Volume-1 Issue-1, April 2021 – Indian Journal of Advanced Mathematics (IJAM)

B1106101221

IJAM Journal — Wed, 11 Aug 2021 07:30:12 +0000

The Indian Journal of Advanced Mathematics (IJAM) has ISSN 2582-8932 (online), an open-access, peer-reviewed, periodical half-yearly international journal, which is published by Lattice Science Publication (LSP) in April and October. The journal aims to publish high-quality peer–reviewed original articles in the area of Mathematics that covers Applied Mathematics, Arithmetic, Algebra, Calculus and Analysis, Geometry and Topology, Trigonometry, Combinatorics, Logic, Number Theory, Numerical Analysis, Dynamical Systems, Differential Equations, Mathematical Physics, Information Theory and Signal Processing, Probability and Statistics, Game Theory, Operations Research, Discrete Mathematics, Business Mathematics and Financial Mathematics. #Applied Mathematics #Arithmetic #Algebra #Calculus and Analysis #Geometry and Topology #Trigonometry #Combinatorics #Logic #Number Theory #Numerical Analysis #Dynamical Systems #Differential Equations #Mathematical Physics #Information Theory and Signal Processing #Probability and Statistics #Game Theory #Operations Research #Discrete Mathematics #Business Mathematics and Financial Mathematics #PhD ademic #Scopus #SCI #LatticeScience #Springer, #ScienceDirect #IEEE #Mendeley #Research #Scholarship #UGC #SSRN #LatticeScience #ESCI #Science #Journal #Conference #SSRN #PubLons

Modified Moments and Maximum Likelihood Estimators for Parameters of Erlang Truncated Exponential Distribution
Kannadasan Karuppaiah¹, Vinoth Raman²

¹Kannadasan Karuppaiah, Assistant Professor, Department of Community Medicine, Melmaruvathur Adhiparasakthi Institute of Medical Sciences and Research, Melmaruvathur – 603319, Tamilnadu, India.

²Vinoth Raman, Assistant Professor, Department of Quality Measurement and Evaluation, Deanship of Quality and Academic Accreditation, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam – 31441. Saudi Arabia.

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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: This study derives the parameter estimation in truncated form of a continuous distribution which is comparable to Erlang truncated exponential distribution. The shape and scale parameter will predict the whole distributions properties. Approximation will be useful in making the mathematical calculation an easy understand for non-mathematician or statistician. An explicit mathematical derivation is seen for some properties of, Method of Moments, Skewness, Kurtosis, Mean and Variance, Maximum Likelihood Function and Reliability Analysis. We compared ratio and regression estimators empirically based on bias and coefficient of variation.

Keywords: Erlang-Truncated Exponential Distribution, Maximum Likelihood Function, Moments, Moment Generating Function, Reliability Analysis.
Scope of the Article: Probability and Statistics

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B1107101221

IJAM Journal — Wed, 11 Aug 2021 07:15:21 +0000

Infinite Teaching (R) In Collection and (R*) By Allegory and Conformity
Ahmad Hedayatpanah Shaldehi¹, Marziyeh hedayatpanah shaldehi², Kolachahi Sabet Mohammad Taghi³, Mohammad Saeed hedayatpanah shaldehi⁴

¹Ahmad hedayatpanah shaldehi, Department of mathematics and Computer, Faculty of Moin Rasht Branch, Technical and Vocational University (TVU), Guilin, Iran.

²Marziyeh hedayatpanah shaldehi, Department of mathematical and Computer, Faculty of Moien Rasht Branch, Technical and Vocational

³Kolachahi Sabet Mohammad Taghi, Electronic Engineering

⁴Mohammad Saeed hedayatpanah shaldehi, Department of mathematics and Computer, Faculty of Shaheed khodadadi Anzali Branch, Technical and Vocational University (TVU), Guilin

Abstract: In given work a scientific base compatibility of polymers, produced by industry have been studied by revealing of thermodynamically regularities of polymer mixtures. The most significant thermodynamic regularities of the mixtures of polyolefin , produced by industry and heterochained polymers have been revealed and on this base the scientific bases of their compatibility have been developed for creation of multicomponent compositional materials with given complex of operating properties. Key words: polymer-polymer mixtures, chlorinated polyethylene (CPE), polymethylmetaacrylate (PMMA), polyethylene of low density (PELD), chlorcarboxylated polyethylene of low density (CCPE) chlorinated PELD (CPE), polyvinyl chloride (PVC), criteria of compatibility, chlorination, upper and lower critical temperature, specific holding of volume, Qibbs mixing energy, parameter of solubility, distribution of macromolecules, chlorine-chlorocontaining polymers, polar groups, thermodynamically compatibility, sorbate, gas-carrier.

Keywords: (CPE), polymethylmetaacrylate (PMMA), polyethylene of low density (PELD), chlorcarboxylated polyethylene of low density (CCPE) chlorinated PELD (CPE), polyvinyl chloride (PVC).
Scope of the Article: Calculus and Analysis

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B1104101121

IJAM Journal — Wed, 11 Aug 2021 07:03:24 +0000

Weighted Average Based Differential Quadrature Method for One-Dimensional Homogeneous First Order Nonlinear Parabolic Partial Differential Equation
Kedir Aliyi Koroche

Kedir Aliyi Koroche, Department of Mathematics, College of Natural and Computational Sciences, Ambo University, Ambo, Ethiopia.

