We obtain a Stone type theorem under the frame of Hilbert C*-module, such that the classical Stone theorem is our special case.
The famous Zalcman–Pang lemma deduces many normality criteria for family of holomorphic functions related with differential polynomials of one complex variable. In this paper, we extend the Zalcman–Pang lemma to the case of high dimension and obtain the normality criteria for family of holomorphic functions of several complex variables related with partial derevatives
such that 
and 
, then G is called a central extension of N by H. In this paper, we classify all groups which are central extensions of N by H, where N is an elementray abelian p-group of order p2 and H is an inner abelian p-group.
In this note, the notion of generalized extension closure of a category is introduced, as a natural generalization of classic extension closure. In particular, we characterize the generalized extension closure of the categories of Nice modules, quasi- Koszul modules and Koszul modules in detail.
For the Newtonian 4-body problems with equal masses, we give a new simple proof for the existence of the hip-hop non-collision and nonplanar periodic solution, where we used the lower bound estimates of Zhang and Zhou on the Lagrangian action on the symmetrical generalized solutions for Newtonian N-body problems.
In this paper, we show the existence of at least one nontrivial solutions for Robin boundary value problems without the P.S. condition, by using minimax methods.
be a real coefficient algebraic polynomial of order r with real roots. Then 
is called to be the differential operator determined by Pr(x), where 
and I is the identical operator. The class 
concerned in this paper is consisted of functions f ∈ Lp(T) whose (r -1)-st derivative is absolutely continuous on T = [-π, π], r-th derivative belongs to Lp(T) and satisfies ||Pr(D)f||p≤1. When Pr(D)=Dr, is the usual Sobolev class 
. In the present paper, the relative n-widths of 
and 
in Lq(T) metric are studied, and the asymptotic estimates of 
and 
are obtained. In our results, we removed the self-conjugate condition of the differential operator considered in Yang Lianhong and Liu Yongping's paper. Furthermore, we consider the periodic convolution classes 
, p = 1 and ∞, the convolution kernels of which are the periodization of PF densities. By the analysis of the kernels, we obtain the asymptotic estimates of 
, p = 1 and ∞.
In this paper, we will investigateMultivariate Riesz Multiwavelet Bases with short support in (L2(Rs))r×1, which have applications in many areas, such as image processing, computer graphics and numerical algorithms. We characterize an algorithm to derive Riesz bases from refinable function vectors. Several other important results about Riesz wavelet bases in (L2(Rs))r×1 are also given.
is a parameter, a∈C[0,1] changes sign, f:[0,1]×→ is Ck function, k≥2, and f(t,0)=0,t∈[0,1].
), where is a prime w-ideal of R.
Computing the Cartan invariant is an important subject in modular representation theories of finite groups. In this paper, using some results from representations of algebraic groups, we obtain the Cartan invariant matrix for the finite symplectic group Sp(4,3).
In this paper, some common fixed points of a pair of self mappings satisfying a Lipschitz type conditions in cone metric space or metric space are proven. The results are more general than the known fixed point theorem of contractive type mappings. Some examples are given, which show that the mappings satisfy the conditions in this paper but cannot satisfy the general contractive type conditions.
The aim of this paper is to study the boundedness of singular integrals and commutators of a singular integral with a BMO function in the Morrey space associated with the Heisenberg group, and give an application to the regularity of weak solutions in the Morrey space for the divergence equation with discontinuous coefficients.
,the is obtained under the condition that the nonlinear term is super-linear or sub-linear, or the nonlinear term is decomposed into super-linear and sub-linear, which imposed some known results.
This paper provides a geometric perspective to study the weighted difference substitutions and introduces the concept of convergence of the sequence of substitution sets. Then it proves the convergence of the sequence of the successive weighted difference substitution sets, from which it is strictly proved that the sequence of the successive weighted difference substitution sets of a positive definite form is positively terminating. Finally, an algorithm for deciding an indefinite form with a counter-example is proposed.
By means of an action of a semigroup on another, we define a new concept called a semigroup with multiplication by scalars or a G-semigroup. This concept and some fundamental results about it are applied to matrix semigroups so that the Gsemigroup of matrices are defined. If S is a matrix semigroup over a field F and G is a multiplicative subsemigroup of F, then we define an action of G on S naturally by the usual multiplication by the scalars which induces a new matrix semigroup which we call the adjoint semigroup of S and denote by [S]. We investigate the relationship between a matrix semigroup and its adjoint semigroup, obtain the following results: under certain conditions, S is a regular (simple, orthodox, inverse, Clifford) semigroup (group) if and only if so is [S]. At last, we characterize the nilpotency and unipotency of the adjoint semigroup of a matrix semigroup and give some necessary and sufficient conditions.
In this paper, some sufficient conditions for a Drazin invertible operator to be still Drazin invertible under a perturbation are established. The expression for the Drazin inverse of the perturbed operator is derived. Moreover, based on the expression, the bound of the relative error is developed.
In this paper, we first investigate method of constructing self-adjoint operators. Then, based on the method, the self-adjoint perturbation of spectra of a class of upper triangular operator matrices is obtained. It can be seen that the self-adjoint perturbation of spectra contains the general perturbation of spectra. Moreover, an interesting example shows that this kind of inclusion may be proper. As an application, these results are developed to infinite dimensional Hamiltonian operators.
The author gives a Mazur–Ulam theorem in non-Archimedean strictly convex 2-normed spaces. She also studies the existence and uniqueness of the best approximation in real linear 2-normed spaces.
In this paper, a new parallel iterative algorithm for two finite families of uniformly L-Lipschitzian mappings is introduced. By using the iterative algorithm, under suitable conditions, some strong convergence theorems to approximating a common fixed point for two finite families of uniformly L-Lipschitzian mappings in the framework of Banach spaces are proved. The results presented in the paper are new which improve and extend the recent results of several authors.
and 
, where 
, with exponents pi, si and weight w satisfying some special conditions. Furthermore, we give concrete estimates of C and K.
