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CIRWORLD en-US JOURNAL OF ADVANCES IN MATHEMATICS 2347-1921 <p>Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the&nbsp;<a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</a>, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.</p> <p>&nbsp;</p> Annual Reviewer Acknowledgement https://cirworld.com/index.php/jam/article/view/7649 <p>The editorial team of the journal would like to thank the reviewers for their work in referring manuscripts during 2018.</p> Kewen Zhao ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-31 2018-08-31 14 2 Further Acceleration of the Simpson Method for Solving Nonlinear Equations https://cirworld.com/index.php/jam/article/view/7415 <p>There are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four.&nbsp; Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method.&nbsp; We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method.</p> Rajinder Thukral ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-05-25 2018-05-25 14 2 7631 7639 10.24297/jam.v14i2.7415 The Trisection of an Arbitrary Angle https://cirworld.com/index.php/jam/article/view/7402 <p>This paper presents an elegant classical geometric solution to the ancient Greek's problem of angle trisection.&nbsp; Its primary objective is to provide a provable construction for resolving the trisection of an arbitrary angle, based on the restrictions governing the problem.&nbsp; The angle trisection problem is believed to be unsolvable for compass-straightedge construction.&nbsp; As stated by Pierre Laurent Wantzel (1837), the solution of the angle trisection problem corresponds to an implicit solution of the cubic equation x cubed minus 3x minus 1 equals 0, which is algebraically irreducible, and so is the geometric solution of the angle trisection problem.&nbsp; The goal of the presented solution is to show the possibility to solve the trisection of an arbitrary angle using the traditional Greek's tools of geometry (a classical compass and straightedge) by changing&nbsp; the problem from the algebraic impossibility classification to a solvable plane geometrical problem.&nbsp; Fundamentally, this novel work is based on the fact that algebraic irrationality is not a geometrical impossibility.&nbsp; The exposed methods of proof have been reduced to the Euclidean postulates of classical geometry.</p> Arthur Clair Rediske ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-05-30 2018-05-30 14 2 7640 7669 10.24297/jam.v14i2.7402 The Neutrosophic Soft Modules https://cirworld.com/index.php/jam/article/view/7401 <p>Molodtsov initiated the concept of soft sets in [17]. Maji et al. defined some operations on soft sets in [13]. Aktas et al. generalized soft sets by defining the concept of soft groups in [2]. After then, Qiu-Mei Sun et al. gave soft modules in [20]. In this paper, the concept of neutrosophic soft module is introduced and some of its basic properties are studied.</p> Kemale Veliyeva Sadi Bayramov ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-05-30 2018-05-30 14 2 7670 7681 10.24297/jam.v14i2.7401 Role of Conservation Laws in the Development of Nonequilibrium and Emergence of Turbulence https://cirworld.com/index.php/jam/article/view/7383 <p>It turns out that the equations of mathematical physics, which consist equations of the conservation laws for energy, linear momentum, angular momentum, and mass, possess additional, hidden, properties that enables one to describe not only a variation of physical quantities (such as energy, pressure, density) but also processes such as origination of waves, vortices, turbulent pulsations and other ones. It is caused by the conservation laws properties.</p> <p>In present paper the development of nonequilibrium in gasdynamic systems, which are described by the Euler and Navier-Stokes equations, will be investigated.&nbsp;</p> <p>Under studying the consistence of conservation laws equations, from the Euler and Navier-Stokes equations it can be obtained the evolutionary relation for entropy (as a state functional).&nbsp; The evolutionary relation possesses a certain peculiarity, namely, it turns out to be nonidentical. This fact points out to inconsistence of the conservation law equations and noncommutativity of conservation laws.</p> <p>Such a nonidentical relation discloses peculiarities of the solutions to the Navier-Stokes equations due to which the Euler and Navier-Stokes equations can describe the processes the development of nonequilibrium and emergence of vortices and turbulence.</p> <p>It has been shown that such processes can be described only with the help of two nonequivalent coordinate systems or by simultaneous using numerical and analytical methods.