African
Journals Online
Global Journal of Mathematical Sciences
Volume 1, No 1 & 2, 2002
Abstracts
NEW THIRD ORDER EXPLICIT RUNDE-KUTTA METHOD WITH
EQUAL NODES
JULIAN IBEZIMAKO MBEGBU AND STELLA CHINYE CHIEMEKE
Department of Mathematics, University of Benin, Benin City, Nigeria
Department of Computer Science, University of Benin, Benin City,
Nigeria.
ABSTRACT
In the light of (4) and (5), a new third order explicit Runge –
Kutta Method with equal nodes and it's computer implementation were
highlighted. The method compared efficiently with the existing third
order explicit Runge – Kutta methods proposed by Kutta, Ralston,
Heun and Nystrom respectively.
Key Word: Explicit Runge – Kutta methods, Stepsize, order
conditions, and parameters
LEAKBACK OF PULSATILE FLOW OF PARTICLE FLUID
SUSPENSION MODEL OF BLOOD UNDER PERIODIC BODY ACCELERATION
R.O. AYENI, E.O. OGHRE AND S.O. AJADI
NATIONAL MATHEMATICAL CENTRE ABUJA, NIGERIA
ABSTRACT
We considered a two-phase model flow of blood subject to both
pulsative pressure gradient due to normal heart action and a periodic
body acceleration. The leakback of flow due to the fact that the
velocity of the red cell is greater than the mean velocity is derived
using the method of characteristics. The variation in body
acceleration amplitude though affects the velocity profile in the
capillary tubes, it has no effect on the leakback in the tubes.
Leakback is mainly determined by the balance of the viscous drag and
the driving force of the applied pressure gradient.
Key words: Leakback, Pulsatile Flow, Fluid Suspension,
Periodic Acceleration, Viscous Drag.
THE TOTAL NUMBER OF PARAMETERS IN THE FINITE
ELEMENT RESCTANGULATION OF A DOMAIN
G. A. OLAYI AND c o EKWUEME
Department of Mathematics, University of Calabar, calabar, Nigeria
Department of Curriculum and Teaching, University of Calabar,
Calabar, Nigeria
ABSTRACT
Rectangular finite elements are important in Finite Element Method.
This paper establishes a general formula for obtaining the total
number of parameters associated with any finite element rectangulation
of a domain. This number is also the dimension of the trail space as
well as the size of the associated linear system.
Key Words: Rectangular finite elements. Finite Element
Methods, Finite elements Parameters.
OBTAINING PROPORTION OF OPTIMUM YIELD WHEN FULL
YIELD IS UNATTAINABLE
E. C. NDUKA and T. A. BAMIDURO
Department of Mathematics / Statistics/ Computer Science.
University of Port Harcourt, Port Harcourt, Nigeria
Department of Statistics University of Ibandan, Ibadan, Nigeria.
ABSTRACT
In a situation where it is not feasible to obtain full yield at
harvest time because it is unattainable or simply unavoidable;
combined methods of calculus of variation and maximum likelihood
estimates are used to obtain a proportion of this yield. This is
obtained for both known (desired) and unknown (estimable) proportions
of the maximum yield on rectangular and square plot – formations.
The reference model is that due to Berry (1967) on intra-row and
inter-row spacing experiment.
Keywords: Berry's model, Calculus of variations,
Maximum likelihood, Plot-formations.
ON THE SEGMENTATION OF THE RESPONSE SURFACES FOR
SUPER CONVERGENT LINE SERIES' OPTIMAL SOLUTIONS OF CONSTRAINED LINEAR
AND QUADRATIC PROGRAMMING PROBLEMS
P. E. CHIGBU AND T. A. UGBE
Department of Statistics, University of Nigeria, Nsukka, Enugu
State, Nigeria
Department of Statistics, University of Nigeria, Nsukka, Enugu
State, Nigeria
Present Address: Department of Mathematics, Statistics, and
Computer Science, University of Calabar Calabar, Nigeria
ABSTRACT
The Solutions of Linear and Quadratic Programming Problems using
Super Convergent Line Series involving the Segmentation of the
Response Surface are presented in the paper. It is verified that the
number of segments, S for which optimal solutions of these problems
selected for verification are obtained are 2 and 4 for the linear and
Quadratic Programming problems, respectively. On the whole the line
search exchange algorithm is exploited.
Key Words: Exchange Algorithm, Response Surface,
Segmentation, Super Convergent Line Series, Support points.
CONSTRUCTION OF EQUIREPLICATE BALANCED
INCOMPLETE BLOCK DESIGNS WITH UNEQUAL BLOCK SIZES
MBA E. I.
