Critical behavior of some measure-valued processes

The so-called weighted occupation time process Y associated with some critical measur-evalued branching process is considered. Y has absolutely continuous states provided that the dimension of the phase space is small enough. The corresponding density functions form a random process η. In some cases there exists a critical dimension such that η. considered in the space-time diagram, is a self-similar random non-negative field. This self-similar field is infinitely divisible but not stable.     

A note on a generalization of Macdonald’s identities forA l andB l

Let η(q) denote the Dedekind’s η-function. Macdonald obtained identities for η(q) ^{dim g} where g is complex simple finite dimensional Lie algebra. The aim of this paper is to obtain generalization of the above identities in the case of g=A _l andB _l. We also get new formulas for the generating functions of the Ramanujan’s τ-function and ?_α-functions.     

具有不变凸多目标规划的η-近似方法

建立了与多目标规划问题等价的η-近似多目标规划问题;对η-近似多目标规划问题引入η-拉格朗日函数和η-鞍点,并给出了η-鞍点与原多目标规划问题有效解之间的关系。     

Agard’s η-distortion function and Schottky’s theorem

The monotoneity properties of certain functions defined in terms of the η-distortion function ηκ(t) in quasiconformal theory are studied and asymptotically sharp bounds are obtained for ηκ(t), thus proving some properties of the upper bound functionK(t, r) in Schottky’s theorem on analytic functions and improving the known explicit bounds forK (t, r).     

Stability of equilibrium solution to inhomogeneous heat equation under a 3-point boundary condition

We consider a one-dimensional heat equation with inhomogeneous term, satisfying three-point boundary conditions, such that the temperature at the end is controlled by a sensor at the point η. We show that the integral solution, in the space of continuous functions satisfying the boundary values, converges to the equilibrium solution. This answers a question posed for nonlinear Laplacians, but in the linear case only.     

Gauss legendre quadrature formulas over a tetrahedron

In this article we consider the Gauss Legendre Quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 ≤ x, y, z ≤ 1, x + y + z ≤ 1} in the Cartesian three‐dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2‐cube: {(ξ, η, ζ)| ? 1 ≤ ζ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points. The effectiveness of the formulas is demonstrated by applying them to the integration of three nonpolynomial, three polynomial functions and to the evaluation of integrals for element stiffness matrices in linear three‐dimensional elasticity. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Multichromatic numbers,star chromatic numbers and Kneser graphs

We investigate the relation between the multichromatic number (discussed by Stahl and by Hilton, Rado and Scott) and the star chromatic number (introduced by Vince) of a graph. Denoting these by χ* and η*, the work of the above authors shows that χ*(G) = η*(G) if G is bipartite, an odd cycle or a complete graph. We show that χ*(G) ≤ η*(G) for any finite simple graph G. We consider the Kneser graphs , for which χ* = m/n and η*(G)/χ*(G) is unbounded above. We investigate particular classes of these graphs and show that η* = 3 and η* = 4; (n ≥ 1), and η* = m - 2; (m ≥ 4). © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 137–145, 1997     

Geodesic G-invex sets and semistrictly geodesic η-preinvex functions

In this article, we introduce semistrictly geodesic η-preinvex functions on Riemannian manifolds, geodesic G-invex sets and study their properties. Our results extend and improve the results of Yang and Li [X. Yang and D. Li, Semistrictly preinvex functions, J. Math. Anal. Appl. 258 (2001), pp. 287–308]. Example is constructed in support of our defnition.     

On the Nonseparable Subspaces of J(η) and C([1, η])

Let η be a regular cardinal. It is proved, among other things, that: (i) if J(η) is the corresponding long James space, then every closed subspace Y ⊆ J(η), with Dens (Y) = η, has a copy of 𝓁₂(η) complemented in J(η); (ii) if Y is a closed subspace of the space of continuous functions C([1, η]), with Dens (Y) = η, then Y has a copy of c₀(η) complemented in C([1, η]). In particular, every nonseparable closed subspace of J(ω₁) (resp. C([1, ω₁])) contains a complemented copy of 𝓁₂(ω₁) (resp.c₀(ω₁)). As consequence, we give examples (J(ω₁), C([1, ω₁]), C(V), V being the “long segment”) of Banach spaces X with the hereditary density property (HDP) (i.e., for every subspace Y ⊆ X we have that Dens (Y) = w*–Dens (Y*)), in spite of these spaces are not weakly Lindelof determined (WLD).     

