ON APPROXIMATION METHODS FOR UNBOUNDED OPERATORS

Department of Mathematics, Cochin University of Science and Technology

A Study of Elementary Operators

Department of Mathematics, Cochin University of Science and Technology

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.

A Study of Morphological Operators with Applications

The present work deals with the A study of morphological opertors with applications. Morphology is now a.necessary tool for engineers involved with imaging applications. Morphological operations have been viewed as filters the properties of which have been well studied (Heijmans, 1994). Another well-known class of non-linear filters is the class of rank order filters (Pitas and Venetsanopoulos, 1990). Soft morphological filters are a combination of morphological and weighted rank order filters (Koskinen, et al., 1991, Kuosmanen and Astola, 1995). They have been introduced to improve the behaviour of traditional morphological filters in noisy environments. The idea was to slightly relax the typical morphological definitions in such a way that a degree of robustness is achieved, while most of the desirable properties of typical morphological operations are maintained. Soft morphological filters are less sensitive to additive noise and to small variations in object shape than typical morphological filters. They can remove positive and negative impulse noise, preserving at the same time small details in images. Currently, Mathematical Morphology allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets.Fuzzy sets have proved to be strongly advantageous when representing in accuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods.

Effectiveness Of Feature Detection Operators On The Performance Of Iris Biometric Recognition System

Iris Recognition is a highly efficient biometric identification system with great possibilities for future in the security systems area.Its robustness and unobtrusiveness, as opposed tomost of the currently deployed systems, make it a good candidate to replace most of thesecurity systems around. By making use of the distinctiveness of iris patterns, iris recognition systems obtain a unique mapping for each person. Identification of this person is possible by applying appropriate matching algorithm.In this paper, Daugman’s Rubber Sheet model is employed for irisnormalization and unwrapping, descriptive statistical analysis of different feature detection operators is performed, features extracted is encoded using Haar wavelets and for classification hammingdistance as a matching algorithm is used. The system was tested on the UBIRIS database. The edge detection algorithm, Canny, is found to be the best one to extract most of the iris texture. The success rate of feature detection using canny is 81%, False Accept Rate is 9% and False Reject Rate is 10%.

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.

Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

Biochemical and molecular characterization of pathogenic vibrios from hatcheries and aquaculture farms

