**Volume 3, No.
2, April 2005.**

1. Relations involving y -functions and H-functions,

*Parveen Agarwal and C.L.Koul*

*Abstract*:
In this paper three relation involving y
- functions y(z) and H-functions of two
variables are established. Some known and new results are also obtained as
application of these relations

2. On weakly concircular Ricci symmetric manifolds,

*U.C.De and Gopal Chandra Ghosh*

*Abstract*:
The object of this paper is to study a new type of Riemannian manifold called
weakly concircular Ricci-symmetric manifold**.**

*Rakesh Kumar and Nagaich,R.K*

*Abstract*:
The object of this paper is to study the axiom of coholomorphic (2p+1) – spheres
for an indefinite RK- manifold.

4. Enumeration of non-isomorphic trellises with at most five points,

*Shashirekha Rai,
S.Parameshwara Bhatta*

*Abstract*:
Computing the number of non-isomorphic lattices with p points p≥1, or to find
asymptotic estimates and bounds for the rate of growth of the number of
non-isomorphic lattices with p points and to enumerate all non-isomorphic
lattices by their diagrams, considered purely as graphs are the questions raised
by Birkhoff.These questions are also wide open for generalized lattices. The
concept of a trellis was introduced by H.L.Skala and E.Fried as a
non-associative generalization of a lattice. In this paper we obtain the number
of non-isomorphic trellises with at most five points by using the
graph-isomorphism concept.

5. On a structure defined by a tensor field F(≠0) of type (1,1) satisfying

*Geeta Verma and Ram Nivas*

*Abstract*:
Inerrability conditions of a structure defined by a tensor field satisfying

have been studied by Gadea and Cordero and others. In this paper we have studied the structure satisfying

where F is a tensor of type (1,1).Certain results on integrability of such structure have also been studied.

6. A note on Hirschhorn’s generalization of the quintuple product identity,

*Abstract*:
We demonstrate that Hirschhorn’s generalization of the quintuple product
identity can be obtained by arguments employed by Hirschhorn himself to
establish a generalization of Winquist’s identity.

7. A bijective proof of a theorem of Andrews and Lewis on partitions,

*Padmavathamma,M.Ruby
Salestina and S.R.Sudarshan*

*Abstract*:
Using an identity of F.H.Jackson,Andrews and Lewis established many new
partition identities.The object of this paper is to give a bijective proof of
one of these.

8. Certain transformations of a class of integrals involving the H-functions of several variables,

*Harish nagar,Kiran Sharma and B.B.Jaimini*

*Abstract*:
In this paper two unified integrals and their multiple integral transformation
formulae involving general classes of polynomials of one and several variables
with the multivariable H-functions are established.As applications of the
results established here some known and new results are also pointed out

9. Brahmagupta polynomials arising from the skew-field of quarternions,

*B.Gayatridevi and R.Rangarajan*

*Abstract*: In this paper it is shown that the Brahmagupta matrix
generating Brahmagupta polynomials in two complex variables and their conjugate
arises naturally from the skew field of quarternions. Number theoretic
properties and special cases of Brahmagupta polynomials are described.

10. Convolution conditions for analytic functions in generalized pinchuk and generalized moulis classes,

*S.Latha and L Shivarudrappa*

*Abstract*: This paper deals with the theorem concerning generalization pf
some results of characterizations in terms of convolution for convex,starlike
and spiral like functions.

11. A study of the behavior of squeeze film between annular plates,

*Rakesh
M.Patel and G.M.Daheri*

*Abstract*: This article reports on the behaviour of squeeze film between
curved annular plates considering curvature of secant form to represent the
film thickness wherein the lower plate is curved.The concerned Reynolds equation
is solved with the associated boundary condition and expressions for
dimensionless pressure,load carrying capacity and response time are
obtained..The results are presented in graphical form.It is observed that while
decreasing values of radii cause increasing values of the response time ,there
is uniform disbrution of pressure and load along the plates as shown by the
parabolic profiles of the graph.

