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Global Journal of Mathematical Sciences

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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