Vol 3 Issue 1 April 2015-September 2015

Abstract: In this article, we discuss the importance of estimating the extinction coefficients for different pass-band filters in the stellar photometry. As the stellar brightness measured by ground based telescopes is reduced due to the scattering and absorption by the atmosphere of the Earth, the extinction correction is required to overcome such attenuation in the stellar brightness. Because of this fact, we also describe the procedure of determining the extinction coefficients for B and V pass-band filters using the CCD images of the Landolt’s standard stars field PG2331+055, which are provided by the Skinakas Observatory. Since the extinction coefficients are estimated by the slope of the graph between the airmass and instrumental magnitudes of a standard star marked as ‘A’ in the field PG2331+055, the stellar magnitudes are calculated by performing the aperture photometry on this standard star ‘A’ whose CCD images were observed in the same night over a wide range of airmass. It is found here that the effect of atmospheric extinction is less in V-filter than in B-filter.

Keywords: Atmospheric coefficients – methods: observations and data analysis – technique: CCD photometry.

Title: Importance of Estimating Extinction Coefficients in Stellar Photometry

Author: Swadesh Chand, Parijat Thakur, Abhijit Mandal

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: Sufficient optimality conditions are derived for nonlinear programming problems in presence of both equality and inequality constraints. This result subsumes the well-known Kuhn-Tucker and Fritz John sufficiency theorems discussed separately in the literature by several authors.

Keywords: Nonlinear programming problems.

Title: Sufficiency in Non Linear Programming: A Unified Problem

Author: DR.BISHMBHER DAYAL

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: It is proposed a new interpretation of the nuclear fusion reaction on the energy produced in stars by including the strong and weak interactions, with which we may explain the union or ligature between protons and neutrons to form atomic nuclei. The initial energy level of protons must be higher than were being estimated for fusion nuclear reactions; this energy is provided by plasma state (hydrogen ions and electrons) existent in stars remaining in the proper atomic nucleus without affecting its actual or inertial mass, because it corresponds to a virtual mass. Therefore, atomic nuclei are configured as an “abstract or inner space”, where the gauge quantum particles are provided with virtual mass; this space is distinct from the “exterior or common” one, in which particles (atoms, molecules and crystal) have real or inertial mass; electromagnetic radiation is compatible with both spaces. The emitted energy (electromagnetic) is due to the variation of “virtual” mass and to high energy photons or gamma rays formed by the union of electrons of the initial hydrogen atoms with positrons originated by the conversion of protons into neutrons, needed for the formation of nuclei. Stellar evolution involves obtaining only the so-called “white dwarf”, because they consist of ordinary matter as any planet.

Keywords: Electromagnetic, Stars.

Title: Stars: A New Approach

Author: Francisco Martínez Flores

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: In this paper we discuss the concepts of inverse split edge domination and total edge domination in fuzzy graph. We determine the inverse split edge domination number γ_IS^ꞌ (G) and the total edge domination number number g¢_t for several classes of fuzzy graph and obtain bounds for the same. We also obtain Nordhaus – Gaddum type results for these parameters.

Keywords: Fuzzy graph; Edge domination; Inverse split edge domination; Total edge Domination.

Title: Inverse Split Edge Domination in Fuzzy Graphs

Author: C.Y. Ponnappan S. Basheer Ahamed, P. Surulinathan

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: The theory of exterior differential systems is applied to study partial differential equations, expressed in the terms of differential forms using Cartan's method. The continuity equation and the Laplace equation are described by these exterior differential systems involving a geometrical perspective.

Keywords: Partial differential equations, exterior derivative, ideal, exterior differential systems, continuity equa-tion.

Title: Exterior Differential System Approach to Continuity Equation

Author: Mansour Hassan Mansour, M. A. Bashir

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: This research aims to determine a model that would predict the future broadband growth in Rwanda over a period of time. More often Organizations/Companies make predictions basing on the available technology based on the available data. But these data predictions more than often are influenced by disruptive technologies. This research was to therefore model the growth of internet broadband in Rwanda, with a view of technological changes and be able to predict the broadband growth irrespective of future technologies. This research   targeted and collected data from all internet licensed operators in Rwanda. This model will help planners especially operators to determine how long a certain technology is likely to last, its output and be able to avoid unnecessary stocks that lead to losses due to obsolete technologies which are overtaken by new technologies. The Gompertz curve was for long been used only to actuaries but more recently, it has been used by many authors as growth curve both for biological and for economic purposes. The intention therefore was to determine the constants, Inflection, Straight line form of equation, Growth rate, Maximum growth rate, Relative growth rate as function, Relative growth rate as function of size.The research found out that the data fits the Gompertz model at 95% of confidence level. The parameters, Lambda λ(inflection growth rate), mu,µ(relative growth rate, A(Maximum growth rate) were computed to able to determine the model and to predict the future internet broadband requirement in Rwanda at any time (t).

Keywords: Inflection, Relative growth rate, Maximum growth rate, Gompertz model and Internet broadband.

