Associated Prime Submodules of Finitely Generated Modules

As generalizations of annihilators and associated primes, we introduce the notions of weak annihilators and weak associated primes, respectively. We first study the properties of the weak annihilator of a subset X in a ring R. We next investigate how the weak associated primes of a ring R behave under passage to the skew monoid ring R*M. Let R be a semicommutative ring, and M an ordered monoid and φ: M → Aut(R) a compatible monoid homomorphism. Then we can describe all weak associated primes of the skew monoid ring R*M in terms of the weak associated primes of R in a very straightforward way.     

On the Classification of Laminations Associated to Quadratic Polynomials

Given any rational map f, there is a lamination by Riemann surfaces associated to f. Such laminations were constructed, in general, by Lyubich and Minsky. In this article, we classify laminations associated to quadratic polynomials with periodic critical point. In particular, we prove that the topology of such laminations determines the combinatorics of the parameter. We also describe the topology of laminations associated to other types of quadratic polynomials.      

Some structural results concerning certain classes of qualitative matrices and their inverses

This paper presents some precise structural results concerning combinatorially symmetric, sign symmetric, and sign antisymmetric invertible matrices whose associated diagraphs are trees. In particular given an invertible sign antisymmetric matrix A whose associated digraph is a tree and the fact that A^-1 is sign antisymmetric, we are able to completely determine the associated digraph of A^-1.     

Inversion of Toeplitz operators,Levinson equations,and Gohberg-Krein factorization—A simple and unified approach for the rational case

The problem of the inversion of the Toeplitz operator T_Φ, associated with the operator-valued function Φ defined on the unit circle, is known to involve the associated Levinson system of equations and the Gohberg-Krein factorization of Φ. A simplified and self-contained approach, making clear the connections between these three problems, is presented in the case where Φ is matrix-valued and rational. The key idea consists in looking at the Levinson system of equations associated with Φ^?1(z^?1), rather than that associated with Φ(z). As a consequence, a new invertibility criterion for Toeplitz operators with rational matrix-valued symbols is derived.     

Structure spinorielle associée à un espace vectoriel quaternionien à droite e sur H, muni d’une forme sesquilinéaire b non dégénérée H-anti hermitienne

This paper, self-contained, deals with the study of Clifford Algebras associated with n-dimensional skew-hermitian spaces over the skew field H. The different structures associated with the spaces S of corresponding spinors are given and the natural imbeddings of associated spinor groups are revealed.     

The Mean-Partition Problem

In mean-partition problems the goal is to partition a finite set of elements, each associated with a d-vector, into p disjoint parts so as to optimize an objective, which depends on the averages of the vectors that are assigned to each of the parts. Each partition is then associated with a d × p matrix whose columns are the corresponding averages and a useful approach in studying the problem is to explore the mean-partition polytope, defined as the convex hull of the set of matrices associated with feasible partitions.     

Convergence and error estimate of cascade algorithms with infinitely supported masks in L p (? s )

The cascade algorithm plays an important role in computer graphics and wavelet analysis.In this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated masks.It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L p-norm.Moreover,the error between the two resulting limit functions is estimated in terms of the masks.     

Algebraic topological methods for the supercritical Q-curvature problem

We study the problem of existence of conformal metrics with prescribed Q-curvature on closed four-dimensional Riemannian manifolds. This problem has a variational structure, and in the case of interest here, it is noncompact in the sense that accumulations points of some noncompact flow lines of a pseudogradient of the associated Euler–Lagrange functional, the so-called true critical points at infinity of the associated variational problem, occur. Using the characterization of the critical points at infinity of the associated variational problem which is established in [42], combined with some arguments from Morse theory, some algebraic topological methods, and some tools from dynamical system originating from Conley's isolated invariant sets and isolated blocks theory, we derive a new kind of existence results under an algebraic topological hypothesis involving the topology of the underling manifold, stable and unstable manifolds of some of the critical points at infinity of the associated Euler–Lagrange functional.     

Continuous planar functions

This paper deals with continuous planar functions and their associated topological affine and projective planes. These associated (affine and projective) planes are the so-called shift planes and in addition to these, in the case of planar partition functions, the underlying (affine and projective) translation planes. We introduce a method that allows us to combine two continuous planar functions ? → ? into a continuous planar function ?² → ?². We prove various extension and embedding results for the associated affine and projective planes and their collineation groups. Furthermore, we construct topological ovals and various kinds of polarities in the associated topological projective planes.     

