EMBEDDINGS OF ONE KIND OF GRAPHS

The purpose of this paper is to display a new kind of simple graphs which belong to B. inwhich any graph has its orientable genus n,n≥3. Furthermore, for any integer k,1≤k≤n,there exists a graph B^kn of B. such that the non-orientable genus of B^kn is k.     

ON BERNSTEIN POLYNOMIALS OF FUNCTIONS OF BOUNDED VARIATION OF ORDER p

1.IntroductionLet f be a function defined on[0,1],then the Bernstein poly-nomial B_n(f,x)of f is T.Popoviciu(see[1])and G.G.Lorentz studied the operator(1.1)and estimated the rate of convergence of B_n(f,x).F.Herzogand J.D. Hill,and others studied the convergence of(1.1)fordiscontinuous functions,they proved that if f is bounded on[0,1]and x is a discontinuity point of the first kind,then     

THEORY OF INFRA-RED ABSORPTION OF MOLECULES

In this paper, we apply the adiabatic approximation model to the IR absorption of molecules. Expressions of the band shape functions for isothermal and isolated systems are obtained and using Einstein model we discuss the dependence of the band shape functions on temperature, normal coodinate shifts and energy.We also obtain a very simple expression of the correlation function when Svv′< 1 and discuss its effect on the band shape function.     

ON NUMBER OF LEAVES ANDBANDWIDTH OF TREES

1.IntroductionFOragraphG=(V,E)oforderp,aonetoonemappingfromVinto{l,2,',p}iscalledanumberingofG.Definition1.1.SupposefisanumberingofG.LetBj(G)=(u57teif(u)--f(v)l.ThebandwidthofG,denotedbyB(G),isdefinedbyB(G)=min{Bf(G)IfisanumberingofG}.Thebandwidthproblemofgraphshasbecomeveryimportantsincethemid-sixties(see[21or[4]).Itisverydifficulttodeterminethebandwidthofagraph.GareyetallllshowedthatthebandwidthproblemisNP-completeevenifitisrestrictedtotreeswithmaximumdegree3.Soitisinterestingtoe…     

PROPERTIES OF FRACTIONAL k-FACTORS OF GRAPHS

In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.     

THEORY OF INFRA-RED ABSORPTION OF MOLECULES

In this paper, we apply the adiabatic approximation model to the IR absorption of molecules. Expressions of the band shape functions for isothermal and isolated systems are obtained and using Einstein model we discuss the dependence of the band shape functions on temperature, normal coodinate shifts and energy.We also obtain a very simple expression of the correlation function when Svv ′<1 and discuss its effect on the band shape function.     

ISOMORPHISMS OF CIRCULANT DIGRAPHS OF DEGREE 3

Abstract. In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In psrticular, we characterize those circulant digraphs of degree 3 which don‘‘t satisfy JkdAm‘‘s conjectttre.     

EXISTENCE OF PERIODIC SOLUTIONS OF SYSTEM OF DIFFERENCE EQUATIONS

This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained.     

CONSTRUCTIONS OF POWER BASES OF CYCLOTOMIC FIELDS

Suppose Q(ζ_m) is the m-th cyclotomic number field, where ζ_m is an m-th primitive root of unity, m>1 any integer. Let a_m=ζ_m+ζ_m~2+...+ζ_m~((m-1)/2) if m is odd and let β_m be the product of the integersl-ζ_m(1相似文献   

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

Algebraic solutions of the Lamé equation, revisited

A minor error in the necessary conditions for the algebraic form of the Lamé equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out (see Baldassarri, J. Differential Equations 41 (1) (1981) 44). It is shown that if the group is the octahedral group S₄, then the degree parameter of the equation may differ by ±1/6 from an integer; this possibility was missed. The omission affects a recent result on the monodromy of the Weierstrass form of the Lamé equation (see Churchill, J. Symbolic Comput. 28 (4-5) (1999) 521). The Weierstrass form, which is a differential equation on an elliptic curve, may have, after all, an octahedral projective monodromy group.     

Totally chiral maps and hypermaps of small genus

An orientably regular hypermap is totally chiral if it and its mirror image have no non-trivial common quotients. We classify the totally chiral hypermaps of genus up to 1001, and prove that the least genus of any totally chiral hypermap is 211, attained by twelve orientably regular hypermaps with monodromy group A₇ and type (3,4,4) (up to triality). The least genus of any totally chiral map is 631, attained by a chiral pair of orientably regular maps of type {11,4}, together with their duals; their monodromy group is the Mathieu group M₁₁. This is also the least genus of any totally chiral hypermap with non-simple monodromy group, in this case the perfect triple covering 3.A₇ of A₇. The least genus of any totally chiral map with non-simple monodromy group is 1457, attained by 48 maps with monodromy group isomorphic to the central extension 2.Sz(8).     

GL(n,K)中一类准可解子群的结构及其在Fuchsian系统中的应用(英文)

本文研究了单值群的可解性与Fuchsian方程可积性之间的关系.利用可解群及GL(n,K)的性质,获得GL(n,K)中一类准可解子群的结构定理,并将之心用于Fuchsian系统的可积性研究之中.     

Realizability of a braid monodromy by an algebraic function in a disk

A braid is called algebraic if it is conjugated to the local braid of an algebraic function at a singular point. It is shown that any homomorphism of a free group into a braid group which takes each generator to an algebraic braid, can be realized as the braid monodromy of an algebraic function in a disk.     

Special Monodromy Groups and the Riemann-Hilbert Problem for the Riemann Equation

In this paper, we solve the Riemann-Hilbert problem for the Riemann equation and for the hypergeometric equation. We describe all possible representations of the monodromy of the Riemann equation. We show that if the monodromy of the Riemann equation belongs to SL(2, ℂ), then it can be realized not only by the Riemann equation, but also by the more special Riemann-Sturm-Liouville equation. For the hypergeometric equation, we construct a criterion for its monodromy group to belong to SL(2, ℤ).__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 753–767.Original Russian Text Copyright ©2005 by V. A. Poberezhnyi.     

Group-groupoids and monodromy groupoids

This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.     

Special solutions of the first and second Painlevé equations and singularities of the monodromy data manifold

A classification of solutions of the first and second Painlevé equations corresponding to a special distribution of poles at infinity is considered. The relation between this distribution and singularities of the two-dimensional complex monodromy data manifold used for the parameterization of the solutions is analyzed. It turns out that solutions of the Painlevé equations have no poles in a certain critical sector of the complex plane if and only if their monodromy data lie in the singularity submanifold. Such solutions belong to the so-called class of “truncated” solutions (intégrales tronquée) according to P. Boutroux’s classification. It is shown that all known special solutions of the first and second Painlevé equations belong to this class.     

A simple proof of the geometric fractional monodromy theorem

A simple proof of the “geometric fractional monodromy theorem” (Broer-Efstathiou-Lukina 2010) is presented. The fractional monodromy of a Liouville integrable Hamiltonian system over a loop γ ? ?² is a generalization of the classic monodromy to the case when the Liouville foliation has singularities over γ. The “geometric fractional monodromy theorem” finds, up to an integral parameter, the fractional monodromy of systems similar to the 1: (?2) resonance system. A handy equivalent definition of fractional monodromy is presented in terms of homology groups for our proof.     

Construction of a Pfaff system of Fuchs type with three singular surfaces on a complex projective space

We construct a multidimensional Pfaff equation of Fuchs type for a given monodromy group on CP ⁿ . The monodromy group is generated by three noncommutating matrices.