Papers

We initiate to fine the 4 - inverse of GM matrix on a set of two distinct positive integers. The eigen value and eigen vectors are determined for the GM matrix.

Y. Matsushima proved that in a compact Kähler-Einstein space, any contravariant analytic vector field is uniquely decomposed in the form of Killing vector fields. A. Lichnerowicz generalised this result for a compact Kähler manifold with constant scalar curvature. S. Sawaki generalised the same result for a compact almost Tachibana-Einstein manifold. In 1959, Tachibana introduced the concept of an almost analytic vector field in the almost complex spaces.

The aim of the paper is to discuss an analytic vector field on an almost hyperbolic Hermitian manifold and to obtain certain expressions of the curvature tensor on an almost hyperbolic Hermitian manifold admitting semi-symmetric metric connection assuming analytic vector field to be killing and affine.

Today, many businesses such as banks, insurance companies, and other service providers realize the importance of Customer Relationship Management (CRM) and its potential to help them acquire new customers retain existing ones and maximize their lifetime value. At this point, close relationship with customers will require a strong coordination between IT and marketing departments to provide a long-term retention of selected customers.

Drastic changes in communication technology are changing the way that traditional banking is done in current economic era. It has been given new shape of traditional banking. The resulting changes will have a great impact on financial sector. Firstly on the reset up of a financial sector network according to the focus of the market, secondly on the design of new products and on the development and the use of alternative distribution channels and finally on the customers' switching behavior^3,7,9,13.

In this paper, we are exploring issues that put in the fundamentals of CRM for franchise's network optimization and discuss mathematical solution for that. Financial Institution's management team could use the findings of this study, in order to determine specific component in designing financial services and products, which would add in customers' satisfaction and reliability. The proposed approach could have significant implications for enlarging the duration of the relationship among customer and financial institution and for maximizing their franchise performance^6,9,12.

There are different issues relating to the reorganization of financial industry are examined. Specifically the performance of a franchise network, the online service's as an alternative distribution channel and the duration of the relationship among customers (individuals or enterprises) are the three interrelated parties. Fuzzy optimization techniques and generalized linear models are used in order to determine financial products and services which are offered to financial clients through traditional and Internet channels, forecasting customers' attitudes (adoption or rejection) to the new products and the time horizon of their cooperation with their sector^1,4,7.

In 1926, H. Levy proved that a second order symmetric parallel non singular tensor on a space of constant curvature is a constant multiple of the metric tensor. R. Sharma generalized Levy's result and studied second order parallel tensor on a Kähler space of constant holomorphic sectional curvature as well as on a compact K-contact manifold without boundary. U.C. De and Debasish Tarafdar showed that for a P-Sasakian manifold M with a symmetric parallel tensor of type (0,2) is also a constant multiple of the metric tensor and there is no parallel 2-form on M.

In this paper, We have studied symmetric and skew-symmetric second order parallel tensor on a Kenmotsu manifold.

In this paper it is shown that semi-T_i reduces to T_i, i = 0, 1, 2, when an appropriate change of topology is invoked.

Takano¹⁴ has studied the decomposition of the curvature tensor field in a recurrent Riemannian space and various significant outcomes of such decomposition in recurrent Riemannian space have been drawn. The innovations of Neo-curvature tensor field in Finsler subspaces have been initiated by Chandra⁴. Moreover, he has defined and studied "Neo-covariant derivatives and its applications" and several interesting theorems concerning to this delighting research article have been derived. Singh¹¹ has defined and studied decomposition of Neo-curvature tensor filed of first order and has discussed various properties of such decomposition.

The present paper is intended to study "A note on decomposition of Neo-curvature tensor filed in recurrent Finsler manifolds", wherein the decomposition of Neo-curvature tensor field will be the composition of one vector and one tensor fields. Also, some theorems on such decomposition will be investigated.

A generalization of multivalued hybrid contraction and Meir - Keeler type multivalued maps are obtained in a metric space. Our result is a generalize concept of commuting and compatible mappings under some conditions and corresponding results of ^{1,2,3,4,5,6,7,8,9,10,11,12,} and many others.

In this paper, inventory replenishment policy is developed for constant deteriorating item and price-dependent demand. The rate of deterioration is taken to be time proportional. A power law form of the price dependence of demand is considered and the numerical example is taken up to illustrate the solution procedure and sensitivity analysis is also carried out.

Many decision making problems may be solved with Heuristic search algorithms. Expert systems taking decisions in competitive situation in uncertain environment/fuzzy environment may take a graph-search algorithm to tackle the situation. To improve the performance of the overall system, a set of important parameters of the decision making system is identified. Optimization methods such as Neural Network (N.N.) is used for the learning of the optimum parameters and also for an improvement of the performance.

Zeeman, in his paper 'Topology of Minkowski Space' made two conjectures :

(1) the topology in Minkowski Space that induces the 3-dimensional Euclidean topology on every space- like hyperplane (S-topology) has G as its group of homeomorphisms, where G is the smallest group generated by the inhomogeneous Lorentz group and dilatation (multiplication by +ve scalars);

(2) the topology on Minkowski space that induces the one-dimensional Euclidean topology on every time-like line (T-topology) also has G as its homeomorphism group.

Since it is known that G is precisely the set of < - automorphism (where < is the causality relation on Minkowski space), we have made an alternative formulation of the second conjecture as follows : every homeomorphism of the T-topology is a < - automorphism.

Here we have dealt with a weaker version of Zecman's conjecture on space topology.