The probability p(s) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [0,1]. The function p is called a numerical event or multidimensional probability. When appropriately structured, sets P of numerical events form so-called algebras of S-probabilities. Their main feature is that they are orthomodular partially ordered sets of functions p with an inherent full set of states. A classical physical system can be characterized by the fact that the corresponding algebra P of S-probabilities is a Boolean lattice. We give necessary and sufficient conditions for systems of numerical events to be a lattice and characterize those systems which are Boolean. Assuming that only a finite number of measurements is available our focus is on finite algebras of S-probabilties.
Let K be a field and S = K[x1, ..., xm, y1,..., yn] be the standard bigraded polynomial ring over K. In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” S-modules with respect to Q = (y1, ..., yn). Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to Q in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to Q are considered., Leila Parsaei Majd, Ahad Rahimi., and Obsahuje seznam literatury
Let $G$ be a finite nonabelian group, ${\mathbb Z}G$ its associated integral group ring, and $\triangle (G)$ its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups $Q_{n}(G)=\triangle ^{n}(G)/\triangle ^{n+1}(G)$ is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.
Let $K = \mathbb {F}_q(T)$ be the rational function field over a finite field of $q$ elements. For any polynomial $f(T)\in \mathbb {F}_q[T]$ with positive degree, denote by $\Lambda _f$ the torsion points of the Carlitz module for the polynomial ring $\mathbb {F}_q[T]$. In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield $M$ of the cyclotomic function field $K(\Lambda _P)$ of degree $k$ over $\mathbb {F}_q(T)$, where $P\in \mathbb {F}_q[T]$ is an irreducible polynomial of positive degree and $k>1$ is a positive divisor of $q-1$. A formula for the analytic class number for the maximal real subfield $M^+$ of $M$ is also presented. Futhermore, a relative class number formula for ideal class group of $M$ will be given in terms of Artin $L$-function in this paper.
The aim of this work is to analyze suitability of existing internet multimedia storage services to use as a covert (steganographic) transmission channel. After general overview we focus specifically on the YouTube service. In particular, we study the feasibility of the recently proposed new steganographic technique \cite{wseas} of hiding information directly in the structure of the mp4-encoded video file. Our statistical analysis of the set of 1000 video files stored by this service show the practical limitations for this type of information hiding.
For a bipartite graph $G$ and a non-zero real $\alpha $, we give bounds for the sum of the $\alpha $th powers of the Laplacian eigenvalues of $G$ using the sum of the squares of degrees, from which lower and upper bounds for the incidence energy, and lower bounds for the Kirchhoff index and the Laplacian Estrada index are deduced.
It is shown that tlie computational power of iion-uniform infinite families of (discrete) neural nets reading their inputs sequentially (so-called neuromata), of polynomial size, equals to PSPACE/poly, and of logarithmic size to LOGSPACE/loy. Thus, such farnilies posses super-Turiug computational power. From computational complexity point of view the above mentioned results rank the respective families of neuromata among the most powerful computational devices known today.
The monotypic genus Seychellesius Carvalho is transferred from the subfamily Cylapinae to Deraeocorinae, tribus Termatophylini Renter. Redescriptions and illustrations of the genus and its single species Seychellesius niger (Distant) are given.
Phylogenetic relationships within the diving-beetle subfamily Hydroporinae are not well understood. Some authors include the genus Pachydrus Sharp, 1882 in the tribe Hyphydrini, whereas others are in favour of excluding Pachydrus from the Hyphydrini and placing it in its own tribe, Pachydrini. Larval characters have been underutilised in phylogenetic studies, mainly because the larvae of many taxa within the family are unknown. In this study, the phylogenetic relationships of Pachydrus are studied based on a cladistic analysis of 34 taxa and 122 morphological larval characters. For this purpose, larvae of P. obesus Sharp, 1882 are described and illustrated in detail for the first time, with particular emphasis on morphometry and chaetotaxy. First and second instars for the genus were unknown. The results support a monophyletic origin of the tribe Hyphydrini excluding Pachydrus, based on four unique character states. On the other hand, Pachydrus is resolved as the sister group of the Hydrovatini. These results suggest Pachydrus should not be placed in the Hyphydrini. Given that the Hyphydrini minus Pachydrus is a distinctive clade, based on this study, it seems useful to recognise this group as Hyphydrini. Including Pachydrus in Hyphydrini would leave the tribe with a single larval apomorphy, as most characters present in the Hyphydrini and Pachydrus are also present in the Hydrovatini. However, in the absence of larvae of Heterhydrus Fairmaire, 1869 and of a more comprehensive and inclusive analysis, we do not propose a formal exclusion of Pachydrus from Hyphydrini at this stage. Pachydrus is a highly distinctive genus within the Hydroporinae and is characterised by several larval apomorphies.