On Truncated Versions of Certain Measures of Inequality and Stability

The present study focuses attention on defining certain measures of income inequality for the truncated distributions and characterization of probability distributions using the functional form of these measures, extension of some measures of inequality and stability to higher dimensions, characterization of bivariate models using the above concepts and estimation of some measures of inequality using the Bayesian techniques. The thesis defines certain measures of income inequality for the truncated distributions and studies the effect of truncation upon these measures. An important measure used in Reliability theory, to measure the stability of the component is the residual entropy function. This concept can advantageously used as a measure of inequality of truncated distributions. The geometric mean comes up as handy tool in the measurement of income inequality. The geometric vitality function being the geometric mean of the truncated random variable can be advantageously utilized to measure inequality of the truncated distributions. The study includes problem of estimation of the Lorenz curve, Gini-index and variance of logarithms for the Pareto distribution using Bayesian techniques.

On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Economics of Human Resource Planning With Special Reference to Higher Education in Kerala

Ongoing changes in global economic structure along information revolution have produced an environment where knowledge and skills or education and training are considered increasingly valued commodities. This is based on the simple notion that nation’s economic progress is linked to education and training. This idea is embodied in the theory of human capital, according to which the knowledge and skill found in labour represents valuable resources for the market. Thus the important assumptions of the Human capital theory are 910 Human capital is an investment for future (2) More training and education leads to better work skills (3) Educational institutions play a central role in the development of human capital(4) the technological revolution is often cited as the most pressing reason why education and knowledge are becoming valuable economic commodities . The objectives of the present study are, the investment and institutional or structural framework of higher education in Kerala, the higher education market and the strengths and weakness of supply demand conditions , cost and the benefits of higher education in Kerala , impact of recent policy changes in higher education,need for expanding higher education market to solve the grave problem of Un employment on the basis of as systematic manpower planning and the higher education and its association with income and employment.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

A Cryptosystem Using the Concepts of Algebraic Geometric Code

Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Error detection and correction can be done efficiently by simple decoding methods using the cryptosystem developed. Approach: Algebraic geometric codes are codes, generated using curves. The cryptosystem use basic concepts of elliptic curves cryptography and generator matrix. Decrypted information takes the form of a repetition code. Due to this complexity of decoding procedure is reduced. Error detection and correction can be carried out efficiently by solving a simple system of linear equations, there by imposing the concepts of security along with error detection and correction. Results: Implementation of the algorithm is done on MATLAB and comparative analysis is also done on various parameters of the system. Attacks are common to all cryptosystems. But by securely choosing curve, field and representation of elements in field, we can overcome the attacks and a stable system can be generated. Conclusion: The algorithm defined here protects the information from an intruder and also from the error in communication channel by efficient error correction methods.

Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Human Resources Development in Higher Education in Kerala

The study is entitled “HUMAN RESOURCES DEVELOPMENT IN HIGHER EDUCATION IN KERALA”. The concept “Human Resource Development” is of high value in business and industry and has been used and applied since years. In industry and business the 'human' element is considred as a resource and hence its development and protection is very essential and inevitable. Of all the factors of production, human resource is the only factor having rational faculty and therefore, it must be handled with utmost care. Right recruitment, right training and right induction followed by faultless monitoring and welfare measures are but decisive factors in business and industry. Altogether there is a constant attention up on human factor there. But this is not a practice at all in education. So far there has not been any such measure of care and close watch and performance analysis of human resource on education front. This may be the main reason for lack of accountability in the sphere of education. The present study reveals the importance of introducing HRD practices in higher educational institutions in Kerala. In order to promise human capital formation through education, it is basic requirement. The higher educational institutions must follow the method of industry and commerce because education can be treated as an industry in service sector. There also we can follow the methods of right recruitment, right training and promotion, delegation, performance analysis and accountability checking of human resource. HRD is a powerful idea of transformation of human being into highly productive and contributing factor The HRD of students is the sum total of HRD of teachers. Reminding the primordial usage 'Yatha Raja Thadha Praja’ the quality of faculty resembles in students. The quality of administrative staff in colleges also affects the quality of higher education. Hence, it is high time to introduce the managerial method of HRD with all its paraphernalia in higher educational institutions so as to assure proper human capital formation in higher education in India.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Human Resources Development in Higher Education in Kerala

The study is entitled “HUMAN RESOURCES DEVELOPMENT IN HIGHER EDUCATION IN KERALA”. The concept “Human Resource Development” is of high value in business and industry and has been used and applied since years. In industry and business the ‘human’ element is considred as a resource and hence its development and protection is very essential and inevitable. Of all the factors of production, human resource is the only factor having rational faculty and therefore, it must be handled with utmost care. Right recruitment, right training and right induction followed by faultless monitoring and welfare measures are but decisive factors in business and industiy. Altogether there is a constant attention up on human factor there. But this is not a practice at all in education. So far there has not been any such measure of care and close watch and performance analysis of human resource on education front. This may be the main reason for lack of accountability in the sphere of education. The present study reveals the importance of introducing HRD practices in higher educational institutions in Kerala. In order to promise human capital formation through education, it is basic requirement. The higher educational institutions must follow the method of industry and commerce because education can be treated as an industry in service sector. There also we can follow the methods of right recruitment, right training and promotion, delegation, performance analysis and accountability checking of human resource. HRD is a powerful idea of transformation of human being into highly productive and contributing factor The HRD of students is the sum total of HRD of teachers. Reminding the primordial usage ‘Yatha Raja Thadha Praja’ the quality of faculty resembles in students. The quality of administrative staff in colleges also affects the quality of higher education. Hence, it is high time to introduce the managerial method of HRD with all its paraphernalia in higher educational institutions so as to assure proper human capital formation in higher education in India.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.

Studies on improved practices of prawn farming for higher production in central Kerala

The thesis entitled "Studies on improved practices of prawn farming for higher production in central Kerala" prepared by the author describes various practices prevailing in the study area in order to elucidate their relative merits. The study on semi-intensive farming at Mundapuram, Kannur was also carried out and included in the thesis for comparison.The author felt it important to make a critical study of the existing culture practices in the central Kerala, a region where it has been existing since time immemorial.Careful analysis of data accrued by the author has helped him to identify strength, weakness, opportunities and threats confronting the shrimp farming. As a result it was possible to evolve an appropriate management technology taking into consideration the various ecological (location specific), social and economical conditions prevalent in the vast study area.

Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Management of Higher Educational Institutions in Kerala

Economists consider education as an investment in man. Education develops human resources necessary for the economic and political growth of any nation. Adam Smith stressed the importance of education and included the acquired and useful activities of all the inhabitants or members of society in his concept of fixed capital.‘ Karl Marx shared with Smith's view when he laid down that the function of education in a socialist society will be to overcome the alienation of the worker from the means of production; while developing the technical skill it will make him a complete man as well as a producer.2 Education is also considered as a powerful instrument for social change. By inculcating moral and spiritual values, it brings changes both in the individual and in the society. It aims at creating a social order founded on the values of freedom, social justice and equal opportunity.3 The objective of this exploratory study is to enquire into the existing system of managing higher educational institutions in Kerala, compare it with the accepted principles of management believed to be applicable to all organisations, and develop a model capable of introducing more effective management practices