Explicit Ramanujan-type approximations to pi of high order

We combine previously developed work with a variety of Ramanujan’s higher order modular equations to make explicit, in very simple form, algebraic approximations to π which converge with orders including 7, 11, 15 and 23.     

Approximation to the expectation of a function of order statistics and its applications

ThisprojectissupportedbytheNationalNaturalScienceFoundationofChinaandDoctoralProgramFoundationofHigherEducation.1.IntroductionLetUI,U2,'bei.i.d.randomvariableswithuniformd.f.ontheinterval(0,l),andforeveryn31,writeUt,,15'5Un,.fortheorderstatisticsofUI,'tUn.SupposethatXI1X2,'arei.i.d.observationsfromanondegenerated.f.F,anddenotebyX.,l5'5X.,.theorderstatisticsofXI,'IX,,'Withoutlossofgenerality,wewillassume0相似文献   

一个映射函数的有理逼近

设０∈Ｇ，Ｇ是有界单连通区域，Γ＝δＧ∈Ｃ（２，α），０＜α＜１．ｗ＝φ（ｚ），φ（０）＝０，φ’（０）＞０是将Ｇ保角映射到│ｗ│＜１内的一个映射函数。本文利用ｗ＝φ（ｚ）的极值性质得到了给定极点的有理函数序列对它的一致逼近阶的估计。     

On ratio block sequences with extreme distribution function

Distribution functions of ratio block sequences formed from sequences of positive integers are investigated in the paper. We characterize the case when the set of all distribution functions of a ratio block sequence contains c ₀, the greatest possible distribution function. Presented results complete some previously published results. Supported by grant MSM 6198898701, and VEGA no. 1/4006/07.     

Booster Method for Singularly-Perturbed One-Dimensional Convection-Diffusion Neumann Problems

An improved numerical method for singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations subject to Neumann-type boundary conditions is proposed. In this method, an asymptotic approximation is incorporated into a finite-difference scheme to improve the numerical solution. Uniform error estimates are derived when implemented in known difference schemes. Numerical results are presented in support of the proposed method.     

用概率统计方法预测洪水水位

河流的水位变化从局部时间看是偶然的，但从长远看，这些偶然的数据常常是必然的结果。在自然条件下取得的水位数据，从本质上看都是随机的，正因为其随机性，统计方法尤为重要。本文试用统计方法分析预测河水的最高洪水水位，这对建筑桥梁、修建堤坝具有一定的参考价值。     

非参数回归函数的kn近邻估计的渐近性质及其Bootstrap逼近

本文研究回归函数的kn-近邻估计的渐近性质,得到了回归函数的kn－近邻估计的渐近正态性和它的Bootstrap统计量的相合性,在高阶矩存在的条件下,我们证明了回归函数的kn-近邻估计的Bootstrap逼近比正态逼近更精确。     

A passage time for greedy-coloring cycles

We consider the progress of the greedy vertex coloring algorithm applied to cycle graphs. In particular we study the asymptotic distribution of the number of vertices colored by the algorithm when the third color is first used (if it is).     

Discrete approximation of integral operators

A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.

     

Behavior of the Effective QCD Coupling in the Infrared Region

The summary of nonperturbative results for the QCD invariant coupling obtained by numerical lattice simulations for the path integral and by solution of the approximate Dyson–Schwinger equations reveals a remarkable variety of IR behaviors of even at the qualitative level. In turn, this raises the question of the correspondence between the results obtained by different groups. We analyze this issue in terms of mass-dependent coupling-constant transformations and conclude that the problem of the IR behavior of the effective QCD coupling and of propagators is not well defined and requires a further clarification.     

两个Smarandache复合函数的混合均值公式

对任意正整数n,Smarandache函数U(n)、V(n)定义为:U(1)=V(1)=1,n>1时,若它的标准分解式是n=p_1~(α_1)p_2~(α_2)…p_r~(α_r),U(n)=1{α_1·p_1α_2·p_2,…,α_r·p_r};V(n)={α_1·p_1,α_2·p_2,…,α_r·p_r}.研究了这两Smarandache函数U(n)与V~m(n)的值分布,并用初等方法及素数分布定理得到了几个较强的渐近公式.     

Gravitational Effects on Light Rays and Binary Pulsar Energy Loss in a Scalar Theory of Gravity

We summarize a scalar bimetric theory of gravity with a preferred reference frame. The dynamics are governed by an extension of Newton's second law. We recover geodesic motion together with Newton's attraction field in the static case and find Schwarzschild's metric in the static spherical case. We build asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximations, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, and we hence obtain the standard predictions of GR for photons. At the 0PM approximation, an isolated system loses energy by quadrupole radiation without any monopole or dipole term. Inserting this loss into the Newtonian two-body problem gives the Peters–Mathews coefficients of the theory.     

Asymptotic method for solving the time-optimal control problem for a nonlinear singularly perturbed system

The time-optimal control problem for a nonlinear singularly perturbed system with multidimensional controls bounded in the Euclidean norm is considered. An algorithm for constructing asymptotic approximations to its solution is proposed. The main advantage of the algorithm is that the original optimal control problem decomposes into two unperturbed problems of lower dimensions.     

Development of the Hubbell Rectangular Source Integral

The integral

A filtering problem with a small nonlinear term

In this paper, we consider a filtering problem where the signal X _t satisfies a slightly nonlinear stochastic differential equation and we want to obtain estimates of X _t. To this end, we decompose the nonlinearity with two techniques—a deterministic one and a stochastic one—and this leads us to two sequences of estimates which can be computed by solving finite dimensional equations. We want to compare their performances: we solve this problem in most cases if we restrict ourselves to sufficiently small times t and we give conditions which permit to conclude also for larger times