12. On dirichlet series solutionsof ordinary differential equation,

*Ashutose Saha and S.De Sarkar*

*Abstract*:
The authors produce two illustrations of
solution of ordinary linear differential equations which influence the utility
of introduction of Dirichlet series solution by Das and Lahiri

13. Fix point theorem for weak compatible of type (A) in fuzzy metric spaces,

*Savita Rathi and Renu Chugh*

*Abstract*: The aim
of this paper is to prove a common fix point theorem for six weak compatible
mappings of type (A) in fuzzy metric space

14. On certain transformations of bi-basic hypergeometric series,

*Esther Christopher*

*Abstract*:
In this paper, making use of a known
series identity and certain transformations of truncated basic hypergeometric
series,we establish certain transformations of bi-basic hypergeometric series.

15. On continued fraction representations for ratio of basic hypergeometric functions,

*Remy Y. Denis, S.N.Singh and S.P.Singh*

*Abstract*:
In this paper we put on record the
continued fraction representations for the ratio of and .We also discuss the corresponding results for the ratio of
two multiple q-series and bi-basic series.

*Fazal Mehdi,
Alveera Mehdi and Mohd. Yahya Abbasi*

*Abstract*: A v module M is said to
be a QT AG module if every finitely generated homomorphic image of M is a
direct sum of uniserial modules.In this paper we investigate the properties
shared by a module M and its submodule .Cardinals and ordinals are key concepts to the study of
infinite structures.Cutler defined Fuchs 5 grpups as a group if and only if its
every infinite pure sub group is contained in a summand of the same
cardinality.We generaste this concept to a module as HF –module and find a QT AG
–module M is a HF-module if and only if is a HF-module

**Volume 3,
No. 1, December 2004**

1. MacMahon’s Partition Analysis X: Plane Partitions With Diagonals,

*G.E. Andrews,
Peter Paule and Axel Riese *

*Abstract*:
We examine two-rowed plane partitions with a new diagonal constraints between
the rows. The related generating function is an infinite product; surprisingly
the numerator factors of the product are not cyclotomic polynomials.

2. q-Gauss summation Via Ramanujan And Combinatorics,

*Bruce C. Berndt,
Ae Ja Yee *

*Abstract*:
Two new proofs of the famous q-Gauss summation theorem are given. The first is
an elaboration of a proof given by Ramanujan in his lost notebook. The second is
combinatorial and uses the theory of partitions.

3. Rogers-Ramanujan Identities For F-Partitions,

*A.K. Agarwal and
G. Narang*

*Abstract*:
Three new infinite classes of partition identities involving generalized
Frobinious partitions (also called F-partitions ) and partitions with “n+t
copies of n” are obtained. Some particular cases which provide Rogers-Ramanujan
type identities are also discussed.

4. Generating Functions of The Laguerre-Bernaoulli Polynomials Involving Bilateral Series,

*M.A. Pathan*

*Abstract*:
The authors derives a newclass of generating functions for 2-variable Lagurre
and Lagurre-Bernoulli polynomials involving bilateral series. By appropriately
specializing a number of known or new partly unilateral and partly bilateral
generating functions are shown to follow as applications of the main results.

5. New Proofs of Jacobi’s Identity,

*Sen-Shan Huang and
Chein-Ming Lu *

*Abstract*:
In this paper, we give two new proofs for Jacobi’s identity by using Jacobi’s
triple product identity and rearrangements of infinite sums.

6. On Certain Bilateral q-series and Ramanujan’s Continued Fractions,

*Remy Y. Denis, S.N.
Singh, Neera A. Herbert*

*Abstract*:
In this paper four equivalent continued fraction representations for the ratio
of two _{2}y_{2} ‘s
have been established. Several known results of Ramanujan as well as certain new
results have also been deduced as special cases of these results.

7. Hypergeometric Proof of A Curious Identity Of Lyons,

*Paule and Riese, C. Krattenthaler*

*Abstract*:
We give a classical hypergeometric proof of an identity of Lyons, Paule and
Riese, which arose in work of Lyons and Steif on determinantal processes, and
which was originally proved by the former authors by the use of computer
algorithms.

