其真商群是周期FC-群的群

利用外FC-群的结果,给出了其真商群为周期FC-群但它本身不具备这种性质的群的结构的满意描述.     

A Note on Shelling

The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial and algebraic structure is well understood for crystals, but less so for non-periodic arrangements such as mathematical quasicrystals or model sets. In this note we summarise several aspects of central versus averaged shelling, illustrate the difference with explicit examples and discuss the obstacles that emerge with aperiodic order.     

A Note on CLT-Groups

In this paper, we characterize finite groups G satisfying that, for every prime power divisor p ⁿ of the order of G, there exists a subgroup H of index p ⁿ (of order p ⁿ ) in G such that H is normal or abnormal in G.     

A Note on Prehomomorphisms

We show that if G is a free group with basis X then any map θ from X to an inverse monoid S extends to a monoid prehomomorphism ψ: G\rightarrow S. As an application we give an affirmative answer to a problem of M. Petrich. 1980 Mathematics Subject Classification: Primary 20M10. September 14, 1999     

A Note on Monomials

We study discontinuous solutions of the monomial equation ${{\frac{1}{n!} \Delta _{h}^{n}f(x) = f(h)}}$ . In particular, we characterize the closure of their graph, ${\overline{G(f)}^{\mathbb{R}^{2}}}$ , and we use the properties of these functions to present a new proof of the Darboux type theorem for polynomials and of Hamel’s theorem for additive functions.     

A Note on Vorticity

The relationship between vorticity and mean angular velocityis explored by methods that do not involve tensors so as toreveal the general relations between any component of vorticityand the mean angular velocity in a perpendicular plane and betweenvorticity and the mean angular velocity of a short line of fluidparticles, over all orientations at a point. Two results aredemonstrated concerning the relation between the moment of momentumof the fluid and suitably defined mean values of the vorticityover a sphere of finite radius. One result concerns the contentsof the sphere, the other a spherical shell.     

A Note on Fibrations

In this paper we generalize a theorem of McAuley-Tulley [2] to show that small homotopies of any topological space can be lifted to small homotopies for any Hurewicz fibration between arbitrary topological spaces. Received: July 7, 2005. Revised: July 13, 2006.     

关于双曲性的一点注记

双曲线性几乎等价于拟－Anosov这一令人惊奇的结果是在文献[1]中由Mane证明的,这里,我们给出这一结果一个较为简洁和直观的证明。     

A Note on t-SFT-rings

We define a nonzero ideal A of an integral domain R to be a t-SFT-ideal if there exist a finitely generated ideal B ? A and a positive integer k such that a ^k  ? B _v for each a ? A _t , and a domain R to be a t-SFT-ring if each nonzero ideal of R is a t-SFT-ideal. This article presents a number of basic properties and stability results for t-SFT-rings. We show that an integral domain R is a Krull domain if and only if R is a completely integrally closed t-SFT-ring; for an integrally closed domain R, R is a t-SFT-ring if and only if R[X] is a t-SFT-ring; if R is a t-SFT-domain, then t ? dim R[[X]] ≥ t ? dim R. We also give an example of a t-SFT Prüfer v-multiplication domain R such that t ? dim R[[X]] > t ? dim R.     

A Note on Reflexivity

We prove some new results on Hadwin's general version of reflexivity that reduce the study of E-reflexivity (or E-hyperreflexivity) of a linear subspace to a smaller linear subspace. By applying our abstract results, we present a simple proof of D. Hadwin's theorem, which states that every C^∗-algebra is approximately hyperreflexive. We also prove that the image of any C^∗-algebra under any bounded unital homomorphism into the operators on a Banach space is approximately reflexive. We introduce a new version of reflexivity, called approximate algebraic reflexivity, and study its properties.     

A Note on NUCOMP

This note is a detailed explanation of Shanks-Atkin NUCOMP--composition and reduction carried out ``simultaneously'--for all quadratic fields, that is, including real quadratic fields. That explanation incidentally deals with various ``exercises' left for confirmation by the reader in standard texts. Extensive testing in both the numerical and function field cases by Michael J Jacobson, Jr, reported elsewhere, confirms that NUCOMP as here described is in fact efficient for composition both of indefinite and of definite forms once the parameters are large enough to compensate for NUCOMP's extra overhead. In the numerical indefinite case that efficiency is a near doubling in speed already exhibited for discriminants as small as .

     

A Note on Shiffman's Theorems

Shiffman proved his famous first theorem, that if A R³ is a compact minimal annulus bounded by two convex Jordan curves in parallel (say horizontal) planes, then A is foliated by strictly convex horizontal Jordan curves. In this article we use Perron's method to construct minimal annuli which have a planar end and are bounded by two convex Jordan curves in horizontal planes, but the horizontal level sets of the surfaces are not all convex Jordan curves or straight lines. These surfaces show that unlike his second and third theorems, Shiffman's first theorem is not generalizable without further qualification.     

关于sn度量空间的注记

The main purpose of this paper is to establish the mapping relation between metric spaces and sn-metric spaces.     

关于次加泛函的一点注记

In this note we obtained a both sufficient and necessary condition there exist non-zero β′ degree abslutely homogeneous, continuous and subadditive unctionals in metric linear spaces (E, ‖·‖_β) for C < β≤β′ ≤1 . APPlying our result, a simpler proof of theorem in[1,§1] was given.     

A Note on Well-posed Problems

A recent result by Ricceri [Ri] states that a ${C^{1,1}_{loc}}$ function ${f : X \to {\mathbb R}}$ , where X is a Hilbert space, attains its minimum on any small closed ball around a point where its derivative does not vanish, and that the unique minimum point belongs to the boundary of the ball. The proof is based on a saddle-point theorem. We show that the result, which we extend to Banach spaces having a norm with modulus of convexity of power type 2, can be obtained by means of a purely variational argument.     

关于AP-内射环的一个注记

本文的主要目的是讨论AP-内射环中的两个问题:(1)环R是正则的当且仅当R是左AP-内射的左PP-环;(2)如果R是左AP-内射环,那么R是内射环当且仅当R是弱内射环.因此我们推广了内射环的一些结果,与此同时我们还取得了一些新的结果.     

A Note on Veraverbeke's Theorem

We give an elementary probabilistic proof of Veraverbeke's theorem for the asymptotic distribution of the maximum of a random walk with negative drift and heavy-tailed increments. The proof gives insight into the principle that the maximum is in general attained through a single large jump.     

A Note on Zorn's Theorem

In this note, we prove that if G is a finite group, then G is p-nilpotent if and only if there exists a positive integer n such that for any x,y∈G.     

关于Ekeland—Caristi定理的一点注记

1.引言 为适应讨论映象满射性等问题的需要,W.O.Ray和A.M.Walker在[1]中对Ekeland—Caristi定理作了新的推广,获得如下的结果: 定理1.1 设(M,d)为完备距离空间,:M→[0,∞)下半连续,C:[0,∞)→[0,∞)连续,不增,且integral from 0 to ∞(C(s)ds=∞)。x_0∈M为某一固定点。若映象g:M→M满足