A complexity measure for families of binary sequences

In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography) it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Lie Atoms and Their Deformations

A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in algebraic geometry, for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms, focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi–Bernoulli cohomology, which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by certain Kodaira–Spencer data. Received: May 2006 Revision: January 2007 Accepted: March 2007     

Characteristic of the Ag(II)/Ag(I) system in the presence of 2,2′:6′,2″-terpyridine in acetonitrile

Summary Composition of complexes of Ag(II) and Ag(I) ions with 2,2:6,2-terpyridine (tp) have been established. It has been found that the Ag⁺ ion forms only one complex Ag(tp)⁺ withtp in acetonitrile; its conditional formation constant: ₀₁=6.6·10⁴ has been determined by the potentiometric method. Equilibria and redox systems formed in solutions due to the complexation of Ag⁺ and Ag²⁺ and oxidation of Ag(II) complexes are described. Their formal potentials have been found by coulometric and voltamperometric examinations. The presence of the Ag(tp) ₂ ³⁺ ion in the anodic oxidized solutions of the complexes Ag(tp)(NO₃)₂ and Ag(tp)₂(NO₃)₂ has been proved. Properties of the system Ag(II)/Ag(I) in the presence of terpyridine in water and in acetonitrile have been compared.

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Charakteristik der Systeme Ag(II)/Ag(I) in Gegenwart von 2,2:6,2-Terpyridin in Acetonitril

Zusammenfassung Die Zusammensetzung der Komplexe von Ag(I)- und Ag(II)-Ionen mit 2,2:6,2-Terpyridin (tp) wurde bestimmt. Das Ag⁺-Ion bildet mittp in Acetonitril nur einen Komplex-Ag(tp)⁺. Seine Konditionalbildungskonstante ₀₁=6.6·10⁴ wurde mit Hilfe der potentiometrischen Methode bestimmt. Es wurden die Gleichgewichte und Redoxsysteme als Resultat der Komplexbildung von Ag(II)- und Ag(I)-Ionen und der Ag(II)-Komplexoxidation charakterisiert und die Formalpotentiale mittels Voltametrie und Coulometrie bestimmt. Die Gegenwart der Ag(tp) ₂ ³⁺ -Ionen wurde in anodisch oxydierten Lösungen der Komplexe Ag(tp)(NO₃)₂ und Ag(tp)₂(NO₃)₂ nachgewiesen. Die Eigenschaften des Systems Ag(II)/Ag(I) in Gegenwart von 2,2:6,2-Terpyridin in Wasser und in Acetonitril wurden verglichen.

     

On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems

In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.     

On shadowing: Ordinary and ergodic

The aim of this paper is to introduce the notion of ergodic shadowing for a continuous onto map which is equivalent to the map being topologically mixing and has the ordinary shadowing property. In particular, we deduce the chaotic behavior of a map with ergodic shadowing property. Moreover, we define some kind of specification property and investigate its relation to the ergodic shadowing property.     

形式Laurent级数域上交错Oppenheim展开的研究

该文介绍了形式Laurent级数域上交错Oppenheim展开的算法,得到了该展开中数字的强(弱)大数定理、中心极限定理和重对数率,并且研究了这些级数部分和的逼近的度.     

Dimensions of Formal Fibers of Height One Prime Ideals

Let T be a complete local (Noetherian) ring with maximal ideal M, P a nonmaximal ideal of T, and C = {Q ₁, Q ₂,…} a (nonempty) finite or countable set of nonmaximal prime ideals of T. Let {p ₁, p ₂,…} be a set of nonzero regular elements of T, whose cardinality is the same as that of C. Suppose that p _i  ∈ Q _j if and only if i = j. We give conditions that ensure there is an excellent local unique factorization domain A such that A is a subring of T, the maximal ideal of A is M ∩ A, the (M ∩ A)-adic completion of A is T, and so that the following three conditions hold: (1) p _i  ∈ A for every i; (2) A ∩ P = (0), and if J is a prime ideal of T with J ∩ A = (0), then J ? P or J ? Q _i for some i; (3) for each i, p _i A is a prime ideal of A, Q _i ∩ A = p _i A, and if J is a prime ideal of T with J ? Q _i , then J ∩ A ≠ p _i A.     

Closure-based constraints in formal concept analysis

We present a method of imposing constraints in extracting formal concepts (equivalently, closed itemsets or fixpoints of Galois connections) from a binary relation. The constraints are represented by closure operators and their purpose is to mimic background knowledge a user may have of the data. The idea is to consider and extract only these itemsets that are compatible with the background knowledge. As a result, the method extracts less clusters, those that are interesting from the user point of view, in a shorter time. The method makes it also possible to extract minimal bases of attribute dependencies in the input data that are compatible with the background knowledge. We provide examples of several particular types of constraints including those that appeared in the literature in the past and present algorithms to compute the constrained formal concepts and attribute implications.