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.     

On the Restricted Order of Asymptotic Bases of Order Two

The restricted order of an asymptotic basis A is the least integer h, if it exists, such that every sufficiently large integer is the sum of h or fewer distinct elements of A. We show that any asymptotic basis of order 2 has a restricted order at most equal to 4. We also provide an example of an additive basis of order 2 whose restricted order is 4.To Jean-Louis Nicolas2000 Mathematics Subject Classification: Primary—11B13     

Minimal Bases in Complete 3-Lattices

In this paper, u-convergence problems for multiple Fourier series with monotone and with positive coefficients in the L_p metrics are considered.     

On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard Manifold

We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold M of dimension n ≥ 2 for a large class of operators containing, in particular, the p-Laplacian and the minimal graph operator. We extend several existence results obtained for the p-Laplacian to our class of operators. As an application of our main result, we prove the solvability of the asymptotic Dirichlet problem for the minimal graph equation for any continuous boundary data on a (possibly non rotationally symmetric) manifold whose sectional curvatures are allowed to decay to 0 quadratically.     

A Note on Asymptotic Minimal Weights for an Integration Rule

Consider an integration rule with abscissas in the intervalof integration and which is exact for all polynomials up toa certain degree. The error of the rule applied to a Hilbertspace of functions analytic within an ellipse containing intervalof integration is a bounded linear functional. In this paperwe the asymptotic weights of the rule which minimize the normof the error functional as the underlying ellipse shrinks tothe interval of integration.     

On Minimal Coalgebras

We define an out-degree for F-coalgebras and show that the coalgebras of outdegree at most κ form a covariety. As a subcategory of all F-coalgebras, this class has a terminal object, which for many problems can stand in for the terminal F-coalgebra, which need not exist in general. As examples, we derive structure theoretic results about minimal coalgebras, showing that, for instance minimization of coalgebras is functorial, that products of finitely many minimal coalgebras exist and are given by their largest common subcoalgebra, that minimal subcoalgebras have no inner endomorphisms and show how minimal subcoalgebras can be constructed from Moore-automata. Since the elements of minimal subcoalgebras must correspond uniquely to the formulae of any logic characterizing observational equivalence, we give in the last section a straightforward and self-contained account of the coalgebraic logic of D. Pattinson and L. Schröder, which we believe is simpler and more direct than the original exposition.     

极小非PNN-群

有限群G称作PNN-群,如果G的每一个极小子群X要么正规于G,要么是自正规化的.本文将讨论PNN-群的性质,并给出极小非PNN-群,也就是本身不是PNN-群,每个真子群都是PNN-群的有限群的完全分类.     

On Normal Integral Bases

in this paper, let K = Q ( ) be an abelian number field,where mi's are distinct square-free integers and Gal (K/Q ) (Z/2Z )n+1, and let k Q(M). When k is imaginary or k is real and has a unit of norm -1, we give a necessaryand sufficient condition for K/k to have a normal integral basis.     

关于定向极小集

本文对定向极小集作了进一步的研究，得到一系列重要性质，文章最后给出连续格为完全分配格的一个充分条件．     

The Minimal Cost of Approximating Linear Operators Using Perturbed Information-The Asymptotic Setting

We study the asymptotic behavior of the minimal cost of computing an ϵ-approximation to linear continuous operators, as ϵ → 0⁺. An approximation is computed based on perturbed values of linear and continuous functionals which can be chosen adaptively. Obtaining a value of a functional with given precision is connected with some cost determined by the cost function. Under some assumptions, we show that the minimal (information) cost of computing an ϵ-approximation grows essentially as fast as the minimal information cost in the worst case setting. It can grow significantly slower only on a boundary set of problem elements. A nonadaptive method with the information cost proportional to the minimal worst case cost is constructed.     

Inapplicability of Asymptotic Results on the Minimal Spanning Tree in Statistical Testing

Penrose has given asymptotic results for the distribution of the longest edge of the minimal spanning tree and nearest neighbour graph for sets of multivariate uniformly or normally distributed points. We investigate the applicability of these results to samples of up to 100 points, in up to 10 dimensions. We conclude that the asymptotic results provide an acceptable approximation only in the uniform case. Their inaccuracy for the multivariate normal case means that they cannot be applied to improve Rohlf's gap test for an outlier in a set of multivariate data points, which depends on the longest edge of the minimal spanning tree of the set.     

Asymptotic Values and Minimal Fine Limits of Subharmonic Functions of Slow Growth

This paper shows that a subharmonic function in the half-spacewhich does not grow too rapidly near the boundary and whichdoes not have asymptotic value + at too many points must havefinite minimal fine limits at a boundary set of positive measure.For harmonic functions, the conclusion may be expressed in termsof non-tangential limits. A related Phragmén–Lindelöftheorem is also established.     

内PN*-群的结构(英文)

若有限群G的每个极小子群及4阶循环子群在G中正规,则称G为PN~*-群.本文给出了有限群的每个真子群都是PN~*-群但其本身不是PN~*-群的完全分类.     

On Minimal Extensions of Rings

Given two rings R ? S, S is said to be a minimal ring extension of R, if R is a maximal subring of S. In this article, we study minimal extensions of an arbitrary ring R, with particular focus on those possessing nonzero ideals that intersect R trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs &; Shapiro, and Ferrand &; Olivier, on commutative minimal extensions.     

On Torsion-Free Minimal Abelian Groups

ABSTRACT

An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. In this article we show that torsion-free groups which are complete in their ?-adic topology or are of p-rank not greater than 1, for all primes p, are minimal. A criterion is found for the minimality of all finite rank and for large classes of infinite rank completely decomposable groups. Separable minimal groups are also considered.     

On Minimal Entropy and Stability

We study n-manifolds Y whose fundamental groups are subexponential extensions of the fundamental group of some closed locally symmetric manifold X of negative curvature. We show that, in this case, MinEnt(Y)ⁿ is an integral multiple of MinEnt(X)ⁿ, and the value MinEnt(Y) is generally not attained (unless if Y is diffeomorphic to X). This gives a new class of manifolds for which the minimal entropy problem is completely solved. Several examples (even complex projective), obtained by gluings and by taking plane intersections in complex projective space, are described. Some problems about topological stability, related to the minimal entropy problem, are also discussed.     

On Identity Bases of Epigroup Varieties

Let C _n and C _n be the varieties of all completely regular and of all completely simple semigroups, respectively, whose idempotent generated subsemigroups are periodic with period n. We use Ol'shanski 's theory of geometric group presentations to show that for large odd n these varieties (and similarly defined varieties of epigroups) do not have finitely axiomatizable equational theories.     

On Differential Bases Formed of Intervals

Translation invariant subbases of the differential basis B ₂ (formed of all intervals), which differentiates the same class of all non-negative functions as B ₂ does, are described. A possibility for extending the results obtained to bases of more general type is discussed.