Author: MODELLING THE GROWTH OF INTERNET BROADBAND IN RWANDA

Title: MARDADI Peter, Dr.KIGABO RUSHUZWA, Dr.Joseph K.MUNG’ATU

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: Semi organic Nonlinear optical material bismuth thiourea zinc acetate (BTZA) single crystals were grown by slow evaporation technique. Solvent used here was water. The solubility range is about 25-45C whose PH value is 3.1.The structural parameters of grown crystal were estimated by XRD. Spectral bands have been compared with thiourea complex using FTIR in the range 400-4000cm-1. FTIR studies confirm the functional groups present in the grown crystal. During the making of this crystal mechanical stress was applied on the crystal while cutting and polishing. Using Vickers’s hardness test hardness of crystal was estimated. NLO property was confirmed using Nd: YAG laser of wavelength 1064nm and efficiency was estimated three times higher than that of KDP.       

Keywords:  Slow evaporation technique, XRD, FTIR, Thermal analysis and SHG.                                                   

Title: Growth and Characteristics of Semi Organic Non-Linear Optical Material –Bismuth Thiourea Zinc Acetate (BTZA) Single Crystals

Author: S.PRIYA

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: In this work, we present a result in the form of a lemma which we name COA-Sowunmi’s Lemma, its proof and application to the stability analysis of the transcendental characteristics equation arising from the perturbation of the steady state of the non-linear age-structured population model of Gurtin and MacCamy [11]. Necessary condition for the asymptotic stability of the equilibrium state of the model is obtained in the form of constrained inequality on the vital parameters of the model. The result obtained is then compared with that of an earlier work by the [4].

Keywords: Characteristic equation, Steady or Equilibrium state, Stability.

Title: COA-SOWUNMI'S LEMMA AND ITS APPLICATION TO THE STABILITY ANALYSIS OF EQUILIBRIUM STATES OF THE NON-LINEAR AGE-STRUCTURED POPULATION MODEL

Author: Akinwande, N.I., Somma, S. A.

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: Intimate partner violence (IPV) against women is a global public health and human rights concern in Rwanda. As reviewed from two national surveys, in Rwanda, women’s experience of physical or sexual IPV in their lifetime almost doubled from 34% in the 2005 DHS, to 56% in the 2010 DHS, while globally IPV rates at 30% and in other sub-Saharan African countries, such as Uganda (40%); Zimbabwe (37%) and Kenya (24), placing Rwanda among the countries with the highest rates of IPV against women in the world, in order to inform the design of IPV prevention programs. A secondary analysis of RDHS 2010 was done and descriptive statistics was used to summarize continuous data, and categorical data, bivariate statistics was used to compare two study groups to provide strong evidence of any study group differences, The test for collinearity was done before fitting Multivariate logistic regression model to produce parsimonious (efficient) multivariable models, backward stepwise logistic regression was used to find the final model. Of the 3042 women included in the analysis 56.6% (n=1718) had experienced at least one form of IPV in the last 12 months prior to the survey. Women corresponding to 51.9% (n=1580) reported to have experienced severe form of IPV whereas other women equivalent to 33% (n=1007) reported a less severe form of IPV. Young women whose husband have not attained high school and having multiple sex partners, living in a high density household in rural areas are more likely to face IPV. IPV prevention programs should increase focus development initiatives to improve access to education for girls and boys may also have an important role in violence prevention.

Keywords: Intimate Partner Violence, Simple Logistic Regression, Multiple Logistic Regression.

Title: MODELING FACTORS ASSOCIATED WITH INTIMATE PARTNER VIOLENCE AGAINST WOMEN IN INTIMATE PARTNERSHIP IN RWANDA

Author: Elysee TUYISHIME, Dr. Joseph K. Mung’atu, Dr. Jairu NDIGA DESIDERIO

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract:  Asymptotically exact and nonlocal third order nonlinear evolution equations are derived for two counter propagating surface capillary gravity wave packets in deep water in the presence of wind flowing over water. From these evolution equations stability analysis is made for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness for some different values of dimensionless wind velocity.

Keywords: Nonlinear evolution equation, capillary gravity, waves, stability analysis. 

Title: Stability Analysis from Third Order Nonlinear Evolution Equations for Counter Propagating Capillary Gravity Wave Packets In The Presence Of Wind Flowing Over Water

Author: A.K. DHAR, J.MONDAL

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: A Single sampling attribute plan cannot be designed satisfying the given strength exactly. It is suggested that a group consisting of at most three single sampling plans be operated at random with certain proportions so that the group as a whole attains the given strength exactly. The problem of choosing at most three plans with the proportion of times they should be operated with minimum average sample size is shown to be a linear programming problem. An example with solution by simplex method is given.

Keywords: Sampling attribute plan, linear programming problem, given strength.

Title: A Group Single Sampling Attributes Plan to Attain a Given Strength

Author: Dr. Bishmbher Dayal Singh

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: The purpose of this project was to analyze the household consumption expenditure in Rwanda. The main objective of this study was to measure the level of household consumption expenditure in Rwanda and to show the contribution of each household consumption expenditure component in the total household consumption expenditure.

The government wants to know where people spend much money for some items for them to be able to budget for food security, non-food and housing consumption expenditure. This information is not always available and people keep changing their spending.

