We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.

We introduce a new type of Self-Organizing Map (SOM) to navigate in the Semantic Space of large text collections. We propose a “hyperbolic SOM” (HSOM) based on a regular tesselation of the hyperbolic plane, which is a non-euclidean space characterized by constant negative gaussian curvature. The exponentially increasing size of a neighborhood around a point in hyperbolic space provides more fre...

For several hyperbolic knots, a relation between certain quantum invariants and the volume of their complements are discovered by R. Kashaev in [2]. In [6], it is shown that Kashaev’s invariants are specializations of the colored Jones polynomials. Kashaev used the saddle point method to obtain certain limit of invariants, and Y. Yokota proved that the equations to determine the saddle points c...

This note presents a comparative study of shock profiles in dissipative systems. Main assumption is that both hyperbolic and parabolic model are reducible to the same underlying equilibrium system when dissipative effects are neglected. It will be shown that the highest characteristic speed of equilibrium system determines the critical value of the shock speed for which downstream equilibrium s...

We derive an asymptotic formula for the number of pairs of consecutive fractions a′/q′ and a/q in the Farey sequence of order Q such that a/q, q/Q, and (Q − q′)/q) lie each in prescribed subintervals of the interval [0, 1]. We deduce the leading term in the asymptotic formula for ’the hyperbolic lattice point problem’ for the modular group PSL(2,Z), the number of images of a given point under t...

We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate to solving a hyperbolic type initial-boundary value problem. We discuss several reductions and specifications of the transformations as well as construction ...

The occurrence of liquid-vapor phase transition and the possible existence of a critical point in complex plasmas--systems that consist of charged micrograins in a neutralizing plasma background--is investigated theoretically. An analysis based on the consideration of the intergrain interaction potential suggests that under certain conditions systems near and at the critical point should be obs...

The critical behavior of electrolyte mixtures was studied using grand canonical Monte Carlo simulations. Mixtures consist of large multivalent macroions and small monovalent co- and counterions. The system can be viewed as a binary mixture of macroions (with their counterions) and salt (co- and counterion pair). The primitive model description was used, in which the ions are point charges with ...

generally, the evaluation and assessment critical condition of rill formation are useful for a better understanding of soil erosion processes. the inherence characteristics of soils, which have much dynamic variations on the hill-slopes and are affected by rill formation, are the soil critical shear stress and soil erodibility factors. this study aims to assess experimental rill incision thresh...

Critical slowing down of the relaxation of the order parameter has phenomenological consequences in early universe cosmology and in ultrarelativistic heavy ion collisions. We study the relaxation rate of long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transit...