Existence of invariant curves with prescribed frequency for degenerate area preserving mappings

We consider small perturbations of analytic non-twist area preserving mappings,and prove the existence of invariant curves with prescribed frequency by KAM iteration.Generally speaking,the frequency of invariant curve may undergo some drift,if the twist condition is not satisfied.But in this paper,we deal with a degenerate situation where the unperturbed rotation angle function r→w+r^(2n+1)is odd order degenerate at r=0,and prove the existence of invariant curve without any drift in its frequency.Furthermore,we give a more general theorem on the existence of invariant curves with prescribed frequency for non-twist area preserving mappings and discuss the case of degeneracy with various orders.

An Adaptive Non-Linear Map and Its Application

A novel adaptive non-linear mapping （ANLM）, integrating an adaptive mapping error （AME） with a chaosgenetic algorithm （CGA） including chaotic variable, was proposed to overcome the deficiencies of non-linear mapping （NLM）. The value of AME weight factor is determined according to the relative deviation square of distance between the two mapping points and the corresponding original objects distance. The larger the relative deviation square between two distances is, the larger the value of the corresponding weight factor is. Due to chaotic mapping operator, the evolutional process of CGA makes the individuals of subgenerations distributed ergodieally in the defined space and circumvents the premature of the individuals of subgenerations. The comparison results demonstrated that the whole performance of CGA is better than that of traditional genetic algorithm. Furthermore, a typical example of mapping eight-dimenslonal olive oil samples onto two-dimensional plane was employed to verify the effectiveness of ANLM. The results showed that the topology-preserving map obtained by ANLM can well represent the classification of original objects and is much better than that obtained by NLM.

NO-ARBITRAGE SYMMETRIES

The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of(idealized) markets.This paper addresses the following basic question:can one characterize the class of transformations that leave the law of no-arbitrage invariant?We provide a geometric formalization of this question in a non probabilistic setting of discrete time-the so-called trajectorial models.The paper then characterizes,in a local sense,the no-arbitrage symmetries and illustrates their meaning with a detailed example.Our context makes the result available to the stochastic setting as a special case.

Maps on Positive Cones of C^(*)-algebras

We prove that a surjective map(on the positive cones of unital C^(*)-algebras)preserves the minimum spectrum values of harmonic means if and only if it has a Jordan *-isomorphism extension to the whole algebra.We represent weighted geometric mean preserving bijective maps on the positive cones of prime C^(*)-algebras in terms of Jordan *-isomorphisms of the algebras.We also characterize order isomorphisms and orthoisomorphisms of the projection lattice of the von Neumann algebra of all bounded linear operators on a Hilbert space,answering an open question arisen by Dye.Finally,we give a description for Fuglede-Kadison determinant preserving maps on the positive cone of a finite von Neumann algebra and improve Gaal and Nayak’s work on this topic.

APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD REGULAR FUZZY NEURAL NETWORKS

Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.

Bijective maps on standard Borel subgroup of symplectic group preserving commutators

Abstract Let F be a field, and let G be the standard Borel subgroup of the symplectie group Sp（2m, F）. In this paper, we characterize the bijective maps φ： G -- G satisfying φ[x, y] = [φ（x）, φ（y）].

Maps Preserving Commutators on the Standard Borel Subgroup of the Unitary Group over a Field

Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving commutators on B2n （F）.