Vol 4 Issue 2 October 2016-March 2017

Abstract: This study examines the use of realistic mathematics approach in improving the understanding of the concept around a rectangular circumference with Realistic Mathematics Approach in class III SD. The results showed that the learning material and the concept of a rectangular circumference Approach Realistic Mathematics can make the students relaxed, happy, and not tense in learning. Lessons are conducted by: (1) shows the objects that are around rectangular and non-rectangular; (2) students complete worksheets using props that have been given; (3) Each group presented the results of their discussion while the other students respond; (4) students construct a rectangular circumference through the guidance of teachers; (5) students solve problems and other realistic problems. Based on the research findings and the provision of the act of learning, it can be concluded that learning by applying realistic mathematics approach can enhance students' understanding of the material around the rectangle.

Keywords: Approach, mathematics, realistic, concept, circumference, a rectangle.

Title: Improve Understanding the Concept of Rectangle Circumference through Realistic Mathematic Approach of Primary Class III (SD)

Author: DRA. KADARIAH

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

Research Publish Journals

Abstract: This paper is devoted to investigate the boundary layer flow and heat transfer in presence of heat generation/absorption, radiation and electrification of particles over a stretching sheet. The governing partial differential equations of the flow field are reduced into first order ordinary differential equations using similarity transformations and then solved numerically using Runge-Kutta method with shooting technique. Numerical results obtained to study the effects of various parameters like Prandtl Number, Eckert Number, Grashof Number, electrification parameter, radiation parameter, and heat source/sink parameter on dimensionless velocity, temperature as well as the skin friction and Nusselt number. Comparison of the obtained results is made with existing literature and graphical study is performed to explain the inter relationship between parameters and velocity, parameters and heat transfer. The rate of heat transfer at the surface and skin friction increases with increasing values of electrification parameter M. Thermal boundary layer thickness of fluid phase increases but thermal boundary layer thickness of dust phase decrease for the enhanced values of diffusion parameter ε. AMS Clasifications: 76T10, 76T15 Keywords: Boundary-Layer, Dusty fluid, Electrification of particles, Heat source / sink, Nusselt number, Radiation, Skin Friction Coefficient, Stretching Sheet, Two-phase flow ,Unsteady Flow. Title: Modeling of Heat and Mass Transfer Analysis of Unsteady Two-Phase Boundary Layer Flow over a Stretching Sheet Author: Aswin Kumar Rauta International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: The shortest path and minimum spanning tree problems are two of the classic problems in combinatorial optimization. Using Dijkstra algorithm for searching shortest path problem is an important content of the application of GIS (Geographic Information System), but it fails to find all the shortest paths. In this work the article based on the Dijkstra algorithm, added some data structure and proposed an algorithm that calculates all the shortest path of one vertex to others, the data structure is relatively simple; while effectiveness of the algorithm is explain through a numerical example. Keywords: Graph, Weighted graph,adjacent matrix, Disjkstra algorithm. Title: Shortest Path Algorithms Author: S.P. Behera, S. Bhattacharjee, D. Mishra International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: Waste water generation in the petroleum refineries and the stringent environmental disposal regulations have called for an intensive waste water management. This study is aimed at finding appropriate way of minimizing waste water generation in the refineries. For this purpose, a typical refinery which utilizes 40.5 te/hr of fresh water in its three basic operations (Distillation, Hydrodesulphurizer and Desalter) was chosen and studied based on single and multiple containment approaches. These methods established that the amount of fresh water required for an operation in the refinery is dependent on the mass transfer of the chosen key reference contaminant. Three key containments, namely H2S, oil and suspended solids where chosen and analysed. The study achieved the aim of simultaneously minimizing both the fresh water consumption and the effluent waste water generation via maximization of the internal water reuse in the operations. The results showed that there is about 37% and 15.4% reduction in waste water generation based on the single and multiple contaminant approaches respectively. The tools applied here are based on the principle of mass transfer. Keywords: Waste Water Generation, Petroleum Refineries, Stringent Environmental. Title: Investigation of Opportunity for Waste Water Minimization in Petroleum Refinery Using Pinch Technology Author: Okafor, I. I., Bassey, E. N International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: Fractal dimension is a valuable mathematical tool to quantify the complexity of geometrical structures. In the context of solar supergranulation, the network of convective cells observed on the solar photosphere, fractal dimension can reveal the dependence of the cell shape complexity on solar rotation, phase, magnetic activity level, and thereby provide insight into the underlying dynamics. This information can be useful for comparing observations with models. In particular, study of supergranular fractal dimension can shed