iosr-Jm   Volume-19 ~ Issue-5 ~ Sep. – Oct. 2023

Abstract : In this article the problem of solving the nonlinear heat equation is raised, this is one of many of which a solution can be found by making a change of variable, or by making a Taylor development around a point to work on, in our In the case it is a transport phenomenon whose equation is non-linear, the reason for being non-linear corresponds to the thermal conductivity of the material, which is a function of the temperature, which is what is generally found in all real cases, since few materials are one hundred percent pure. For this type of case in particular, a method is used which consists of modifying the thermal conductivity function using the Gustav Robert Kirchhoff transform, which....

Key Word: Heat Equation, Kirchhoff, Poisson Equation, Nonlinear Heat Equation, Temperature, Thermal Conductivity

[1]. J. P. Holman, Transferencia De Calor, (1999), Mcgraw-Hill Book Company. Inc., Pp129-141
[2]. J. A. Ortega H., M. A. Gutiérrez V. (2000), Formulaciones Variacionales En La Transferencia De Calor, Vol. 14 Serie En Ciencia E Ingeniería (Sepi-Esime-Zac), Pp 20-40,337-338,
[3]. Shoichiro Nakamura, (1992), Métodos Numéricos Aplicados Con Software, Prentice-Hall, Pp 471-485,
[4]. M. Necati. Ozisik, (1980), Heat Conduction (Wiley, New York,).
[5]. M. Necati. Ozisik. (1989)., Boundary Value Problems Of Heat Conduction, Dover Publication, Inc, New York

Abstract : The present paper consists of Theory and classification of.......

Key Word: Vector space, field, algebra, Lie algebra, simplicity, semisimplicity, representation, weight, module

[1]. James Humphreys, Numerical Mathematics (Introduction To Lie Algebras And Representation Theory), Springer, 1980
[2]. Serre J-P, Complex Semisimple Lie Algebras, Springer (2006).
[3]. N. J. Vilenkin, Special Functions And The Theory Of Group Representations, Providence RI: American Mathematical Society, 1968.
[4]. Jacques Faraut, Analyse Sur Les Groupes De Lie : Une Introduction, Calvage Et Mounet, 2006.
[5]. Fulton W., Harris J, Representation Theory: A First Course, Springer (2001)

Abstract : In this paper, we will discuss modeling of severity on motor vehicle insurance claims for third party liability guarantees with comprehensive coverage at PT. The 2019 X uses the Generalized Inverse-Lindley distribution. The Generalized Inverse-Lindley distribution is a non-composite distribution with α and λ parameter. The parameters in the Generalized Inverse-Lindley distribution are estimated through the maximum likelihood estimator method using the Newton-Raphson iteration numerical method. Distribution fit testing is carried out using the Kolmogorov-Smirnov test. The data used is secondary data from the recording results of the insurance company PT. X....

Key Word: Motor Vehicle Insurance, Third Party Liability, Generalized Inverse-Lindley Distribution, Newton-Raphson, Kolmogorov-Smirnov

[1] N. Indra, "Pelaksanaan Asuransi Kebakaran Pada Pt. Asuransitakaful Umum Cabang Padang," 2015.
[2] A. N. Hidayah, "Pengaruh Klaim, Hasil Investasi, Risk Based Capital (Rbc) Terhadap Laba Perusahaan Asuransi Syariah Di Indonesia Tahun 2016," 2018.
[3] Y.-K. Tse, "Nonlife Actuarial Models Theory, Methods And Evaluation," 2009.
[4] R. S. Nastiti And A. K. Mutaqin, "Penerapan Model Komposit Weibull-Pareto Pada Data Klaim Asuransi Harta Benda Skripsi Oleh Raisha Shahelia Nastiti Npm: 10060115027 Program Studi Statistika Fakultas Matematika Dan Ilmu Pengetahuan Alam Universitas Islam Bandung 2021," 2021.
[5] A. Asgharzadeh, S. Nadarajah, And F. Sharafi, "Generalized Inverse Lindley Distribution With Application To Danish Fire Insurance Data," Commun. Stat. - Theory Methods, Vol. 46, No. 10, Pp. 5001–5021, May 2017,
Doi: 10.1080/03610926.2015.1096394.

Abstract : Local rough set (LRS) is one of the effective tool to enhance the limitations of classical rough set theory. In recent years many scholars interested to focused on LRS. At present there is no specific literature reviews of this LRS and applications. This review paper first explores a summary of current LRS from three basic aspects, such as basic models, local fuzzy rough sets and other applications. This review, lists about the distinct promising issues of LRS which are helpful to the future works.

