On the theory of vapor — Liquid — Crystal phase transitions

An approach is discussed which allows one to describe within the framework of the single model the aggregative states of a system of atoms obeying the Fermi statistics. A phase diagram is obtained containing both the critical point where the distinctions between the liquid and vapor vanish and the triple point where the liquid, vapor, and crystal are in equilibrium.     

Shape preservation regions for six-dimensional spaces

We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables, two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order that the space has shape preserving representations for curves. We describe the shape preserving regions for both families. To our friend Mariano Gasca on occasion of his 60th birthday Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

Pairwise Correlations in a Multicomponent Anisotropic Liquid

We investigate a multicomponent anisotropic liquid system. The first spatial moment of the direct correlation function is taken into account to obtain asymptotic expressions for the pairwise correlation functions. In this approximation, we obtain the pairwise correlation functions that describe the system behavior not only in the critical-state neighborhood but also in the noncritical domain. We show that the critical parameters for the anisotropic system differ from those for the isotropic system.     

Existence and multiplicity of solutions for a nonlinear Neumann problem

We consider a Neumann problem of the type -εΔu+F ^′(u(x))=0 in an open bounded subset Ω of R ⁿ , where F is a real function which has exactly k maximum points. Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them. Received: October 30, 1999 Published online: December 19, 2001     

Codiameters of 3‐connected 3‐domination critical graphs

A graph G is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3‐connected 3‐domination critical graph of order n. In this paper, we show that there is a path of length at least n?2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002     

Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ _c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca₃Rh₄Sn₁₃, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ _c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca₃Rh₄Sn₁₃ has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.     

第一临界情形下的三次系统局部结构的判断准则

讨论了第一临界情形下的平面三次系统高次奇点的局部拓朴结构，并给出利用多项式系数的判断准则。     

Stability of bars made of linear elastic materials with voids

Summary Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.