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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>The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations. The submitting author is responsible for securing any permissions needed for the reuse of copyrighted materials included in the manuscript.</p> <p>While the advice and information in this journal are believed to be true and accurate on the date of its going to press, neither the authors, the editors, nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.</p> Further Acceleration of the Simpson method for solving nonlinear equations http://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 http://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 http://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]. Aktaş 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 ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-05-30 2018-05-30 14 2 7670 7681 10.24297/jam.v14i2.7401 The Role of conservation laws in the development of nonequilibrium and emergence of turbulence. Peculiarities of calculating nonequilibrium flows http://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 Solutıon Algorıthm for Interval Transportatıon Problems vıa Tıme-Cost Tradeoff http://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 Sİvri 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 http://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 http://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> Osama Mahmoud Hollah ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-06-13 2018-06-13 14 2 7729 7743 10.24297/jam.v14i2.7365