</p> Ludmila Ivanovna Petrova ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-05-30 2018-05-30 14 2 7682 7690 10.24297/jam.v14i2.7383 A Solution Algorithm for Interval Transportation Problems via Time-Cost Tradeoff https://cirworld.com/index.php/jam/article/view/7417 <p>In this paper, an algorithm for solving interval time-cost tradeoff transportation problemsis presented. In this problem, all the demands are defined as intervalto determine more realistic duration and cost. Mathematical methods can be used to convert the time-cost tradeoff problems to linear programming, integer programming, dynamic programming, goal programming or multi-objective linear programming problems for determining the optimum duration and cost. Using this approach, the algorithm is developed converting interval time-cost tradeoff transportation problem to the linear programming problem by taking into consideration of decision maker (DM).</p> Inci Albayrak Mustafa Sivri Gizem Temelcan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-06-12 2018-06-12 14 2 7691 7701 10.24297/jam.v14i2.7417 Generalized Rayleigh-quotient Formulas for the Real Parts, Imaginary Parts, and Moduli of the Eigenvalues of Diagonalizable Matrices https://cirworld.com/index.php/jam/article/view/7373 <p>In the present paper, generalized Rayleigh-quotient formulas for the real parts, imaginary parts,&nbsp;and moduli of the eigenvalues of diagonalizable matrices are derived. These formulas are new and&nbsp;correspond to similar formulas for the eigenvalues of self-adjoint matrices obtained recently. Numerical&nbsp;examples underpin the theoretical findings.</p> Ludwig Kohaupt ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-06-13 2018-06-13 14 2 7702 7728 10.24297/jam.v14i2.7373 Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment https://cirworld.com/index.php/jam/article/view/7365 <p>This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions).<br>The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.</p> H. A. Ferganya O. M. Hollahb ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-06-13 2018-06-13 14 2 7729 7743 10.24297/jam.v14i2.7365 Model Higgs Bundles in Exceptional Components of the Sp(4,R)-Character Variety https://cirworld.com/index.php/jam/article/view/7444 <p>We establish a gluing construction for Higgs bundles over a connected sum of Riemann&nbsp; surfaces in terms of&nbsp; solutions to the Sp(4,R)-Hitchin equations using the linearization&nbsp;of a relevant elliptic operator. The construction can be used to provide model Higgs bundles&nbsp;in all the 2g-3 exceptional components of the maximal Sp(4,R)-Higgs bundle moduli space,&nbsp;which correspond to components solely consisted of Zariski dense representations. This also<br>allows a comparison between the invariants for maximal Higgs bundles and the topological&nbsp;invariants for Anosov representations constructed by O. Guichard and A. Wienhard.</p> Georgios Kydonakis ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-06-29 2018-06-29 14 2 7744 7786 10.24297/jam.v14i2.7444 Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces https://cirworld.com/index.php/jam/article/view/7461 <p>In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil&nbsp; et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples.</p> Mohammed Saleh Malfi Fathi Hishem Khedr Mohamad Azab Abd Allah ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-06-30 2018-06-30 14 2 7787 7805 10.24297/jam.v14i2.7461 The Asymptotic Behavior of Solutions of Second order Difference Equations With Damping Term https://cirworld.com/index.php/jam/article/view/7467 <p>&nbsp;</p> <p>The author presents some sufficient conditions for second order difference equation</p> <p>with damping term of the form</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<sub><strong>&nbsp;^</strong></sub>(a<sub>n</sub> <sub><strong>^</strong></sub>(x<sub>n</sub> + cx<sub>n-k</sub>)) + p<sub>n<strong>^</strong></sub>x<sub>n</sub> + q<sub>n</sub>f(x<sub>n+1-l</sub>) = 0</p> <p>An example is given to illustrate the main results.</p> <p><strong>2010 AMS Subject Classification: 39A11</strong></p> <p><strong>Keywords and Phrases:</strong> Second order, difference equation, damping term.</p> Jai Kumar S K. Alagesan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-07-03 2018-07-03 14 2 7806 7811 10.24297/jam.v14i2.7467 Estimates of Solutions to Nonlinear Evolution Equations https://cirworld.com/index.php/jam/article/view/7445 <p>Consider the equation</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;u’(t) = <em>A </em>(t, u (t)),&nbsp; &nbsp;u(0)= U<sub>0&nbsp;</sub>;&nbsp; &nbsp;u' := du/dt&nbsp; &nbsp; &nbsp;(1).&nbsp;&nbsp;</p> <p>Under some assumptions on the nonlinear operator A(t,u) it is proved that problem (1) has a unique global solution and this solution satisfies the following estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ||u (t)|| &lt; µ (t) <sup>-</sup><sup>1</sup>&nbsp; &nbsp; &nbsp;for every&nbsp;<em>t belongs to R<sub>+ </sub></em>= [0,infinity).