light on the turbulence of the magneto-convective process that generates the magnetic structures. Here we briefly review recent research on this topic in the last decade. Keywords: Fractal dimension, mathematical tool. Title: Fractal Dimension of Supergranulation Author: Rajani G, Sowmya G M, Yamuna M, Panivani Udayshankar, R. Srikanth International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: In this article we study topological groups and their separation axioms. The theory of topological groups is rich in terms of its own profound results and also in terms of its application. We study topological groups mainly to illustrate how the introduction of an algebraic structure on a space affects and enriches its topological properties. As the name implies, a topological group is a topological space whose underlying set is also endowed with a group structure. A topological group is a mathematical object with both an algebraic structure and topological structure. Topological group along with continuous group action are used to study continuous symmetries which have many applications. Keywords: Filter base, interior of a set, Neighborhood system, semi topological group, separation axioms, and topological group. Title: A Study on Topological Groups and Their Separation Axioms Author: Swatilekha Nag International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: Levels of heavy metals: lead, chromium, manganese, zinc, copper and cadmium which were incorporated as glazes in the production of ceramic wares were analyzed in different ceramic materials using atomic absorption spectrophotometric method. The ceramic materials analyzed were spoon, pot, soup bowl, plate, mug and cup. Atomic absorption spectrophotometric analysis of the ceramic wares sampled revealed varying concentrations of these metals. The results obtained for the six metals in six ceramic samples ranged between 13.7075 mg/kg and 140.905mg for lead; 101.565 and 233,01 mg/kg for chromium, 0.1325 and 3.63 mg/kg for cadmium; 44.3325 and 1449.047 mg/L for manganese; 61.0625 and 1033 mg/kg for zinc; and 0.2350 and 6.260 mg/kg for copper. The levels of lead, manganese, zinc, chromium and copper in all the wares analyzed were above the permissible limits while the levels of chromium in all the wares analyzed with the exceptions of mug were above the permissible limits of World Health Organization (WHO) and Society of Glass and Ceramic Decorators. The result implies that the continuous domestic use of these wares pose potential danger to the end user. Consumption of food and drinks from these ceramic wares has attendant health implications owing to the toxicity of these metals, which could include; kidney and liver damage, loss of appetite, insomnia, chest pain, diarrhea, renal dysfunction, pneumonia and impotence in both men and women. The results were subjected to Pearson correlation analysis to see if some metals were interrelated with each other. The negative correlation observed between these metals indicated that the metals were probably not from the same source and that the presence of one does not affect the presence of other significantly. Similarly, the positive correlation between the metals indicated that they may probably be either of the same source or that the presence of one may affect the other. Keywords: Ceramic, heavy metals, leaching, permissible limits. Title: Determination of Some Heavy Metals from Domestic Ceramic Products Used In Kaduna, Nigeria Author: IDRIS M.K, OYEWALE A O, HAUWA M.S.H International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: Relativistic setting up is nothing more than a mathematical game between definitions and identities turned into principles or physical laws; in this sense, relationship of physical quantities from distinct moving systems is reduced to a fixed system regarding a moving one, so that the time or mass estimated from such a system are given by definition and they can only acquire physical meaning when are considered from the fixed frame. Lorentz’s transformation is only valid for electromagnetic phenomena and for subatomic particles, such as electron, which by virtue of the wave-corpuscle duality, can manifest its wavelike nature; its extension to classical particles is non-viable. The only mass to consider is the relativistic one, variable (it depends on velocity), but must be “virtual”. However, that virtualitiy confers to the same a great operative capacity under which it is possible to determine the energy levels working in weak, strong and electromagnetic interactions, as well as those produced in the nuclear reactions. The confusión comes of having mixed two spaces conceptually different: a) ordinary or common one, in which we can use space and time to obtain the velocity as a kinematic characteristic of any particle; b) fields (functions), whose arguments (phases), contain the dynamic variables (energy and momentum) through frequency and wavenumber as essential parameters, which relationship results in the propagation of light’s speed, as an universal constant, quite independent of any velocity. Keywords: Relativity, Relationship of Physical Quantities, Principles or Physical Laws. Title: Relativity: The Real Meaning Author: Francisco Martínez Flores. International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: Remotely sensed images acquired from National Centre for Remote Sensing (NCRS) Jos, using NigeriaSat 1 imagery were processed (filtering, edge enhancement, digitization etc.) to delineate the major geological ring structures/trends such as lineaments and drainage patterns of Jos Plateau. In addition, to decipher the relationship, if any, between the ring structures and the tectonism in the Plateau. The data was geo-referenced in accordance to topographic map coordinates of the