8. Integral Formulas For The H-Functions Generalized Fractional Calculus,

*R.K. Saxena, J.
Ram and D.L. Sauthar*

*Abstract*:
The object of this article is to derive the images of the product of the
H-function, in which its argument contains a factor
, and a general class of polynomials defined by Srivastava
[5] under the multiple Erdelyi-Kober operator due to Galue et
al. [2, p.90]. The results obtained are general in character and includes
as special cases, the results for Riemann-Liouville operator [8], Saigo operator
[5] and the operator defined by Kalla and Kiryakova [3].

9. On Integral Means Inequalities Involving A Certain Class Of Integral Operators,

*R.K. Raina, Deepak
Bansal*

*Abstract*:
The present paper investigates the integral means inequalities for the functions
belonging to certain subclasses which are analytic in the open unit disc, and
involve a class of operators of fractional integration. Several special cases
and applications are also considered.

10. An Infinite Family Of Mock Theta Functions,

*S. Ahmad Ali*

*Abstract*:
Two new functions A(a,q) and
B(b,q) have been introduced
which yield the tenth order mock theta functions found in the Ramanujan’s ‘Lost’
Notebook as their particular cases. It has been shown that one of these two
functions represents an infinite family of the mock theta functions associated
with two mock theta functions of order ten. An identity connecting the bilateral
forms of these functions have also been established.

11. A Note On Certain Entries Of Ramanujan,

*Shyamli Gupta*

*Abstract*:
In this paper, we establish the generalization of entry 42 and 43 of chapter
XII of Ramanujan’s second notebook.

12. New Results Concerning The Analysis Of Voigt Functions,

*M. Kamarujjama, M.
Khursheed Alam and Dinesh Singh *

*Abstract*:
This paper aims at presenting a set of new results concerning the analysis of
Voigt functions and its generalization (or unification) from the viewpoint of
integrals and series. A multiple series expansion (or generating function) of
the generalized (or unified) Voigt functions are also considered by means of
generating function of hyper-Bessel’s functions.

**Volume 2 No.
3, August 2004.**

1. On Abelian Type
Results At ¥ And 0^{+} For
Modified Stielitjes Transformation,

*S. B. Gaikwad, M.
S. Chaudhary*

*Abstract*:
In this paper, using distributional Steiltje’s transform given in [1] which
enabled us to use the strong theory of the space of tempereddistributions S^{/
}and using notion of the quasi-asymptotic behaviorof distributions from {fÎS^{/},
sup fÌ[0,¥)},
introduced by Zavialov in [7], the author in [1] along with some general
results for asymptotic behavior of distributional Stieltjes transform at 0 and
¥, we obtain Modified Stieltjes
transformation; relation between classical Steiltjes and Modified Stieltjes
transformations. Further using the Modified Stieltjes transformation, we prove
some Abelian type results at ¥ and 0^{+}
.

2. An Iterative Algorithm For Implicit Complementarity Problem In Banach Space,

*K. R. Kazmi and F.
A. Khan*

*Abstract*:
In this paper, we establish an equivalence relation between a class of implicit
complementarity problems and a class of implicit Wiener-Hopf equations in
uniformly smooth Banach space. This relation is used to suggest
and analyze an iterative algorithm for finding the approximate solutions of
implicit complemantarity problems. Further, we prove the existence of solutions
of this class of problems and discuss the convergence of iterative sequences
generated by the iterative algorithm.

3. Some Fixed Point Theorems For Fuzzy Multi-Valued Mappings,

*T. Basu, Pradip
Kumar Maiti*

*Abstract*:
In this paper, we have proved two fixed-point theorems for fuzzy multi-valued
mappings. These are extentions of two theorems for single-valued mappings in
metric space.

