in essence) of five research papers [2, 3,10, 12, 13] that follow as particular cases of our findings. In the end,
we record a new fractional derivative formula involving the product of the Hermite polynomials, the Laguerre polynomials and
the product ofr different Whittaker functions as a simple special case of our first formula. 相似文献
23.
Nikola Popović Dirk Praetorius Anja Schlömerkemper 《Continuum Mechanics and Thermodynamics》2007,19(1-2):67-80
The mathematical and physical analysis of magnetoelastic phenomena is a topic of ongoing research. Different formulae have
been proposed to describe the magnetic forces in macroscopic systems. We discuss several of these formulae in the context
of rigid magnetized bodies. In case the bodies are in contact, we consider formulae both in the framework of macroscopic electrodynamics
and via a multiscale approach, i.e., in a discrete setting of magnetic dipole moments. We give mathematically rigorous proofs
for domains of polygonal shape (as well as for more general geometries) in two and three space dimensions. In an accompanying
second article, we investigate the formulae in a number of numerical experiments, where we focus on the dependence of the
magnetic force on the distance between the bodies and on the case when the two bodies are in contact. The aim of the analysis
as well as of the numerical simulation is to contribute to the ongoing debate about which formula describes the magnetic force
between macroscopic bodies best and to stimulate corresponding real-life experiments.
相似文献
24.
Hongmei Liu Wenshu Zhou Shuyan Ding 《Journal of Difference Equations and Applications》2017,23(7):1204-1218
By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers. 相似文献
25.
26.
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
27.
Marek Bożejko Anna Dorota Krystek Łukasz Jan Wojakowski 《Mathematische Zeitschrift》2006,253(1):177-196
In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution
is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined
with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive.
Partially sponsored with KBN grant no 2P03A00723 and RTN HPRN-CT-2002-00279. 相似文献
28.
Clifford分析中奇异积分的Poincaré-Bertrand置换公式 总被引:3,自引:0,他引:3
借助于多元复分析的思想,本文证明了Cliford分析中奇异积分的Poincaré-Bertrand置换公式. 相似文献
29.
F. Garcia M. Net B. García-Archilla J. Sánchez 《Journal of computational physics》2010,229(20):7997-8010
A numerical study of several time integration methods for solving the three-dimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The codes are validated with a known benchmark, and their efficiency is studied. The results show that the use of high-order methods, especially those with time step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions. 相似文献
30.
This article provides a new theory for the analysis of the particle Gibbs (PG) sampler (Andrieu et al., 2010). Following the work of Del Moral and Jasra (2017) we provide some analysis of the particle Gibbs sampler, giving first order expansions of the kernel and minorization estimates. In addition, first order propagation of chaos estimates are derived for empirical measures of the dual particle model with a frozen path, also known as the conditional sequential Monte Carlo (SMC) update of the PG sampler. Backward and forward PG samplers are discussed, including a first comparison of the contraction estimates obtained by first order estimates. We illustrate our results with an example of fixed parameter estimation arising in hidden Markov models. 相似文献