Naraguta Sheet, and convolution models in ILWIS 3.1 software program were specifically employed to enhance and facilitate the recognition of the linear features in the area. Structural analysis shows that numerous fractures and lineation occurs at the northwestern, central and southwest of the satellite image. The strikes and lengths of all lineaments were measured and computed to obtain the rose diagram. The important structural trends are NE-SW, N-S and NW-SE, which corresponds to the directions and positions of the paleo-tectonic fracture zones in the area and mineralization tracks. Areas where basement rocks outcrop or underlay just beneath to the surface (i.e. areas with thin overburden) are known for the high lineament frequencies they exhibit, whereas, areas with little or no lineament frequencies are characteristic of areas with deeply buried basement rocks. Cross-referencing the lineament densities and Younger granites occurrences in Jos Plateau, a correlation is found between them emblematic of tectonic control most likely connected with paleo-tectonic structures; thus, associating their emplacement with the epeirogenic uplift. Mineralization in the Plateau is inferred to have been controlled by the same correlation. Keywords: Lineaments, fracture, faults, complexes, granites, structures. Title: Interpretation of Ring Structures in Jos Plateau Using NigeriaSat 1 Imagery Author: CHUKWUEMEKA C. ONYEANUNA International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: Rwanda runs the risk of slowing further progress toward the achievement of MDG-1 to eradicate extreme hunger and poverty. Thus there was needed to understand factors that influence and determine food security in Rwanda. A probit regression procedure was employed on household cross sectional data surveyed by WFP Comprehensive Food Security and Vulnerability Analysis and Nutrition Survey 2012 in a joint initiative between the Rwandan National Institute of Statistics and the Ministry of Agriculture and Animal Resources. The backward elimination and stepwise methods determined automatically which variables to keep or drop from the model. Of the seven variables fitted in the model; Sex of household head and Education level of household head as demographic determinants of household food security and Size of land, Access to nearest market, Livestock ownership and climatic adaptation as the economic determinants of household food security were found to be statistically significant. Marginal effects showed that households with education level of head of household and households owning livestock were more likely to be food secure than their counterparts. Correctly classified of 75.72% And the area under the receiver operating characteristic (ROC) curve of 0.71 indicated that the model was correctly specified. These results have policy implications for Food Security Status of Households in developing countries like Rwanda. Keywords: Probit, food security, Rwanda. Title: MODELING KEY DETERMINANTS OF THE HOUSEHOLD FOOD SECURITY IN RWANDA: PROBIT REGRESSION APPROACH Author: NDAKAZA Jean Napoleon, Dr. Joseph K. Mung’atu, Dr. NDENGO Marcel, HAGENIMANA Felix, GASHEJA Christophe, HARERIMANA jean de Dieu International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: The ultimate goal of the study was to find out statistical linear model which predictor variables exactly discriminate or separate women and men groups in wage non-farm employment sector in Rwanda. Linear discriminant method was used with numerical data given by third EICV conducted from 2010-2011 published by NISR in 2012. Discriminant analysis assigns observations to one of the pre-defined groups based on the knowledge of the multi-attributes. For this study I had a single classification variable as sex (male and female) that were divided into two groups of male workers and female workers in non-farm works and the distribution with each group was multivariate normal. The research’s sample was limited to the age between 18 and 65 years old by which women and men who are engaged in the wage nonfarm employment sector. This implied that 7,353 individuals belonged to the actual sample size with 3,772 (51.3%) women and 3,581 (48.7%) men. Majority of respondents were between 18 and 32 years old. 80% of the respondents had been to school and the level of Diploma is at 1%, Bachelor with 0.7%. 55% of the NFE workers are in the trade businesses. In the Non-Farm Employment sector. The SPSS was used to perform tests including the ANOVA test, test of variance, test of equality of group means, the Box’s M test, the Wilks’ Lambda test and Canonical discriminant analysis. Dependent variable was the sex type of male and female which was categorical and independent variables were: Type of non-farm activity (enterprise group), Education level, Income, Income-Unit of time, Expenditure, Expenditure-Unit of time, Duration, Urban/Rural location, and Poverty. The best predictors variables of the discrimination between women and men in the NFE sector were: Education level, Income, Income-Unit of time, Expenditure, Expenditure-Unit of time, Urban/Rural location, and Poverty and the weak predictor variables were: Duration in the business and Industry group of jobs. Keywords: discrimination, women, men, nonfarm employment sector and statistical linear model. Title: Linear Discriminant Modeling of Wage Nonfarm Employment between Women and Men in Rwanda Author: Anatole Mulindwa, Joseph K. Mungatu Phd, Marcel Ndengo Phd, International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: The model uses observed data from 1976 to 2013 on FDI, GDP, Industrial added value, Savings. Unit root test was conducted in order to know if the data are stationary. The co-integration approach was employed to investigate the long-run relationship between