Another Proof of the Brezis-Lieb Lemma

Yanjin Chen, Yue Zhang

Sch J Phys Math Stat | 53-56

DOI : 10.36347/sjpms

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The Breis-Lieb Lemma was first came up with by the famous French mathematician Haim Brezis and
American mathematician Elliott Lieb, it is an improvement of Fatou's Lemma, which has numerous applications mainly
in calculus of variations when it faced the problem whether an infimum or supremum can be achieved. In this paper we
use the Clarkson's inequality combined with the Fatou's Lemma to prove the Brezis-Lieb lemma

Original Research Article

**April 22, 2017**

Effects of Radiation and Chemical Reaction on MHD Flow Past Over Vertical Plate with Variable Temperature and Mass Diffusion

U. S. Rajput, Gaurav Kumar

Sch J Phys Math Stat | 35-43

DOI : 10.36347/sjpms

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In the present paper, we study the effects of radiation and chemical reaction on flow past an oscillating vertical
plate with variable wall temperature and mass diffusion in the presence of transversely applied uniform magnetic field
and Hall current. The flow model consists of unsteady flow of a viscous, incompressible and electrically conducting
fluid. The plate temperature and the concentration level near the plate increase linearly with time. The fluid model under
consideration has been solved by Laplace transform technique. The model contains equations of motion, diffusion
equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have
been considered. The numerical data obtained is discussed with the help of graphs and tables. The numerical values
obtained for skin-friction, Sherwood number and Nusselt number have been tabulated. We found that the values obtained
for velocity, concentration and temperature are in concurrence with the actual flow of the fluid.

Original Research Article

**May 22, 2017**

Lower Triangular Vector Bilinear Autoregressive Time Series Model

Iberedem A. Iwok

Sch J Phys Math Stat | 44-52

DOI : 10.36347/sjpms

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This work proposed a strategy for fitting a subset form of a vector bilinear model. In this case, lower triangular
portion of the vector linear and non-linear components of a vector autoregressive bilinear structure was considered. The
workability of the method was illustrated using a 3 – dimensional vector of time series. The models were found to fulfil
the assumptions of model adequacy and each time dependent variable depended only on a subset of lagged time varying
quantities under consideration. Apart from being parsimonious, the fitted models were found to perform better than the
parent vector bilinear autoregressive models as revealed by some statistical comparative analysis.

Measurement of Beliefs, Attitudes, Emotions and Valuation in Training About the Teaching of Mathematics

Carlos Eduardo Valdivieso Taborga, Oscar Álvaro Valdivieso Taborga

Sch J Phys Math Stat | 57-78

DOI : 10.36347/sjpms

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This investigation focuses on beliefs, attitudes, emotions and valuation in training about mathematics of 200
students from Universidad Privada Boliviana (UPB) in Bolivia. An instrument was designed to measure these aspects by
verifying the structure proposed by Caballero and Blanco[1] and by Caballero, Guerrero and Blanco[2], using
confirmatory factor analysis (CFA), consisting of 6 factors, 19 dimensions and 75 items. The scores obtained in each
factor and dimension were analyzed, showing that the students from UPB have beliefs, attitudes, emotions and valuations
about their training in mathematics that are positive and of a moderate level, and are increasing as the student goes into
higher mathematics subjects level. A structural equation modeling (SEM) was performed to observe the relationships
among the 6 factors studied. The most remarkable finding was that the factor of the role of the teacher of mathematics in
teaching and the factor of beliefs that the student has as an apprentice of mathematics are the most influential in his
valuation of his training in this area. Subsequently, a much shorter measuring instrument was proposed, with 6 factors, 11
dimensions and 31 items, making an exploratory factorial analysis for the elimination of items and dimensions, due to the
fact that a robust structure was not obtained through the CFA. Also, we obtained personal and academic profiles of the
students of UPB that presents positive characteristics about mathematics. Finally, some implications were analyzed that
help to improve the academic management of the UPB.

Hybrid Orthonormal Bernstein and Block-Pulse Functions for solving nonlinear Volterra integral equations

Mohamed A. Ramadan, Mohamed R. Ali

Sch J Phys Math Stat | 87-95

DOI : 10.36347/sjpms

Abstract
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In this paper, A numerical method based on an set of general, orthonormal Bernstein functions coupled with
Block-Pulse Functions on the interval [0,1] to solve non linear Volterra integral equations of the second kind,
numerically. First we introduced the proposed hybrid method, then we used it to transform the integral equations to
the system of algebraic equations. The obtained numerical results of the proposed methods are compared with exact
solution to show the convergence and advantages of the new method. the operational matrix of integration together with
Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra integral equations into some algebraic
equations, the numerical example illustrate the efficiency and accuracy of this method.
Keywords: Orthonormal Bernstein functions; Block-pulse functions; nonlinear Volterra integral equations; integration of
the cross product, product matrix, coefficient matrix