Small clique and large chromatic number

In this paper, we will exhibit old and new results concerning distance graphs with simaltaneously small clique and large chromatic numbers.     

Small sublattices with large dominions

Two examples of finite sublattices with infinite dominions are given. It is proven that this cannot occur in a finitely generated lattice variety. Received May 10, 2001; accepted in final form October 6, 2005.     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

Renormalization group approach to 1D cellular automata with large updating neighborhoods

We study self‐similarity in one‐dimensional probabilistic cellular automata (PCA) by applying a real‐space renormalization technique to PCA with increasingly large updating neighborhoods. By studying the flow about the critical point of the renormalization, we may produce estimates of the spatial scaling properties of critical PCA. We find that agreement between our estimates and experimental values are improved by resolving correlations between larger blocks of spins, although this is not sufficient to converge to experimental values. However, applying the technique to PCA with larger neighborhoods, and, therefore, more renormalization parameters, results in further improvement. Our most refined estimate produces a spatial scaling exponent, found at the critical point of the five‐neighbor PCA, of ν = 1.056 which should be compared to the experimental value of ν = 1.097. © 2014 Wiley Periodicals, Inc. Complexity 21: 206–213, 2015     

Small set in a large box

Let K ? ?^d be a compact convex set which is an intersection of half-spaces defined by at most two coordinates. Let Q be the smallest axes-parallel box containing K. We show that, as the dimension d grows, the ratio diam Q/ diam K can be arbitrarily large. We also give examples of compact sets in Banach spaces which are not contained in any compact contractive set.     

Small embedding characterizations for large cardinals

We show that many large cardinal notions can be characterized in terms of the existence of certain elementary embeddings between transitive set-sized structures, that map their critical point to the large cardinal in question. As an application, we use such embeddings to provide new proofs of results of Christoph Weiß on the consistency strength of certain generalized tree properties. These new proofs eliminate problems contained in the original proofs provided by Weiß.     

Small eigenvalues of large Hermitian moment matrices

We consider an infinite Hermitian positive definite matrix M which is the moment matrix associated with a measure μ with infinite and compact support on the complex plane. We prove that if the polynomials are dense in L²(μ) then the smallest eigenvalue λn of the truncated matrix Mn of M of size (n+1)×(n+1) tends to zero when n tends to infinity. In the case of measures in the closed unit disk we obtain some related results.     

Small braids with large ultra summit set

In [1, Open question 2], the following question was posed: Is the size of the ultra summit set of the conjugacy class of a rigid pseudo-Anosov braid bounded above by a polynomial in the braid length and the number of strands? A negative answer to this question is given.     

Small deviation of Brownian motion with large drift

In this article, we obtain exact asymptotics of the sojourn probability of Brownian motion with large drift on a small curvilinear strip in a finite time interval.     

Fuzzy automata and life

Boolean cellular automata may be generalized to fuzzy automata in a consistent manner. Several fuzzy logics are used to create 1‐dimensional automata and also 2‐dimensional automata that generalize the game of life. These generalized automata are investigated and compared to their Boolean counterparts empirically and using rule entropy and repeated input response functions. Fuzzy automata offer new mechanisms for classification of classical automata and can be used for insight into their qualitative behavior. © 2002 Wiley Periodicals, Inc.     

Probabilistic automata

This paper is a survey of the most important results in the theory of probabilistic automata obtained from the start of the development of the theory through 1974. References are given to the basic papers on the topics discussed.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 15, pp. 79–122, 1978.     

Small strain deformations of elastic beams and rods including large deflections

A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending and twisting of a rod or beam by end loads and by its own weight. The theory provides solutions for geometries and loadings between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff s theory for rods, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior.

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Zusammenfassung Eine konsistente Theorie, bei der linearelastisches Verhalten und Verzerrungen klein vorausgesetzt, jedoch große Verschiebungen und Drehungen zugelassen sind, wird auf die Verbiegung und Verdrehung eines Stabes unter Endlasten und Eigengewicht angewendet. Die Theorie ergibt Lösungen für Geometrien und Belastungen im mittleren Bereich zwischen dem Gültigkeitsbereich der infinitesimalen Theorie und jenem der strukturellen Theorien wie die Kirchhoff'sche Stabtheorie im Bereich der kleinen Verzerrungen und des linear-elastischen Verhaltens.

     

Codification schemes and finite automata

This paper is a note on how Information Theory and Codification Theory are helpful in the computational design of both communication protocols and strategy sets in the framework of finitely repeated games played by bounded rational agents. More precisely, we show the usefulness of both theories to improve the existing automata bounds on the work of Neyman (1998) Finitely repeated games with finite automata, Mathematics of Operations Research, 23 (3), 513–552.     

On free and torsion-free automata

In this paper we define free, torsion-free and torsion-free completely on an automaton. We prove some properties of them which are important     

Lattice valued relations and automata

A lattice-valued relation, lvr for short, from a set X to a set Y is a function from the Cartesian product of X and Y to a lattice. This concept is a generalization of other structures, notably tolerance spaces, nets and automata, separately investigated by the authors elsewhere. It is adequate to admit a natural definition of homogeneity and a classification of homogeneous lvr's by their isomorphism groups. The main result of the present paper is a proof of this classification. The application of this to automata, also interpretable as lvr's, is described, and an example given. We conclude with a brief discussion of the lvr theory of fuzzy and stochastic automata.     

Homology theories and tolerance automata

We present three possible approaches to a homology theory of automata. Two of these require the state to possess a tolerance. This permits us to proceed by analogy with either the simplicial or the cubical theories of the topological category. The third approach describes a homology theory of automata as such.Fixed simplex theorems are stated. It is suggested that homology theory might be used to classify automata.