4. A Computational Study Of The Two-Layered Model For Blood Flow Through A Circular Tube Hemodialyser,

*Manoj Kumar Gupta
and Sanjeev Kumar*

*Abstract*:
Hemodialysis is a very important phenomenon during the study of the blood,
because it removes metabolic wastes uric acid etc. from the blood. The most of
the wastes removed during the process are contained in plasma. So to analyze the
hemodialysis, one must first understand the flow behavior of the
blood in the tubes, therefore, we are considering a two-layered model of the
blood flow through a circular tube hemodialyser. Since the viscosity of the
plasma layer near the wall acts as a natural lubricant for the blood flow. In
dialysis, we have flows in which have peripheral plasma layer with less red
cells. Such flows are called two layered. Since red blood cells contain an iron
compound, so the blood may be considered as a magnetic flow. It
has been already studied that a magnetic field can push red cells away from the hemodialyser membrane, see [1,3-5]. We solved numerically this problem using the
finite difference techniques and obtained the result for blood velocity for the
different values of pressure force. For related work, see [2].

5. On Generalized Implicit Vector Variational-Like Inequalities,

*Abdul Khaliq and
Sonam Krishan *

*Abstract*:
In this paper, we introduce a class of generalized implicit vectorvariational-like
inequality problems in Hausdorff topologicalvector spaces which contain implicit
vector equilibrium problems, implicit vector variational inequalities and
implicit vector complementarity problems as special cases. We derive some new
existence results by using KKM-Fan theorem. The results of this paper generalize
and unify the corresponding results of several authors and can be considered as
a significant extension of the previous known results.

6. Abelian Theorems For The Generalized And Distributional Generalized Mehler-Fock Transformations,

*P. K. Banerji and
Deshna Loonker *

*Abstract*:
In this paper, we establish some Abelian theorems for the generalized and
distributional generalized Mehler-Fock transformation, as an initial value and a
final value theorem.

7. A Heuristic Approach For Solving Multi Objective Linear Integer Programming Problem,

*Teg Alam and Abdul
Bari *

*Abstract*:
This paper gives an approach for finding integer solution to multi objective
linear integer programming problem. Special cuts are developed to reach the
integer optimum after covering the multi objective integer programming into a
single objective linear integer programming. An example is given in the last to
illustrate the procedure.

8. Integral Representation Of Bivariate Laguerre And Jacobi Polynomials With Matrix Argument in The Complex Case,

*P. L. Sethi and
Virendra S. Bhati*

*Abstract*:
In this paper, some theorems have been discussed for bivariate Laguerre and
Jacobi polynomials for hermitian positive definite matrices. These theorems have
not been discussed previously. Few theorems have a wide range of applications in
the field of multivariate analysis.

**Volume 2 No.
2, April
2004 **

1. Lie Theoretic Generating Functions Of Two-Index Generalized Hermite Polynomials,

*Mohannad J. S.
Shahwan *

*Abstract*:
The aim of the present paper is to establish new generatingfunctions for
two-index generalized Hermite polynomials (G.H.P.) H_{m,n}(x,y,z,w,k) by
giving suitable interpretations to the indices (n) and (m). A few
special cases of interest are also discussed which would yield inevitably to
many new results of the theory of special functions.

2. A Note On Bailey’s Transform,

*Pankaj Srivastava*

*Abstract*:
In this paper, transformation formulae for poly-basichypergeometric functions
have been established by making use of Bailey’s Transform.

3. Bayesian Estimator Of Reliability For Generalized Burr Life
Distribution Under Time Censoring, *R. S. Srivastava,
Vijay Kumar and Narayan Kumar Joshi *

*Abstract*:
In this paper, we have obtained the Bayesian estimators of the reliability of
generalized Burr distribution with time censoring. These estimators are obtained
under linex loss function considering the non-informative and beta prior
distribution of the reliability function. The proposed estimators are useful
where the components fallow the Generalized Burr Distribution failure model and
equal importance is not given to under estimation. The expression
of estimators of reliability has also been obtained under squared
error loss function.

4. On A Structure
Defined By A Tensor Field x Of Type
(1,1) Satisfying x^{p} –a^{2}x^{p-q}
= 0, *Ram Nivas, Mohd
Nazrul Islam Khan *

*Abstract*:
Integrability conditions of a structure defined by a (1,1) tensor field
f^{4}
±f^{2} =0 have been studied by
Gadea and Cordeo [3] and others. Upadhyay and Gupta [2] studied integrability
conditions of

x (K,-(K-2))structure manifold. In this
paper, we have studied the integrability conditions of a structure satisfying
x^{p} –a^{2}x^{p-q}
= 0 (x¹0, p,q odd),
x a tensor field of type (1,1) and ‘a’
is a complex number not equal to zero.

