IR finite one-loop box scalar integral with massless internal lines

The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments. Received: 31 January 2002 / Published online: 26 April 2002     

An expansion in the exponent for compound binomial approximations

The purpose of this paper is two-fold. First, we introduce a new asymptotic expansion in the exponent for the compound binomial approximation of the generalized Poisson binomial distribution. The dependence of its accuracy on the symmetry and shifting of distributions is investigated. Second, for compound binomial and compound Poisson distributions, we present new smoothness estimates, some of which contain explicit constants. Finally, the ideas used in this paper enable us to prove new precise bounds in the compound Poisson approximation. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 1, pp. 67–110, January–March, 2006.     

Moment problem for effect algebras

We present a solution to the moment problem for effect algebras, concerning mean values of all powers of an observable concentrated on the interval [0, 1] for states from a convex set. We give a solution for particular examples, e.g., for the set of all effect operators. We examine how this problem is related to a socalled E-property. Finally, we give a solution for observables studied in the operational approach to physical theories.     

Influence of solute mobility on dislocation motion I. Basic model

Dislocation motion in the real lattice of alloys is highly complex. In a certain temperature range the dynamic strain ageing phenomena have been reported. In this paper the influence of mobile solute atoms (as obstacles) on the motion of dislocation is analysed. Both processes are assumed to be thermally activated. A new model based on this assumption is proposed. The dislocation velocity and the friction stress (due to solute-dislocation interactions) are calculated. A change in the friction stress caused by solute mobility is discussed.     

Use of new composite materials for the determination of Cu, Cd, Mo, As, and Sb in biological samples by radiochemical neutron activation analysis

Summary  Vezetéknév     

Approximation by a binomial type law

Kaunas Academy of Agriculture, 4324 Noreikiškés, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 221–228, April–June, 1992.     

The world according to Rényi: thermodynamics of multifractal systems

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs-Shannon entropy into more general framework—Rényi’s information entropy. We address the renormalization issue for Rényi’s entropy on (multi)fractal sets and consequently show how Rényi’s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Rényi’s information entropy and thermodynamics of multifractals. Important issues such as Rényi’s entropy versus Tsallis-Havrda-Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed.