Collectionwise normality and selections into Hilbert spaces

A T₁-space X is countably paracompact and collectionwise normal if and only if every l.s.c. mapping from X into a Hilbert space with closed and convex point-images has a continuous selection. This settles a conjecture posed by M. Choban, V. Gutev and S. Nedev [M. Choban, S. Nedev, Continuous selections for mappings with generalized ordered domain, Math. Balkanica (N.S.) 11 (1-2) (1997) 87-95].     

Generic adjoints in comtrans algebras of bilinear spaces

As a first step towards a general structure theory for comtrans algebras (modeled loosely on the Cartan theory for Lie algebras), this paper investigates comtrans algebras of bilinear spaces. Attention focuses on invariants associated with comtrans algebras, and the extent to which these invariants may serve to specify the algebras up to isomorphism within certain classes. Over fields whose characteristic differs from two, comtrans algebras of symmetric forms are determined up to isomorphism by the eigenvalues of generic adjoints, while comtrans algebras of symplectic forms are determined by the dimensions of maximal abelian subalgebras. Examples show that the multiplicity of zero as a root of the characteristic polynomial is generally independent of the dimension of a maximal abelian subalgebra.     

Reduction principles in the theory of selections

In the present article many theorems about existence of continuous selections for a set-valued mapping into the metrizable spaces are extended to mappings into non-metrizable spaces.     

Nonparametric methods for unbalanced multivariate data and many factor levels

We propose different nonparametric tests for multivariate data and derive their asymptotic distribution for unbalanced designs in which the number of factor levels tends to infinity (large a, small n_i case). Quasi gratis, some new parametric multivariate tests suitable for the large a asymptotic case are also obtained. Finite sample performances are investigated and compared in a simulation study. The nonparametric tests are based on separate rankings for the different variables. In the presence of outliers, the proposed nonparametric methods have better power than their parametric counterparts. Application of the new tests is demonstrated using data from plant pathology.     

Rigidity in motivic homotopy theory

We show that extensions of algebraically closed fields induce full and faithful functors between the respective motivic stable homotopy categories with finite coefficients.     

The Ulm method under mild differentiability conditions

The Ulm method is considered to approximate a solution of a nonlinear operator equation F(x) = 0. We study the convergence of this method when F′ is ω-conditioned and prove that the R-order of convergence is at least 1 + p if ω is quasi-homogeneous of type ω(tz)≤ t ^p ω(z), for z > 0, tϵ[0,1] and pϵ[0,1]. Preparation of this paper was partly supported by the Ministry of Education and Science (MTM 2005-03091).     

Bézout rings with almost stable range 1

Elementary divisor domains were defined by Kaplansky [I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949) 464-491] and generalized to rings with zero-divisors by Gillman and Henriksen [L. Gillman, M. Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82 (1956) 362-365]. In [M.D. Larsen, W.J. Lewis, T.S. Shores, Elementary divisor rings and finitely presented modules, Trans. Amer. Math. Soc. 187 (1) (1974) 231-248], it was also proved that if a Hermite ring satisfies (N), then it is an elementary divisor ring. The aim of this article is to generalize this result (as well as others) to a much wider class of rings. Our main result is that Bézout rings whose proper homomorphic images all have stable range 1 (in particular, neat rings) are elementary divisor rings.     

Influence of permutizers of subgroups on the structure of finite groups

A group G is said to satisfy the maximal permutizer condition if the permutizer of any maximal subgroup M of G in G, P_G(M), is G. In this paper, we characterize the supersolubility of finite groups by using the maximal permutizer condition. We also get some results for when both G/N and N are supersoluble, which implies that G is supersoluble. Our results unify or generalize some known results.     

Intermediary rings in normal pairs

We establish in this paper a result that gives the number of intermediary rings between R and S where (R,S) is a normal pair of rings. This result answers in particular a question which was left open in [A. Jaballah, Finiteness of the set of intermediary rings in a normal pair, Saintama Math. J. 17 (1999) 59-61]. Further applications are also given.