Vibrio are important during hatchery rearing. aquaculture phase and post-harvest quality of shrimps. Vibrio spp are of concern to shrimp farmers and hatchery operators because certain species can cause Vibriosis. Vibrio species are of concern to humans because certain species cause serious diseases.With the progress in aquaculture, intensive systems used for shrimp aquaculture create an artificial environment that increases bacterial growth. To maintain the productivity of such an intensive aquaculture, high inputs of fish protein have to be employed for feeding together with high levels of water exchange and the massive use of antibiotics/ probiotics / chemicals. It seems that the combination of these conditions favours the proliferation of vibrios and enhances their virulence and disease prevalence. The risk of a microbial infection is high, mainly at larval stages. The effect and severity are related to Vibrio species and dose, water, feed, shrimp quality and aquaculture management.Consumption of seafood can occasionally result in food-bome illnesses due to the proliferation of indigenous pathogens like Vibrio.Of the l2 pathogenic Vibrio species, 8 species are known to be directly food associated. Strict quality guidelines have been laid by the importing nations, for the food products that enter their markets. The microbiological quality requirement for export of frozen shrimp products is that V.cholerae, V.parahaemolyticus and V. vulnificus should be absent in 25g of the processed shrimp (Export Inspection Council of India, 1995). The mere presence of these pathogenic Vibrios is sufficient for the rejection of the exported product.The export rejections cause serious economic loss to the shrimp industry and might harm the brand image of the shrimp products from the countiy.There is a need for an independent study on the incidence of different pathogenic vibrios in shrimp aquaculture and investigate their biochemical characteristics to have a better understanding about the growth and survival of these organisms in the shrimp aquaculture niche. PCR based methods (conventional PCR, duplex PCR, multiplex-PCR and Real Time PCR) for the detection of the pathogenic Vibrios is important for rapid post-harvest quality assessment. Studies on the genetic heterogeneity among the specific pathogenic vibrio species isolated from shrimp aquaculture system provide; valuable information on the extent of genetic diversity of the pathogenic vibrios, the shrimp aquaculture system.So the present study was undertaken to study the incidence of pathogenic Vibrio spp. in Penaeus monodon shrimp hatcheries and aquaculture farms, to carry out biochemical investigations of the pathogenic Vibrio spp isolated from P. monodon hatchery and. aquaculture environments, to assess the effect of salt (NaCl) on the growth and enzymatic activities of pathogenic Vibrio spp., to study the effect of preservatives, and chemicals on the growth of pathogenic Vibrio spp. and to employ polymerase chain reaction (PCR) methods for the detection of pathogenic V ibrio spp.Samples of water (n=7) and post-larvae (n=7) were obtained from seven Penaeus monodon hatcheries and samples of water (n=5), sediment (n=5) and shrimp (n=5) were obtained from five P. monodon aquaculture farms located on the East Coast of lndia. The microbiological examination of water, sediment, post-larvae and shrimp samples was carried out employing standard methods and by using standard media.The higher bacterial loads were obtained in pond sediments which can be attributed to the accumulation of organic matter at the pond bottom which stimulated bacterial growth.Shrimp head. (4.78 x 105 +/- 3.0 x 104 cfu/g) had relatively higher bacterial load when compared to shrimp muscle 2.7 x 105 +/- 1.95 x 104 cfu/g). ln shrimp hatchery samples, the post-larvae (2.2 x 106 +/- 1.9 x 106 cfu/g) had higher bacterial load than water (5.6 x 103 +/- 3890 cfu/ml).The mean E.coli counts were higher in aquaculture pond sediment (204+/-13 cfu/g) and pond water (124+/-88 cfu/ml). Relatively lower Escherichia coli counts were obtained from shrimp samples (12+/-11 to 16+/-16.7 cfu/g). The presence of E.coli in aquaculture environment might have been from the source water. E.coli was not detected in hatchery waters and post-larvae.

Message Integrity in the World Wide Web: Use of Nested Hash Function and a Fast Stream Cipher

The focus of this work is to provide authentication and confidentiality of messages in a swift and cost effective manner to suit the fast growing Internet applications. A nested hash function with lower computational and storage demands is designed with a view to providing authentication as also to encrypt the message as well as the hash code using a fast stream cipher MAJE4 with a variable key size of 128-bit or 256-bit for achieving confidentiality. Both nested Hash function and MAJE4 stream cipher algorithm use primitive computational operators commonly found in microprocessors; this makes the method simple and fast to implement both in hardware and software. Since the memory requirement is less, it can be used for handheld devices for security purposes.

`A Study on Ultra L-topologies and Lattices of L-topologies'

The thesis is divided into nine chapters including introduction. Mainly we determine ultra L-topologies in the lattice of L- topologies and study their properties. We nd some sublattices in the lattice of L-topologies and study their properties. Also we study the lattice structure of the set of all L-closure operators on a set X.

A Faster 2D Technique for the design of Combinational Digital Circuits Using Genetic Algorithm

Combinational digital circuits can be evolved automatically using Genetic Algorithms (GA). Until recently this technique used linear chromosomes and and one dimensional crossover and mutation operators. In this paper, a new method for representing combinational digital circuits as 2 Dimensional (2D) chromosomes and suitable 2D crossover and mutation techniques has been proposed. By using this method, the convergence speed of GA can be increased significantly compared to the conventional methods. Moreover, the 2D representation and crossover operation provides the designer with better visualization of the evolved circuits. In addition to this, a technique to display automatically the evolved circuits has been developed with the help of MATLAB