Papers

In the paper `Fine topologies for Minkowski space', Williams¹ has suggested a fine topology for M, the four-dimensional flat space-time, with the following properties: (i) the induced topology on each time like line and light like line is Euclidean and (ii) the group of C^1­ -homeomorphisms of this topology is G. While suggesting this topology, Williams has argued that defining a topology in terms of lines rather than in terms of timelike lines and spacelike hyperplanes^2,3,4 has certain advantages. For example, this procedure lends itself to possible generalization to curved space-times where curves are significant, whereas, spacelike hypersurfaces are of little physical significance. However, William's topology has an unsatisfactory feature. If we imagine the path of a particle as the continuous image of I, the closed unit interval, then such a path in Williams' topology is a finite connected union of timelike intervals. Since photons travel along lightlike lines, it follows that photons are excluded from the category of particles whose paths are intuitively thought of as continuous images of I. In this paper we show that one can define a fine topology (that is, a topology which is finer than the Euclidean topology) on Minkowski space in terms of lines such that (1) the C¹-group of homeomorphisms is G and (ii) any continuous image of I is a connected union of a finite number of timelike and (or) lightlike intervals. Thus, we are able to remove the unsatisfactory features of Williams' topology while retaining its defining features. One of the unsatisfactory features of this topology (as well as of Williams' topology) is that we have to make the C¹ assumption while deriving the group of homeomorphisms. It is reasonable to conjecture that without the C¹ hypothesis, the group of homeomorphisms will be too wild.

In this paper necessary conditions of normal efficient solutions for a class of multiobjective sum of variational and fractional variational problems with nonlinear equality and inequality constraints and also sufficient conditions for efficient solutions are established.

The use of stochastic model in this study of HIV infection, transmission the spread of AIDS is quite common .The time to seroconversion from the point of infection depends upon what is known as antigenic diversity which act against the immune ability of an individuals. If the antigenic diversity causes a particular level which is known as the antigenic diversity threshold, the immune system collapses and seroconversion takes place at once. To propose a stochastic model to study the damage process acting on the immune system is non- linear. The mean time to seroconversion and its variance are derived and the numerical illustrations are provided.

Restricting the particular type of background metric, it is found that there is no contribution from cosmic strings to the Bianchi I, V and VIo models in Rosen's Bimetric Relativity. Thus empty space time solutions can be obtained.

In this paper we introduce a new class of sets namely *gs-closed sets which settled in between the class of g*-closed sets²² and the class of gs-closed sets¹³ then we study many basic properties of *gs-closed sets together with the relationship of these sets with some other sets. Applying these sets we introduce and study new class of spaces namely T_s-spaces, T_s*-spaces and *T_s-spaces. Further we introduce and study *gs-continuous maps and *gs-irresolute maps. Finally we introduce the concept of *gs-compactness and *gs-connectedness in topological spaces and study some of their properties.

In this paper we improve result of Rashwan by removing the condition of continuity and replacing the compatibility of mappings of type (A) by weak compatibility.

In this paper I have established the result on product summability of Borel and Cesaro of first order
1. Difinitions and notation
Definition 1: An infinite series  with the sequence {Sn} of its partial sums is said to be summable (C,1) if (1.1) lim  n ® ¥ i.e. lim sn ® S where sn =  n ® ¥

Definition 2 : An infinite series  with the sequence {Sn} of its partial sums is said to be summable by Borel exponential means or sammable

(B) to a finite number S, if

(1.2) Bp 

Definition 3: An in finite series  with the sequence of its partial sums {Sn} is called (B) (C,1) to a finite number S, if

(1.3) 

where sn stands for the (C,1) transform of Sn is given above.

Let f(x) be a 2p periodic function of x and integrable (L) over the interval

(-p,p). Suppose that Fourier series associated with f (x) is

Then the series

obtained by diff. (1.4) w. r to x is know a the derived Fourier series of f(x) and is not necessarily a Fourier Series

For fixed x ans S, we shall frequently use the following notation
f(x+t) + f(x-t) - 25
y0 = f(x+t) - f(x-t)
g(t) = y0(t)/4sin (t/2)

In this paper, using varying arguments and Sãlãgean derivative we define the subclasses V_n (A,B) and K_n (A,B) of analytic functions. For functions belonging to these classes, we obtain coefficient estimates, distortion bounds and many more properties.

MHD mixed convection flow over an inclined plane with viscous dissipation and ohmic effects have been analyzed in this paper. Nearly an approximate solution for the velocity, temperature and skin friction are obtained by using perturbation method. The analytical results are examined more in detail with respect to the participating parameters that arises out of the situation. It is observed that, as Grashoff number decreases, the velocity of the fluid medium decreases. In addition to the above, it is also seen that Schmidt number also contributes to the decrease in fluid velocity. Further, it is seen that both parameters Schmidt number and Grashoff number has a significant role in the decrease of fluid velocity and for back flow. Also, it is noticed that the increase in the Prandtl number contributes to the increase in the velocity field. Even when the Schmidt number is decreasing the trend continues to the same. Further, it is seen that as Schmidt number decreases, even though the nature of the velocity profiles remains same, the parabolic nature seems to have been lost. For the case of relatively very small values of Prandtl number, it is noted that the velocity profiles are found to be perfectly linear and having negative slope. It is noticed that, the effect of velocity is not that significant when the magnetic intensity remains constant. However, as the magnetic intensity increases for a constant value or Prandtl number, not a significant change is observed.

In this paper we study the problems of People With Disabilities (PWDs) using special FCMs. We use both the data collected about PWDs using a linguistic questionnaire and experts opinion to analyze the problem. This paper has 3 sections. Section one defines the Combined Special Fuzzy Cognitive Maps (CSFCMs) Model. Section two uses this new model to analyze the problems faced by PWDs. The conclusions based on our study are given in section three of this paper.