Key Word: Rough Set, LRS, Local Fuzzy Rough Set, Attribute reduction

[1]. A Fatih Ozcan, M Mustafa Beydaˇgı, And Ilhan I¸Cen. Comparison Of Rough Sets And Local Rough Sets In Data Analysis. New Trends In Mathematical Sciences, 10(2):1–13, 2022.
[2]. Didier Dubois And Henri Prade. Rough Fuzzy Sets And Fuzzy Rough Sets. International Journal Of General System, 17(2-3):191–209, 1990.
[3]. Guoping Lin, Linlin Xie, Jinjin Li, Jinkun Chen, And Yi Kou. Local Double Quantitative Fuzzy Rough Sets Over Two Universes. Applied Soft Computing, Page 110556, 2023.
[4]. Guoqiang Wang, Tianrui Li, Pengfei Zhang, Qianqian Huang, And Hongmei Chen. Double-Local Rough Sets For Efficient Data Mining. Information Sciences, 571:475–498, 2021
[5]. Jia Zhang, Xiaoyan Zhang, Weihua Xu, And Yanxue Wu. Local Multigranulation Decision-Theoretic Rough Set In Ordered Information Systems. Soft Computing, 23:13247–13261, 2019.

Abstract : In this paper, the goodness-of-fit tests for the Suja distribution with one parameter was studied based on a complete sample. The maximum likelihood method is utilized to obtain the estimator of the parameter. Also, simulation was carried out using different sample sizes and different values of the parameter. In addition, the goodness of fit test statistics was calculated for proposed models to find out the best of it for data COVID-19 in Saudi Arabia.

Key Word: Suja distribution, maximum likelihood, goodness-of-fit test, complete sampling

[1]. Abu-Zinadah, H. H. (2014). Goodness-Of-Fit Tests For The Exponentiated Gompertz Distribution. International Journal Of Innovation In Science And Mathematics, 2(4), 2347–9051.
[2]. Abu-Zinadah, H., & Binkhamis, A. (2020). Goodness-Of-Fit Tests For The Beta Gompertz Distribution. Thermal Science, 24(Suppl. 1), 69-81.
[3]. Al-Omari, A. I., Alhyasat, K., Ibrahim, K., & Abu Bakar, M. A. (2019). Power Length-Biased Suja Distribution: Properties And Application. Electronic Journal Of Applied Statistical Analysis, 12(2), 429-452.
[4]. Alshenawy, R. (2020). A New One Parameter Distribution: Properties And Estimation With Applications To Complete And Type II Censored Data. Journal Of Taibah University For Science, 14(1), 11-18.
[5]. Shanker, R. (2017). Suja Distribution And Its Application. International Journal Of Probability And Statistics, 6(2), 11-19.
[6]. Shankar, P. M. (2019). Pedagogy Of Chi‐Square Goodness Of Fit Test For Continuous Distributions. Computer Applications In Engineering Education, 27(3), 679-689.

Abstract : In this paper, some characterizations of Abel rings are introduced such as a ring R is an Abel ring if and......

[1]. Y. Lee, Armendariz rings and semicommutative rings. Comm. Algebra, 2002, 30(2): 751-761.
[2]. Z. K. Liu, W. L. Fan, Principal quasi-Baerness of skew power series rings. J. Math. Resea. Exposi., 2005, 25(2): 197-203.
[3]. J. C. Wei, L. B. Li, Quasi-normal rings. Comm. Algebra, 2010, 38(5): 1855-1868.
[4]. W. X. Chen, On semiabelian π-regular rings. Intern. J. Math. Sci., 2007, 23: 1-10.
[5]. Q. S. Cheng, L. Y. Wang, J. C. Wei, Strongly left min-abel rings. J. Yangzhou Univ., 2010, 13(1): 6-9.

Abstract : A new COVID-19 SIR model introduced by Rahim ud Din and Ibrahem A. Algehyne describes the interaction between susceptible S(t), Infected I(t) and Recovered R(t) populations. This model is represented in nonlinear ordinary differential system of equations. In this paper, numerical simulations are calculated by Matlab and compared with the results by numerical fourth order Runge-Kutta (RK4) and Nonstandard Finite Difference Scheme (NSFD).

Keywords: SIR; Covid; NFDS; RK4

[1]. Algehyne, E. A., & Ud Din, R. (2020). On Global Dynamics Of COVID-19 By Using SQIR Type Model Under Nonlinear Saturated Incidence Rate. Alexandria Engineering Journal, 60(1), 393-399.
[2]. Algehyne E. And R. Ud Din. (2021). Mathematical Analysis Of COVID-19 By Using SIR Model With Convex Incidence Rate. University Of Malakand And Tabuk Saudi Arabia.
[3]. Bogoch, I. I., Watts, A., Thomas-Bachli, A., Huber, C., Kraemer, M. U., Khan, K. (2020). Pneumonia Of Unknown Etiology In Wuhan, China: Potential For International Spread Via Commercial Air Travel. Journal Of Travel Medicine, 27(2).
[4]. DUMAS L., (Modélisation Mathématique De L'épidémie De COVID-19. Laboratoire De Mathématiques De Versailles, Université De Versailles Saint Quentin (UVSQ).
[5]. Goel, N. S., Maitra, S. C., Montroll, E. W. (1971). On The Volterra And Other Nonlinear Models Of Interacting Populations. Reviews Of Modern Physics, 43(2), P 231

Abstract : In mathematics, the search for exact formulas giving all the prime numbers, certain families of prime numbers or the n-th prime number has generally proved to be vain, which has led to contenting oneself with approximate formulas [8]. The purpose of this article is to give a new proof of the Riemann hypothesis [4] by y introducing a new extension of the of the Riemann zeta function....

