‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...

The success of beetles is mainly attributed to the possibility to hide the hindwings under the sclerotised elytra. The acquisition of the transverse folding function of the hind wing is an important event in the evolutionary history of beetles. In this study, the morphological and functional variances in the hind wings of 94 leaf beetle species (Coleoptera: Chrysomelinae) is explored using geom...

We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern’s probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabili...

It is demonstrated how a Hyperset Theory (satisfying P.Aczel's Anti-Foundation Axiom) naturally arises from the idea of World-Wide Web (WWW). Alternatively, Web serves as an illustration and possible application of the abstract notion of antifounded sets. A -language of Bounded Hyperset Theory is presented as a query language to the Web or, more generally, to Web-like Data Bases (WDB). It is sh...

This study presents a psycholinguistically motivated evaluation method for phoneme classifiers by using non-categorical perceptual data elicited in a Japanese sibilant matching 2AFC task. Probability values of a perceptual [s]-[S] boundary, obtained from 42 speakers over a 7-step synthetic [s]-[S] continuum, were compared to probability estimates of Gaussian mixture models (GMMs) of Japanese [s...

An ordered partition with k blocks of [n] := {1, 2, . . . , n} is a sequence of k disjoint and nonempty subsets, called blocks, whose union is [n]. In this article, we consider Steingŕımsson’s conjectures about Euler-Mahonian statistics on ordered partitions dated back to 1997. We encode ordered partitions by walks in some digraphs and then derive their generating functions using the transfer-m...

0. INTRODUCTION. Although the word problem for free lattices is well known to be solvable (cf. Dean [1]), the question still remains open to characterize the finite partial lattices P for which the free lattice F (P ) over P is finite. There are partial answers to this question. In Wille [5] the problem is solved for the partial lattices P that are both meet– and join–trivial in the sense that ...

An upward drawing of a tree is a drawing such that no parents are below their children. It is order-preserving if the edges to children appear in prescribed order around each vertex. Chan showed that any tree has an upward order-preserving drawing with width O(logn). In this paper, we consider upward order-preserving drawings where edges are allowed to have bends. We present a linear-time algor...

The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that defines IndependentSet. This result can also be understood as that every sentence that defines a NP-complete problem P can be decomposed in two disjuncts suc...

We introduce a new framework for a descriptive complexity approach to arithmetic computations. We define a hierarchy of classes based on the idea of counting assignments to free function variables in first-order formulae. We completely determine the inclusion structure and show that #P and #AC0 appear as classes of this hierarchy. In this way, we unconditionally place #AC0 properly in a strict ...