Vol 7 Issue 2 October 2019-March 2020

Abstract: Numerical solution methods of ordinary differential equations in numerical analysis is an important topic, which is usually used for many differential equations that is difficult to find their exact and analytic solution or the equation which cannot be represented in explicit form. There are many methods of numerical solution of ordinary differential equations such as; Taylor method, Euler method, Hunn method and Runge-Kutta method with first, second, third, fourth and higher orders respectively. Taylor's method is very accurate for numerical solution of differential equations, but it is rarely used because of the need for computations of successive derivatives. Euler's method has more errors but needs less computation. The Runge-Kutta method is a suitable and the most commonly used method with less computational steps and accurate calculation. The Runge-Kutta method is the generalized form of the Euler method which is used for numerical solution of ordinary differential equations. In this paper, the numerical solutions of ordinary differential equations are solved by Taylor, Euler and Runge-Kutta fourth-order methods and then their exact solutions are compared using tables and graphs.

Keywords: Ordinary Differential Equations, Numerical Solution of Equations, Exact Solution of Equations, Taylor’s Method, Euler’s Method, Runge-Kutta Method.

Title: Study of Numerical solution of Ordinary Differential Equation by Taylor, Euler and Runge-Kutta methods

Author: Sayed Abdul Bashir Osmani

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: In this paper, we have investigated some features of anisotropic accelerating Bianchi type-V cosmological models in the presence of perfect fluid, variable gravitational and cosmological constants towards the gravitational field equations for scale covariant theory of Gravitation. With the help of special law of variation of Hubble’s parameter proposed by Berman (1983) which yields constant deceleration parameter of the models, we achieve a physically realistic solution to the field equations. Some geometrical and physical aspects of derived model are discussed with the help of solution and make the models at late times turn out to be flat Universe.

Keywords: Bianchi type-V cosmological model; scale covariant theory of gravitation.

Title: Bianchi type-V Cosmological model with  and  in Scale Covariant Theory of Gravitation

Author: R. S. Rane, G. C. Bhagat

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: In modern world, the technology is rising upwards at large scale and the leading the day is Nano-Technology. Hence it appealed to us that we should contribute to the science with our little efforts.

Nickel Nano-ferrites i.e. NiCo Nanoparticles were prepared by using sol-gel synthesis method using Ni(NO3)2 .6H20 (Nickel Nitrate), Fe (NO3)3 .9H20 (Ferric Nitrate),Cobalt Nitrate Co(No3)2.6H20 ( C6H807.H20 (Citric Acid) as fuel agent, NH3 (Ammonia) as pH balancing agent and followed by calcinations at certain temperature. The pH of three samples prepared were varied in order to understand changes in properties. Multiple techniques (XRD, 2 Probe) were commanded to characterize the crystal structures, electrical properties and magnetic properties of NiCo.

Keywords: Nano-Technology, Nano-ferrites, NiCo, pH, characterize.

Title: SYNTHESIS OF NI-CO NANO FERRITE USING SOL-GEL METHOD

Author: HITESH PATIL

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: The paper presents a review of Differential Transform Method (DTM) to solve non-linear heat equations. The method reduces the large amount of computational methods when non-linear problems need to be solved. The solutions obtained are exact to the high power of derivatives. After a brief discussion of the methods available, the method was used to solve an example with two variables. Approximate and exact solutions were developed for two derivatives, and the accuracy of DTM is evident in solving non-linear heat equations. 

Keywords:  Non-linear equations, heat equation, differential transform method.

Title: Using Differential Transform Method to Solve Non-Linear Heat Equation

Author: Yousef A. S.  M. Alsulaiman

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: This study described the theory and mechanism for the simultaneous determination of major, minor and trace elements involved in Neutron Activation Analysis, applied to geological and environmental samples as a sensitive and non−destructive tool. Using Neutron Source, the gamma−rays emitted due to neutron capture have been applied for the investigation of the elemental constituents and concentrations of major, minor and trace elements in such samples. Neutron Activation Analysis is of increasing importance in the field of element characterization in environmental and geological samples for a number of reasons that were documented and reviewed by several scientific researchers. NAA serve in the local industry and economy in each regional area of the country. It presents a sensitive multi-element technique which is valuable for major, minor and trace element analysis due to its precision and accuracy. The basic theory and detailed information on how NAA works in the analysis of above samples was presented in this paper. 

Keywords: mechanism, Neutron Activation Analysis, geological and environmental samples.

