JOURNAL OF ADVANCES IN MATHEMATICS Interested in submitting to this journal? We recommend that you review the About the Journal page for the journal's section policies, as well as the Author Guidelines. Authors need to register with the journal prior to submitting or, if already registered, can simply log in and begin the five-step process. en-US <p>Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the&nbsp;<a href="">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> (Prof. Kewen Zhao) (John Miller) Thu, 31 May 2018 16:32:00 +0000 OJS 60 Further Acceleration of the Simpson method for solving nonlinear equations <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## Fri, 25 May 2018 00:00:00 +0000 The Trisection of an Arbitrary Angle <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## Wed, 30 May 2018 05:08:11 +0000 The Neutrosophic Soft Modules <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## Wed, 30 May 2018 00:00:00 +0000 Role of conservation laws in the development of nonequilibrium and emergence of turbulence <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## Wed, 30 May 2018 00:00:00 +0000 A Solution Algorithm for Interval Transportation Problems via Time-Cost Tradeoff <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## Tue, 12 Jun 2018 06:38:30 +0000 Generalized Rayleigh-quotient formulas for the real parts, imaginary parts, and moduli of the eigenvalues of diagonalizable matrices <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## Wed, 13 Jun 2018 05:51:42 +0000 Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment <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## Wed, 13 Jun 2018 00:00:00 +0000 Model Higgs Bundles in Exceptional Components of the Sp(4,R)-Character Variety <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## Fri, 29 Jun 2018 00:00:00 +0000 Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces <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## Sat, 30 Jun 2018 08:56:48 +0000 The Asymptotic Behavior of Solutions of Second order Difference Equations With Damping Term <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## Tue, 03 Jul 2018 00:00:00 +0000 Estimates of Solutions to Nonlinear Evolution Equations <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## Tue, 03 Jul 2018 00:00:00 +0000 Regional Boundary Gradient Detectability in Distributed Parameter Systems <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## Wed, 04 Jul 2018 07:35:12 +0000 Regional Boundary Strategic Sensors Characterizations <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 ##submission.copyrightStatement## Mon, 09 Jul 2018 09:15:13 +0000 On Solutions and Heteroclinic Orbits of Some Lotka-Volterra Systems <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## Mon, 30 Jul 2018 07:41:23 +0000 Global existence and uniqueness of the solution to a nonlinear parabolic equation <p>Consider the equation</p> <p>&nbsp;u’ (t)&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## Mon, 30 Jul 2018 00:00:00 +0000