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Category: Issue 2

An Estimator for Population Mean Using Power Transformation and Auxiliary Information

RAJ. K. GANGELE and SHAILESH K. CHOUBE
Department of Mathematics and Statistics Dr. Sir Hari Singh Gour University Sagar, M.P. (INDIA

ABSTRACT:

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.

KEYWORDS: Finite population, Study variable, Auxiliary variable, Bias, Variance.


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...

A Common Fixed point Theorem for fuzzy Type mapping in Hilbert space

RAJESH SHRIVASTAVA*, ANIL RAJPUT** and SHIV KUMAR SINGH***

*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)

ABSTRACT:

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

KEYWORDS: fuzzy mapping, Hilbert space, fixed point, approximate quantity.


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

C-Field Cosmological models with bulk viscosity and variable G in flat FRW space-time

RAJ BALI and MEGHNA KUMAWAT
Department of Mathematics, University of Rajasthan Jaipur-302055 (INDIA)

ABSTRACT:

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.

KEYWORDS: C-field Cosmology, bulk viscosity, variable G PACS Nos.: 98.80. Cq, 98.80. Hw.


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...

Quasi-P Normal operators linear operators on Hilbert space for which T+T* And T*T commute

DIPSHIKHA BHATTACHARYA1 and NARENDRA PRASAD2
1,2Ramgarh College, Ramgarh Dept. of Mathematics Dist. Ramgarh Jharkhand, 829122 (V.B.U B Hazaribagh) (INDIA

ABSTRACT:

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*

KEYWORDS: Quasi normal operator,Binormal operator,Hilbert Space


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* =...

MHD flow of visco-elastic [Oldroyd (1958) model] liquid of first order through porous media between two parallel flat plates

RAVINDRA KUMAR1, K.K. SINGH and A.K. SHARMA2
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

ABSTRACT:

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.

KEYWORDS: visco-elastic liquid


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...

Optimization of Multi-Objective Routing Models for Multiple Level and Multi-Tiered Networks

RAVIENDER SINGH and ARIF NADEEM*
Department of Mathematics Bareilly College Bareilly (M J P R University Bareilly) (INDIA)

ABSTRACT:

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.

KEYWORDS: Vehicle Routing, Time Windows, Raw Data


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...

Non compatible mappings in fuzzy metric spaces

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

ABSTRACT:

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.

KEYWORDS: fuzzy metric spaces


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...

Random algebraic polynomials with non-identically distributed normal coefficients

1S. BAGH and 2M.K. PAL
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

ABSTRACT:

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.

KEYWORDS: Random algebraic polynomial, Expected number of zeroes 2010 AMS Subject classification: Primary 34F60 , Secondary 30B20


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 stochastic model with variable threshold in HIV infection

S. VIJAYA
Department of Mathematics, Annamalai University (INDIA)

ABSTRACT:

n 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.

KEYWORDS: HIV infection,stochastic model,variable threshold


n 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....

Integrability Conditions of a Generalised almost contact manifold

LATA BISHT* and SANDHANA KUMARI**
*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

ABSTRACT:

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

KEYWORDS: Integrability,contact manifold


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