Minimal covers of the prisms and antiprisms

This paper contains a classification of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion of their topological structure, and completes the enumeration of such covers for convex uniform polyhedra. Additionally, this paper addresses related structural questions in the theory of string C-groups.     

A theorem about snakes for weak Cartesian systems

It is shown that Karlin's theorem about snakes remains true for polynomials in any weak Cartesian system of continuous functions on a compact set without any change in the statement, and the existence part is valid for arbitrary weak Chebyshev systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 315–321, March, 1995.     

A theorem about affine maps in Banach spaces

It is shown that a weakly compact convex set in a strictly convex space cannot be decomposed into two non-empty, disjoint sets which are similar to each other in the sense that one is the image of the other under a non-expansive affine map.     

A geometric proof of a theorem about non-dual renormings

We give a simple geometric proof of a result by Davis and Johnson that every nonreflexive Banach space admits an equivalent norm in which is not isometric to a dual space. Moreover, our renorming keeps unchanged the original norm on a given finite-codimensional subspace and makes this subspace norm-one complemented.

     

On a theorem about orderability

The purpose of this note is proving a result of Nogura and Shakhmatov [4, Theorem 4]. Furthermore, a characterization of connected spaces with a selection is given. Work supported by the research project “Metodi e problemi in Analisi Reale” of the Italian Ministero dell'Università e della Ricerca Scientifica e Tecnologica.     

On a theorem about projectivities

The main result of this paper is a theorem about projectivities in then-dimensional complex projective spaceP ⁿ (n 2). Puttingn = 2, we showed in [3] that the theorem of Desargues inP ⁿ is a special case of this theorem. And not only the theorem of Desargues but also the converse of the theorem of Pascal, the theorem of Pappus-Pascal, the theorem of Miquel, the Newton line, the Brocard points and a lot of lesser known results in the projective, the affine and the Euchdean plane were obtained from this theorem as special cases without any further proof. Many extensions of classical theorems in the projective, affine and Euclidean plane to higher dimensions can be found in the literature and probably some of these are special cases of this theorem inP ⁿ. We only give a few examples and leave it as an open problem which other special cases could be found.     

A theorem and a question about epicomplete archimedean lattice-ordered groups

An archimedean ?-group is called epicomplete (or universally σ-complete, or sequentially inextensible) if it is divisible, σ-complete and laterally σ-complete. Various characterizations of such G are known in case the G have weak order units. The “theorem” of the title is a characterization of such G which have no weak order unit; it involves the requirement that G have a certain kind of representation. The “question” of the title is whether every epicomplete G has such a representation.     

A remark about the Orlicz-Pettis theorem and the statistical convergence

In this paper we obtain a new version of the Orlicz-Pettis theorem by using statistical convergence. To obtain this result we prove a theorem of uniform convergence on matrices related to the statistical convergence.     

A short proof of a theorem of dirac's about hadwiger's conjecture

A Short proof is given of the theorem that every grph that does not have K₄ as a subcontraction is properly vertex 3-colorable.     

A note on Miller's theorem about maps out of classifying spaces

Let be a connected infinite loop space whose fundamental group is a torsion group and let be a finite nilpotent -complex. The main result of this paper is that the space of based maps from to the profinite completion of is weakly contractible.

     

Remark on Tono's theorem about cuspidal curves

We give an upper bound for the number of cusps of a plane affine or projective curve via its first Betti number.     

Some results about a theorem of Shidov

Abstract The authors characterize the finite groups in which , the intersection of the maximal non-nilpotent subgroups of G, is nilpotent, but different from Φ(G). Further, if is a saturated formation and if is the intersection of all maximal subgroups of G not belonging to , a necessary and sufficient condition is given for to be nilpotent different from Φ(G). Keywords: Frattini subgroup, Maximal subgroups, Saturated formation Mathematics Subject Classification (2000): 20B05, 20D10, 20D25,20E28     

非齐次树上马氏双链的一个强极限定理

树指标随机过程已成为近年发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上马氏双链的一个强极限定理.