Boundary Value Problems with a Parameter of Differential Equations with Deviated Arguments

The aim of the present paper is to study boundary value problems with a parameter of differential equations with deviated arguments. The existence, uniqueness and continuous dependence of the solution on the right-hand side of our problem are considered.     

A class of B-(p,r)-invex functions and mathematical programming

Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems.     

Molecular dynamics simulation of phase transition in AgNO3

Structural phase transition in AgNO₃ at high temperature is simulated by molecular dynamics. The simulations are based on the potentials calculated from the Gordon-Kim modified electron-gas formalism extended to molecular ionic crystals. AgNO₃ transforms into rhombohedral structure at high temperature and the phase transition is associated with the rotations of the NO₃ ions and displacements of the NO₃ and Ag ions.     

Ueber den Einfluß des Filtrierens auf Hydrosole

Ohne ZusammenfassungVorgelegt der Akad. d. Wiss. in Krakau in der Sitzung vom 6. Mai 1918.Am Schlusse erachte ich es als meine Pflicht, Herrn Prof. Godlewski sowohl für die Anregung zur vorliegenden Arbeit als auch für wohlwollende Weisungen und Ratschläge im Laufe der Untersuchungen meinen aufrichtigen Dank auszusprechen.     

Spectral Gap for Stable Process on Convex Planar Double Symmetric Domains

We study the semigroup of the symmetric α-stable process in bounded domains in R ². We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap.