Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Decay chain differential equations: Solution through matrix algebra

A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. (C) 2009 Elsevier B.V. All rights reserved.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.

MapScript: A map algebra programming language incorporating neighborhood analysis

Map algebra is a data model and simple functional notation to study the distribution and patterns of spatial phenomena. It uses a uniform representation of space as discrete grids, which are organized into layers. This paper discusses extensions to map algebra to handle neighborhood operations with a new data type called a template. Templates provide general windowing operations on grids to enable spatial models for cellular automata, mathematical morphology, and local spatial statistics. A programming language for map algebra that incorporates templates and special processing constructs is described. The programming language is called MapScript. Example program scripts are presented to perform diverse and interesting neighborhood analysis for descriptive, model-based and processed-based analysis.

Free field and parafermionic realizations of twisted su(3)(k)((2)) current algebra

Free field and twisted parafermionic representations of twisted su(3)(k)((2)) current algebra are obtained. The corresponding twisted Sugawara energy-momentum tensor is given in terms of three (beta, gamma) pairs and two scalar fields and also in terms of twisted parafermionic currents and one scalar field. Two screening currents of the first kind are presented in terms of the free fields.

Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

Effects of the solute ionization on the adsorption of aromatic compounds from dilute aqueous solutions by activated carbon

Adsorption of four dissociating aromatic compounds and one nondissociating compound on a commercial activated carbon is investigated systematically. All adsorption experiments were carried out in pH-controlled aqueous solutions. The adsorption isotherms are fitted to the binary homogeneous Langmuir model, where the concentrations of the molecular and the ionic species in the liquid phase are expressed in terms of the sum of the two and the degree of solute ionization. Examination of the relationships between the solution pH, the degree of ionization of the solutes, and the model parameters is found to give new insights into the adsorption process. Furthermore, this is used to correlate the variation of the monolayer capacity with the solution pH.

Effects of surface chemistry on aromatic compound adsorption from dilute aqueous solutions by activated carbon

Adsorption of one nondissociating and four dissociating aromatic compounds onto three untreated activated carbons from dilute aqueous solutions were investigated. All adsorption experiments were preformed in pH-controlled solutions. The experimental isotherms were analyzed using the homogeneous Langmuir model. The surface chemical properties of the activated carbons were characterized using a combination of water adsorption, X-ray photoemission spectroscopy, and mass titration. These data give rise to a new insight into the adsorption mechanism of aromatic solutes, in their molecular and ionic forms, onto untreated activated carbons. It was found that, for the hydrophilic activated carbons, the dominant adsorption forces were observed to be dipolar interactions when the solutes were in their molecular form whereas dispersive forces, such as pi-pi interactions, were most likely dominant in the case of the basic hydrophobic carbons. However, when the solutes were in their ionic form adsorption occurs in all cases through dispersive forces.

Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme

A new algebraic Bethe ansatz scheme is proposed to diagonalize classes of integrable models relevant to the description of Bose-Einstein condensation in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra. (C) 2003 American Institute of Physics.

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.

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.

Using relational algebra on the specification of real world ETL processes

Modeling Extract-Transform-Load (ETL) processes of a Data Warehousing System has always been a challenge. The heterogeneity of the sources, the quality of the data obtained and the conciliation process are some of the issues that must be addressed in the design phase of this critical component. Commercial ETL tools often provide proprietary diagrammatic components and modeling languages that are not standard, thus not providing the ideal separation between a modeling platform and an execution platform. This separation in conjunction with the use of standard notations and languages is critical in a system that tends to evolve through time and which cannot be undermined by a normally expensive tool that becomes an unsatisfactory component. In this paper we demonstrate the application of Relational Algebra as a modeling language of an ETL system as an effort to standardize operations and provide a basis for uncommon ETL execution platforms.