On minimal Hausdorff and minimal Urysohn functions

In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.     

On minimal non-MSN-groups

A finite group G is called an MSN-group if all maximal subgroups of the Sylow subgroups of G are subnormal in G. In this paper, we determinate the structure of non-MSN-groups in which all of whose proper subgroups are MSN-groups.     

On minimal simple lattices

The class of simple lattices, excluding the two-element lattice, is preordered by placing L₀L₁ iff L₀ belongs to the variety generated by L₁. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices.Presented by G. McNulty.Research supported by National Science Foundation Grant DMS 89 04014.     

On minimal strong blocks

It is shown that storng blocks, i.e., digraphs that are strongly connected and have no cutnodes have an ear-decomposition. This result is used to prove that the number q of arcs of minimal strong blocks is bounded by p ≤ q ≤ 2p – 3 and that minimal strong blocks contain at least two nodes with indegree and outdegree equal to one.     

On minimal universal trees

In this paper we solve the problem of finding a minimal n-universal rooted tree. We show that the number(n) of vertices of a minimal n-universal rooted tree coincides with the quantity of trees of a special form (uniform trees), the number of whose vertices n. We derive a recursion formula for computing the value of(n). We also specify the construction of a minimal universal tree for an arbitrary set of uniform trees.Translated from Matematicheskie Zametki, Vol. 4, No. 3, pp. 371–379, September, 1968.We should like to express our gratitude to Yu. I. Lyubich for his attention and valuable advice.     

On minimal exposed faces

In this paper we consider the problem of the non-empty intersection of exposed faces in a Banach space. We find a sufficient condition to assure that the non-empty intersection of exposed faces is an exposed face. This condition involves the concept of inner point. Finally, we also prove that every minimal face of the unit ball must be an extreme point and show that this is not the case at all for minimal exposed faces since we prove that every Banach space with dimension greater than or equal to 2 can be equivalently renormed to have a non-singleton, minimal exposed face.     

On minimal strongly KC-spaces

In this article we introduce the notion of strongly KC-spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space (X, τ) is maximal countably compact if and only if it is minimal strongly KC, and apply this result to study some properties of minimal strongly KC-spaces, some of which are not possessed by minimal KC-spaces. We also give a positive answer to a question proposed by O.T. Alas and R.G. Wilson, who asked whether every countably compact KC-space of cardinality less than c has the FDS-property. Using this we obtain a characterization of Katítov strongly KC-spaces and finally, we generalize one result of Alas and Wilson on Katìtov-KC spaces. This research was supported by NSFC of China (No. 10671173).     

On minimal non- -groups

A finite group G is called an J N J-group if every proper subgroup H of G is either subnormal in G or self-normalizing. We determinate the structure of non-J N J-groups in which all proper subgroups are J N J- groups.     

On finite minimal non-nilpotent groups

A critical group for a class of groups is a minimal non- -group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol'fand's theorem on maximal Schmidt groups.

     

On block minimal residual methods

In the present work, we give some new results for block minimal residual methods when applied to multiple linear systems. Using the Schur complement, we develop new expressions for the approximation obtained, for the corresponding residual and for the Frobenius residual norm. These results could be used to derive new convergence properties for the block minimal residual methods.     

On minimal complements in groups

The Ramanujan Journal - Let $$W,W'subseteq G$$ be non-empty subsets in an arbitrary group G. The set $$W'$$ is said to be a complement to W if $$Wcdot W'=G$$ and it is minimal if no...     

On a minimal factorization conjecture

Let be a proper holomorphic map from a connected complex surface S onto the open unit disk D⊂C, with 0∈D as its unique singular value, and having fiber genus g>0. Assume that in case g?2, admits a deformation whose singular fibers are all of simple Lefschetz type. It has been conjectured that the factorization of the monodromy f∈Mg around ?⁻¹(0) in terms of right-handed Dehn twists induced by the monodromy of has the least number of factors among all possible factorizations of f as a product of right-handed Dehn twists in the mapping class group (see [M. Ishizaka, One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists, J. Math. Soc. Japan 58 (2) (2006) 585-594]). In this article, the validity of this conjecture is established for g=1.