Baric changes in refractive indices of K<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> crystals

The influence of uniaxial pressure applied along the principal crystallophysical directions on the dispersion and temperature dependences of the refractive indices n _i of K₂ZnCl₄ crystals has been investigated. The n _i values are found to be fairly sensitive to uniaxial pressure, whereas an uniaxial stress does not change the behavior of the dispersion and temperature dependences of n _i . The baric changes in n _i have been studied. The electronic polarizability α _i , refractions R, and parameters of UV oscillators (λ_0i , B _1i ) of mechanically deformed K₂ZnCl₄ crystals have been calculated. The contributions of UV and IR oscillators to n _i (λ) have been estimated for different temperatures, spectral regions, and stresses. A significant baric shift of the points of the paraelectric phase-incommensurate phase-commensurate phase transitions to different temperature ranges, depending on the direction of pressure application, is found; this shift is due to the effect of uniaxial stress on the K₂ZnCl₄ crystal structure.     

The Features of the Characteristics of Forced Whispering-Gallery Modes in an Ellipsoidal Dielectric Resonator with Small Eccentricity

We study experimentally the whispering-gallery modes excited in a dielectric ellipsoidal resonator by a lumped-parameter radiation source and through distributed coupling of a dielectric resonant structure with a dielectric waveguide. Peculiarities of the formation of mode fields and spectra for different mutual locations of the resonator and the exciting element are pointed out. The influence of the derivative of the ellipsoid-surface curvature on the behavior of the energy characteristics of forced modes is found.     

On weak compactness of bounded sets in Banach and locally convex spaces

We investigate the compactness of one class of bounded subsets in Banach and locally convex spaces. We obtain a generalization of the Banach-Alaoglu theorem to a class of subsets that are not polars of convex balanced neighborhoods of zero. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp 731–739, June. 2000.     

Electron-positron annihilation and speculations on the renormalization group of strong interactions

Implications of recent measurements of the electron-positron annihilation cross section for other deep inelastic processes are discussed within the context of conventional field theory and conventional current algebra. Canonical scaling laws for deep inelastic electron and neutrino scattering are predicted to fail for $\text{Q}{}^2\text{? 15–25 GeV}{}^2$. Other easily measured consequences of a violation of scale invariance at short distances are discussed. Comments and speculations concerning the renormalization group of strong interactions are made.     

Chiral symmetry restoration in baryon rich environments

Chiral symmetry restoration in an environment rich in baryons is studied by computer simulation methods in SU(2) and SU(3) gauge theories in the quenched approximation. The basic theory of symmetry restoration as a function of chemical potential is illusstrated and the implementation of the ideas on a lattice is made explicit. A simple mean field model is presented to guide one's expectations. The second order conjugate-gradient iterative method and the pseudo-fermion Monte Carlo procedure are convergent methods of calculating the fermion propagator in an environment rich in baryons. Computer simulations of SU(3) gauge theory show an abrupt chiral symmetry restoring transition and the critical chemical potential and induced baryon density are estimated crudely. A smoother transition is observed for the color group SU(2).     

Twisted reduced chiral models at large N

We construct and study the twisted reduced SU(N)×SU(N) chiral model in two dimensions. The equivalence of the reduced model to the field theory is established by examining the Dyson-Schwinger equations and weak coupling perturbation expansion. We evaluate the internal energy and two-point correlation function by extensive Monte Carlo simulations for N=12, 24 and 36. We find a non-analyticity near the weak coupling edge of the crossover region in which the system flips back and forth between the “normal” state and one characterised by a strongly disordered correlation function.     

S-convergence in the theory of homogenization of problems of optimal control

We give a definition of homogenized problems of optimal control in terms of variational S-limits and establish sufficient conditions for a family of problems of optimal control described by nonlinear operator relations to be compact with respect to the operation of homogenization.