Making nontrivially associated modular categories from finite groups

We show that the non-trivially associated tensor category constructed from left coset representatives of a subgroup of a finite group is a modular category. Also we give a definition of the character of an object in a ribbon category which is the category of representations of a braided Hopf algebra in the category. The definition is shown to be adjoint invariant and multiplicative. A detailed example is given. Finally we show an equivalence of categories between the non-trivially associated double D and the category of representations of the double of the group D(X).Comment: Approx 43 pages, uses LaTeX picture environmen

A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations

The present paper is devoted to the development of a new scheme to solve the initial-boundary value Korteweg-de Vries equation which models many physical phenomena such as surface water waves in a channel. The scheme consists of Jacobi dual-Petrov Galerkin-Jacobi collocation method in space combined with Crank-Nicholson-leap-frog method in time such that at each time step only a sparse banded linear algebraic system needs to be solved. Numerical results are presented to show that the proposed numerical method is accurate and efficient for Korteweg-de Vries equations and other third-order nonlinear equations

Sequencing, Analysis, and Annotation of Expressed Sequence Tags for Camelus dromedarius

Despite its economical, cultural, and biological importance, there has not been a large scale sequencing project to date for Camelus dromedarius. With the goal of sequencing complete DNA of the organism, we first established and sequenced camel EST libraries, generating 70,272 reads. Following trimming, chimera check, repeat masking, cluster and assembly, we obtained 23,602 putative gene sequences, out of which over 4,500 potentially novel or fast evolving gene sequences do not carry any homology to other available genomes. Functional annotation of sequences with similarities in nucleotide and protein databases has been obtained using Gene Ontology classification. Comparison to available full length cDNA sequences and Open Reading Frame (ORF) analysis of camel sequences that exhibit homology to known genes show more than 80% of the contigs with an ORF>300 bp and ~40% hits extending to the start codons of full length cDNAs suggesting successful characterization of camel genes. Similarity analyses are done separately for different organisms including human, mouse, bovine, and rat. Accompanying web portal, CAGBASE (http://camel.kacst.edu.sa/), hosts a relational database containing annotated EST sequences and analysis tools with possibility to add sequences from public domain. We anticipate our results to provide a home base for genomic studies of camel and other comparative studies enabling a starting point for whole genome sequencing of the organism

Sequencing, Analysis, and Annotation of Expressed Sequence Tags for \u3ci\u3eCamelus dromedarius\u3c/i\u3e

Despite its economical, cultural, and biological importance, there has not been a large scale sequencing project to date for Camelus dromedarius. With the goal of sequencing complete DNA of the organism, we first established and sequenced camel EST libraries, generating 70,272 reads. Following trimming, chimera check, repeat masking, cluster and assembly, we obtained 23,602 putative gene sequences, out of which over 4,500 potentially novel or fast evolving gene sequences do not carry any homology to other available genomes. Functional annotation of sequences with similarities in nucleotide and protein databases has been obtained using Gene Ontology classification. Comparison to available full length cDNA sequences and Open Reading Frame (ORF) analysis of camel sequences that exhibit homology to known genes show more than 80% of the contigs with an ORF\u3e300 bp and ~40% hits extending to the start codons of full length cDNAs suggesting successful characterization of camel genes. Similarity analyses are done separately for different organisms including human, mouse, bovine, and rat. Accompanying web portal, CAGBASE (http://camel.kacst.edu.sa/), hosts a relational database containing annotated EST sequences and analysis tools with possibility to add sequences from public domain. We anticipate our results to provide a home base for genomic studies of camel and other comparative studies enabling a starting point for whole genome sequencing of the organism

Influence of weakly H-subgroups of minimal subgroups on the structure of finite groups

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H) \ Hg H for all g in G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and  H \ K is an H-subgroup in G. In this paper, we use weakly H-subgroup condition on minimal subgroups to study the structure of the finite group G. Some earlier results are improved and extend

Lie Groups Analysis and Contact Transformations for Ito System

Generalized Ito systems of four coupled nonlinear evaluation equations are proposed. New classes of exact invariant solutions by using Lie group analysis are obtained. Moreover, we investigate the existence of a one-parameter group of contact transformations for a generalized Ito system. Consequently, we study the relationship between one-parameter group of a contact transformation and a one-parameter Lie point transformation for a generalized Ito system

The Influence of Cc-normality Subgroups on the Structure of Finite Groups

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