Kraftfeldrechnungen an linearen Oligopyrrolen: 2,2′-Bipyrrol, 2,2′-Furylpyrrol und Prodigiosen

Using a specific force field model, relative stabilities of 2,2-bipyrrole and 2,2-furylpyrrole conformers as well as of prodigiosene tautomers, configurations, and conformations, are studied. 2,2-Bipyrrole adopts anantiperiplanar conformation in accord with other theoretical calculations and experimental findings. Its rotational barrier calculated by this method compares favourably to the one derived by other means. For the parent prodigiosene the (Z)sp,sp arrangement is found to be the most stable one. The two possible tautomers within its dipyrrin fragment do not show a significant energy difference.

     

ELECTRON PARAMAGNETIC RESONANCE STUDIES OF SINGLE CRYSTAL SODIUM HEXAMOLYBDOCHROMATE (Ⅲ)Cr~(3+)/Na_3(AlMo_6O_(24)H_6)·8H_2O

An X-band EPR study on a Na_3(CrMo_6O_(24)H_6)·8H_2O single crystal diluted by its isomor-phic compound Na_3(AlMo_6O_(24)H_6)·8H_2O at room temperature is reported. Using the least squares-fitting method to simulate the EPR data for principal planes, the Hamiltonian parameterswere obtained. The principal values of the g tensors are g_(ZZ) = 1.904, g_(XX)= 1.973, g_(YY)=1.933. The zero field splitting tensor parameters are D = 0.275 cm~(-1), E = 0.05 cm~(-1). The fielddependence of Cr~(3+) energy levels with field at different angles from the principal axes whenthe field is along the principal planes is calculated based on these experimental parameters.The isofrequency plots of calculated field vs. angle are also shown. They agree well with theexperimental results.     

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. He also reviews the related analytic extension results, conjectures and problems. He discusses the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of q-traces and pseudo-q-traces of products of intertwining operators. He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.     

Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation

In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Through the phase portraits, in addition to periodic wave solutions and solitary wave solutions, we also obtain explicit periodic singular wave solutions, singular wave solutions and kink wave solutions, which were not found in the previous works. The dynamical behavior of these solutions and their internal relations are revealed through asymptotic analysis. The results will help supplement the study of field equation.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Unification of electromagnetism and gravitation: The equations of electrodynamics derived from the Riemann tensor in general relativity

The equations of free-space electrodynamics are derived directly from the Riemann curvature tensor and the Bianchi identity of general relativity by contracting on two indices to give a novel antisymmetric Ricci tensor. Within a factore/h, this is the field-strength tensor G of free-space electrodynamics. The Bianchi identity for G describes free-space electrodynamics in a manner analogous to, but more general than, Maxwell's equations for electrodynamics, the critical difference being the existence in general and special relativity of the Evans-Vigier fieldB ⁽³⁾.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

Normsets and determination of unique factorization in rings of algebraic integers

The image of the norm map from to (two rings of algebraic integers) is a multiplicative monoid . We present conditions under which is a UFD if and only if has unique factorization into irreducible elements. From this we derive a bound for checking if is a UFD.

     

Atom-probe field ion microscopy

The atom probe field ion microscope (AP-FIM) is a combination of a field ion microscope and a time-of-flight mass spectrometer with a single ion detection sensivity. With the field ion microscope topology of a surface, surface reactions and surface modifications can be studied in atomic detail. By time-of-flight measurements surface layers and interface layers can be chemically analyzed atom by atom and atomic layer by atomic layer. Compositional variations according to surface or interface segregation, precipitations, or surface changes in corrosion or in electrochemical layer formation etc. can be studied quantitatively on a subnanometer scale. Some of our studies on related problems will be decribed briefly.