Title: Scientific Review on theory and Mechanism of Neutron Activation Analysis in Geological and Environmental Samples

Author: BUHARI SAMAILA, SHEHU ALHASSAN ALHJI

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: The movement of galaxies is not radial (running away) but transverse, according to relativistic Doppler Effect and its implication in the Hubble Law, so the Universe is not expanding.

The existence of “dark matter” may be linked to the  relativistic mass, which is of electromagnetic and virtual nature that  can be assumed by Quantum Theory, but not by Classical Mechanics;  in this sense, it may  also  explain the Cosmic Background Radiation, which are produced by a  large number of distant galaxies that are distributed  according to the  homogeneity an isotropy of the Cosmos.

General Theory of Relativity fails in its claim to convert  Gravitation into the relevant force, because it is mathematically inconsistent, so it could be explained  that “black holes” are not inferred from the Schwarzschild metric and the  “cosmic scale factor”, taken out from the Robertson-Walker metric  is no more than a  mathematical device: the evidence adduced is of little reliability, since they cannot be repeated, which is the necessary condition for an experimental science.

The Cosmos is arranged according to the paradigm of Dualitiy and not that of Unification, because the very small structures (subatomic particles) and the  larger ones (galaxies) are subject to  Quantum Theory thanks to Relativity, while the macroscopic bodies  obey to Gravitation  and  Classical Mechanics.

Keywords: Doppler effect,  relativistic mass and matter,  gravity and light, Quantum Universe.

Title: UNIVERSE: AN EXPANSION MODEL?

Author: Francisco Martínez Flores

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: The levels of heavy metals were assessed in three randomly chosen dump sites. Nine soil samples were drawn at the depth of 0-15 cm, 15-30 cm and 30-45 cm on each of the three randomly chosen locations and plant samples from three locations from the dumpsites, one plant from each site. The result of the analysis carried out showed that Iron (Fe) has the highest total mean concentration in both the soil and plants from the three dumpsites with the mean values of 763.86 mg/kg and 148.86 mg/kg respectively. The total mean concentrations for lead (Pb) in soil and plant samples were 0.35 mg/kg and 0.23 mg/kg respectively. The total mean concentration of Manganese (Mn) in the soil and plant samples was 11.70 mg/kg and 2.37 mg/kg respectively. Zinc, in the order of concentration had total mean concentrations of 4.01 mg/kg and 2.24 mg/kg for soil and plant samples respectively. Cadmium (Cd) had the least total mean concentration from the soil samples with the value of 0.0078 mg/kg, although it was absent in the soil samples of Sites A and B, and also not detected in all of the plant samples. Assessments of some physicochemical properties of these metals were also carried out. The results show that the soils around the dumpsites were slightly alkaline with mean pH of 7.4. The soil moisture, Organic carbon and organic matter contents had mean values of 1.92%, 1.19% and 2.06%, while the plants moisture and ash contents were 14.78% and 63.29% respectively.

Keywords: Heavy metals, Metalloids, dumpsites, physicochemical parameters, Environmental Contamination.

Title: DETERMINATION OF HEAVY METAL CONCENTRATIONS IN SOIL AND PLANTS OF THREE WASTE DUMPSITES IN ILORIN KWARA STATE, NIGERIA

Author: Anyiam Ngozi Donald

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: The concepts of matter and antimatter require a new interpretation, after having shown that the relativistic mass of quantum particles is of electromagnetic nature, virtual and indeterminate, which can not be accepted by Classical Mechanics, but may be assumed by Quantum  Fields Theory thanks to Uncertainty Principle.

By applying this principle in interactive processes of the radiation (photons) with electrons, it may be shown that those particles with negative mass  (positrons)  are moving  at  higher velocities  than  that of light in vacuum, which coincides with the analysis carried out by means of  a reformulation of the relativistic equations, avoiding the space-like or negative interval (non-causal);  so  the particles called Tachyons may be identified with Antiparticles  (positrons), based on  the  peculiar behavior  of   electrons and photons,  in relation to   energy and momentum.

Keywords: superluminal particles o taquiones, positrons and electrons, photons.

