Nonstandard decision methods for the solvability of real polynomial equations

For a multivariate polynomial equation with coefficients in a computable ordered field, two criteria of this equation having real solutions are given. Based on the criteria, decision methods for the existence of real zeros and the semidefiniteness of binaly polynomials are provided. With the aid of computers, these methods are used to solve several examples. The technique is to extend the original field involved in the question to a computable non-Archimedean ordered field containing infinitesimal elements. Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project.     

Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals

For an ideal I??[x] given by a set of generators, a new semidefinite characterization of its real radical I(V _?(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover, we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety V _?(I) as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gröbner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.     

On L-fuzzy ideals in semirings II

We study some properties of L-fuzzy left (right) ideals of a semiring R related to level left (right) ideals     

Generalized Hadamard Matrices

The paper studies a generalized Hadamard matrix H = (g _{i j}) of order n with entries gi j from a group G of order n. We assume that H satisfies: (i) For m k, G = {g _{m i} g k i ^-1 i = 1,...., n} (ii) g _1i = g _i1 = 1 for each i; (iii) g _ij ^-1 = g _ji for all i, j. Conditions (i) and (ii) occur whenever G is a(P, L) -transitivity for a projective plane of order n. Condition (iii) holds in the case that H affords a symmetric incidence matrix for the plane. The paper proves that G must be a 2-group and extends previous work to the case that n is a square.     

On（N,U）-Coherence of Modules and Rings

Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U.     

Noncommutative Grassmannian <Emphasis Type="Italic">U</Emphasis>(1) sigma model and a Bargmann-Fock space

We consider a Grassmannian version of the noncommutative U(1) sigma model specified by the energy functional E(P) = ‖[a, P]‖ _HS ² , where P is an orthogonal projection operator in a Hilbert space H and a: H → H is the standard annihilation operator. With H realized as a Bargmann-Fock space, we describe all solutions with a one-dimensional range and prove that the operator [a, P] is densely defined in H for a certain class of projection operators P with infinite-dimensional ranges and kernels. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 347–357, December, 2007.     

Polynomials of Least Deviation from Zero

A new family of polynomials of least deviation from zero is defined on the unit disk B. Lower bounds for best approximations in the space L _p (B), p ≥ 1, are given.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 308–313.Original Russian Text Copyright © 2005 by V. A. Yudin.     

Fermi resonance-algebraic model for molecular vibrational spectra

A Fermi resonance-algebraic model is proposed for molecular vibrations, where aU(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent moleculeXY ₂ and a moleculeXY ₃ is successfully applied to fitting the recently obsenred vibrational spectrum of the water molecule and arsine (AsH₃), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations. Project supported by the National Natural Science Foundation of China (Grant No. 19377103) and the Chinese Academy of Sciences.     

A note about the cyclotomic polynomial Фpq（x） and some related results

Abstract. The expression of cyclotomic polynomial Фpq （x） is concerned for a long time. A simple and explicit expression of Фpq （x） in Z[x] has been showed. The form of the factors of Фpq （x） over F2 and the upper, lower bounds of their Hamming weight are provided.     

Asymptotically optimal sequential estimation of regular functionals of several distributions based on generalized U-statistics

For the several sample problem, a vector of estimable parameters is considered. For a fixed total sample size, a multistage (sequential) procedure based on generalized U-statistics is developed for choosing a partition of this sample size into individual sample size for which the generalized variance of the estimator of the parameter vector is asymptotically minimized.     

A compound of the generalized negative binomial distribution with the generalized beta distribution

This paper presents a compound of the generalized negative binomial distribution with the generalized beta distribution. In the introductory part of the paper, we provide a chronological overview of recent developments in the compounding of distributions, including the Polish results. Then, in addition to presenting the probability function of the compound generalized negative binomial-generalized beta distribution, we present special cases as well as factorial and crude moments of some compound distributions.     

Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity

In this paper, we consider nondifferentiable multiobjective fractional programming problems. A concept of generalized convexity, which is called (C,α,ρ,d)-convexity, is first discussed. Based on this generalized convexity, we obtain efficiency conditions for multiobjective fractional programming (MFP). Furthermore, we establish duality results for three types of dual problems of (MFP) and present the corresponding duality theorems.     

A polynomial algorithm for finding (<Emphasis Type="Italic">g,f</Emphasis>)-colorings orthogonal to stars in bipartite graphs

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). A (g, f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a (g, f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.     

Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems

We introduce some definitions related to semicontinuity of multivalued mappings and discuss various kinds of semicontinuity-related properties. Sufficient conditions for the solution sets of parametric multivalued symmetric vector quasiequilibrium problems to have these properties are established. Comparisons of the solution sets of our two problems are also provided. As an example of applications of our main results, the mentioned semicontinuity-related properties of the solution sets to a lower and upper bounded quasiequilibrium problem are obtained as consequences.     

Enlargements and generalized topologies

The paper discusses the generalization of a construction described in [6] for the case when the starting point topology is replaced by a generalized topology. Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786.     

Infrared absorption line intensities forU(5) model of linear triatomic molecules

The symmetry of the rotation-vibration spectra for linear triatomic molecules is described by means of the groupU(5). The rotation-vibration levels of linear triatomic molecules HCN and COS are calculated. The infrared absorption line intensities are calculated for the COS molecule. The results are in good agreement with the experimental values.     

Ideal <Emphasis Type="Italic">C</Emphasis>-totally real submanifolds in Sasakian space forms

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen classified Lagrangian immersions in complex space forms, which are ideal. In the present paper, we investigate ideal C-totally real submanifolds in a Sasakian space form. Mathematics Subject Classification (2000) 53C40, 53C25     

Z-Join Spectra of Z-Supercompactly Generated Lattices

The main result of this paper is a generalization of the classical equivalence between the category of continuous posets and the category of completely distributive lattices, based on the fact that the continuous posets are precisely the spectra of completely distributive lattices. Here we show that for so-called hereditary and union complete subset selections Z, the category of Z-continuous posets is equivalent (via a suitable spectrum functor) to the category of Z-supercompactly generated lattices; these are completely distributive lattices with a join-dense subset of certain Z-hypercompact elements. By appropriate change of the morphisms, these equivalences turn into dualities. We present two different approaches: the first one directly uses the Z-join ideal completion and the Z-below relation; the other combines two known equivalence theorems, namely a topological representation of Z-continuous posets and a general lattice theoretical representation of closure spaces.     

Structure Theorem of Kummer étale K-group

In this paper we develop a K-theory of log schemes by using vector bundles on the Ket site. Then, for a wide class of log varieties, we describe the structure of their K-groups in terms of the usual algebraic K-groups.