5. A Note On
Raina-Nahar Multivariable Function, *S. P. Goyal, J.K.
Prajapat*

*Abstract*:
This note considers application of a multivariable function of Raina and Nahar
(and its integral representation) to derive Weyl fractional integrals of
particular functions.

6. Fractional
q-Derivative and Certain Basic Hypergeometric Transformations, *R. K. Yadav and S.
D. Purohit*

*Abstract*:
The present paper deals with the derivation of certain transformations for the
hypergeometric functions, as an application of q-Leibnitz rule for the n^{th}
order derivatives of a product of two functions. As q®1^{-},
the results given earlier by Manocha and Sharma [6] follows as a particular case
of our results. In the next section, we have deduced the q-Rodrigues formula for
the q- Laguerre polynomial as another application of fractional q-derivative.

7. Bayesian
Estimation Of The Shape Parameter And Reliability Of Generalized Pareto
Distribution Using Precautionary Loss Functionn With Censoring, *R. S. Srivastava,
Vijay Kumar and Arun Kumar Rao *

*Abstract*:
In this paper, we have obtain the Bayes estimators of the shape parameter and
reliability function of generalized Pareto Distribution. The loss function used
is precautionary. A number of prior distributions have been considered and
Bayesian estimates have been compared with the corresponding estimates with
squared error loss function.

8. Numerical Simulation Of Fluid Inertia On Slider Bearing Lubricant With
Heat conduction To The Pad, *P. Srinivasa Rao,
B.V. Rathish Kumar and Prawal Sinha *

*Abstract*: A
numerical study of thermo hydrodynamic performance of a high speed slider
bearing with heat conduction to the stationary pad has been analyzed. The couple
partial differential equations governing the fluid mass, momentum and energy
conservations along with heat conduction equation for the stationary pad,
assuming temperature dependent density and viscosity are solved usingStreamline
Upwind Petrov-Galerkin Finite Element Method to yield various bearing
characteristics. The influence of fluid inertia on the performance of a slider
bearing lubrication under various values of the tilt parameter, k has been
studied. Also, the influence of thermal flux along with fluid-solid interface
has been studied. The study reveals that the influence of fluid inertia has
greatly there is a marginal variation in thermal flux values across fluid-solid
interfaces.

9. A Unified Mock Theta Function, *S. Ahmad Ali*

*Abstract*:

10. Response To
Moving Load At Elastic/ Micropolar Solid Interface, *Rajneesh Kumar,
Praveen Ailawalia *

*Abstract*:
The steady state response of a micropolar elastic solid overlying an elastic
half space subjected at the plane interface to a moving point load has been
studied. The eigen value approach using FourierTransforms has been employed and
the transform has been inverted by using a numerical technique. The displacement
and stress components in the physical domain are obtained numerically. The
numerical results are illustrated graphically for adhesive (elastic) and
aluminum (micropolar) solid.

**Volume 2 No.
1, December, 2003.**

1. Existence Of
Solutions For Generalized Vector Variational-Like Inequalities, *A. Khaliq and A.
Raouf*

*Abstract*:
In this paper, we establish some existence theorems for a new class of
generalized vector variational-like inequalities in Banach space and in
Hausdorff topological vector space under compact and noncompact assumptions on
underlying convex sets.

2. Generating
Functions Of Biorthogonal Polynomials Suggested By Generalized Hermite
Polynomials, *P. G. Andhare, M.
S. Chaudhary*

*Abstract*:
In present paper, we obtain the generating function and bilateral generating
function for biorthogonal polynomials suggested by the generalized Hermite
polynomials.

3. A Fixed Theorem For Mappings, *D. Gopal and A. S.
Ranadive*

*Abstract*:
In this paper two fixed point theorems for three mappings have been proved.