Title: ANTIMATTER AND TACHYONS

Author: Francisco Martínez Flores

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: In this paper, a deterministic mathematical model is formulated using epidemiological model approach composed by mutually exclusive spreader compartments of ISR (ignorant – spreaders – stiflers), which provides excellent explanations of the “psychological” effect with rumor spreading in emergency event. We showed that as time evolves rumor will seize spreading when R_o<1 or persists if R_o>1 by studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium. Finally, numerical simulation was performed in order to validate the analytical result and recommendations are explored in the case study of rumors propagated on unknown disease attacking students of College of Education Waka Biu upon arriving from Biology field trip that took place at Yankari game reserve in august 2019.

Keywords: Rumor spreading, Psychological effect, Reproduction number, Rumour free equilibrium, Rumor endemic equilibriums.

Title: Mathematical Model of the dynamics of Rumor Spreading with Psychological Effect in Emergency Event

Author: Mohammed Fori, Samuel Musa, Ibrahim Yakubu Mshalia, Salihu Saleh

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: The study entitled “Analysis of Errors in Solving Mathematical Problems Involving Fractions among Grade 7 Students of Zamboanga National High School West used a descriptive qualitative research method. It identified the causes of errors prevalent among Grade 7 students of Zamboanga City High School-West in solving mathematical problems involving fractions. It also identified students’ error types and patterns, as well as corrective instructions/strategies to address the errors. Of the total population of 1,997, only 333 Grade 7 students of Zamboanga National High School-West were chosen through random sampling as participants for the diagnostic examination.  Stage I of the study was a diagnostic test that determined the error types and patterns committed by the participants in solving mathematical problems involving fractions. In stage 2, 8 of the 333 participants in the diagnostic examination, were purposively chosen for the interview intended to probe into the causes of errors.  Newman’s Error Analysis (NEA) Techniques was used to determine the participants’ prevalent error types/patterns. The findings revealed that the participants’ most prevalent error was transformation error which totalled 1,417 or 50.6 percent of the total errors.  This was followed by procedural or basic facts error which totalled 941 or 33.6 percent.  It was also found out that the underlying causes of errors committed are the following: conceptions and preconceptions to the present Mathematics classroom that was not corrected previously, teacher’s pedagogical skills or teacher competence, lapses in concentration or hasty reasoning, lack of long term learning, poor exposure on such kind of word problems.  Based on the findings, this study proposed corrective instructions/strategies which may be adopted by mathematics teachers in addressing learning problems related to the prevalent errors identified.

Keywords: corrective measures, causes of error, error patterns, error types, fractions.

Title: ANALYSIS OF ERRORS IN SOLVING MATHEMATICAL PROBLEMS INVOLVING FRACTIONS

Author: LILIA B. BAYOS

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: This theory is supported on 8 propositions- acceptances and it is built of them.

It is developing the results of the nuclear magnetic resonance, it is correcting it and goes on the new constants of the micro-cosmos. It doubts the experiments results of Thompson’s cathode rays tube and of Millikan or the tunnel rays tube and it is on magnetic resonance reason e/m.

The theory is developing the Hydrogen theory and the Balmer’s formula, and it is correcting the Bohr’s theory.  New theory is coming from them and for the structure of the photons. This structure, explains the Maxwell’s equations and it is explained of them.

New law in the reverse cubic power is coming from the logic application, for the attracted masses or charges they are rotated round the center of their mass and it is moderating the law of Newton.     

Keywords:  Atomic Nuclear, Molar Theory, Hydrogen theory.

Title: THE NEW ATOMIC NUCLEAR AND MOLAR THEORY

Author: ALEKOS CHARALAMPOPOULOS

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: The Paper Examines The Differential Transform Method (DTM) And Applies It To Solve Heat-Like Equations Using Variable Coefficients. DTM Reduces Complex Partial Differential Equations To Simple Closed Form Equations. The Method Is Used In A Number Of Engineering Applications. In This Paper, The Modalities And Process Are Examined And Then Applied To Solve Two Numerical Problems.

Keywords: Solve Heat-Like, Differential Transform Method (DTM).

Title: Solve Heat-Like with Variable Coefficients by the Differential Transform Method

Author: Jassim Saleh Albasri

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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Abstract: In this article, we study two types of two dimensional line integral problems. The closed forms of the two types of line integrals can be determined by using a complex integral formula. In addition, we provide two examples to do calculation practically. The research method used in this paper is to get the results by hand first, and then calculate the approximate values of the answers by Maple.

Keywords: Line integrals, Complex integral formula, Closed forms, Maple.

Title: A New Method for Evaluating Two Dimensional Line Integrals Using Maple

Author: Chii-Huei Yu

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

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