Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

Criminal justice system in pondicherry - a comparative critical study of the past and the presen

The Union Territory of Pondicherry prior to its merger with the Indian Union was a French Colony. The erstwhile territory of Pondicherry along with its hamlets, namely, KARAIKKAL, MAHE and YANAM was administered by the French Regime. Before it was established by French in 1 6 74 A.D. it was part of Vijayanagara Empire. Prior to this, Pondicherry was a part of the Kingdom of Chola and Pallava Kings. During French Regime, the laws which were in force in France in relation to administration of civil and criminal justice were extended to the erstwhile Territory of Pondicherry. Thus while Pondicherry stood influenced by the Inquisitorial system since the beginning of the 18th century, the neighboring states forming part of the Indian Union since Independence came under the Influence of the British system, viz. accusatorial system. The territory of Pondicherry, for administrative reasons, came to be merged with the Indian Union in the early 60's. Following the merger, the Indian administration sought to extent its own laws from time to time replacing erstwhile French Laws, however, subject to certain savings. Thus the transitional period witnessed consequential changes in the administration of the territory, including the sphere of judicial system. Since I 963, the Union Territory of Pondicherry was brought under the spell of the Indian Legal System The people in Pondicherry ' thus have had the benefit of experiencing both the svstems. Their experiences will be of much help to those who undertake comparative studies in law. The plus and minus points of the respective systems help one to develop a detachment that helps independent evaluation of the svstents. The result of these studies could be relevant in revitalising our criminal systems.The present system is evaluated in the light of the past system. New dimensions are added by way' of an empirical study also.

Impact of Information Communication Technology (ICT) on Professional Development and Educational Needs of Library Professionals in the Universities of Kerala

The shift from print to digital information has a high impact on all components of the academic library system in India especially the users, services and the staff. Though information is considered as an important resource, the use of ICT tools to collect and disseminate information has been in a slow pace in majority of the University libraries This may be due to various factors like insufficient funds, inadequate staff trained in handling computers and software packages, administrative concerns etc. In Kerala, automation has been initiated in almost all University libraries using library automation software and is under different stages of completion. There are not much studies conducted about the effects of information communication technologies on the professional activities of library professionals in the universities in Kerala. It is important to evaluate whether progress in ICT has had any impact on the library profession in these highest educational institutions. The aim of the study is to assess whether the developments in information communication technologies have any influence on the library professionals’ professional development, and the need for further education and training in the profession and evaluate their skills in handling developments in ICT. The total population of the study is 252 including the permanently employed professional library staff in central libraries and departmental libraries in the main campuses of the universities under study. This is almost a census study of the defined population of users. The questionnaire method was adopted for collection of data for this study, supplemented by interviews of Librarians to gather additional information. Library Professionals have a positive approach towards ICT applications and services in Libraries, but majority do not have the opportunities to develop their skills and competencies in their work environment. To develop competitive personnel in a technologically advanced world, high priority must be given to develop competence in ICT applications, library management and soft skills in library professionals, by the University administrators and Library associations. Library science schools and teaching departments across the country have to take significant steps to revise library science curriculum, and incorporate significant changes to achieve the demands and challenges of library science profession.

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.

Studies on some fish larvae of the arabian sea and bay of bengal

Though several scientific expeditions surveyed tha Indian ocean. their findings on larval fishes were fragmentory and incomplete. During the International Indian ocean expedition (1960-1965) zooplankton samples were collected from vast area at the lndian ocean adopting standard procedures by participating vessels. These planktons provided an opportunity for a general study of the zooplanltton as well as their anotomy. abundance and distribution.. Realising the imortance of the analysis and classification of fish larvae at the family level being one of the most important information required then for the Indian Ocean region the fish larval portion sorted out from the above zooplankton samples was allocated to the author by the UNESCO consultative committee for the Indian Ocean Biological centre. In spite of the emhasis laid on The study of the family scombridae. owing to the paucity of the scombridae material in tne collection. much could not be done about it.However the record and description of the very early stages of morakel larvae made in 1967 as part of this study was the first of its kind. The present study on the distribution aspects o fish larva of such large area in the Indian ocean is also unique and first of its kind