Spectra of certain types of polynomials and tiling of integers with translates of finite sets

We investigate Fuglede's spectral set conjecture in the special case when the set in question is a union of finitely many unit intervals in dimension 1. In this case, the conjecture can be reformulated as a statement about multiplicative properties of roots of associated with the set polynomials with (0,1) coefficients. Let alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022314X03001471-si1.gif"> be an N-term polynomial. We say that {θ₁,θ₂,…,θ_N−1} is an N-spectrum for A(x) if the θ_j are all distinct and

alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022314X03001471-si2.gif">     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a alt="Gamma" align="BASELINE" BORDER="0">-semiring to study alt="Gamma" align="BASELINE" BORDER="0">-semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a alt="Gamma" align="BASELINE" BORDER="0">-semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various alt="Gamma" align="BASELINE" BORDER="0">-semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

About the Notion of Semiring of Sets

We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved.     

Iterative Algebras without Projections

We deal with iterative algebras of functions of alt=" $$k$$ " align="middle" border="0"> -valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of alt=" $$m$$ " align="middle" border="0"> -valued logic, for alt=" $$k >m$$ " align="middle" border="0"> , without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of alt=" $$k$$ " align="middle" border="0"> -valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is.     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

On the commutator of the Marcinkiewicz integral

alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X02004985-si1.gif"> boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X02004985-si2.gif"> and the alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X02004985-si3.gif"> boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Herstein定理的推广

1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使[x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.