export and variables mentioned above. But we first assessed the order of integration of variables, and then assessed co integration among the variables (Long-run relationship) and short-run adjustments to retain the long-run equilibrium. Finally we have analyzed the dynamic relationship between export and hypothesized determinant. After differencing data the unit root test show that the series became stationary, it means the series are found to be integrated of order one i.e I(1) . To the other side Foreign Direct Investment (FDI) become stationary at level. The co-integration is possible because we found that among five series, four are integrated at the same highest order which is order one in our case. The results gave an indication for the existence of a long-run relationship between exports (EXPO), Foreign Direct Investment (FDI), Gross Domestic Product (GDP), and Industrial value added (IVA) and Savings (SAV). The size of the speed of adjustment (-0.80) shows that the economy will converge towards the long run equilibrium in approximately one year following a shock. The empirical results shows that Foreign Direct Investment, Gross Domestic Product, Industrial Value Added are statistically significant in short run. To the other side Savings is not statistically significant; this is because short term deposits are used for early future consumption but not for investment perspectives. The value of R-squared ( R2 ) shows that about 80 % of the variation in exports is explained by the combined effect of all variables considered. It also indicates that the explanatory variables contribute significantly in explaining the exports activity. This is the indicator of a good model which can be used for policy implication. Keywords: Export, Vector Error Correction Model, Stationarity, Long-run and short-run relationship. Title: Applying Vector Error Correction to Model Export in Rwanda Author: GASHEJA Christophe, Dr. Joseph MUNG’ATU, INGABIRE Joselyne, NDAKAZA Jean Napoleon, HAGENIMANA Felix International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: The models of single-channel recycling and dual-channel recycling are builded respectively, which are based on the closed loop supply chain (CLSC) of manufacturer and retailer. Under the decentralized decision-making, the Sterberg model is investigated in the models of single-channel recycling and dual-channel recycling, respectively. And then the optimal pricing and profit in different power-dominated rules are obtained. Meanwhile, under the same dominant model, the optimal price and profit of manufacturer and retailer under the single-channel recycling and the dual-channel recycling are studied. The results show that under the dual-channel recycling model, when some parameters meet certain conditions, the collection rate of the manufacturer is always greater than that of the retailer under different dominant model; the manufacturer and the retail can obtain the optimal profits under their own dominant model, under the retail-managed (manufacturer- managed) model, the manufacturer (the retailer) can obtain the minimum profit. It’s found that whether it is the manufacturer-managed or retailer-managed, the profits of retailers under the dual-channel recycle are higher than that under the single-channel recycle. Dual-channel recycling model is more advantageous to benign development and stable operation of closed-loop supply chain. Keywords: CLSC; Dual-channel recycling; Optimal pricing decision; Sterberg model. Title: Complexity Analysis of Pricing Policies in the Dual-Channel and Single-Channel Recycling Author: Xiaolin Ma International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: In this paper, a mathematical model of is presented and analyzed to gain more insight in the dynamism of Poverty and Prostitution in Nigeria. The model incorporates an infected compartment that gives a non – violent approach as intervention from the government. The stability of the system is analyzed for the existence of the Prostitute free equilibrium and existence of the Local stability of the Prostitution free equilibrium was investigated via the threshold parameter [Reproduction number ] obtained using the Next generation Matrix technique. The result shows that the is locally asymptotically stable at reproduction number less than unity and unstable whenever . Numerical simulation was performed using reasonable sets of values from existing literatures and the results shows that high rate of government intervention will proclaim a drastic decrease to the minimum point the number of the Poverty and Prostitution population which will triggers the truncation of infection in the population. Keywords: Mathematical model, Prostitution, Poverty, Local stability, Reproduction number. Author: F. O Akinpelu, M. M Ojo International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals

Abstract: The model of dual-channel recycling is builded, which is based on the closed loop supply chain (CLSC) of manufacturer and retailer. Under the decentralized decision-making, the Sterberg model is investigated. And then the optimal pricing and profit in different power-dominated rules are obtained. Meanwhile, under the same dominant model, the optimal price and profit of manufacturer and retailer based on the model are studied. The results show that under the dual-channel recycling model, when some parameters meet certain conditions, the collection rate of the manufacturer is always greater than that of the retailer under different dominant model. Keywords: CLSC; Dual-channel recycling; Sterberg model; optimal pricing. Title: Research on the Complexity of the Dual-Channel Recycling Closed Loop Supply Chain Author: Xiaolin Ma International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Research Publish Journals