Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable the relativistic dynamic equation for systems with an invariant plane becomes a non-linear analytic equation in one complex variable. We obtained explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock hypothesis and using these solutions, we were able to describe the space-time transformations between two uniformly accelerated and rotating systems. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Additivity of melting curves

Universality of some melting indicators, in the context of two successful models of the solid and the liquid, gives rise to simple semi-empirical melting equations that describe additivity of melting curves. Computer inverse power melting results are used to reproduce the melting characteristics of argon to a good accuracy.     

Super-Resolved Raman Spectra of Toluene and Toluene–Chlorobenzene Mixture

In this paper, we present a method for “super-resolved” Raman spectroscopy which improves the resolution of obtained spectra. Experimental investigations were carried out on the spectra of toluene and a toluene–chlorobenzene mixture. A tunable Fabry–Perot filter is added to the detection channel and by measuring the spectra for several states of the filter a spectrum of higher resolution can be obtained after a decoding process. We demonstrate both a reduced linewidth in the pure toluene spectra and partial separation of the two overlapping peaks in the mixture.     

The Fermat–Torricelli Problem, Part I: A Discrete Gradient-Method Approach

We give a discrete geometric (differential-free) proof of the theorem underlying the solution of the well known Fermat–Torricelli problem, referring to the unique point having minimal distance sum to a given finite set of non-collinear points in d-dimensional space. Further on, we extend this problem to the case that one of the given points is replaced by an affine flat, and we give also a partial result for the case where all given points are replaced by affine flats (of various dimensions), with illustrative applications of these theorems.     

Error bounds for asymptotic approximations of the partition function

We consider Markovian queueing models with a finite number of states and a product form solution for its steady state probability distribution. Starting from the integral representation for the partition function in complex space we construct error bounds for its asymptotic expansion obtained by the saddle point method. The derivation of error bounds is based on an idea by Olver applicable to integral transforms with an exponentially decaying kernel. The bounds are expressed in terms of the supremum of a certain function and are asymptotic to the absolute value of the first neglected term in the expansion as the large parameter approaches infinity. The application of these error bounds is illustrated for two classes of queueing models: loss systems and single chain closed queueing networks.     

On the isoperimetric inequalities for Reuleaux polygons

We give a unifying approach to the Blaschke-Lebesgue Theorem and the Firey-Sallee Theorem on Reuleaux polygons in the Euclidean plane.     

Applications of Galerkin's method to bifurcation and two-point boundary value problems

The modeling of physical systems inherently involves constructing a mathematical approximation from observable data and/or a priori assumptions. This study refines some recent work on causal interpolation and causal approximation as system modeling techniques. Sufficient conditions for causal interpolators to approximate continuous causal systems are established. State realizations for minimal norm causal interpolators are also established.     

The isometries ofC p n,m intoC P

We characterize the isometries ofC _p ^n,m intoC _P (l≦p<∞, p ≠ 2, 2≦n,m). In particular, we find that ifX ?C _P is isometric toC _p ^n,m , then there exists a contractive projection from C_p ontoX.