New “large” groups of type I

All unitary representations of certain infinite-dimensional, completely disconnected groups of type I are described.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 16, pp. 31–52, 1980.     

Spectral Characterizations of the Lovász Number and the Delsarte Number of a Graph

This paper gives spectral characterizations of two closely related graph functions: the Lovász number and a generalization ¹ of Delsarte's linear programming bound. There are many known characterizations of the Lovász number , and each one corresponds to a similar characterization of ¹ obtained by extremizing over a larger or smaller class of objects.The spectral characterizations of and ¹ given here involve the largest eigenvalue of a type of weighted Laplacian that Fan Chung introduced.     

The Binding Number of a Graph

The binding number of a graph is an important characteristic quantity of agraph.In1973 Woodall first introduced the concept of the binding number ofa graph and then gave the binding number of some special graphs in[1].In1981 Kane,Mohanty and Hales gave the binding number of some product graphsin[2].Wang Jianfang,Tian Songlin,Liu Ziuqiang(1983-1987)gave the bin-ding number of some multi-product graphs,and it is the limit character.Up to     

A “Birkhoff-Lewis” type result for a class of Hamiltonian systems

This paper contains results concerning the existence of long periodic solutions of nonautonomous Hamiltonian systems near the origin.Sponsored by M.P.I. (fondi 60% Problemi diff. nonlineari e teoria dei punti critici fondi 40% Eq. diff. e calcolo delle variazioni)     

On a Class of Number Fields of Eisenstein Type

In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial xp ?m(m is p-th powerfree and p | m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.     

On Quasi-valuation Rings of Rational Number Field

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On the Crossing Number of Circular Graphs

1.IntroductionInVLSIchipdesign,thetwo-layerroutingofgraphGplayanimportantrole.Thatis,theupperlayercanonlybeusedforverticalwiringandthesecondlaer,theloweroneonlyforhorizontalwiring.Soweconsidertheplanarprojectionofth.etwolayers,i.e.,consideratwodimensionalgridasapropergraphmodel.ThenoneobviousconditiontoberequiredisthateveryvertexofGhasitsdegreeatmost4.Withoutlossofgeneralitylweonlyconsider4regUlargraphs.IfGisaplanargraphwitha(G)S4,alinearalgorithmhadbeenprovidedforfindingarectilineajrrout…     

A quantum particle under the action of “white noise” type forces

We obtain the Schrödinger equation for the wave function of a particle interacting with the external field having a potential containing a component of the white noise type and the Kolmogorov equations for the distribution of a wave function.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 907–914, July, 1993.     

Optimal transmission of “television type” gaussian signals through a noiseless feedback channel

Using the methods and results of the theory of conditionally Gaussian filtering of stochastic processes and fields, an optimal scheme of “television type” signal transmission through a noiseless feedback channel is constructed under the usual power conditions, the signals being evolutionary Gaussian fields θ={θ_t(x)),tε[0,T),xεDεRⁿ . Explicit representations for optimal coding and decoding functionals, which are optimal in the sense of a special square criterion, and the expression for the error of signal reproduction are given.     

Erratum to “On type 1 representable lattices of dimension at most 4”

The main result in the paper mentioned above, that every lattice of length at most 4 and representable by commuting equivalence relations, is also representable by subgroups of an Abelian group, can be easily derived from known results due to B. Jónsson. Moreover, we correct some misleading statements.     

The Complete Chromatic Number of Maximal Outerplane Graphs

Let G be a maximal outerplane graph and X0(G) the complete chromatic number of G. This paper determines exactly X0(G) for △(G)≠5 and proves 6≤X0.(G)≤7 for △(G) = 5, where △(G) is the maximum degree of vertices of G.     

The Linking Number of Link with Two Components

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On groups of type Φ

We define a group G to be of type Φ if it has the property that for every -module G, proj. G < ∞ iff proj. H G < ∞ for every finite subgroup H of G. We conjecture that the type Φ is an algebraic characterization of those groups G which admit a finite dimensional model for , the classifying space for the family of the finite subgroups of G. We also conjecture that the type Φ is equivalent to spli being finite, where spli is the supremum of the projective lengths of the injective -modules. Here we prove certain parts of these conjectures. The project is cofounded by the European Social Fund and National Resources–EPEAK II–Pythagoras. Received: 21 June 2006     

Properties of Some Kind of Number Theoretical Function（Ⅱ）

For any given positive integer n ≥ 1, the Euler function φ（n） is defined to be the number of positive integers not exceeding n, which is relatively prime to n. o：（n） is defined to be the number of different prime divisors of n. In order to know the solvability of the function of φ（φ（φ（n））） = 2^ω（n）, properties of the number theoretical function φ（φ（n）） is studied in the paper.     

On the Equation and the Number of Solution of Znam's Problem

§1. In 1972,St.Znam posed the problem whether for every s>1 thereexist integers x_i>1,i=1,…,s such that x_i is a proper divisor of the numberx_1…x_(i-1)x_(i 1)…x_s 1 for i=1,…, s.Without loss of generality, we may assume1相似文献   

Radiation damping of “whispering gallery” type oscillations in the case of a sharp variation of the radius of curvature of the boundary

One investigates the radiation damping of whispering gallery waves. For a prolate ellipse it is shown that, in the neighborhood of the minimum of the radius of curvature, the solution, obtained with the aid of the complex ray method, coincides with the asymptotics of the exact eigenfunction. One isolates a class of boundaries for which one can use the complex ray method for the computation of the eigenvalues.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 129, pp. 149–151, 1983.The author is grateful to I. A. Molotkov for discussions.     

Singularity of the “swallow-tail” type and the glass-glass transition in a system of collapsing hard spheres

In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added). We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid-glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the “swallow-tail” type corresponding to the glass-glass transition.