The
chromatic number of a commutative groupoid
W.B. Vasantha* and K. Paramasivam
Abstract: In this paper, we study the coloring problem of a commutative
groupoid and define the chromatic number of a commutative groupoid. We construct
a class of commutative groupoids using the set of all integers modulo n, on
which different closed binary nonassociative operations are defined and we prove
the following results:
1. For n = 2m, the chromatic number of the commutative groupoid Zn is m.
2. For n = p2, the chromatic number of the commutative groupoid Zn is p.
3. For n = pq, where p,q are primes such that 2<p<q, the chromatic number of the
commutative groupoid Zn is p.
Key words: Commutative groupoid, coloring, chromatic number.
Initial
Value Method for Two-dimensional Jet of Incompressible Viscous Fluids
Hema C. Surati and M. G. Timol
Abstract: Using group theoretic technique, the similarity solution for
two-dimensional jet flow of viscous incompressible fluids to derived. The
similarity equations governing the flow is non-linear boundary value problem (BVP)
with homogeneous boundary conditions is further transform to BVP with non
homogeneous boundary conditions and finally whole BVP is transformed into
initial value problem (IVP). Simple Taylor's series method is used to solve IVP.
It is observed that velocity of set increase with similarity independent
variable.
On almost contact hyperbolic
structures
Latika Bhatt and K.K. Dube
Abstract: Hyperbolic Kaehlerian space has been studied by Prvanovic4.
Rasevaski5 was the first to consider such spaces. Almost hyperbolic Hermitian
manifolds studied by Dube2. Upadhyay and Dube studied almost contact hyperbolic
structure6. Almost r-contact hyperbolic structure studied by Dube and Niwas3.
In the present paper we have defined hyperbolic Cosymplectic, nearly hyperbolic
Cosymplectic, almost hyperbolic Sasakian, quasi hyperbolic Sasakian, nearly
hyperbolic Sasakian, K-contact hyperbolic Remannian manifold, almost contact
hyperbolic normal metric manifold, almost contact hyperbolic pseudo normal
metric manifold, almost contact nearly hyperbolic normal metric manifold, quasi
hyperbolic normal manifold, generalized hyperbolic Cosymplectic, generalized
nearly hyperbolic Cosymplectic manifold and generalized quasi hyperbolic
Sasakian manifold.
Study of blood flow
through a stenosed capillary using Casson's fluid model
S.U. SIDDIQUI and SAPNA
Abstract: The Problem of blood flow through a capillary with axially
non-symmetric but radially symmetric stenosis at some distance from the entry
with mild local narrowing has been studied by characterizing blood as Casson's
fluid model. The effect of shape of stenosis (m) on physiological
characteristics of blood flow has been investigated. The variation of resistance
to flow and apparent viscosity with shape parameter (m), stenosis size (d/Ro),
stenosis length (Lo/L), and yield stress (to) has been shown graphically. It has
been found that the resistance to flow (l) decreases as the shape of stenosis
(m) changes (stenosis shape parameter m increases) and the maximum resistance
attained in the case of symmetric stenosis (m = 2). Resistance to flow decreases
as stenosis grows for increasing shape parameter. It is seen that apparent
viscosity decreases as stenosis shape parameter (m) increases, and apparent
viscosity increases as length of stenosis increases. It is also observed that as
shape parameter increases apparent viscosity decreases . It is of interest to
note that apparent viscosity decreases as the stenosis grows and as yield stress
increases apparent viscosity decreases for the shape of stenosis (m = 3). This
analysis incorporates a more realistic representation for blood flow in small
diameter tubes.
Solutions of field equations
Rij = 0 for [
–t]–type
and [t/]–type waves in
four dimensional space-time (I)
J. K. Jumale, K. D. Thengane and D. N. Warade*
Abstract: Considering for dimensional plane symmetric space-time
the plane wave
solutions of field equations Rij = 0 in empty region of space-time
for [-t]-type
and [t /
]-type plane waves are found as
An equivalent solution
are obtained by employing the concept of curvature tensor and Ricci tensor for
both types of waves.
A General Principle
for Mann Iteration
Anil Rajput and S. K. Malhotra*
Abstract: Let E be a closed convex subset of a Metric Space X T a selfmap
of E, A a lower Triangular Matrix. The general Mann Iteration of T are
defined by
x0 = v0Î
E, xn+1 = Tvn ,
we prove that, If A is equivalent to convergence, {xn} converges, and
T satisfies a generic type condition, then {xn} converges to a fixed
point of T. A similar theorem is proved for a pair of self maps. A number of
theorems in the literature are special cases of these results.
Steady three-dimensional
flow and heat trasfer along an infinite hot vertical porous surface in the
presence of heat source, uniform free stream and periodic suction
P. R. Sharma, Indu Gupta and M. K. Sharma*
Abstract: Steady three-dimensional laminar flow and heat transfer of an
incompressible fluid along an infinite hot vertical porous surface in the
presence of heat source, uniform free stream and sinusoidal suction velocity is
investigated. The governing equations of motion and energy are solved by using
perturbation technique. The velocity components, pressure distribution and
temperature distribution are derived. The mean and main velocity components and
temperature fields are shown through graphs. The expressions of skin - friction
coefficients along X*- and Z*- axes and Nusselt number at the surface are
derived, discussed and their numerical values for various values of physical
parameters are presented through Tables.
