Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

Certain bilateral generating relations for generalized hypergeometric functions

Recently, we introduced a class of generalized hypergeometric functionsI n:(b _q)/α:(a _p) (x, w) by using a difference operator Δ _x,w , where . In this paper an attempt has been made to obtain some bilateral generating relations associated withI _n ^ga (x, w). Each result is followed by its applications to the classical orthogonal polynomials.     

A characterization ofL n (q) by the normalizers' orders of their sylow subgroups

LetG be a finite group. If for every primer, whereR ₁ Syl _r G andR ₂ Syl _r (L _n (q)), thenG L _n (q).     

Boundedness of solutions of nonlinear systems of differential equations

We first give an example to illustrate that the results in [12] concerning the boundedness of solutions of nonlinear oscillatory equations are not true. And then we obtain sufficient or necessary conditions for the boundedness of solutions of the nonlinear system of differential equations

Characterizations of generalized Hermite and sieved ultraspherical polynomials

A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.

     

Normal subgroups of

We classify the normal subgroups of of index less than 960; they are all congruence subgroups.

     

Generalized evaluation subgroups of product spaces relative to a factor

For any -complexes and , we show that . We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.

     

Crumpled laminations and manifolds of nonfinite type

Using a group-theoretic construction due to Bestvina and Brady, we build -manifolds which admit partitions into closed, connected -manifolds but which do not have finite homotopy type.

     

Carleson measure characterization of Bloch functions

We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized Carleson measure;f B ₀ if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized vanishing Carleson measure, whereD f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province.     

纤维素基磁性聚偕胺肟树脂的研究——锌副族金属离子在树脂上的吸附

研究了Ｚｎ２＋、Ｃｄ２＋、和Ｈｇ２＋离子在碱式纤维素基磁性聚偕胺肟树脂（ＢＭＡＯ）上的吸附动力学。结果表明，吸附速度受粒内扩散所控制。测得粒内扩散系数分别是１．２２×１０－４、２．４２×１０－４和３．９０×１０－４ｃｍ２·ｓ－１；Ｈｇ２＋离子在树脂上的吸附行为符合Ｆｒｅｕｎｄｌｉｃｈ和Ｌａｎｇｍｕｉｒ等温吸附方程；浓集因数随Ｈｇ２＋离子浓度降低而上升，有利于从稀溶液中除去Ｈｇ２＋离子。将树脂加至Ｚｎ２＋、Ｃｄ２＋或Ｈｇ２＋离子浓度为５０ｐｐｍ的溶液中，离子去除率分别是９６．１、９９．９和９９．３％。