Keywords: .Prime Number, number theory, distribution of prime numbers, the law of prime numbers, the Gamma function, the Mertens function, quantum mechanics, black Holes, holomorphic function, Hilbert-Polya's conjecture, the Riemann hypothesis

[1] N. M. KATZ and P. SARNAK , Random Matrices, Frobenius Eigenvalues, and Monodromy. Colloq.Publ. 45, Amer. Math. Soc., Providence, 1999.
[2] N. M. KATZ and P. SARNAK ,zeroes of zeta functions and symmetry, Bulletin (New Series) of the american mathematical society, Volume 36,
Number 1, January 1999, Pages 1–26.
[3] Roshdi Rashed, Entre arithmétique et algèbre : Recherches sur l'histoire des mathématiques arabes, journal Paris, 1984.

Abstract : In this paper, the concept of fuzzy C-almost P-Space is introduced and studied. The conditions under which fuzzy P -spaces and fuzzy almost P -spaces become fuzzy C-almost P- spaces are obtained. It is established that fuzzy C-almost P-spaces are neither fuzzy hyperconnected spaces nor fuzzy open hereditarily irresolvable spaces. Fuzzy regular Oz -spaces are fuzzy C-almost P-spaces and fuzzy Oz and fuzzy P-spaces, are fuzzy C-almost P-spaces..

Keywords: Fuzzy 𝐺𝛿 -set, fuzzy 𝜎 -nowhere dense set, fuzzy 𝜎 - boundary set, fuzzy hyperconnected space, fuzzy Oz-space, fuzzy P-space, fuzzy almost P-space, fuzzy open hereditarily irresolvable space

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Abstract :The purpose of this paper is to explore an Ordinary Differential Equation (ODE) model of cancer immunotherapy. Initially, we provide an overview of cancer immunotherapy treatment method, as well as key mathematical concepts. Subsequently, we conduct a comprehensive analysis of the model proposed by De Pillis et al., which describes tumor growth in the absence of treatment. Without treatment, (as we restricted our study here in this paper) tumor development (cancer cell growth) occurs rapidly, leading....

Keywords: SIR; immunotherapy, cancer, cancer cells, immune cells, treatment. NSFD; RK4.

[1]. Abbal, M., And Pr Henri Roche, "Immunité Et Cancer," DFGSM3 2012/2013.
[2]. Altrock, P., M., Lin L. Liu, And Franziska Michor, "The Mathematics Of Cancer: Integrating Quantitative Models," Page 730.
[3]. Costes,V., F.P. Chatelet, "La Cellule Cancéreuse Et Le Tissu Cancéreux (Chapitre 8)," Mai 2005, Page 01.
[4]. Goel, N. S., Maitra, S. C., Montroll, E. W. (1971). On The Volterra And Other Nonlinear Models Of Interacting Populations. Reviews Of Modern Physics, 43(2), P 231.
[5]. Hahnfeldt,P., D. Panigrahy, J. Folkman, And L. Hlatky, "Tumor Development Under Angiogenic Signaling: A Dynamical Theory Of Tumor Growth, Treatment Response, And Postvascular Dormancy," Cancer Research, Vol. 59, No. 19, Pp. 4770-4775, 1999.

Abstract :In this paper, we introduce intuitionistic fuzzy generalized semi-pre-compactness (IFGSP-compactness) in intuitionistic fuzzy topological spaces. This structure of compactness is based on intuitionistic fuzzy generalized semi-pre-open set. We investigate some of its characterizations and properties. We identify the relations between fuzzy compactness and IFGSP-compactness in intuitionistic fuzzy topological spaces.

Keywords: Intuitionistic fuzzy generalized semi-pre-open set, Intuitionistic fuzzy generalized semi-pre-compactness

[1]. Atanassov K. T., (1986) Intuitionistic Fuzzy Sets, Fuzzy Sets And Systems, 20, 87-96.
[2]. Atanassov K. T., (2022) New Topological Operator Over Intuitionistic Fuzzy Sets, Journal Of Computational And Cognitive Engineering, 1(3) 94-102.
[3]. Bayramov S., Gunduz C., (2012), Intuitionistic Fuzzy Topology On Function Spaces, Annals Of Fuzzy Mathematics And Informatics, 3 (2), 19-30.
[4]. Christy Jenifer J*, Kokilavani V, (2023) IFG#Α-CS In Intuitionistic Fuzzy Topological Spaces, Ratio Mathematica, 46, 63-69.
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