</p> <p>Here µ(t) &gt; 0,&nbsp; &nbsp;µ <em>belongs to&nbsp;</em>&nbsp;C<sup>1 </sup>(R<sub>+</sub>), is a suitable function and the norm ||u || is&nbsp;the norm in a Banach space X with the property ||u (t) ||’&nbsp; &nbsp;&lt;=&nbsp; ||u’ (t) ||.</p> Alexander G. Ramm ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-07-03 2018-07-03 14 2 7812 7817 10.24297/jam.v14i2.7445 Regional Boundary Gradient Detectability in Distributed Parameter Systems https://cirworld.com/index.php/jam/article/view/7478 <p>The aim of this paper is study and explore the notion of&nbsp; the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space,&nbsp; we give various new results related with different measurements. In addition, we provided a description of the regional boundary exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems.</p> Raheam Al Saphory Mrooj Al Bayati ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-07-04 2018-07-04 14 2 7818 7833 10.24297/jam.v14i2.7478 Regional Boundary Strategic Sensors Characterizations https://cirworld.com/index.php/jam/article/view/6368 <p>This paper, deals with the linear infinite dimensional distributed parameter systems in a Hilbert space where the dynamics of system is governed by strongly continuous semi-groups. More precisely, for parabolic distributed systems the characterizations of regional&nbsp; boundary strategic sensors have been discussed and analyzed in different cases of regional&nbsp; boundary observability in infinite time interval. Furthermore, the results so obtained are applied in two-dimensional systems and sensors studied under which conditions guarantee regional boundary observability in a sub-region of the system domain boundary.&nbsp; Also, the authors show that, the existent of a sensor for the diffusion system is not strategic in the usual sense, but it may be regional&nbsp; boundary strategic of this system.</p> Raheam Al-Saphory Hind K. Kolaib ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-07-09 2018-07-09 14 2 7834 7850 10.24297/jam.v14i2.6368 On Solutions and Heteroclinic Orbits of Some Lotka-Volterra Systems https://cirworld.com/index.php/jam/article/view/7499 <p>In this work, a principle for getting heteroclinic orbit of a dynamical system has been proposed when the solution is known in a compact form. The proposed principle has been tested through its application to a three species Lotka-Volterra system, which may appear as a mathematical model of human pathogen system. The domain in parameter &nbsp;space involve in the model, and the region of initial condition &nbsp;for the existence of heteroclinic orbit have been derived.</p> Supriya Mandal Madan Mohan Panja Santanu Ray ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-07-30 2018-07-30 14 2 7851 7859 10.24297/jam.v14i2.7499 Global existence and uniqueness of the solution to a nonlinear parabolic equation https://cirworld.com/index.php/jam/article/view/7503 <p>Consider the equation</p> <p>&nbsp;u’ (t)&nbsp; - <img src="/public/site/images/editor/delta2.png">&nbsp;u + | u |<sup>p </sup>u = 0, u(0) = u<sub>0</sub>(x), (1),</p> <p>where u’ := du/dt , p = const &gt; 0, x E R<sup>3</sup>, t &gt; 0.</p> <p>&nbsp;Assume that u<sub>0</sub> is a smooth and decaying function,</p> <p>&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;||u<sub>0</sub>|| =&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; sup&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;|u(x, t)|.</p> <p><sub>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </sub>x E R<sub>3</sub> ,t E&nbsp;R+&nbsp;&nbsp;&nbsp; &nbsp;</p> <p>It is proved that problem (1) has a unique global solution and this</p> <p>solution satisfies the following estimate</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ||u(x, t)|| &lt; c,</p> <p>where c &gt; 0 does not depend on x, t.</p> Alexander G. Ramm ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-07-30 2018-07-30 14 2 7860 7863 10.24297/jam.v14i2.7503 Stability of Cubic Functional Equation in Random Normed Space https://cirworld.com/index.php/jam/article/view/7614 <p>In this paper, we present the Hyers-Ulam stability of Cubic functional equation.</p> <p><img src="/public/site/images/editor/7614.png"></p> <p>where n is greater than or equal to 4, in Random Normed Space.</p> Sandra Pinelas V. Govindan K. Tamilvanan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-30 2018-08-30 14 2 7864 7877 10.24297/jam.v14i2.7614 Another Proof of Beal's Conjecture https://cirworld.com/index.php/jam/article/view/7587 <p>Beal's Conjecture : The equation z<sup>a</sup> = x<sup>b</sup>+y<sup>c</sup> has no&nbsp;solution in relatively prime positive integers x; y; z with a, b and c odd primes at least 3. A proof of this longstanding conjecture is&nbsp;given.