含极大η-单调算子的广义非线性混合似变分包含组的扰动算法和稳定性

研究了一类含极大η-单调算子的广义非线性混合似变分包含组.依据不动点理论和极大η-单调算子的预解算子技巧,在Hilbert空间中提出了一种求这类变分不等式组的逼近解的扰动迭代算法,并证明了这类算法的收敛性和稳定性.所得结果是新的,并推广和统一了近期文献中的一些相关结论.     

给定匹配数和独立数时图零度的上界

设G是一个有n个点的简单图,分别记η(G),m(G)和α(G)为图G的零度、匹配数和独立数.设θ(G)是一个非负整数,定义为使图G成为二部图至少需要从G的边集中删去的边数.本文运用二部划分运算,证明了对于有n个点并且不含有圈长为2的倍数的圈为子图的简单图G,有η(G)≤n-2m(G)+20(G)和η(G)≤2α(G)+2θ(G)-n.     

Characterization of Almost η-Ricci–Yamabe Soliton and Gradient Almost η-Ricci–Yamabe Soliton on Almost Kenmotsu Manifolds

Acta Mathematica Sinica, English Series - The prime object in this article is to study an almost η-Ricci–Yamabe soliton and gradient almost η-Ricci–Yamabe soliton within the...     

Some Limit Theorems for the Cell Load in the Generalized Allocation Scheme

Lithuanian Mathematical Journal - In the paper, we consider the generalized allocation scheme and study the asymptotic behaviors of the extreme η(N?s), where η(N?s) denotes...     

一个局部带优先权的最大多物资网络流问题

给出一个局部带优先权的最大多物资网络流问题(MMFP-LPRI),证明它的解存在,并给出其η-松弛解的定义.通过做辅助网络,并运用程丛电等根据Korte和Vygen于2000年在Young,Garg和K(o|¨)nemann等工作的基础上给出的求最大多种物资网络流问题的ε-近似解的多项式方案设计的一个算法作为子程序进行二分收索建立了一个求所给问题的η-松弛解的拟多项式算法.最后,进行算法分析,证明了所设计的算法的输出结果确实是MMFP-LPRT的一个η-松弛解.     

关于凸体覆盖的Hadwiger猜想的两个等价形式

令K是一个内部(记作intK)包含原点o的凸体,bdK为其边界,m为覆盖K所需的intK的平移的最小个数.本文证明,存在正实数η和含于η(bdK)的m元点集C1使得C1+int K覆盖K;存在正实数η′、实数γ∈(0,1)和含于η′(bd K)的m元点集C2使得C2+γK覆盖K.基于这两个事实,本文得到关于凸体覆盖的Hadwiger猜想的两个等价形式.本文还引入一个可以替代宗传明提出的攻克Hadwiger猜想的数量方案中的γm(K)的新泛函.     

一个修正的Benjamin方程的行波解的存在性

运用集中紧性和Nehari约束方法,证明了对任意L〉0和c〉0,修正的Benjamin方程 ηt＋（f（η））x＋LHηxx＋ηxxx=0,x,t／∈R 有一个孤立波η（x,t）=u（x-ct）.     

High-precision evaluation of the regular and irregular Coulomb wavefunctions

Steed's method for the calculation of both the regular and irregular Coulomb functions for positive energy, F_λ(η,x),G_λ(η,x), and their derivatives, is extended into the region of very high precision (～ 30S). Other methods in general use result in less than one half of this precision. The test-case results of Strecok and Gregory for G₀(η,x) and G′₀(η,x) to 22S over a restricted range of parameter values close to the transition line are almost completely verified. Limiting forms of the functions are given for x < x_TP (the turning point) and an heuristic estimate of the errors in the functions is obtained. The method is valid for real η, including η = 0 (i.e. the spherical Bessel functions), and for real λ > ?1; thus cylindrical Bessel functions, Airy functions, and even the real Gamma function can also be obtained to high accuracy. For each of these, in the oscillating region (where appropriate) results are available to within about 2S of the machine accuracy; in the monotonic region the loss of accuracy is quantitatively predictable.     

New proximal algorithms for a class of (A,η)-accretive variational inclusion problems with non-accretive set-valued mappings

In this work, by using Xu’s inequality, Nalder’s results, the notion of(A,η)-accretive mappings and the new resolvent operator technique associated with(A, η)- accretive mappings due to Lan et al., we study the existence of solutions for a new class of(A, η)-accretive variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.     

Decomposition of spaces of modular forms

Structural theorems for spaces of modular forms with respect to congruence subgroups are proved. The Dedekind η-function plays an important role in our study.