Stability of Random Sums and Extremes

This study is about the stability of random sums and extremes.The difficulty in finding exact sampling distributions resulted in considerable problems of computing probabilities concerning the sums that involve a large number of terms.Functions of sample observations that are natural interest other than the sum,are the extremes,that is , the minimum and the maximum of the observations.Extreme value distributions also arise in problems like the study of size effect on material strengths,the reliability of parallel and series systems made up of large number of components,record values and assessing the levels of air pollution.It may be noticed that the theories of sums and extremes are mutually connected.For instance,in the search for asymptotic normality of sums ,it is assumed that at least the variance of the population is finite.In such cases the contributions of the extremes to the sum of independent and identically distributed(i.i.d) r.vs is negligible.

Data Security in Fault Tolerant Hard Real Time Systems- Use of Time Dependant Multiple Random Cipher Code

The present research problem is to study the existing encryption methods and to develop a new technique which is performance wise superior to other existing techniques and at the same time can be very well incorporated in the communication channels of Fault Tolerant Hard Real time systems along with existing Error Checking / Error Correcting codes, so that the intention of eaves dropping can be defeated. There are many encryption methods available now. Each method has got it's own merits and demerits. Similarly, many crypt analysis techniques which adversaries use are also available.

Some Properties of Weighted Distributions for Truncated Random Variables

The present study gave emphasis on characterizing continuous probability distributions and its weighted versions in univariate set up. Therefore a possible work in this direction is to study the properties of weighted distributions for truncated random variables in discrete set up. The problem of extending the measures into higher dimensions as well as its weighted versions is yet to be examined. As the present study focused attention to length-biased models, the problem of studying the properties of weighted models with various other weight functions and their functional relationships is yet to be examined.

Resource abundance and Survival of indigenous ornamental fishes of central Kerala with emphasis on handling and packing stress in Puntius filamentosus(VALENCIENNES)

This thesis Entitled Resource abundance and survival of indigenous ornamental fishes of central kerala with emphasis on handling and packing stress in puntius filamentosus (valenciennes).Kerala state is endowed with 41 west flowing and three east flowing rivers originating in the Western Ghats. These rivers and their vast network of tributaries and distributaries harbour rich and diversified fish fauna. Most of the freshwater fishes available in Kerala are highly appreciated as ornamental fishes in the national and international markets.Today the ornamental fish industry is one of the largest industries all over the world. The demand for ornamental fishes has been increasing steadily with the enlargement of the industry, such that the current demand for indigenous ornamental fishes have exceeded the supply. This has led to serious concern about the resources available in the country that can be utilised judiciously for the economic benefit of the state. With an aim to fill up the lacuna, a database of freshwater ornamental fishes of Kerala was created as part of the present study. Ornamental fishes destined for export marketing should thrive well in the aquarium conditions.The study reiterates fishes caught from different environmental conditions and feeding habits have a greater ability to adapt and acclimatise to an entirely new environment and food habits. Marketing studies based on the statistics available with Marine Products Export Development Authority show that these species are not being exported at the required level over the past 6 years, when compared to the availability in the water bodies of Kerala. Sustainable utilisation of these resources from the wild using modern management principles and code of conduct for responsible fishing are advisable until captive breeding technology is popularised.

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Microstructure and random magnetic anisotropy in Fe–Ni based nanocrystalline thin films

Nanocrystalline Fe–Ni thin films were prepared by partial crystallization of vapour deposited amorphous precursors. The microstructure was controlled by annealing the films at different temperatures. X-ray diffraction, transmission electron microscopy and energy dispersive x-ray spectroscopy investigations showed that the nanocrystalline phase was that of Fe–Ni. Grain growth was observed with an increase in the annealing temperature. X-ray photoelectron spectroscopy observations showed the presence of a native oxide layer on the surface of the films. Scanning tunnelling microscopy investigations support the biphasic nature of the nanocrystalline microstructure that consists of a crystalline phase along with an amorphous phase. Magnetic studies using a vibrating sample magnetometer show that coercivity has a strong dependence on grain size. This is attributed to the random magnetic anisotropy characteristic of the system. The observed coercivity dependence on the grain size is explained using a modified random anisotropy model

Testing Isotropy and a related Random Walk problem

One comes across directions as the observations in a number of situations. The first inferential question that one should answer when dealing with such data is, “Are they isotropic or uniformly distributed?” The answer to this question goes back in history which we shall retrace a bit and provide an exact and approximate solution to this so-called “Pearson’s Random Walk” problem.

Molecular genetic profiling of functional genes of pearl oyster, Pinctada fucata

There are a number of genes involved in the regulation of functional process in marine bivalves. In the case of pearl oyster, some of these genes have major role in the immune/defence function and biomineralization process involved in the pearl formation in them. As secondary filter feeders, pearl oysters are exposed to various kinds of stressors like bacteria, viruses, pesticides, industrial wastes, toxic metals and petroleum derivatives, making susceptible to diseases. Environmental changes and ambient stress also affect non-specific immunity, making the organisms vulnerable to infections. These stressors can trigger various cellular responses in the animals in their efforts to counteract the ill effects of the stress on them. These include the expression of defence related genes which encode factors such as antioxidant genes, pattern recognition receptor proteins etc. One of the strategies to combat these problems is to get insight into the disease resistance genes, and use them for disease control and health management. Similarly, although it is known that formation of pearl in molluscs is mediated by specialized proteins which are in turn regulated by specific genes encoding them, there is a paucity of sufficient information on these genes.In view of the above facts, studies on the defence related and pearl forming genes of the pearl oyster assumes importance from the point of view of both sustainable fishery management and aquaculture. At present, there is total lack of sufficient knowledge on the functional genes and their expressions in the Indian pearl oyster Pinctada fucata. Hence this work was taken up to identify and characterize the defence related and pearl forming genes, and study their expression through molecular means, in the Indian pearl oyster Pinctada fucata which are economically important for aquaculture at the southeast coast of India. The present study has successfully carried out the molecular identification, characterization and expression analysis of defence related antioxidant enzyme genes and pattern recognition proteins genes which play vital role in the defence against biotic and abiotic stressors. Antioxidant enzyme genes viz., Cu/Zn superoxide dismutase (Cu/Zn SOD), glutathione peroxidise (GPX) and glutathione-S-transferase (GST) were studied. Concerted approaches using the various molecular tools like polymerase chain reaction (PCR), random amplification of cDNA ends (RACE), molecular cloning and sequencing have resulted in the identification and characterization of full length sequences (924 bp) of the Cu/Zn SOD, most important antioxidant enzyme gene. BLAST search in NCBI confirmed the identity of the gene as Cu/Zn SOD. The presence of the characteristic amino acid sequences such as copper/zinc binding residues, family signature sequences and signal peptides were found out. Multiple sequence alignment comparison and phylogenetic analysis of the nucleotide and amino acid sequences using bioinformatics tools like BioEdit,MEGA etc revealed that the sequences were found to contain regions of diversity as well as homogeneity. Close evolutionary relationship between P. fucata and other aquatic invertebrates was revealed from the phylogenetic tree constructed using SOD amino acid sequence of P. fucata and other invertebrates as well as vertebrates

Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space