An algebra and conceptual model for semantic tagging of collaborative digital libraries

Cost-effective semantic description and annotation of shared knowledge resources has always been of great importance for digital libraries and large scale information systems in general. With the emergence of the Social Web and Web 2.0 technologies, a more effective semantic description and annotation, e.g., folksonomies, of digital library contents is envisioned to take place in collaborative and personalised environments. However, there is a lack of foundation and mathematical rigour for coping with contextualised management and retrieval of semantic annotations throughout their evolution as well as diversity in users and user communities. In this paper, we propose an ontological foundation for semantic annotations of digital libraries in terms of flexonomies. The proposed theoretical model relies on a high dimensional space with algebraic operators for contextualised access of semantic tags and annotations. The set of the proposed algebraic operators, however, is an adaptation of the set theoretic operators selection, projection, difference, intersection, union in database theory. To this extent, the proposed model is meant to lay the ontological foundation for a Digital Library 2.0 project in terms of geometric spaces rather than logic (description) based formalisms as a more efficient and scalable solution to the semantic annotation problem in large scale.

Linear algebra: selected problems

Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

代數學Dai shu xue.De Morgan's Algebra.

Traduction Chinoise par Alexander Wylie (1815-1887), rédigée par Li Shan lan, de Hai ning. Préface Chinoise par Wylie (1859) ; préface anglaise, écrite par le même à Shang hai (octobre 1859), contenant un historique des mathématiques en Chine. Imprimé en caractères mobiles, dans la maison Mo hai (1859).Livre préliminaire + 13 livres.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.

Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

Validación matemática de un nuevo método para salvación de algunos tipos de problemas relacionados con algebra lineal

Tesis (Maestría en Ingenieria Industrial con Especialidad en Sistemas) UANL

Algebra [por] Miguel Angel Garza Tamez... [y otros]

UANL

Algebra [por] Miguel Angel Garza Tamez... [y otros]

UANL