The least square nucleolus is a general nucleolus

This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the least square nucleolus is a general nucleolus (Maschler et al. (1992)). Received: December 1998/Revised version: July 1999     

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.     

《泛函分析》中两个定理的教学与应用

本文讨论《泛函分析》中 Schauder不动点定理和 Arzela-Ascoli定理的教学方法并把它们用于互助生态模型得到两物种共存的一个充分条件 .     

一个具有时滞和功能反应的非自治阶段结构的捕食模型

研究一个具有时滞和功能反应的非自治阶段结构的捕食模型,其中食饵种群分两个阶段——幼年和成年,且捕食种群只捕成年食饵.通过利用微分不等式、比较定理和构造适当的Lyapunov泛函,得到该模型的永久持续生存和绝灭的充分条件,同时也得到了周期系统存在唯一全局渐近稳定的周期解的充分条件.     

Two phase algorithms for the bi-objective assignment problem

In this paper, we present several algorithms for the bi-objective assignment problem. The algorithms are based on the two phase method, which is a general technique to solve multi-objective combinatorial optimisation (MOCO) problems.     

一类动态规划的解法及其在Turbo码解码中的应用

研究一类多阶段动态规划问题,给出了求最优解的方法.将这种多阶段动态规划应用于Turbo译码中,不仅可以减少运算量,还可以避免传统的Turbo译码算法需要进行指数运算以及其随着迭代次数的增加容易出现的数据溢出问题,因此是一种十分有效的方法,是对系统工程理论应用领域的拓宽.     

A sufficient condition for the existence of limit values of solutions of an elliptic equation on the boundary

We find a sufficient condition for the existence of a limit value of an elliptic equation solution on the domain boundary. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 436–449, December, 2008.     

ABOUT HYBRID BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DISCRETE DELAYS

In this paper, hybrid bidirectional associative memory neural networks with discrete delays is considered. By ingeniously importing real parameters di > 0(i = 1,2,···,n) which can be adjusted, we establish some new sufficient conditions for the dynamical characteristics of hybrid bidirectional associative memory neural networks with discrete delays by the method of variation of parameters and some analysis techniques. Our results generalize and improve the related results in [10,11]. Our work is significant...     

Thallium(III) coordination compounds: chemical information from 205Tl NMR longitudinal relaxation times

²⁰⁵Tl longitudinal relaxation rate measurements were performed on several thallium(III) complexes with the composition Tl(OH)_n(H₂O)_6?n^(3?n)+ (n = 1,2), Tl(Cl)_n(H₂O)_m?n^(3?n)+, Tl(Br)_n(H₂O)_m?n^(3?n)+ (m = 6 for n = 1–2, m = 5 for n = 3, m = 4 for n = 4), Tl(CN)_n(H₂O)_m?n^(3?n)+ (m = 6 for n = 1–2, m = 4 for n = 3–4) in aqueous solution, at different magnetic fields and temperatures. ¹³C and ²D isotopic labelling and ¹H decoupling experiments showed that the contribution of the dipolar relaxation path is negligible. The less symmetric lower complexes (n < 4) had faster relaxation rate dominantly via chemical shift anisotropy contribution which depended on the applied magnetic field: T₁ values are between 20 and 100 ms at 9.4 T and the shift anisotropy is Δσ = 1000–2000 ppm. The tetrahedral complexes, n = 4, relax slower; their T₁ is longer than 1 s and the spin–rotation mechanism is probably the dominant relaxation path as showed by a temperature dependence study. In the case of the TlCl₄^? complex, presumably a trace amount of TlCl₅^2? causes a large CSA contribution, 300 ppm. Since the geometry and the bond length for the complexes in solution are known from EXAFS data, it was possible to establish a correlation between the CSA parameter and the symmetry of the complexes. The relaxation behaviour of the Tl–bromo complexes is not in accordance with any known relaxation mechanism. Copyright © 2002 John Wiley & Sons, Ltd.