The project studied the distribution of the household consumption expenditure data and the mean differences between household consumption expenditure by component, by urban and rural areas, by sex of head of household and by household composition size and household adult equivalent size.

The research found out that the distribution of household consumption expenditure data was not approximately normally distributed, and Kigali city was the province with higher household consumption expenditure mean and the last was southern province. The research also revealed that, in Rwanda, households spent much money in food consumption, followed by non-food and the last was alcohol. The statistical hypothesis tests found out that the household consumption expenditure mean differences between components, urban and rural areas, household headed by male and female, and between household adult equivalent and household composition size were statistically significant at 95% confidence level.

Keywords: Parametric and non-parametric Test, Test of Normality, Household Consumption expenditure, Household size, Adult equivalent household size.

Title: Parametric and Non-Parametric Design Based Tests Analysis of the Level and Differentials of Household Consumption Expenditure in Rwanda (2010-2011)

Author: Roger KAMANA, Dr. Joseph K. Mung’atu , Dr. Marcel Ndengo

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: The aim of this study is to determine the radioactivity content of different types for building materials. Twenty four samples, from both local and foreign product were collected and measured using gamma spectrometry system. The activity concentrations have been determined for radium (226Ra), thorium (232Th) and potassium (4OK) in each sample. The samples were crushed and dried in controlled furnace for around twenty four hours, and then stored for four weeks in plastic Marinelli beakers. From the measured gamma-ray spectra, activity concentrations of marble building materials 238U (0.72– 43.2Bq/kg), 232Th (0.20 –33.10 Bq/kg), 226Ra (0.43–33.1 Bq/kg) and 40K (0.70–897.2 Bq/kg) for granite 238U (0.04–315.3 Bq/kg), 232Th (0.02–186.1 Bq/kg), 226Ra (0.03–147.2 Bq/kg) and 40K (0.30 – 1482.6 Bq/kg) The results are compared with the published data of other countries and with the world average limits. It is concluded that the measured radioactivity of building materials are within acceptable levels and does not poses any risk from radiation protection point of view. The results indicated that all the samples collected used as building materials in Alkharj area are safe in general for the radioactivity levels.

Keywords: Radioactivity concentration, building materials, Radium Equivalent, Radiation Hazard, Annual dose.

Title: Study of Natural Radioactivity for Some Building materials used in Al Kharj Area

Author: Ismael. A. Wadi, Mubarak Dirar, Ahmed Elhassan, Wasil .A.Abdalla

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: The purpose of this project was to analyze time that patients can spend waiting for service in Muhima District hospital. The main objective for this research was to provide necessary information to policy makers aimed to contribute in wellbeing of population by reducing waiting time for service because in excessive cases, long queues can delay appropriate decision for a specific disease that can cause occurrence of death while patient still waiting for service. This project examined, first the waiting time of patients in outpatient department by using queuing model after calculating the mean number of arrivals per hour and the mean number of patients served per hour. Further results from questionnaire from staff were analyzed in order to know their opinions about the waiting time in outpatient department. The results showed that the system utilization factor is greater than one. This means that the queue grew without bound. There were a big number of patients waiting in the queue and they waited for a long time before being seen by a physician. The correlation analysis revealed a significant negative correlation between days and patient arrivals which means that there were many patients on Monday more than Friday. The reasons given by staff interviewed were the big number of patients visiting this department and the shortage of staff. To reduce the waiting time, we suggested increasing the number of physicians and nurses in outpatient department and strengthening the capacity building of health care providers. The hospital should develop a staffing plan and put more effort in the beginning of the week for efficient use of available resources.

Keywords: Queuing model, Waiting time, Customer arrival, Customer service, Birth and Death process, Outpa- tient Department.

Title: Queuing Model for Healthcare Services in Public Health Facilities (A Case Study of Muhima Hospital)

Author: Augustin Dushime, Dr. Joseph K. Mung’atu, Dr. Marcel Ndengo

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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Abstract: Pure nickel ferrite (NiFe2O4) and magnesium substituted nickel ferrite (Ni1-xMgxFe2O4) with particles size in Nano-meter range were synthesized by using auto combustion technique. In this study, it has been observed that with increase in sintering temperature, the estimated bulk density of the materials increases. The XRD patterns of the samples show the formation of single phase materials and the lattice parameters estimated using XRD patterns.  FT-IR spectra shows two small peaks in the band region 400-1000 cm-1 (vibrational) and another peaks in the band range 1000- 4000 cm-1 in all the samples, characteristics of spinel structure. From Raman spectra, the Raman shift of pure NiFe2O4 and MgxNi1-xFe2O4 are comparable with the experimental values reported in literature. The Raman spectra gives five Raman active modes (A1g + Eg + 3F2g) which are expected in the spinel structure.

Keywords:  Combustion Method, Spinel structure,  XRD, FTIR, Raman Spectroscopy.

Title: Characterization of Magnesium Substituted Nickel Ferrites Nano-Particles Synthesized Using Combustion Technique

Author: Manojit De, Ganesh Bera, H. S. Tewari

International Journal of Mathematics and Physical Sciences Research

ISSN 2348-5736 (Online)

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