Abstract: In this paper, the weighted average-based differential quadrature method is presented for solving one-dimensional homogeneous first-order non-linear parabolic partial differential equation. First, the given solution domain is discretized by using uniform discretization grid point. Next, by using Taylor series expansion we obtain central finite difference discretization of the partial differential equation involving with temporal variable associated with weighted average of partial derivative concerning spatial variable. From this, we obtain the system of nonlinear ordinary differential equations and it is linearized by using the quasilinearization method. Then by using the polynomial-based differential quadrature method for approximating derivative involving with spatial variable at specified grid point, we obtain the system of linear equation. Then they obtained linear system equation is solved by using the LU matrix decomposition method. To validate the applicability of the proposed method, two model examples are considered and solved at each specific grid point on its solution domain. The stability and convergent analysis of the present method is worked by supported the theoretical and mathematical statements and the accuracy of the solution is obtained. The accuracy of the present method has been shown in the sense of root mean square error norm and maximum absolute error norm and the local behavior of the solution is captured exactly. Numerical versus exact solutions and behavior of maximum absolute error between them have been presented in terms of graphs and the corresponding root mean square error norm and maximum absolute error norm presented in tables. The present method approximates the exact solution very well and it is quite efficient and practically well suited for solving the non-linear parabolic equation. The numerical result presented in tables and graphs indicates that the approximate solution is in good agreement with the exact solution.

Keywords: Non-linear parabolic equation, Burger equation, Differential quadrature method, weighted average, Stability and Convergent Analysis, Root mean square and Maximum absolute error.
Scope of the Article: Numerical Analysis

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A1109101221

IJAM Journal — Wed, 11 Aug 2021 06:51:23 +0000

Energy Absorption Capacity of Rigid Polyurethane Foam under Impact Load
Kedir Mohamedraja Seid

Kedir Mohamedraja Seid, Material Engineer in Addis Ababa city roads authority. MSc on structural engineering from university of Addis Ababa science and Technology College of civil engineering and architecture.

Manuscript received on 04 April 2021 | Revised Manuscript received on 08 April 2021 | Manuscript Accepted on 15 April 2021 | Manuscript published on 30 April 2021 | PP: 8-14 | Volume-1 Issue-1, April 2021 | Retrieval Number:100.1/ijam.A1109101121
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: Vehicles has multiple safety mechanisms such as air bags, sit belts and ABS brakes to protect lives of occupants. Also, road safety and management offers various solutions like speed breakers and road side barriers to supplement and minimize damages of errand vehicle crashes. This thesis work presents mainly finite element analysis of a rigid polyurethane foam under impact loading. Energy absorption capacity of a rigid polyurethane foam was quantified both under impact load of a drop hammer; and a passenger car with mass of 1200 kg and 2000 kg and approach speed 30km/hr. and 50km/hr. scenario. In the absence of field crash tests principle of energy conservation were used to validate developed finite element models. FEA results showed road side barrier designed with an equivalent design static force of 377 KN and a rigid polyurethane foam thickness of 60.5 cm offers a forgiving road side barrier scenario by absorbing energy and re-directing impacting passenger car into inward lanes. Also, FEA results revealed thickness of a rigid polyurethane foam affects energy-absorbing capacity of a rigid polyurethane foam. For 50 km/hr. impacting speed, as thickness of a rigid polyurethane foam decreased by 33%, the material energy absorption capabilities lost by 100% whereas 33 % thickness increment resulted in 33 % additional energy absorption capacity.

Keywords: Rigid polyurethane foam, LS-DYNA, Energy absorption, Vehicle impact.

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A1108101221

IJAM Journal — Wed, 11 Aug 2021 06:37:49 +0000

Solution of Integral Equations Involving Bessel Maitland Functions using Fractional Integral Operators
Prachi Jain¹, Vandana Jat²

¹Prachi Jain, Department of Mathematics, Motilal Vigyan Mahavidyalaya, Bhopal – 462008, Madhya Pradesh, India.

²Vandana Jat, Govt. College Patharia (Damoh) – 470666, Madhya Pradesh, India.

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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: In this paper, we have solved integral equation involving Bessel Maitland function. In case of single kernel the equations have been transforming by using Erdélyi-Kober operators to one having Fox’s H-function while the equations having summation of two or more Bessel Maitland functions have been transformed into a summation of two or more Hfunctions as kernel. In first case the solutions are expressed in terms of H-function while in second, the solutions are in terms of Saxena’s I-function. These results may be useful in finding solutions of problems in mathematical physics and engineering which are expressed as integral equations. Theparticular cases are also obtained.2010 Mathematics Subject Classification:33C70, 31B10, 33C60, 26A33.

Keywords: Bessel Maitland function, Erdélyi Koberfractional integral operators, Fox’s H- function, Saxena’s I-function.

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