Multiple Categories: The Equivalence of a Globular and a Cubical Approach

We show the equivalence of two kinds of strict multiple category, namely the well-known globular ω-categories, and the cubical ω-categories with connections.     

Global existence of a classical solution for a large class of free boundary problems in one space dimension

We prove global classical solvability and a uniqueness theorem for a wide class of one dimensional free boundary problems in which the evolution of the free boundarys(t) is controlled by the derivatives up to the second order ofu (u together withs(t) is an unknown of our problem) and by a functional ofs(t) itself. In the Introduction it is showed the physical background from which such problems arise.Work partially supported by the Italian M.U.R.S.T. National Project Problemi non lineari...     

Symmetric K-Theory Spectra of C*-Categories

We define K-theory groups and symmetric K-theory spectra associated to ₂-graded C ^*-categories and show that the exterior product of K-theory groups can be expressed in terms of the smash product of symmetric spectra.     

NIL PROBLEMS REVISITED FOR ALMOST NILPOTENT RINGS

Abstract

We begin with the notion of K-flat projectivity. For each biframe L we then introduce a binary relation ?L on it. The K-flat projective biframes are exactly such biframes with each element a of the total (first, second) part approximated by the elements x of the total (first, second) part, x?_L a and the relation ?_L being stable wrt. the meet operation on L. Further on, we introduce the notion of a K-comonad and characterize K-flat projective biframes as those biframes having a coalgebra structure for the K-comonad. The K-coherent biframes and K-flat projective biframes are coreflective in all biframes.     

On error bounds of polynomial complementarity problems with structured tensors

The recently introduced polynomial complementarity problem (PCP) is an interesting generalization of the tensor complementarity problem (TCP) studied extensively in the literature. In this paper, we make a contribution to analysing the error bounds of PCPs with structured tensors. Specifically, we first show that the solution set of PCPs with a leading ER-tensor is nonempty and compact. Then, we analyse lower bounds of solutions of PCPs under the strict semicopositiveness, thereby gainfully establishing error bounds of PCPs, which, to the best of our knowledge, are not studied in the current PCPs and TCPs literature. Moreover, it is noteworthy that, due to the special structure of PCPs, our error bounds are better than the direct results obtained by applying the theory of non-linear complementarity problems to PCPs.     

k-Eulerian Posets

A poset P is called k-Eulerian if every interval of rank k is Eulerian. The class of k-Eulerian posets interpolates between graded posets and Eulerian posets. It is a straightforward observation that a 2k-Eulerian poset is also (2k+1)-Eulerian. We prove that the ab-index of a (2k+1)-Eulerian poset can be expressed in terms of c=a+b, d=ab+ba and e ^2k+1=(a–b)^2k+1. The proof relies upon the algebraic approaches of Billera-Liu and Ehrenborg-Readdy. We extend the Billera-Liu flag algebra to a Newtonian coalgebra. This flag Newtonian coalgebra forms a Laplace pairing with the Newtonian coalgebra ka,b studied by Ehrenborg-Readdy. The ideal of flag operators that vanish on (2k+1)-Eulerian posets is also a coideal. Hence, the Laplace pairing implies that the dual of the coideal is the desired subalgebra of ka,b. As a corollary we obtain a proof of the existence of the cd-index which does not use induction.     

On co-positive,semi-monotoneQ-matrices

In this paper we consider not necessarily symmetric co-positive as well as semi-monotoneQ-matrices and give a set of sufficient conditions for such matrices to beR ₀-matrices. We give several examples to show the sharpness of our results. Construction of these examples is based on the following elementary proposition: IfA is a square matrix of ordern whose first two rows are identical and bothA ₁₁ andA ₂₂ areQ-matrices whereA _ii stands for the principal submatrix ofA obtained by deleting rowi and columni fromA, thenA is aQ-matrix.Dedicated to our colleague and friend B. Ramachandran on his sixtieth birthday.Corresponding author.     

Differential Criterion of Complete Regular Local Rings

Abstract

In the paper by Furuya and Niitsuma [Furuya, M., Niitsuma, H. (2002a). On m -adic higher differentials and regularities of Noetherian complete local rings. J. Math. Kyoto Univ. 42(1):33–40], we gave a regularity criterion of complete Noetherian local rings in terms of the concept of m -adic higher differentials with some assumptions of separability on the residue fields of the local rings. The aim of this paper is to try to weaken “the separability assumptions” in a premise of the theorems in Furuya and Niitsuma (2002a).     

Systems of linear differential equations symmetric with respect to transformations nonlinear in a function

We show that if a system of first order linear differential equations with constant coefficients admits an operator whose coordinates responsible for the transformation of independent variables depend on functions then it admits an operator whose coordinates responsible for the transformation of functions depend nonlinearly on functions.     

One Setting for All: Metric, Topology, Uniformity, Approach Structure

For a complete lattice V which, as a category, is monoidal closed, and for a suitable Set-monad T we consider (T,V)-algebras and introduce (T,V)-proalgebras, in generalization of Lawvere's presentation of metric spaces and Barr's presentation of topological spaces. In this lax-algebraic setting, uniform spaces appear as proalgebras. Since the corresponding categories behave functorially both in T and in V, one establishes a network of functors at the general level which describe the basic connections between the structures mentioned by the title. Categories of (T,V)-algebras and of (T,V)-proalgebras turn out to be topological over Set.     

The Commutators of Fractional Integrals on Besov Spaces

Abstract   In this paper we consider the commutators of fractional integrals

Linear Volterra Integral Equations as the Limit of Discrete Systems

We consider the multidimensional abstract linear integral equation of Volterra type x（t） （*）∫Rtα（s)x(s)ds=f(t),t∈R,（1）as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Bauach space-valued defined on a compact interval R of R^n Rt is a subinterval of R depending on t ∈ R and (*) f denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems, The Henstock integral setting enables us to consider highly oscillating functions.     

辫子T-范畴的构造

本文首先引入了一类新的范畴_AYD_G^H, 这个范畴是一簇范畴{_AYD^H(α,β)}_(α,β)∈G的非交并, 获得了范畴{_AYD^H(α,β)}_(α,β)∈G是一个辫子T-范畴当且仅当(A,H,Q)是一个G-偶结构, 推广了2005年Panaite和Staic的主要结论. 最后, 当H是有限维时, 构造了一个拟三角T-余代数{A#H^*(α,β)}_(α,β)∈G, 它的表示范畴与{_AYD^H(α,β)}_(α,β)∈G是同构的.     

On the Peripheral Spectrum of Order Continuous,Positive Operators

Let E be an order complete Banach function lattice and T a positive, eventually compact, order continuous operator on E. We study necessary conditions under which the peripheral spectrum of T is fully cyclic in terms of certain bands of the underlying Banach function lattice E. A set of sufficient conditions is also given. Examples are presented to demonstrate our methods.