</p> James E. Joseph Bhamini P. Nayar ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-30 2018-08-30 14 2 7878 7879 10.24297/jam.v14i2.7587 Cycles Cohomology and Geometrical Correspondences of Derived Categories to Field Equations https://cirworld.com/index.php/jam/article/view/7581 <p>The integral geometry methods are the techniques could be the more naturally applied to study of the characterization of the moduli stacks and solution classes (represented cohomologically) obtained under the study of the kernels of the differential operators of the corresponding field theory equations to the space-time. Then through a functorial process a classification of differential operators is obtained through of the co-cycles spaces that are generalized Verma modules to the space-time, characterizing the solutions of the field equations. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic bundles category with a special connection (Deligne connection). Using the classification theorem given by geometrical Langlands correspondences are given various examples on the information that the geometrical invariants and dualities give through moduli problems and Lie groups acting.</p> Francisco Bulnes ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-30 2018-08-30 14 2 7880 7892 10.24297/jam.v14i2.7581 Some Remarks on a Class of Finite Projective Klingenberg Planes https://cirworld.com/index.php/jam/article/view/7527 <p>In this article, we deal with a class of projective Klingenberg planes constructed over a plural algebra of order m. Thanks to this, the incidence matrices for some special cases of the class are obtained. Next, the number of collineations of the certain classes are found. Besides, an example of a collineation for these classes are given. Finally, we achieve to carry the obtained results to more general case.</p> Atilla Akpinar Isa Dogan Elif Demirci Zeynep Sena Gurel Bercem Boztemur ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-30 2018-08-30 14 2 7893 7902 10.24297/jam.v14i2.7527 The Universal Coefticient Theorem in the Category of Fuzzy Soft Modules https://cirworld.com/index.php/jam/article/view/7599 <p>This paper begins with the basic concepts of chain comlexes of fuzzy soft modules. Later, we introduce short exact sequence of fuzzy soft modules and prove that split short exact sequence of fuzzy soft chain complex. Naturally, we want to investigate whether or not the universal coefficient theorems are satisfied in category of fuzzy soft chain complexes. However, in the proof of these theorems in the category of chain complexes, exact sequence of homology modules of chain complexes is used. Generally, sequence of fuzzy soft homology modules is not exact in fuzzy chain complexes. Therefore in this study, we construct exact sequence of fuzzy soft homology modules under some conditions. Universal coefficients theorem is proven by making use of this idea.</p> Sebuhi Abdullayev S. A. Bayramov ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-09-15 2018-09-15 14 2 7893 7904 10.24297/jam.v14i2.7599 On Almost Alpha Kenmotsu (k,u)-Spaces https://cirworld.com/index.php/jam/article/view/7662 <p>In this paper, the geometry of almost alpha Kenmotsu (k,u)-spaces are studied. Finally, we give an illustrative example on almost alpha Kenmotsu (k,u)-space of dimension .</p> Hakan Öztürk S. Öztürk ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-09-29 2018-09-29 14 2 7905 7911 10.24297/jam.v14i2.7662 A New Technique for Simulation the Zakharov–Kuznetsov Equation https://cirworld.com/index.php/jam/article/view/7559 <p>In this article, a new technique is proposed to simulated two-dimensional Zakharov–Kuznetsov equation with the initial condition. The idea of this technique is based on Taylors' series in its derivation. Two test problems are presented to illustrate the performance of the new scheme. Analytical approximate solutions that we obtain are compared with variational iteration method (VIM) and homotopy analysis method (HAM). The results show that the new scheme is efficient and better than the other methods in accuracy and convergence.</p> Mohammed Sabah Abdul-Wahab A. S. J. Al-Saif ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-09-29 2018-09-29 14 2 7912 7920 10.24297/jam.v14i2.7559 Approximation of General Form for a Sequence of Linear Positive Operators Based on Four Parameters https://cirworld.com/index.php/jam/article/view/7573 <p>In the present paper, we define a generalization sequence of linear positive operators based on four parameters which is reduce to many other sequences of summation–integral older type operators of any weight function (Bernstein, Baskakov, Szász or Beta). Firstly, we find a recurrence relation of the -th order moment and study the convergence theorem for this generalization sequence. Secondly, we give a Voronovaskaja-type asymptotic formula for simultaneous approximation. Finally, we introduce some numerical examples to view the effect of the four parameters of this sequence.