Adhesion in elastic-plastic spherical microcontact

An elastic-plastic adhesion model for a metallic deformable sphere pressed by a rigid flat is presented. Analytical dimensionless expressions for the local separation outside the contact area and for the adhesion force are provided covering a large range of interference values from a point contact to a fully plastic contact. Two main dimensionless parameters of the problem are identified and their effect on the adhesion is investigated. The significance of the adhesion in the elastic-plastic contact force balance is discussed and the regimes where adhesion is important or negligible are pointed out. A comparison of the present results with a previously published approximate elastic-plastic model shows substantial differences in the local separation and in the adhesion force.     

On Isotropic Points in K2SO4 Impurity Crystals

Optics and Spectroscopy - The temperature, spectral and baric dependences of birefringence Δni of potassium sulfate crystals doped with 1.7% of copper are studied. It is established that the...     

On quadratic scalarization of vector optimization problems in Banach spaces

We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar non-linear optimization problems can be by-turn approximated by quadratic minimization problems.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.