广义Ginzburg-Landau方程和Rangwala Rao方程的显式精确解

该文通过适当代换并结合假设待定法，求出了具高阶非线性项的Liénard方程a″(ξ)+la(ξ)+ma\+\{2p+1\}(ξ)+na\+\{4p+1\}(ξ)=0的三类精确解. 据此求出了广义Ginzburg Landau方程、Rangwala Rao方程及若干 导数schr〖AKo¨D〗dinger型方程的孤波解和三角函数型周期波解.     

Boolean algebras and uniform convergence of series

Several classical results on uniform convergence of unconditionally Cauchy series are generalized to weakly unconditionally Cauchy series. This uniform convergence is characterized through subalgebras and subfamilies of . A generalization of the Orlicz-Pettis theorem is also proved by mean of subalgebras of .     

Weakly Associated Prime Filtration

Let R be a (not necessarily Noetherian) commutative ring and let M be a (not necessarily finitely generated) R-module. We characterize the modules with only finitely many weakly associated primes as those modules M admitting a chain 0 = M ₀ M ₁ ... M _n = M of submodules together with prime ideals p₁, p₂,...,p _n such that the set of weakly associated primes of M _i /M _i-1 is equal to {p _i } for all 1 i n. Let M = gr_a(M) = _n0a ⁿ M/a ⁿ⁺¹ M be the corresponding graded module over the graded ring R = gr_a(R) = _n0a ⁿ /a ⁿ⁺¹. It is shown that the union of the set of weakly associated primes of.....     

Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups

Let X be a Banach space with a weak uniform normal structure and C a non–empty convexweakly compact subset of X. Under some suitable restriction, we prove that every asymptoticallyregular semigroup T = {T(t) : t ∈¸ S} of selfmappings on C satisfying

${\mathop {\lim \inf }\limits_{S \mathrel\backepsilon t \to \infty } }{\left| {{\left\| {T(t)} \right\|}} \right|} < {\text{WCS}}(X)$

has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and\({\left| {{\left\| {T(t)} \right\|}} \right|}\) is the exact Lipschitz constant of T(t).     

多目标规划弱较多有效解的充要条件

本文构造欧氏空间上的一个连续泛函，建立关于非凸锥H的分离定理，给出多目标规划弱较多有效解的充要条件．     

Regularity Results for the Generalized Beltrami System

Abstract For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class (1 < r < n). By changing the generalized Beltrami system into a class of a divergent elliptic system with nonhomogeneous items, we obtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolev class. Furthermore, we also establish a higher regularity of its weak solution if the regularity hypotheses of two characteristic matrices are improved. Supported by the National Natural Science Foundation of China (49805005) and by the research foundation of Northern Jiaotong University (2002SM061)     

QCM based sensor for detecting volumetric properties of liquids

We introduce a microacoustic sensor, which combines the quartz crystal microbalance, a liquid-filled cavity and an intermediate artificial layer with effective acoustic properties. Each of the three components fulfils a specific task. The quartz vibrates in its thickness shear mode and acts as source and detector of shear waves, which penetrate the intermediate artificial layer and excite a resonance in the liquid-filled cavity. Both the piezoelectric transducer and the liquid-filled cavity are high-Q resonators with well-adjusted resonance frequencies very close to each other. The intermediate artificial layer couples the two resonators in a distinct manner via control of the propagation of acoustic waves between the quartz crystal and the liquid-filled cavity layer. The origin of the sensor signal is a change of the resonance frequency of the liquid-filled cavity caused by variations of acoustic properties of the liquid analyte inside the cavity, first of all speed of sound. This resonance appears as second resonance peak in the admittance spectrum of the quartz crystal.     

Banach space properties sufficient for normal structure

In this paper we establish lower bounds for the weakly convergent sequence coefficient WCS(X) of a Banach space X, in terms of some well known moduli and coefficients. By mean of these bounds we identify several properties, of geometrical nature, which imply normal structure. We show that these properties are strictly more general than other previously known sufficient conditions for normal structure.