Orthogonal systems of spline wavelets as unconditional bases in Sobolev spaces

We exhibit the necessary range for which functions in the Sobolev spaces $L_p^s$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle–Lemarié wavelets. We also consider the natural extensions to Triebel–Lizorkin spaces. This builds upon, and is a generalization of, previous work of Seeger and Ullrich, where analogous results were established for the Haar wavelet system.     

Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

     

Existence of maximal points with respect to ordered bipreference relations

The maximality of a point with respect to an ordered pair of arbitrary preference relations is introduced. Necessary and sufficient conditions for the existence of maximal points are given.The authors are grateful for the referee's comments which led to an improved presentation of the paper.     

An alternative approach to the uniqueness of unconditional basis of for

We give an alternative and much simpler proof of the uniqueness of unconditional basis (up to equivalence and permutation) in the quasi-Banach spaces ℓ_p(c₀) for 0<p<1 and its complemented subspaces with unconditional basis. The new approach uses the fact that the Banach envelope of these spaces is not sufficiently Euclidean with the lattice structure induced by its unconditional basis.     

计算网络最小割的问题的注记

对网络最小割的计算进行了研究,给出了简化求最小割的理论依据.     

Fréchet spaces with unconditional base

A nonnormable ?-space possessing an unconditional basis is not necessarily isomorphic to a generalized Köthe space.     

Minimal bases and maximal nonbases in additive number theory

An asymptotic basis $\text{A}$ of order h is minimal if no proper subset of $\text{A}$ is an asymptotic basis of order h. Examples are constructed of minimal asymptotic bases, and also of an asymptotic basis of order two no subset of which is minimal.If $\text{B}$ is a set of nonnegative integers which is not a basis (resp. asymptotic basis) of order h, but such that every proper superset of $\text{B}$ is a basis (resp. asymptotic basis) of order h, then $\text{B}$ is a maximal nonbasis (resp. maximal asymptotic nonbasis) of order h. Examples of such sets are constructed, and it is proved that every set not a basis of order h is a subset of a maximal nonbasis of order h.     

阶极小渐近基

Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~*(W) the set of all finite,nonempty subsets of W.Fix integer g≥2,let A_g(W) be the set of all numbers of the form sum f∈Fa_fg~f where F∈F~*(W)and 1≤a_f≤g-1.For i=0,1,2,3,let W_i = {n∈N|n≡ i(mod 4)}.In this paper,we show that the set A = U_i~3=0 A_g(W_i) is a minimal asymptotic basis of order four.     

Structure of Gröbner bases with respect to block orders

In this paper we study the structure of Gröbner bases with respect to block orders. We extend Lazard's theorem and the Gianni-Kalkbrenner theorem to the case of a zero-dimensional ideal whose trace in the ring generated by the first block of variables is radical. We then show that they do not hold for general zero-dimensional ideals.

     

网络最小割计算的一点注记

给出了具有单一源和单一汇网络割的数目,完善了一些文献中的不完整之处.     

Maximal and Minimal Semilattices on Ordered Sets

The map which takes an element of an ordered set to its principal ideal is a natural embedding of that ordered set into its powerset, a semilattice. If attention is restricted to all finite intersections of the principal ideals of the original ordered set, then an embedding into a much smaller semilattice is obtained. In this paper the question is answered of when this construction is, in a certain arrow-theoretic sense, minimal. Specifically, a characterisation is given, in terms of ideals and filters, of those ordered sets which admit a so-called minimal embedding into a semilattice. Similarly, a candidate maximal semilattice on an ordered set can be constructed from the principal filters of its elements. A characterisation of those ordered sets that extend to a maximal semilattice is given. Finally, the notion of a free semilattice on an ordered set is given, and it is shown that the candidate maximal semilattice in the embedding-theoretic sense is the free object.     

Reflexivity with maximal ideal axes

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. We in this note study rings with the reflexivity whose axis is given by maximal ideals (simply, an RM ring) which are a generalization of symmetric rings. It is first shown that the reflexivity of a ring and the RM ring property are independent of each other, noting that both of them are generalizations of ideal-symmetric rings. We connect RM rings with reflexive rings in various situations raised naturally in the procedure. As a generalization of RM rings, we also study the structure of the reflexivity with the maximal ideal axis on idempotents (simply, an RMI ring) and then investigate the structure of minimal non-Abelian RMI rings (with or without identity) up to isomorphism.     

乘积空间中非线性算子的极大极小不动点定理及迭代法*

本文研究了乘积空间中非线性算子的极大极小不动点和迭代法.作为我们结果的推论,一些耦合不动点定理被获得、它们推广了由郭大钧和Lankshmikantham获得的耦合不动点定理.(见Nonlinear Anal、11(1986),623-632)和由兰在[4]、[6]中获得的结果.     

On the Markov equivalence of maximal ancestral graphs

Necessary and sufficient conditions for a maximal ancestral graph (MAnG) to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its equivalent DAG is given for the first time.     

There do not exist minimal algebras between C*(X) and C(X) with prescribed real maximal ideal spaces

Let C(X) be the algebra of all real-valued continuous functions on a completely regular Hausdorff space X, and C*(X) the subalgebra of bounded functions. We prove that for any intermediate algebra A between C*(X) and C(X), other than C*(X), there exists a smaller intermediate algebra with the same real maximal ideals as in A. The space X is called A-compact if any real maximal ideal in A corresponds to a point in X. It follows that, for a noncompact space X, there does not exist any minimal intermediate algebra A for which A is A-compact. This completes the answer to a question raised by Redlin and Watson in 1987.     

Minimal generators for symmetric ideals

Let be the polynomial ring in infinitely many indeterminates over a field , and let be the symmetric group of . The group acts naturally on , and this in turn gives the structure of a module over the group ring . A recent theorem of Aschenbrenner and Hillar states that the module is Noetherian. We address whether submodules of can have any number of minimal generators, answering this question positively.

     

Unconditional reproducing kernel bases in de Branges spaces

We describe unconditional bases of the form {k(z,λ _n ):λ _n ∈Λ}, Λ∩?=? in de Branges spaces, where k is the reproducing kernel.     

Absolutely bounded matrices and unconditional convergence

We characterize the so-called absolutely bounded matrices in terms of the (strong) unconditional convergence of their standard decompositions. There is a similar characterization of absolutely compact matrices, and both characterizations are closely related to some natural multiplication operators. Rudiments of the duality theory for the algebra of all absolutely bounded matrices are included.