4. Growth
Properties Of A Class Of Entire Double Dirichlet Sequences, *Artee *

*Abstract*:
In this paper, we have defined the growth (order and type) of complex double
sequences analogous to the respective definitions in the theory of integral
functions represented by double Dirichlet series with fixed sequence {l_{m}}
and {m_{n}} of exponents. We
have considered a class P of entire double dirichlet sequences (EDDS)
and have examined their growth properties. Distribution of elements of P over
the universal set U of all EDDS has been investigated and has been depicted by
Venn diagram.

5. On Strongly Multiplicative Graphs, *Chandrashekhar
Adiga, H. N. Ramaswami and D. D. Somashekara,*

*Abstract*:
In this note we show that every wheel is strongly multiplicative. Also we give a
formula for l(n), the maximum number of
edges in a strongly multiplicative graph of order n.

6. Effects Of Slip
Parameters On Magnetopolar Free Convection Flow, *Poonam Gupta and
N. C. Jain *

Abstract: This
paper is connected with steady free convection flow of an electrically
conducting viscous incompressible magneto polar fluid through a porous medium,
over a semi-infinite vertical porous plate under slip boundary conditions for
velocity and temperature. Using perturbation technique expressions
for velocity field, temperature field, skin friction and rate of heat transfer
have been obtained. Effects of Grashof number (G), permeability parameter
(K), magnetic parameter (M), rarefaction parameters (h_{1}
and r_{1}) and rotational parameters (a
and l) are discussed in detail and also
shown graphically.

7. On M-Projectively
Recurrent Sasakian Manifolds, *A. A. Sheikh and
Sudipta Biswas *

*Abstract*:
The object of this paper is to study M-projectively recurrent Sasakian
manifolds.

8. A Study Of Mathematical Models Of Production Functions, *R. C. Srivastava
and U. K. Gupta*

*Abstract*:
In this paper we study the production and cost function in generalized form. The
formulation and generalization may be used to study the production behavior and
cost structure of any industry.

9. Problems Of
Functions Of Bounded Boundary and Radial Rotations, *Susheel Chandra*

*Abstract*:
Coefficient problems related to the functions of bounded boundary and radial
rotations in the unit disc have been obtained.

**
Volume 1 No. 3, August 2003.**

1. Some
Generalization Of Closed Modules, *Fazal Mehdi and
Alveera Mehdi*

*Abstract*: A
closed module is defined as the module, which is a direct sum of the summands of
its basic sub modules. In a h-reduced S_{2}-module the closed sub
modules of M coincide with the sub modules of M which are complete with respect
to the h-topology. On the other hand a S_{2}-module M =
N Å K, where N is closed and K is
direct sum of uniserial modules, need not be closed. This motivates the
generalization of closed modules to semi closed modules. As a
direct sum of a closed and h-divisible module is quasicomplete module with
respect to h-topology, this motivates the generalization of closed modules to
quasiclosed module. _{ }

2. On Certain
Transformation Formulae For Abnormal q-Series, *Remy Y. Denis,
S.N.singh, S.P.Singh *

*Abstract*:
In this paper, making use of Bailey’s transform and certain known summations, an attempt has been made to establish certain transformation
formulae for abnormal q-series.

3. On Generating
function For the Two Variable Modified Lagurre Polynomials, *Subuhi Khan and
Ghazala Yasmin*

*Abstract*:
In this paper, using Weisner’s group-theoretic method, we derive generating
relations for the two variable modified Laguerre polynomials (TVMLP). Certain
special cases of interest are also discussed which would yield many new and
known generating relations for the polynomials related to TVMLP.

4. On A
Generalization Of Iyer’s Sequence Space G,
*J.K.Srivastava and
P.K.Srivastava*

*Abstract*:
Let X be a Banach space and p = (p_{k}) be a sequence of positive real
numbers. X-valued sequence space E(X,p,R), R > 0, and E(X,p) are introduced and
some of their topological properties are investigated. For these spaces operator
version Kothe Toeplitz duals and continious duals are characterized and
equivalance of weak and strong convergence is investigated.

5. Double Series
Representation Of Mock Theta Functions, *Pankaj Srivastava.*

*Abstract*:
In this paper, making use of a known results we established double series
representations of various mock-theta functions.