DEPARTMENT OF STATISTICS,
UNIVERSITY OF NIGERIA, NSUKKA,
ENUGU STATE, NIGERIA
ABSTRACT
There are three major concepts of balancing in incomplete block
designs viz variance balancing, pair wise balancing and efficiency
balancing. The necessary and sufficient condition for a design to be
balanced is that the matrix C of the adjusted intra block normal
equation shall have all its off diagonal elements equal and all its
diagonal elements equal. This will serve as a major test of balance in
this work. Also a necessary condition is for the rank of C =t-1
because if the rank of C=(t-s), where s>1, then a set of [s-1}
independent contrast are not estimable, but if the rank of
C=t-1; then every contrast is estimated hence the design will be
connected. The paper concentrates on the quadruplicate balanced
incomplete block designs.
Keywords: Balanced incomplete block design (BIBD),
variance-balanced block design (VBBD), treatments, C-matrix, connected
design.
THE WEB OPTION AND
RESEARCH IN PHYSICS
ANYALEWECHI D. ASIEGBU
DEPARTMENT OF MATHEMATICAL AND PHYSICAL SCIENCESMICHAEL OKPARA
UNIVERSITY OF AGRICULTURE-UMUDIKE
ABSTRACT
Various options and opportunities offered by
the web to the study and practice of physics have been reviewed.
Rather than work individually the web provides the option of working
as a team. Rather than go from place to place in search of physics
information the browsing technique of the web is seen to provide the
option of obtaining any kind of information across the globe from
one's office or workstation. Websites are seen as global reservoir of
ordinary and expensive information, pricelessly accessible by the
privileged and less privileged. Favoured as well is the option of
passing physics instructions across the web rather than the classroom
alone. The web is seen to have broken the restriction imposed by
distance on global communication so that all kinds of physics
materials can be shared across the globe. Study shows that the web has
a lot of options and opportunities for the broad field of physics.
Keywords: Web, Physics- information,
Website, Option, Globe
ON THE PRECISION OF AN ESTIMATOR OF MEAN FOR
DOMAINS IN DOUBLE SAMPLING FOR INCLUSION PROBABILITIES
GODWIN A. UDOFIA
Department Of Mathematics/Statistics and Computer Science,
University of Calababr, Calabar, Nigeria.
ABSTRACT
In sample surveys, estimates are often required for small
subclasses of the population under study. In many sample situations,
the size of the domain and hence the number of sample units that fall
in the domain are unknown before the start of the survey. In this
paper, we examine the effect of the randomness of the domain size on
the precision of an estimator for the domain under double sampling for
inclusion probabilities. It is assumed that the population can be
divided into different strata. The results show that there is a
positive contribution to the variance of the estimator which varies
from one stratum to another. This addition vanishes where the domain
coincides with a stratum. The total sampling variance depends only on
components of variance for the domain and is inversely related to the
total sample size in each phase of the survey.
Key Words: Domain, Double Sampling, Unequal Probabilities.
STOCHASTIC SIMULATION OF HOURLY AVERAGE WIND
SPEED IN UMUDIKE, SOUTH-EAST NIGERIA.
*M. U. Igboekwe &** C. O. Omekara
Department of Mathematical and Physical Sciences
Michael Okpara University of Agriculture, Umudike, P.M.B 7267
Umuahia,
Abia State, Nigeria.
ABSTRACT
Ten years of hourly average wind speed data were used to build a
seasonal autoregressive integrated moving average (SARIMA) model. The
model was used to simulate hourly average wind speed and recommend
possible uses at Umudike, South eastern Nigeria. Results showed that
the simulated wind behaviour was reproducible and matched well with
the characteristics of the experimental values. The model may thus be
used to forecast wind speed and its impact on the environment of
Umudike, very accurately. Specifically the wind speed values have the
capacity of propelling a wind bound generating plant capable of
serving as a back-up power to the national grid.
Key words: Simulation; wind speed; SARIMA Model; Forecasts;
Back-up Power.
ESTIMATION FOR DOMAINS IN DOUBLE SAMPLING WITH
PROBABILITIES PROPORTIONAL TO KNOW SIZE
G. A. UDOFIA
Department of mathematics, Statistics and Computer Science,
University of Calabar, Calabar, Nigeria
ABSTRACT
Available publications show that the variance of an estimator of a
domain parameter depends variance of the study variable for the domain
elements and on the variance of the mean of that variable for element
of the domain in each constituent stratum. In this article, we show
that the variance of an estimator of a domain total for a small domain
of study in double sampling with probabilities proportional to size
(pps) when the size, Xn' is know before the start of the
survey depends only on the variance of the estimator by knowledge of X
is greater when both the proportion of non-domain elements and the
deviation of mean of the study variable for the domain elements in
each stratum form the population mean for the domain are large while
the study variable varies little among the domain elements in each
stratum.
Key Words: Domain, Double, Sampling, Unequal, Probabilities
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