Let F be a local/global field. Let E and K be quadratic semisimple F–algebras. Let φ and λ be characters/grössencharacters of E× and K×. We define a local/global symbol ( φ λ ) to be essentially the root number of the representation BCK/F (AIE/F (φ))⊗ λ−1. In the spirit of quadratic reciprocity, we prove that ( φ λ )( λ φ ) = φ(−1)λ(−1). We then derive some consequences of this reciprocity for ...

In this papec we propose a new method of recognizing mathematical formulae. The method is robust against the recognition errors of characters and the variation of the printing styles of the documents. The outline is as follows: we first construct a network with vertices representing the characters (symbols), linked each other by several edges with labels and costs representing the possible rela...

Cultural background can crucially influence human behavior. For virtual characters, that are supposed to imitate human behavior in a natural manner, integrating cultural background came into focus the recent years. Unlike earlier approaches, this paper presents a hybrid approach of modeling a Bayesian network that generates culture-specific behaviors for virtual characters. For the hybrid appro...

In 1979, Lusztig proposed a cohomological construction of supercuspidal representations of reductive p-adic groups, analogous to Deligne–Lusztig theory for finite reductive groups. In this paper we establish a new instance of Lusztig’s program. Precisely, let X be the Deligne–Lusztig (ind-pro-)scheme associated to a division algebra D over a non-Archimedean local field K of positive characteris...

This paper presents a literature review on English OCR techniques. English OCR system is compulsory to convert numerous published books of English into editable computer text files. Latest research in this area has been able to grown some new methodologies to overcome the complexity of English writing style. Still these algorithms have not been tested for complete characters of English Alphabet...

One focus of developmental biology is to understand how genes regulate development, and therefore examining the phenotypic effects of gene mutation is a major emphasis in studies of zebrafish and other model organisms. Genetic change underlies alterations in evolutionary characters, or phenotype, and morphological phylogenies inferred by comparison of these characters. We will utilize both exis...