A new characterization of for countable spectra of (LB)-spaces

The derived projective limit functor Proj¹ is a very useful tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations).

We provide a new characterization for vanishing Proj¹ on projective spectra of (LB)-spaces which improves a classical result of V. P. Palamodov and V. S. Retakh.

     

The boundary layer solutions of the interface problem considering the strain gradient

According to the classical elastic theory, there is always a discontinuity of rotation angle on the interface between different materials. This illogic result can be overcome by the strain gradient plasticity theory. In the light of this theory, there is a group of boundary layer solutions near the interface, which have made important adjustment of the classical results. This project is supported by National Natural Science Foundation of China (19891180).     

A parametric view on the Mangasarian–Fromovitz constraint qualification

The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers. Received May 8, 1995 / Revised version received February 12, 1998 Published online February 25, 1999     

On a certain property of the BurkillSCP-integral

We establish a necessary condition for theSCP-integrability of a function and use it to construct an example of a function possessing a continuousSCP-majorant andSCP-minorant on a closed interval, but nonintegrable over this interval in the sense of theSCP-integral. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 599–606, April, 1999.     

The boundary element method applied to elastic contact problems with friction

In the current paper the boundary integral equations (BIE) for elastic contact problems with friction are derived from the incremental virtual work principle. After introducing contact conditions of adhesion and slip into BIE all variants on boundary are made to discretize by quadratic isoparametric boundary element. In the current paper not only an auto-increment loading law is presented but also the iterative calculation laws for open, slip and adhesion condition are given. The results of numerical examples are satisfactory.     

The effect of repulsive interactions on Bose-Einstein condensation

One-dimensional Bose gases that interact via a repulsive two-body interaction and show Bose-Einstein condensation at the free level are studied. It is shown that the introduction of this interaction, however small, destroys the condensate. It is also shown that the free energy of an interacting Bose gas does not depend on the boundary conditions(including attractive boundary conditions) in the van der Waals limit.     

Synthesis of Nitroalkanes from Alkylhalides under Mild and Nonaqueous Conditions by Using Polymer Supported Nitrites

Alkyl halides are efficiently converted to their corresponding nitroalkanes under mild and nonaqueous conditions by using polymer supported nitrites. The polymeric reagent is regenerable.     

On a Class of Ordinary Differential Equations of Various Orders on a Graph

Mathematical Notes -     

Anode-Shape Determination with Allowance for Electrolyte Properties in Problems of Dimensional Electrochemical Machining of Metals

Based on the boundary-element technique, a method for determining the contour of an anode-workpiece with a prescribed shape of a cathode-tool is suggested for plane problems of dimensional electrochemical machining of metals. Within the scope of the assumptions made, the original problem is reduced to the problem of a fictitious flow of an ideal fluid with free surfaces. The allowance for the machining mode and electrolyte properties yields a nonlinear condition at the free surface.     

On Selfsimilar Jordan Curves on the Plane

We study the attractors of a finite system of planar contraction similarities S _j (j=1,...,n) satisfying the coupling condition: for a set {x ₀,...,x _n} of points and a binary vector (s ₁,...,s _n ), called the signature, the mapping S _j takes the pair {x ₀,x _n} either into the pair {x _j-1,x _j } (if s _j =0) or into the pair {x _j , x _j-1} (if s _j =1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis.