Journal of Mahani Mathematical Research
Volume:11 Issue: 1, Winter and Spring 2022

‎‎Lifetime performance index ‎is widely used as process capability index to evaluate the performance and potential of a process‎. ‎In manufacturing industries‎, ‎the lifetime of a product is considered to be conforming if it exceeds a given lower threshold value‎, ‎so‎ nonconforming products are those that fail to exceed this value.‏ Nonconformities are ‎so ‏‎important‎ that affect the safe or effective use of the products. ‏‎This article deals with ‎the processes‎ that ‎the ‎products' ‎lifetime is related to a two-component system, ‎distributed ‎as Farlie-Gumbel-Morgenstern (FGM) copula-based bivariate ‎exponential‎ ‎and ‎presen‏‎ts‎‎ the ‎probability ‎of ‎non-conforming ‎products‎. Also, bootstrap upper confidence bounds are constructed and their performance are investigated in simulation study. In addition, Monte Carlo scheme is applied to do hypothesis testing on it. Finally, two example sets are presented to demonstrate the application of the proposed index.‎

In this paper a new mathematical model for COVID-19, including Improved people who are susceptible to get infected again, is given. And it is used to investigate the transmission dynamics of the corona virus disease (COVID-19). Our developed model consists of five compartments, namely the susceptible class, S(t)S(t), the exposed class, E(t)E(t), the infected class, I(t)I(t), the quarantine class, Q(t)Q(t) and the recover class, R(t)R(t). The basic reproduction number is computed and the stability conditions of the model at the disease free equilibrium point are obtained. Finally, We present numerical simulations based on the available real data for Kerman province in Iran.

The main object of this paper is to define a new class of univalent functions and two subclasses of this class along with the Pascal distribution associated with convolution and subordination structures. We obtained a number of useful properties such as, coefficient bound, convolution preserving and some other geometric properties

‎Process capability indices are used widely throughout the world to give a quick indication of a process capability in a format that is easy to use and understand‎. ‎A process capability index CpCp that constructed for measuring the quality is an effective tool for assessing process capability‎, ‎since this index can reflect whether a centering process is capable of reproducing items meeting the specifications limits‎. ‎The minimax approach is proposed in this paper for testing capability on the basis of precision index Cp when the producer goal is avoiding the largest possible risk‎. ‎Motivations and benefits of proposing minimax approach are discussed for capability test‎. ‎Also‎, ‎the proposed method clarified by an industrial application.

We consider the locally convex product cone topologies and prove that the product topologyof weakly cone-complete locally convex cones is weakly cone-complete. In particular, we deduce that a product cone topology is barreled whenever its components are weaklycone-complete and carry the countable neighborhood bases.

Let  MnMn be  the set of all nn-by-nn real  matrices, and let  RnRn be  the set of all nn-by-11 real (column) vectors. An nn-by-nn matrix R=[rij]R=[rij] with nonnegative entries is called row stochastic, if ∑nk=1rik∑k=1nrik is equal to 1 for all ii, (1≤i≤n)(1≤i≤n). In fact, Re=eRe=e, where e=(1,…,1)t∈Rne=(1,…,1)t∈Rn.  A matrix R∈MnR∈Mn  is called integral row stochastic, if each row has exactly one nonzero entry, +1+1, and other entries are zero.  In the present paper,  we provide an algorithm for constructing integral row stochastic matrices, and also we show the relationship between this algorithm and majorization theory.

Recently, it has been shown that the density based empirical likelihood concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics. In this article, we propose a density based empirical likelihood goodness of fit test for the Cauchy distribution. The properties of the test statistic are stated and the critical points are obtained. Power comparisons of the proposed test with some known competing tests are carried out via simulations. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can confidently apply in practice. Finally, a financial data set is presented and analyzed.

Abstract. In this paper, we define and investigate a new class of spirallike harmonic functions defined by a Salagean differential operator and we obtain a coefficient inequality for the functions in this class. Following, we investigated convolution and obtain the order of convolution consistence for certain spirallike harmonic univalent functions with negative coefficients.

The uncertain functional differential equation (UFDE) is a type of functional differential equations driven by a canonical uncertain process. Uncertain functional differential equation with infinite delay (IUFDE) have been widely applied in sciences and technology. In this paper, we prove an existence and uniqueness theorem for IUFDE intheinterval [t0,T][t0,T], underuniform Lipschitz condition and weak condition. Also, the novel existence and uniqueness theorem under the linear growth condition and the local Lipschitz condition is proven. In the following, a more general type of UFDE considers, which the future state is determined by entire of the past states rather than some of them. Finally, the existence and uniqueness theorem is considered on theinterval [t0,∞][t0,∞].

In this study, a neutrosophic N−N−subalgebra, a (implicative) neutrosophic N−N− filter, level sets of these neutrosophic N−N−structures and their properties are introduced on a Sheffer stroke BE-algebras (briefly, SBE-algebras). It is proved that the level set of neutrosophic N−N− subalgebras ((implicative) neutrosophic N−N−filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then we present relationships between upper sets and neutrosophic N−N−filters of this algebra. Also, it is given that every neutrosophic N−N−filter of a SBE-algebra is its neutrosophic N−N−subalgebra but the inverse is generally not true. We study on neutrosophic N−N−filters of SBE-algebras by means of SBE-homomorphisms, and present relationships between mentioned structures on a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of N−N−functions and some properties are examined.

ELEL-hypergroups  were defined by Chvalina 1995. Till now, no exact statistics of ELEL-hypergroups have been done. Moreover, there is no classification of ELEL-hypergroups and EL2EL2-hypergroups even over small sets. In this paper we classify all ELEL-(semi)hypergroups over sets with two elements obtained from quasi ordered semigroups. Also, we characterize all quasi ordered HvHv-group and   then we enumerate the number of EL2EL2-HvHv-hypergroups and EL2EL2-hypergroups of order 22.

Let Mm,nMm,n be the set of all mm-by-nn real matrices‎. ‎A matrix RR in Mm,nMm,n with nonnegative entries is called strictly sub row stochastic if the sum of entries on every row of RR is less than 1‎. ‎For A,B∈Mm,nA,B∈Mm,n‎, ‎we say that AA is strictly sub row Hadamard majorized by BB (denoted by A≺SHB)A≺SHB) if there exists an mm-by-nn strictly sub row stochastic matrix RR such that A=R∘BA=R∘B where X∘YX∘Y is the Hadamard product (entrywise product) of matrices X,Y∈Mm,nX,Y∈Mm,n‎. ‎In this paper‎, ‎we introduce the concept of strictly sub row Hadamard majorization as a relation on Mm,nMm,n‎. ‎Also‎, ‎we find the structure of all linear operators T:Mm,n→Mm,nT:Mm,n→Mm,n which are preservers (resp‎. ‎strong preservers) of strictly sub row Hadamard majorization‎.