微分算子扰动问题的值域研究

本文研究作用在C2周期函数空间上的微分算子u→u″ g(u) ,其中g(u)为连续有界函数.我们将证明上述微分算子的值域限制在周期函数空间的“超曲面”中.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Exceptional set of a representation with fractional powers

We prove that for any given c, 1 < c < 17/11, almost all natural numbers are representable in the form [x ^c] + [p ^c], where x is a natural number and p is a prime.     

Commutators, C0-semigroups and resolvent estimates

We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C₀-semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator [H,iA] is not comparable to H. The applications include the spectral theory of zero mass quantum field models.     

Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

Little Grothendieck's theorem for sublinear operators

Let SB(X,Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider π₂(X,Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K),H) is in π₂(C(K),H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open.     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

每个算子都是两个强不可约算子的和

本文证明了可分无穷维 Hilbert空间上每个有界线性算子均可写成两个强不可约算子之和 .这回答了文献 [9]中提出一个公开问题     

Finite-Dimensional Approximations for Scattering Theory Operators in the Wave-Packet Representation

We consider some types of packet discretization for continuous spectra in quantum scattering problems. As we previously showed, this discretization leads to a convenient finite-dimensional (i.e., matrix) approximation for integral operators in the scattering theory and allows reducing the solution of singular integral equations connected with the scattering theory to some suitable purely algebraic equations on an analytic basis. All singularities are explicitly singled out. Our primary emphasis is on realizing the method practically.