Papers

Department of Mathematics and Statistics  Dr. Sir Hari Singh Gour University Sagar, M.P. (INDIA

In this paper we have suggested a family of ratio-cum product estimator when the population coefficient of variation (Cx) alongwith population means (X ) of the auxiliary variable x is known in advance. Its bias and variance to the first degree of approximation are obtained. For an appropriate weight ‘w’ and a good range of -values, it is shown that the suggested estimator is more efficient than the set of estimators viz. usual unbiased estimator, usual ratio and product estimators, Sisodia and Dwivedi’s5 estimator, Bansal and Singh’s1 estimator, Chakraborty’s2 type estimator, Vos’s8 type estimator and Sahai and Ray4 type estimator, some of which are in fact particular members of it.

*Govt. Science & Commerce Benazeer College, Bhopal (INDIA)
**Bhabha Engineering Research Institute – MCA, Bhopal (INDIA)
***Sagar Institute of Science and Technology, Bhopal (INDIA)
*(email: rajeshraju0101@rediffmail.com)  **(email: dranilrajput@hotmail.com)  ***(email:lekh13@yahoo.com)

In this paper we worked out fixed point theorem for fuzzy mapping on Hilbert space.

Department of Mathematics, University of Rajasthan Jaipur-302055 (INDIA)

Cosmological models with variable gravitational constant (G)  and bulk viscosity in C-field cosmology for flat FRW space-time are investigated. To get the deterministic model of the universe, we have assumed G = Rn where R is the scale factor and n is a constant. Under this assumption, we have investigated two C-field cosmological models for two cases: (i)  = constant, (ii)  = constant, R 3R  where  is the coefficient of bulk viscosity,  the expansion in the model. The physical and geometrical aspects of the models and the effect of bulk
viscosity related with the observation are discussed.
 .

^1,2Ramgarh College, Ramgarh Dept. of Mathematics Dist. Ramgarh Jharkhand, 829122 (V.B.U B Hazaribagh) (INDIA

Binormal operator: We say that an operator T on a Hilbert
Space H is bi-normal if TT* and T*T commute
i.e [T*T, TT*] = 0
I.e T*T TT* = TT*T*T = 0
Where T* is the ad joint of T
Quasi normal operator : We say that an operator T on a Hilbert
Space H is quasi normal operator if T and T*T commute
i.e [T , T*T] = 0
I.e TT*T = T*TT
Quasi– P-normal operator : An operator T on a Hilbert Space
H is said to be quasi P-normal operator if T+T* and T*T Commute
i.e [T+T* , T*T] = 0
I.e (T+T*) T*T = T*T(T+T*)
I.e TT*T+ T*T*T = T*TT+T*TT*

¹Department of Mathematics, Agra College, Agra U.P. (INDIA)
²Department of Mathematics, K.K.P.G.College Etawah U.P. (INDIA)
Email ID: rkpal.maths@gmail.com ; kk.singh@bsacet.org Email ID: aksharma.maths@gmail.com

Present paper is concerned with the oscillatory motion of conducting visco-elastic [Oldroyd (1958) model] liquid of first order through porous medium between two infinite flat plates both of which execute simple harmonic motion in the plane of plates with different amplitudes and frequencies under the influence of an uniform magnetic field applied perpendicular to the flat plates. Some particular cases have also been discussed in detail.

Department of Mathematics Bareilly College Bareilly (M J P R University Bareilly) (INDIA)

In the present work, The authors describe two types of problem. One is the vehicle routing problem with time windows and the second problem is the pickup and delivery problem with time windows. for Optimization we use dynamic programming and branch and bound method. They will not be able to solve large-scale problems. So, we review three types of approximation algorithms. Construction methods try to build a feasible solution starting from the raw data. Iterative improvement methods start from a feasible solution and seek to improve it through a sequence of local modifications. Incomplete optimization methods use a combination of enumeration of the solution space and heuristic rules.

*CSA, Govt. PG College, Sehore (INDIA)
**Millennium Group of Institutions, Bhopal (INDIA)
email: dranilrajput@hotmail.com, pkdwivedi76@gmail.com

In this paper we have proved some common fixed point theorems for the class of four non compatible mappings in fuzzy
metric spaces. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm.

1Department of Statistics, Sambalpur University, Orissa (INDIA)
2Institute of Management & Information Science, Bhubaneswar, Orissa (INDIA)
E-mail: sbagh55@hotmail.com, E-mail: manas.sbp@gmail.com

The asymptotic estimate for the expected number of real zeros of a random
algebraic polynomial Qn ( x ,  ) =
j
n
j
j x
j
n
a
1 / 2
0
) ( 

Where the coefficients () j a are independently normally distributed
random variables defined on a probability space ( , F, P ) ,   
is known. In this paper we provide the asymptotic value for the expected
number of zeros of the integration of Qn (x, ) with respect to x.

Department of Mathematics, Annamalai University (INDIA)

In the study of HIV infection the progression of the disease takes place with the passage of time. This is due to the increasing the antigenic diversity level of the Retrovirus. As and when the total antigenic diversity crosses a threshold level, the sero conversion takes place. The threshold itself is considered to be a random variable. In this paper assuming that the antigenic diversity threshold satisfies the property known as Setting the Clock Back to Zero (SCBZ) property, the
expected time to sero conversion and its variance are derived. The results are augumented with suitable numerical illustrations.

*HOD of Applied Science Department, Bipin Tripathi Kumaon Institute of Technology, Dwarahat (Uttarakhand) (INDIA)
**Assistant Professor in Bipin Tripathi Kumaon Institute of Technology, Dwarahat (Uttarakhand) (INDIA).
Email: dr.latabisht@gmail.com, Email: sandhana_shanks@rediffmail.com

In this Paper, we have obtained the integrability conditions for a generalized almost contact manifold some related result have also been discussed.