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We report on the observation of quantized surface spin waves in periodic arrays of magnetic Ni81Fe19 wires by means of Brillouin light scattering spectroscopy. At small wavevectors (q_1 = 0 - 0.9*100000 cm^-1 ) several discrete, dispersionless modes with a frequency splitting of up to 0.9 GHz were observed for the wavevector oriented perpendicular to the wires. From the frequencies of the modes and the wavevector interval, where each mode is observed, the modes are identified as dipole-exchange surface spin wave modes of the film with quantized wavevector values determined by the boundary conditions at the lateral edges of the wires. With increasing wavevector the separation of the modes becomes smaller, and the frequencies of the discrete modes converge to the dispersion of the dipole-exchange surface mode of a continuous film.
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel - including the Bargmann-Fock representation - and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z 2 -graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.
An asymptotic-induced scheme for nonstationary transport equations with thediffusion scaling is developed. The scheme works uniformly for all ranges ofmean free paths. It is based on the asymptotic analysis of the diffusion limit ofthe transport equation. A theoretical investigation of the behaviour of thescheme in the diffusion limit is given and an approximation property is proven.Moreover, numerical results for different physical situations are shown and atheuniform convergence of the scheme is established numerically.
We present a method for making use of past proof experience called flexiblere-enactment (FR). FR is actually a search-guiding heuristic that uses past proofexperience to create a search bias. Given a proof P of a problem solved previouslythat is assumed to be similar to the current problem A, FR searches for P andin the "neighborhood" of P in order to find a proof of A.This heuristic use of past experience has certain advantages that make FRquite profitable and give it a wide range of applicability. Experimental studiessubstantiate and illustrate this claim.This work was supported by the Deutsche Forschungsgemeinschaft (DFG).
MP Prototype Specification
(1997)
A first explicit connection between finitely presented commutative monoids and ideals in polynomial rings was used 1958 by Emelichev yielding a solution tothe word problem in commutative monoids by deciding the ideal membership problem. The aim of this paper is to show in a similar fashion how congruenceson monoids and groups can be characterized by ideals in respective monoid and group rings. These characterizations enable to transfer well known resultsfrom the theory of string rewriting systems for presenting monoids and groups to the algebraic setting of subalgebras and ideals in monoid respectively grouprings. Moreover, natural one-sided congruences defined by subgroups of a group are connected to one-sided ideals in the respective group ring and hencethe subgroup problem and the ideal membership problem are directly related. For several classes of finitely presented groups we show explicitly howGröbner basis methods are related to existing solutions of the subgroup problem by rewriting methods. For the case of general monoids and submonoidsweaker results are presented. In fact it becomes clear that string rewriting methods for monoids and groups can be lifted in a natural fashion to definereduction relations in monoid and group rings.
The concept of algebraic simplification is of great importance for the field of symbolic computation in computer algebra. In this paper we review somefundamental concepts concerning reduction rings in the spirit of Buchberger. The most important properties of reduction rings are presented. Thetechniques for presenting monoids or groups by string rewriting systems are used to define several types of reduction in monoid and group rings. Gröbnerbases in this setting arise naturally as generalizations of the corresponding known notions in the commutative and some non-commutative cases. Severalresults on the connection of the word problem and the congruence problem are proven. The concepts of saturation and completion are introduced formonoid rings having a finite convergent presentation by a semi-Thue system. For certain presentations, including free groups and context-free groups, theexistence of finite Gröbner bases for finitely generated right ideals is shown and a procedure to compute them is given.