Hamiltonians associated with the third and fifth Painlevé equations

We obtain a Painlevé-type differential equation for the simplest rational Hamiltonian associated with the fifth Painlevé equation in the case γ ≠ 0, δ = 0. We prove the existence of Hamiltonians of a nonrational type associated with the fifth Painlevé equation in the case γ ≠ 0, δ = 0. We obtain a generalization of the Garnier and Okamoto formulas for rational Hamiltonians associated with the third Painlevé tequation.     

The strong derivative of the best approximation operator

ABSTRACT

This article is devoted to the derivation of sampling series associated with eigenvalue problems. No examples of sampling theorems associated with odd order problems are known except when the order is one. Here we give necessary and sufficient conditions for the boundary conditions to be self adjoint. Then sampling series associated with odd order self adjoint and non self adjoint problems are given. The sampling representations associated with non self adjoint odd order problems are derived provided that the boundary condition are regular.     

Simplectic spreads and finite semifields

It is well known that associated with a translation plane π there is a family of equivalent spreads. In this paper, we prove that if one of these spreads is symplectic and π is finite, then all the associated spreads are symplectic. Also, using the geometric intepretation of the Knuth’s cubical array, we prove that a symplectic semifield spread of dimension n over its left nucleus is associated via a Knuth operation to a commutative semifield of dimension n over its middle nucleus.      

On the Hilbert Evolution Algebras of a Graph

Evolution algebras are a special class of nonassociative algebras exhibiting connections with various fields of mathematics. Hilbert evolution algebras generalize the concept in the framework of Hilbert spaces. This allows us to deal with a wide class of infinite-dimensional spaces. We study Hilbert evolution algebras associated to a graph. Inspired by the definitions of evolution algebras we define the Hilbert evolution algebra that is associated to a given graph and the Hilbert evolution algebra that is associated to the symmetric random walk on a graph. For a given graph, we provide the conditions for these structures to be or not to be isomorphic. Our definitions and results extend to the graphs with infinitely many vertices. We also develop a similar theory for the evolution algebras associated to finite graphs.

     

Some limit theorems for negatively associated random variables

Let {X _n , n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the L ^p -convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.     

Uniqueness of Dirichlet forms associated with systems of infinitely many Brownian balls in ℝ d

Summary. Dirichlet forms associated with systems of infinitely many Brownian balls in ℝ ^d are studied. Introducing a linear operator L ₀ defined on a space of smooth local functions, we show the uniqueness of Dirichlet forms associated with self adjoint Markovian extensions of L ₀. We also discuss the ergodicity of the reversible process associated with the Dirichlet form. Received: 18 July 1996/In revised form: 13 February 1997     

Approximating the jump discontinuities of a function by its Fourier-Jacobi coefficients

In the present paper we generalize Eckhoff's method, i.e., the method for approximating the locations of discontinuities and the associated jumps of a piecewise smooth function by means of its Fourier-Chebyshev coefficients.

A new method enables us to approximate the locations of discontinuities and the associated jumps of a discontinuous function, which belongs to a restricted class of the piecewise smooth functions, by means of its Fourier-Jacobi coefficients for arbitrary indices. Approximations to the locations of discontinuities and the associated jumps are found as solutions of algebraic equations. It is shown as well that the locations of discontinuities and the associated jumps are recovered exactly for piecewise constant functions with a finite number of discontinuities.

In addition, we study the accuracy of the approximations and present some numerical examples.

     

Beyond hyperinvariance for compact operators

We introduce a new class of operator algebras on Hilbert space. To each bounded linear operator a spectral algebra is associated. These algebras are quite substantial, each containing the commutant of the associated operator, frequently as a proper subalgebra. We establish several sufficient conditions for a spectral algebra to have a nontrivial invariant subspace. When the associated operator is compact this leads to a generalization of Lomonosov's theorem.     

Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables

In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund’s strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesàro’s and Riesz’s sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409–412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105–112, 2000), Li et al. (J. Theor. Probab. 8, 49–76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169–178, 1993) are also improved and extended to the negatively associated setting.