International Journal of Mathematics and Mathematical Sciences

Journal Information
ISSN / EISSN : 0161-1712 / 1687-0425
Published by: Hindawi Limited (10.1155)
Total articles ≅ 5,193
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Latest articles in this journal

Anthony Joe Turkson, Francis Ayiah-Mensah, Vivian Nimoh
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-16; https://doi.org/10.1155/2021/9307475

Abstract:
The study recognized the worth of understanding the how’s of handling censoring and censored data in survival analysis and the potential biases it might cause if researchers fail to identify and handle the concepts with utmost care. We systematically reviewed the concepts of censoring and how researchers have handled censored data and brought all the ideas under one umbrella. The review was done on articles written in the English language spanning from the late fifties to the present time. We googled through NCBI, PubMed, Google scholar and other websites and identified theories and publications on the research topic. Revelation was that censoring has the potential of biasing results and reducing the statistical power of analyses if not handled with the appropriate techniques it requires. We also found that, besides the four main approaches (complete-data analysis method; imputation approach; dichotomizing the data; the likelihood-based approach) to handling censored data, there were several other innovative approaches to handling censored data. These methods include censored network estimation; conditional mean imputation method; inverse probability of censoring weighting; maximum likelihood estimation; Buckley-Janes least squares algorithm; simple multiple imputation strategy; filter algorithm; Bayesian framework; β -substitution method; search-and-score-hill-climbing algorithm and constraint-based conditional independence algorithm; frequentist; Markov chain Monte Carlo for imputed data; quantile regression; random effects hierarchical Cox proportional hazards; Lin’s Concordance Correlation Coefficient; classical maximum likelihood estimate. We infer that the presence of incomplete information about subjects does not necessarily mean that such information must be discarded, rather they must be incorporated into the study for they might carry certain relevant information that holds the key to the understanding of the research. We anticipate that through this review, researchers will develop a deeper understanding of this concept in survival analysis and select the appropriate statistical procedures for such studies devoid of biases.
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-8; https://doi.org/10.1155/2021/4492480

Abstract:
This article deals with the study of mathematical models and the assessment of the stability of the motion of ships, investigating properties of the system such as kinetics and stability. This is essential for the selection of suitable control methods according to the requirements set out for the problem. Some control methods require the author to specify control parameters before the operation of the system can be started. Therefore, the survey of the article is useful for the above problem. Control methods through simulation results (PID controller, lag compensator, and lead compensator) give me results that reflect properties of the system (the stability of the operation cycle of the ship model). In addition, control methods for this model, which serve for research and education, are also presented below. Simulation is done by Matlab.
Michael R. Schwob, Peter Shiue, Rama Venkat
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-10; https://doi.org/10.1155/2021/5754439

Abstract:
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.
Ali El Mfadel, , M’Hamed Elomari
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-6; https://doi.org/10.1155/2021/7488524

Abstract:
In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.
, Peter J.-S. Shiue, Rama Venkat
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-11; https://doi.org/10.1155/2021/6396792

Abstract:
This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three-variable Frobenius-related problems. The first method is used to reduce the equation of order three from a three-variable Frobenius-related problem to be a system of equations with two fixed variables. The second method reduces the equation of order three into three equations of order two, for which an algorithm is designed with an interesting open problem on solutions left as a conjecture.
Abba Mallam Hassane, Barro Diakarya, Yaméogo WendKouni, Saley Bisso
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-9; https://doi.org/10.1155/2021/7648093

Abstract:
In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.
Robert Gardner, Narendra Kumar Govil, Prasanna Kumar
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-4; https://doi.org/10.1155/2021/2263550

Abstract:
For a polynomial p z of degree n , it follows from the maximum modulus theorem that max z = R ≥ 1 p z ≤ R n max z = 1 p z . It was shown by Ankeny and Rivlin that if p z ≠ 0 for z < 1 , then max z = R ≥ 1 p z ≤ R n + 1 / 2 max z = 1 p z . In 1998, Govil and Mohapatra extended the above two inequalities to rational functions, and in this paper, we study the refinements of these results of Govil and Mohapatra.
K. L. Duggal
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-9; https://doi.org/10.1155/2021/6141587

Abstract:
In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M , g , f , λ , ξ by a real tensor field f of type 1,1 , a real function λ such that f 3 = λ 2 f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Blair proved that the vector field ξ of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general, ξ of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. Contrary to the odd-dimensional contact manifolds, we construct several examples of even- and odd-dimensional semi-Riemannian and lightlike CPF-manifolds and propose two problems for further consideration.
, Tri Atmojo Kusmayadi, Baki Swita, Minsi Romala, Friska Damanik
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-8; https://doi.org/10.1155/2021/8483926

Abstract:
A graph G is called cycle books B 4 , m , 2 if G consists of m cycles C 4 with a common path P 2 . Figueroa-Centeno, Ichishima, and Muntaner-Batle conjecture that the graph B 4 , m , 2 is super edge-magic total if and only if m is even or m ≡ 5 mod 8 . In this article, we prove this conjecture for m ≥ 36 and m = 0 mod (2).
Kins Yenoke, , Mohammed M. Ali Al-Shamiri, R. C. Thivyarathi
International Journal of Mathematics and Mathematical Sciences, Volume 2021, pp 1-8; https://doi.org/10.1155/2021/5101021

Abstract:
A mapping ℸ : V G ⟶ N ∪ 0 for a connected graph G = V , E is called a radial radio labelling if it satisfies the inequality ℸ x − ℸ y + d x , y ≥ rad G + 1 ∀ x , y ∈ V G , where rad G is the radius of the graph G . The radial radio number of ℸ denoted by r r ℸ is the maximum number mapped under ℸ . The radial radio number of G denoted by r r G is equal to min { r r ℸ / ℸ is a radial radio labelling of G }.
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