6. Some Some
Multiple Gaussian Hypergeometric Generalizations Of Buschman-Srivastava Theorem,
*M.I.Qureshi,
M.Sadiq, M.A.Pathan *

*Abstract*:
Some generalizations of Bailey theorem [1, p.246(2.11)] involving the product of
two Kummer’s functions _{1}F_{1}, are obtained by usingWatson
theorem [14, p.95(26)] and Srinivasa’s identities [12, pp.194-197; see also 14,
p.214(8), p.217(12)]. Its special cases yields various new transformations and
reduction formulae involving Pathan’s quadruple hypergeometric functions F^{(3)},
F^{(4)}, Lauricella’s quadruple hypergeometric function
, Exton’s multiple hypergeometric functions
,Erdelyi multiple hypergeometric function H_{n,k} ,
triple hypergeometric function , Appell’s double hypergeometric function of second kind F_{2}
, Srivastava-Daoust function. Some known results of Buschman and Srivastava [4, p.439; see
alsop 13, p.31(47)] and Bailey [3, p.239(4.4); see also 13, p.323(191)], are
obtained.

7. Some New
Sequence Space Generated By Orlicz Functions, *Metin Basarir *

*Abstract*:
In this paper, we define some new spaces of lacunary sequences of invariant
means generated by a sequence of Orlicz functions M = (M_{k}). We
discuss some topological properties and establish some inclusion relations
between them.

8. Certain
Transformations And Reduction Formulae For Hypergeometric Functions, *M.A.Pathan and
S.I.Laskar*

*Abstract*:
In this paper, certain interesting results involving Kampe de Feriet and
Appell’s hypergeometric functions are derived by using some known summation
formulae.

**Volume 1 No. 2**, **April 2003**.

1. On a
generalized statistical distribution association with product of Generalized
hypergeometric functions, *R.K. Saxena, Jeta
Ram and J.D. Goree*

*Abstract*: A
new statistical distribution association with the product of Gauss Hypergeometric
function and ‘r’ generalized hypergeometric Function is introduced and studied,
which provides the extension of the work of Saigo et.al. [J.Frac.calc. 7(1995),
35-40]

2. Application of
directed signature scheme, *Sunder Lal, Manoj Kumar*

*Abstract*:
Directed signature scheme is applicable when the signed message Contains
information sensitive, because only receiver can directly Verify the signature
and that he/she can prove its validity to any Third party, whenever necessary.
This paper presents two applications of directed signature scheme:-

(i) Directed-Delegated Signature Scheme. This scheme combines the idea of proxy signatures with directed signature scheme.

(ii)
Allocation of registration number.** **This scheme proposes a
registration number cannot be forged and misused.

3. Laurent
coefficients for cubic theta function, *S.Bhargava and
Syeda Noor Fathima*

*Abstract*:
The purpose of the paper is to establish the interesting fact that the Laurent
coefficient of two-parameter cubic analogues of the Jacobi’s theta
functions.This is a sequel to an earlier work of the first author and at the
same time generalized a recent work of S.Cooper.

4. Existence of
solution and iterative algorithm for a generalized Implicit complementarity
problem in banach space, Kaleem *Raza Kazmi
and Mohd. Iqbal Bhat*

*Abstract*:
In this paper, we study a generalized implicit complementarity problem 9in
short, GICP) in uniformly smooth Banach space and show that it is equivalent to
a fixed-point problem. Using this equivalence we analyze an interative algorithm
for GICP.further, we prove the existence of solution and discuss the convergence
analysis of the developed interative algorithm. The theorems presented in this
paper generalized, improve and unify the corresponding known results for the
complementarity problems in Hilbert spaces.

5. On certain
transformation of poly-basic Bilateral Hypergeometric, *Remy Y. Denis, S.N.singh, S.P.Singh*

*Abstract*:
In this paper we have established certain transformation of basic hypergeometric
series with more than one base. Some of these lead to the relationship between
product of two q-series. These result, in turn, lead to very interesting
transformations of bi-basic and poly-basic series.

