A Reader's Guide to Gacs's “Positive Rates” Paper

Peter Gacs's monograph, which follows this article, provides a counterexample to the important Positive Rates Conjecture. This conjecture, which arose in the late 1960's, was based on very plausible arguments, some of which come from statistical mechanics. During the long gestation period of the Gacs example, there has been a great deal of skepticism about the validity of his work. The construction and verification of Gacs's counterexample are unavoidably complex, and as a consequence, his paper is quite lengthy. But because of the novelty of the techniques and the significance of the result, his work deserves to become widely known. This reader's guide is intended both as a cheap substitute for reading the whole thing, as well as a warm-up for those who want to plumb its depths.     

Some geometric and dynamical properties of the Urysohn space

This is a survey article about the geometry and dynamical properties of the Urysohn space. Most of the results presented here are part of the author's Ph.D. thesis and were published in the articles [J. Melleray, Stabilizers of closed sets in the Urysohn space, Fund. Math. 189 (1) (2006) 53-60; J. Melleray, Compact metrizable groups are isometry groups of compact metric spaces, Proc. Amer. Math. Soc. 136 (4) (2008) 1451; J. Melleray, On the geometry of Urysohn's universal metric space, Topology Appl. 154 (2007) 384-403]; a few results are new, most notably the fact that Iso(U) is not divisible.     

SOME DYNAMICAL PROPERTIES OF THE UNIVERSAL UNFOLDING OF PITCHFORK

From the point of view of dynamics,the phenomenon of mode jumpingin the imperfect pitchfork problem is discussed.The dynamical mechanism of modeljumping of structures,such as plate and shell,that is brought about by the extremurninstability,is explained.Finally,we give numerical simulation to show the validity ofour results.     

On random frequent universality

We give a probabilistic construction of frequently hypercyclic or universal entire functions using Birkhoff?s ergodic Theorem. We apply the same ideas to construct random frequently universal vectors for the polynomials of the weighted backward shift on the classical real or complex ?^p${?}^p$ space.     

Overlap Cycles for Steiner Quadruple Systems

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is well known that Steiner quadruple systems of order v, or SQS(v), exist if and only if . Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole, et al. Using Hanani's SQS constructions, we show that for every with there exists an SQS(v) that admits a 1‐overlap cycle.     

Developing an algorithm for compression, multiplexing and enhancement of multiple images

Image compression is one of the important fields that has useful applications in data storage and transmission. In this research a new algorithm is developed and tested for multiple-image compression and enhancement. The algorithm, in addition, is applied to multiple noisy images. Also, the effect of compression ratio on the peak signal to noise ratio (PSNR) is explored by applying different compression ratios. The developed algorithm gives good compression and noise immunity. It can be used for storage/transmission of encrypted and compressed information.     

Multi-linear variable separation approach to nonlinear systems

The multi-linear variable separation approach is reviewed in this article. The method has been recently established and successfully solved a large number of nonlinear systems. One of the most exciting findings is that the basic multi-linear variable separation solution can be expressed by a universal formula including two (1+1)-dimensional functions, and at least one is arbitrary for integrable systems. Furthermore, the method has been extended in two different ways so as to enroll more low dimensional functions in the solution.      

Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

李超代数与Frobenius代数

利用限制李超代数的新定义,给出了李超代数的p-包络的一些相关结果,并将李代数中表示理论的一些结果推广到李超代数上,进而研究了限制李超代数与Frobenius代数的关系．