In Search of Alternatives to Higgs Fields

Field equations of the S² sigma model (“the A3 model”) with spontaneously broken Z(2) symmetry are presented for (D+1)-dimensional space–time. The A3 model is an extension of the sine-Gordon equation (SGE) and supports kink-like U(1) charged solitons which are a generalization of neutral solitons of the SGE. The natural question arises — is the A3 model completely integrable in (1+1)-dimensional space–time? The Lorentz-invariant scalar A3 field can be viewed as a promising alternative to the Higgs field.     

Response to high acidity and basicity at a platinum electrode in chronopotentiometry

A simple and rapid method is developed to determine the high acidity and the basicity of solutions by chronopotentiometry with a platinum working electrode. The acidity range from 5.0 mol/l H⁺ to 1.0 mol/l OH⁻ can be measured by the adjustment of deposition potential and time. The response mechanism to acidity and basicity has been explored. The transition potential plateau in chronopotentiograms is caused from the oxidation of hydrogen adsorbed on electrode surface.     

Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

Template atom transfer radical polymerization of a diaminopyrimidine‐derivatized monomer in the presence of a uracil‐containing polymer

Uracil‐derivatized monomer 6‐undecyl‐1‐(4‐vinylbenzyl)uracil and diaminopyrimidine‐derivatized monomer 2,6‐dioctanoylamido‐4‐methacryloyloxypyrimidine (DMP) were synthesized and polymerized by atom transfer radical polymerization (ATRP). A well‐defined, highly soluble, uracil‐containing polymer, poly[6‐undecyl‐1‐(4‐vinylbenzyl)uracil] (PUVU), was prepared in dioxane at 90 °C with CuBr/1,1,4,7,10,10‐hexamethyltriethylenetetramine as the catalyst and methyl α‐bromophenylacetate as the initiator. PUVU was further used as a template for the ATRP of DMP. The enhanced apparent rate constant of the DMP polymerization in the presence of PUVU indicated that the ATRP of DMP occurred along the PUVU template. The template polymerization produced a stable and insoluble macromolecular complex, PUVU/poly(2,6‐dioctanoylamido‐4‐methacryloyloxypyrimidine). An X‐ray diffraction study confirmed that the complex had strandlike domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6607–6615, 2006     

SD对壳模型: 偶偶Pt核低激发态性质

利用SD对壳模型讨论了偶偶Pt核低激发态的集体性质. 结果发现在该模型下, 利用一个仅含有3个参数的哈密顿量, 可以很好地再现偶偶Pt核低激发谱的集体性质.     

Recognition of ring pairs in the data analysis of Cherenkov detectors

We present a new algorithm for the identification of ring pairs in Cherenkov detectors. The approach combines linear regression methods for the construction of an appropriate reference quantity, methods from statistics for the evaluation of hypotheses and Monte Carlo simulation runs for the tuning of threshold levels.     

无限维Banach空间的一个特征

证明如下结果，设Ｘ是Ｂａｎａｃｈ空间，则Ｘ是无限维的充分必要的条件是存在不含内点的非空凸集Ｂ，使得Ｂ不在任何一个闭超平面上。     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.