</p> Khalid Dhaman Abbod Ali J. Mohammad ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-09-29 2018-09-29 14 2 7921 7936 10.24297/jam.v14i2.7573 Some Generalizations of Green’s Relations in Rings and Modules https://cirworld.com/index.php/jam/article/view/7772 <p>In semigroups theory Green’s relations, introduced by J. Green, are a very important and useful tool for developing the semigroup theory. They characterise the element of a semigroup or a ring in terms of the principal ideals they generate.</p> <p>In contrast to early semigroup theory , where, as we have seen, ideas from ring’s were applied to semigroups, Green’s relation’s have also been applied to ring’s (Hollings, 2014). In ring theory Green’s relation’s are introduced by (Petro,2002) In this paper at first we generalize Green’s relations in rings.</p> <p>After this we notice that there exist an one to one correspondence between the ideals of a ring and this type of new relations we introduced.Then we compare them with Green’s relations in rings. At last we define some new relations in module theory, which mimic Green’s relations in rings, as an attempt to get tools in studying modules.&nbsp;</p> Florion Cela ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-10-01 2018-10-01 14 2 7937 7945 10.24297/jam.v14i2.7772 Stochastic Analysis of Two Non-identical Unit Parallel System Incorporating Waiting Time and Preventive Maintenance https://cirworld.com/index.php/jam/article/view/7763 <p>The reliability of two non-identical unit’s parallel system with two kinds of failures common cause failure and partial failures is inspected. Moreover, the preventive maintenance and waiting time to repair, a significant aspect of reliability analysis, has also been incorporated. The proposed system is assumed to a function properly if at least one of the unit is in operate mode. The system goes for preventive maintenance at random apaches. Supplementary variable technique and Laplace transform have used for solution. Our results are compared with the previous results to observe the effect of preventive maintenance and failure rates on system performance.</p> Shaaban Ebrahim Abu-Youssef Fatima A. Assed ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-10-10 2018-10-10 14 2 7946 7964 10.24297/jam.v14i2.7763 Green's Relations in Rings and Completely Simple Rings https://cirworld.com/index.php/jam/article/view/7781 <p>In this paper we prove that which of Green's relations $\mathcal{L,R,H}$ and $\mathcal{D}$ in rings preserve the minimality of quasi-ideal. By this it is possible to show the structure of the classes generated by the above relations which have a minimal quasi ideal. For the completely simple rings we show that they are generated by the union of zero with a $\mathcal{D}$-class. Also we emphasize that a completely simple ring coincides with the union of zero with a $\mathcal{D}$-class if and only if it is a division ring.</p> Florion Cela ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-10-11 2018-10-11 14 2 7965 7974 10.24297/jam.v14i2.7781 Attracting Sets Of Nonlinear Difference Equations With Time-Varying Delays https://cirworld.com/index.php/jam/article/view/7668 <p>In this paper, a class of nonlinear difference equations with time-varying delays is considered. Based on a generalized discrete Halanay inequality, some sufficient conditions for the attracting set and&nbsp;the global asymptotic stability of the nonlinear difference equations with time-varying delays are obtained.</p> Danhua He ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-10-13 2018-10-13 14 2 7975 7982 10.24297/jam.v14i2.7668 Composition Of Songs Using Symmetric Group https://cirworld.com/index.php/jam/article/view/7514 <p>Mathematics of music and sound production brings to bear the physical and practical application of Mathematics in the field of Music. The composition of songs involves the principle of key scaling, their respective interval as calculated with the aid of an appropriate key division which suites the generality of songs&nbsp;composed in different keys with the keyboard. Melodies, harmonies and rhythms produced in the stage of rendition is characterized by transposition and inversion of key to suite each song.&nbsp;With the aid of keyboard, elements of Symmetric group are used to compose songs.</p> Adenike Olusola Adeniji ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-10-13 2018-10-13 14 2 7983 8003 10.24297/jam.v14i2.7514