Analysis of Some Single and Two Commodity Inventory Problems

This thesis is devoted to the study of some stochastic models in inventories. An inventory system is a facility at which items of materials are stocked. In order to promote smooth and efficient running of business, and to provide adequate service to the customers, an inventory materials is essential for any enterprise. When uncertainty is present, inventories are used as a protection against risk of stock out. It is advantageous to procure the item before it is needed at a lower marginal cost. Again, by bulk purchasing, the advantage of price discounts can be availed. All these contribute to the formation of inventory. Maintaining inventories is a major expenditure for any organization. For each inventory, the fundamental question is how much new stock should be ordered and when should the orders are replaced. In the present study, considered several models for single and two commodity stochastic inventory problems. The thesis discusses two models. In the first model, examined the case in which the time elapsed between two consecutive demand points are independent and identically distributed with common distribution function F(.) with mean  (assumed finite) and in which demand magnitude depends only on the time elapsed since the previous demand epoch. The time between disasters has an exponential distribution with parameter . In Model II, the inter arrival time of disasters have general distribution (F.) with mean  ( ) and the quantity destructed depends on the time elapsed between disasters. Demands form compound poison processes with inter arrival times of demands having mean 1/. It deals with linearly correlated bulk demand two Commodity inventory problem, where each arrival demands a random number of items of each commodity C1 and C2, the maximum quantity demanded being a (< S1) and b(of linearly correlated demand is also discussed

Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

On Distance Energy of Graphs

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

A Note on Energy of Some Graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

Some classes of Turker equivalent graphs

Two graphs G and H are Turker equivalent if they have the same set of Turker angles. In this paper some Turker equivalent family of graphs are obtained.

A Study Of Frames In The Fuzzy And Intuitionist Fuzzy Contexts

The fuzzy set theory has a wider scope of applicability than classical set theory in solving various problems. Fuzzy set theory in the last three decades as a formal theory which got formalized by generalizing the original ideas and concepts in classical mathematical areas and as a very powerful modeling language, that can cope with a large fraction of uncertainties of real life situations. In Intuitionistic Fuzzy sets a new component degree of non membership in addition to the degree of membership in the case of fuzzy sets with the requirement that their sum be less than or equal to one. The main objective of this thesis is to study frames in Fuzzy and Intuitionistic Fuzzy contexts. The thesis proved some results such as ifµ is a fuzzy subset of a frame F, then µ is a fuzzy frame of F iff each non-empty level subset µt of µ is a subframe of F, the category Fuzzfrm of fuzzy frames has products and the category Fuzzfrm of fuzzy frames is complete. It define a fuzzy-quotient frame of F to be a fuzzy partition of F, that is, a subset of IF and having a frame structure with respect to new operations and study the notion of intuitionistic fuzzy frames and obtain some results and introduce the concept of Intuitionistic fuzzy Quotient frames. Finally it establish the categorical link between frames and intuitionistic fuzzy topologies.

Queues with retrial/self-generation of priorities /postponement of work and some related reliability problems

Application of Queueing theory in areas like Computer networking, ATM facilities, Telecommunications and to many other numerous situation made people study Queueing models extensively and it has become an ever expanding branch of applied probability. The thesis discusses Reliability of a ‘k-out-of-n system’ where the server also attends external customers when there are no failed components (main customers), under a retrial policy, which can be explained in detail. It explains the reliability of a ‘K-out-of-n-system’ where the server also attends external customers and studies a multi-server infinite capacity Queueing system where each customer arrives as ordinary but can generate into priority customer which waiting in the queue. The study gives details on a finite capacity multi-server queueing system with self-generation of priority customers and also on a single server infinite capacity retrial Queue where the customer in the orbit can generate into a priority customer and leaves the system if the server is already busy with a priority generated customer; else he is taken for service immediately. Arrival process is according to a MAP and service times follow MSP.

Inherent Powers of the High Court under Section 482 of the Code of Criminal Procedure 1973

This thesis is shows the result of the research work on the inherent Powers of the High Court in criminal jurisdiction. The criminal justice system in India recognizes inherent powers only of the High Court. The Theory and Philosophy of inherent powers are concerned the Distinction between civil and Criminal laws are of very little consequence. In formulating the research programme the confusion created by the concept of inherent powers and its application by High Court form the central point. How fully the concept is understood, how correctly the power is used, and how far it has enhanced the rationale of the administration of criminal justice, what is its importance and what are the solutions for the inherent power to earn a permanent status in the province of criminal jurisprudence are the themes of this study. The precipitation of new dimensions is the yardstick to acknowledge the inherent powers of the High Court and Supreme Court. It is of instant value in criminal justice system. This study concludes innovativeness provided by the inherent powers has helped the justice administration draw inspiration from the Constitution. A jurisprudence of inherent powers has developed with the weilding of inherent powers of the Supreme Court and the High Court. It is to unravel mystery of jurisprudence caused by the operation of the concept of inherent powers this research work gives emphasis. Its significance is all the more relevant when the power is exercised in the administration of criminal justice. Application or non application of inherent powers in a given case would tell upon the maturity and perfection of the standard of justice