Coupling Parameters and the Form of the Potential via Noether Symmetry

We explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present we find a general exact solution for the Einstein equations. We also show that non Noether symmetries can be found. Finally, we present an extension of the procedure to the Kantowski-Sachs metric which is particularly interesting in the case of degenerate Lagrangian.     

The Kramers–;Wannier Symmetry and S-Duality in the Two-Dimensional g03A6;4 Theory

We show that the exact beta function of the two-dimensional g⁴ theory possesses two dual symmetries. These are the Kramers–Wannier symmetry d(g) and the strong–weak-coupling symmetry, or the S-duality f(g), connecting the strong- and weak-coupling domains lying above and below the fixed point g ^*. We obtain explicit representations for the functions d(g) and f(g). The S-duality transformation f(g) allows using the high-temperature expansions to approximate the contributions of the higher-order Feynman diagrams. From the mathematical standpoint, the proposed scheme is highly unstable. Nevertheless, the approximate values of the renormalized coupling constant g ^* obtained from the duality equations agree well with the available numerical results.     

High-Energy Relations Between Elastic Scattering Amplitudes of Particles and Antiparticles

We find conditions under which the ratio of particle and antiparticle total scattering cross sections as s. If the forward elastic scattering amplitudes become purely real asymptotically, then their ratio tends to –1. We prove that /_–(s)1 for ₊(s)/m ², where m is the -meson mass. We show that the asymptotic relations obtained have finite-energy analogues for some processes.     

Some Non-trivial Symmetry Classes of Tensors Associated with Certain Characters

Let G be a finite group and a set of n elements. Assume that G acts faithfully on and let V be a vector space over the complex field , with dim V = m 2. It is shown that for each irreducible constituent of permutation character of G, the symmetry class of tensors associated with G and is non-trivial. This extends a result of Merris and Rashid (see [6, Theorem 2]).1995 AMS subject classification primary 20C30 secondary 15A69This research was in part supported by a grant from IPM.     

The replica-symmetric solution without replica trick for the Hopfield model

We derive the saddle-point equations for the order parameters of the Hopfield model in the case of replica symmetry without using the replica trick, but assuming that the Edwards-Anderson parameter is a self-averaging quantity.     

Density Functional Theory (DFT) studies on the ground state of NO_3(~2A''''_2) radical and the first triplet state of NO_3~ cation

Density Functional Theory (DFT) studies on the ground states (2A'2) of NO3 radical and on the ground state (1A1') and the first triplet state (3E") of NO3 cation provide an unambiguous prediction about their geometrical structure-, the ground states of both NO3 radical and NO3 cation have D3h symmetry and the geometrical configuration of the first triplet state 3E" of NO3 cation has C2v symmetry. It is shown that as far as the ionization energy calculations on NO, radical are concerned, the results are only slightly different, no mater that gradient corrections of the exchange-correlation energy are included during self-consistent iterations or they are included as perturbations after the self-consistent iterations.     

螺旋型高分子链晶体结构所属空间群的演变规律性

本文利用有色对称的理论讨论了螺旋型高分子链晶体结构所属空间群的演变规律性。得出：（１）有序链结构的空间群是无序链结构空间群的有色空间群；（２）对称性较低的螺旋链所属空间群是高对称螺旋链所属空间群的有色空间群；（３）从而得出空间群演变的方向、途径和结果，总结出其演变的规律性。     

Molecular Exciton Approach to Anisotropic Absorption and Circular Dichroism II. The Partial Optic Axis and its Application in Molecular Exciton Theory

Summary. The first part of the present communication develops the general theory of the partial optic axis, which is an excitation specific structural feature first proposed as an aid to the choice of chromophoric reference points in a molecular exciton approach to optical rotatory power, and discusses its applicability to symmetry analyses in the light of the distinction between the three categories for anisotropic optical rotatory power, i.e. chiral, achiral optically active, and achiral optically inactive molecular structures. The second part of the communication discusses the special role played by the concept of the partial optic axis in the evaluation of the anisotropic chromophoric intensity contributions in a molecular exciton approach, in particular in relation to the use of the chromophoric symmetry for the systematic selection and characterization of the intensity contributions.Permanent address: Holmebjerg 5, DK-2950 Vedbæk, Denmark