Steady blood flow through a
narrow exponentially diverging tube with magnetic effect
V. P. RATHOD and G. G. RAJPUT
Abstract: The problem of steady blood flow in the presence of transverse
magnetic field through a narrow exponentially diverging tube is considered. The
solution to this problem has been obtained in Bessel - Fourier series form. The
velocity profiles are drawn for different values of Hartman number A, couple
stress parameter and diverging parameter y1. It is of interest to note that as
the magnetic effect is increased the velocity of the blood is decreased. Thus,
by deaccelerating the velocity certain cardiovascular diseases and diseases
related to accelerated blood circulation like hypertension can be treated by the
application of magnetic field.
Key words: diverging tube, blood flow, velocity profile, Hartman number, couple
stress.
Similarity Solutions for
Heat Conduction Equation Via Group Theory
Hema C. Surati and M. G. Timol
Abstract: The similarity transformations for the Heat Conduction equation
are investigated used in Group theoretic method. The entire theory has been
presented in a simple manner so that, it could be beneficial to the Engineering
specialists. The special group of transformations likes scaling, translation and
the spiral group of transformations is used to investigate proper similarity
transformations to transform partial differential equation governing the Heat
Conduction Equation into Similarity Equation, which is ordinary differential
equation. Finally, a more general new group of transformation is proposed which
includes the earlier group transformations as its special cases.
Free convection of an
elastico-viscous fluid confined between two vertical wavy walls
RITA CHOUDHURY, HEMENDRA SARMA* and ALOK DAS**
Abstract: The flow of an elastico-viscous fluid in porous medium confined
between two long vertical wavy walls has been studied in this paper. The wave
length of the wavy walls is assumed to be large with amplitudes of two wavy
walls being different. Regular perturbation technique is used to solve the
problem where perturbation parameter is inversely proportional to the wave
length. The analytic expression for dimensionless shearing stress at both the
walls has been obtained and numerically worked out for different values of the
parameters involved in the solution.
Key Words : Elastico-viscous, Porous Medium, Wavy walls, Wave length,
Shearing Stress, Regular perturbation technique. 1991 AMS Mathematics Subject
Classification: 76A05, 76A10
Solutions of field equations
Rij = 0 for [
–
]–type and [/]–type
waves in four dimensional space-times
Pangul N. D. and Thengane K. D.
Abstract: Investigating for dimensional plane symmetric space-time, plane wave
solutions of field equations Rij = 0 for [–]-type
and [t/]-
type plane waves are obtained as
Furthermore, an equivalent plane wave solutions are obtained by using the
concept of curvature tensor and Ricci tensor for the same space-time.
A study of nutritional
transport in pulsatile blood flows through time dependent stenotic tube
P.N. TANDON, REKHA BALI, S.U. SIDDIQUI and A.K. SHUKLA
Abstract: Representing blood by couple stress fluid and introducing m 1d
symmetric stenosis in a small diameter tube, a study of nutritional transport
has been made in this paper. The governing equations have been solved by a
Picard’s type iterative procedure. Variations of the local concentration with
various parameters involved in the analysis has been presented through graphs
and discussed. It has been observed that the rheological parameters of the fluid
model representing concentration and shape and size of suspended microstructures
dominate the nutritional transport. In the stenotic region, the diffusional
process hinders owing to the closure of pores and this, in turn, prevents proper
nutritional supply to the cells in the deeper region in the tissue.
Propagation of spherical
shock waves in non-ideal atmosphere
S. N. OJHA and S. B. TIWARI
Abstract: Using the method of self - similar motion, the propagation of
spherical shock waves has been discussed in non - ideal gas. It has been
observed that the non - ideal factor affects greatly the flow behind the shock
waves.
Power series collocation
methods of several orders for initial value problems
J. O. Fatokun
Abstract: This paper concerns the derivation of some Multistep methods
for solving initial value problems. Earlier reports by P. Onumanyi et al.9 and
Awoyemi D.O.2, show that collocation methods are derived through the use of
canonical polynomials.
In this paper, power series is used as the approximation to the solution of the
general first order initial value problem y' = f(x, y); y(a) = a..
For every k-step method derived, it turns out to be of order k+1. This report
presents cases of k=1, 2, 3, and 4. The order, error constants, convergence and
stability properties are examined for each method.
Key words: Collocation methods, Initial Value Problems Power Series,
Convergence and Stability.
AMS subject classification 65L05
A study of p-filters of
orthomodular lattices
E.K.R. NAGARAJAN
Abstract: In this paper we define a binary operation
Ä on an
orthomodular lattice, we study about same properties of this operation
Ä. We also
prove that a filter F of an orthomodular lattice is a p-filter if, and only if,
(bÄa)Äb
Î
F for all aÎF
and for all bÎL.
Further, we prove that a C b if, and only if, bÄ(aÄa)
= (bÄa)Äa.
We also prove that (aÄb)Äc
= aÄ(bÄc)
if a commutes with both b and c.
Key words: Ortholattice, Orthomodular lattice, p-filter, perspectivity,
commutativity.
On two point boundary value
problems for X = A X + X B
M.S.N. MURTY and B.V. APPARAO
Abstract: This paper presents criteria for the existence and uniqueness
of solutions of two point boundary value problems associated with the system of
matrix differential equations by applying the technique of Kronecker product of
matrices and with the help of a Green’s matrix.