6. Extrapolated
iteration for a certain class o nonlinear Equation, *Rabindra Nath Sen,
Pulak Guhathakurta*

*Abstract*:
The extrapolated Newton-SOR method has been discussed. This method is used to
solve nonlinear equation having special structures. The method has been shown to
be iteratively faster than the Newton-SOR method discussed by Ortega and
rheinboldt.

7. A Unified mock
theta function, *S.Ahmad Ali *

*Abstract*:

8. A study of
certain integrals relating Ramanujan’s formula, *Mridula Garg and
Shweta Mittal*

*Abstract*:
The aim of the present paper is to develop and extend an interesting integral
obtained by Ramanujan with the help of his master theorem. In the present paper
we evaluate three unified integral involving the product of the
general class of polynomial, the generalized sequence of function and the H-
function of several variables with general arguments. Our
findings are believed to be new and are capable of yielding of
large number of integral involving several polynomials and special functions as
their particular cases.

1. On Reducibility
of Certain q-Double Hypergeometric Series and Clausen Type Identities, *Remy Y. Denis*

*Abstract*:
In this paper, a method has been developed to establish certain
transformations of double q-series in terms of basic hypergeometric functions of
one variable. These results lead to certain interesting Clausen type identities.
We also discuss certain continued fractionRepresentations involving q-series.

2. Two Variable
Modified Laguerre Polynomials And Their Generating Relations, *M.A.Pathan, Subuhi
Khan and Ghazala* Yasmin

*Abstract*:
In this paper, the notion of two variable modified Laguerre poly-nomials (TVMLP)
L_{a,b,m,n}
(x,y) is given and their generating relations are derived. The process involves
the problem of framing TVMLP into the context of the representation
w,m
of a Lie algebra G(0,1). Certain new and known generating relations for the
poly-nomials related to TVMLP are also obtained as special cases.

3. A Certain Class
Of Multiple Generating Functions Involving Mittag-Leffler’s Functions, *M. Kamarujjama and
M. Khursheed Alam *

*Abstract*: A
set of certain class of multiple generating function involving Mittag-Leffler’s
functions E_{a} , E_{a,b
} and related function f(a,b;z)
of wright is given. Some interesting (known and new) multiple enerating
functions are also obtained as special cases.

4. Unsteady MHD
Flow Of A Generating Viscoelastic Oldroydian luid, *P.R.Sengupta*

*Abstract*:
The aim of this paper is to study the unsteady MHD flow of generalized visco-elastic
fluids through a porous rectangular duct. From this generalized investigation we
have deduced the different problems of flow in cases of oldroyd first order,
second order, n-th order fluids; Rivlin-Ericksen first order, second order, n-th
order fluids and ordinary viscous fluid. The numerical
calculation of the velocity profile for oldroyd Fluid has been made in the forms
of tables and graphs.

5. Some Remarks On
Wiener-Hopf Equations and Variational Inequalities In Banach Spaces, *Kaleem Raza Kazmi
and Mohd. Iqbal Bhat*

6. Bilateral
Generating Relations For Certain Hypergeometric Functions, *P.K.Banerji and F.B.F.Mohsen
*

*Abstract*:
This paper establishes some bilateral generating relations for hypergeometric
functions of two, three and four variables. Some Particular cases have been
explored.

7. The
Askey-wilson operation and the _{6}F_{5}
summation formula, *Shaun Cooper *

The summation formula

can be proved by expanding each
term in the identity by the binominal theorem, equating
coefficients of x^{n} on both sides and relabelling parameters. The aim
of this paper is to use the Askey- Wilson operator D_{q} and its index
lad to give a similar proof of the summation
formula for a terminating, very well poised _{6}F_{5}
series.

8. N- high
submodules and h-topology, *Fazal Mehdi and
Alveena Mehdi*

*Abstract*: A
sub-module K of M is N-high if K is maximal with the property KÇN
= 0 where N is a sub-module of M. In this paper we study N-high submodules in
the light of h-topology. In h-topology, H_{k}(M), k =1,2,…,¥
form a neighborhood system for zero. We characterize the submodules N of a
h-reduced S_{2}-model M for which all N-high submodules are bounded. We
further characterizethe submodule N of the same module M for which all h-pure
N-high submodules are bounded.