Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Studies on a syntax based approach for translation between structurally different languages and the development of a prototype for Malayalam to English translation

This thesis summarizes the results on the studies on a syntax based approach for translation between Malayalam, one of Dravidian languages and English and also on the development of the major modules in building a prototype machine translation system from Malayalam to English. The development of the system is a pioneering effort in Malayalam language unattempted by previous researchers. The computational models chosen for the system is first of its kind for Malayalam language. An in depth study has been carried out in the design of the computational models and data structures needed for different modules: morphological analyzer , a parser, a syntactic structure transfer module and target language sentence generator required for the prototype system. The generation of list of part of speech tags, chunk tags and the hierarchical dependencies among the chunks required for the translation process also has been done. In the development process, the major goals are: (a) accuracy of translation (b) speed and (c) space. Accuracy-wise, smart tools for handling transfer grammar and translation standards including equivalent words, expressions, phrases and styles in the target language are to be developed. The grammar should be optimized with a view to obtaining a single correct parse and hence a single translated output. Speed-wise, innovative use of corpus analysis, efficient parsing algorithm, design of efficient Data Structure and run-time frequency-based rearrangement of the grammar which substantially reduces the parsing and generation time are required. The space requirement also has to be minimised

The median function on graphs with bounded profiles

The median of a profile = (u1, . . . , uk ) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of . It is shown that for profiles with diameter the median set can be computed within an isometric subgraph of G that contains a vertex x of and the r -ball around x, where r > 2 − 1 − 2 /| |. The median index of a graph and r -joins of graphs are introduced and it is shown that r -joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.

HWR for Indian Languages: A Comprehensive Survey

Few major Research works are going in the field of Handwriting Word Recognition (HWR) of Indian languages. This paper surveys the major works of offline/online handwritten word recognition. Techniques involved in word recognition are also discussed. Major works carried out in Bangla, Urdu, Tamil and Hindi are mentioned in this paper. Advancement towards HWR in other Indian languages are also discussed. Application of offline HWR is also discussed