Journal of Mathematics Research
http://ccsenet.org/journal/index.php/jmr
<p><strong><em>Journal of Mathematics Research </em></strong>(ISSN: 1916-9795; E-ISSN 1916-9809) is an open-access, international, double-blind peer-reviewed journal published by the Canadian Center of Science and Education. This journal, published <strong>bimonthly</strong> (<span>February, April, June, August, October and December</span>) in <strong>both print and online versions</strong>, keeps readers up-to-date with the latest developments in all aspects of mathematics.</p><div class="Section1"><strong>The scopes of the journal </strong>include, but are not limited to, the following topics: statistics, approximation theory, numerical analysis, operations research, dynamical systems, mathematical physics, theory of computation, information theory, cryptography, graph theory, algebra, analysis, probability theory, geometry and topology, number theory, logic and foundations of mathematics. <em> </em></div><div class="Section1"><p>This journal accepts article submissions<strong> <a href="/journal/index.php/jmr/information/authors">online</a> or by <a href="mailto:jmr@ccsenet.org">e-mail</a> </strong>(jmr@ccsenet.org).</p></div><div class="Section1"><br /><br /><strong><strong><em><img src="/journal/public/site/images/jmr/jmr.jpg" alt="jmr" width="201" height="264" align="right" hspace="20" /></em></strong><strong>ABSTRACTING AND INDEXING:</strong></strong></div><div class="Section1"><strong><br /></strong></div><div class="Section1"><ul><li>BASE (Bielefeld Academic Search Engine)<strong><br /></strong></li><li><strong>EBSCOhost</strong></li><li>Google Scholar</li><li>JournalTOCs</li><li>LOCKSS</li><li><strong>MathEDUC</strong></li><li><strong><a href="http://www.ams.org/dmr/JournalList.html">Mathematical Reviews</a>® (<a href="http://www.ams.org/mathscinet">MathSciNet</a>®)</strong></li><li>MathGuide</li><li>NewJour</li><li>OCLC Worldcat</li><li>Open J-Gate</li><li><strong>ProQuest</strong></li><li>SHERPA/RoMEO</li><li>Standard Periodical Directory</li><li>Ulrich's</li><li>Universe Digital Library</li><li><strong><a href="https://zbmath.org/journals/?q=se:00006772">Zentralblatt MATH</a></strong></li></ul></div><div class="Section1"><strong><br /></strong></div><div class="Section1"> </div>Canadian Center of Science and Educationen-USJournal of Mathematics Research1916-9795Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication. <br />Copyrights for articles published in CCSE journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.Key Role of Dimensional Analysis Homogeneity in Proving Riemann Hypothesis and Providing Explanations on the Closely Related Gram Points
http://ccsenet.org/journal/index.php/jmr/article/view/59341
Riemann zeta function is the famous complex number infinite series consisting of a real and an imaginary part. Non-trivial zeros and Gram points are best seen as mathematically derived entities of this function when its variable Sigma has a value of $\frac{1}{2}$. The presence [but not the actual locations] of the complete set of infinite non-trivial zeros is characterized by the criterion that the sum total of the simultaneous real and imaginary parts in Riemann zeta function equates to zero. In an identical manner this slightly altered criterion for the presence [but not the actual locations] of the complete set of infinite Gram points is that this 'sum total' now refer to the lesser requirement that only the individual imaginary part in Riemann zeta function equates to zero. The key role played by Dimensional analysis homogeneity to rigorously prove Riemann conjecture/hypothesis has been fully outlined in our landmark research paper published earlier on Page 9 - 21 in the preceding Volume 8, Number 3, June 2016 issue of this journal. Those resulting methodology previously employed by us are now mathematically used in an analogical procedure to delineate its role in successfully supplying crucial explanations for Gram points. In this research article, we use the notation \{Non-critical lines\}-Gram points to signify those 'near-identical' (virtual) Gram points when Sigma value is not $\frac{1}{2}$.John Y. C. Ting
Copyright (c) 2016 Journal of Mathematics Research
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2016-07-252016-07-2584110.5539/jmr.v8n4p1The Shift Invariant Discrete Wavelet Transform (SIDWT) with Inflation Time Series Application
http://ccsenet.org/journal/index.php/jmr/article/view/61732
<p>Analysis of time series used in many areas, one of which is in the field economy. In this research using time series on inflation using Shift Invariant Discrete Wavelet Transform (SIDWT).Time series decomposition using transformation wavelet namely SIDWT with Haar filter and D4. Results of the transformation, coefficient of drag coefficient wavelet and scale that is used for modeling time series. Modeling done by using Multiscale Autoregressive (MAR). In a certain area, inflation to it is an important that he had made the standard-bearer of economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. Inflation can be analyzed using methods Shift Invariant Discrete Wavelet Transform (SIDWT) which had been modeled for them to use Mulitiscale Autoregressive (MAR) with the R2 value 93.62%.</p>Suparti SupartiRezzy Eko CarakaBudi WarsitoHasbi Yasin
Copyright (c) 2016 Suparti Suparti, Rezzy Eko Caraka, Budi Warsito, Hasbi Yasin
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2016-07-252016-07-25841410.5539/jmr.v8n4p14Computational Algorithms for Solving Spectral/$hp$ Stabilized Incompressible Flow Problems
http://ccsenet.org/journal/index.php/jmr/article/view/60151
In this paper we implement the element-by-element preconditioner and inexact Newton-Krylov methods (developed in the past) for solving stabilized computational fluid dynamics (CFD) problems with spectral methods. Two different approaches are implemented for speeding up the process of solving both steady and unsteady incompressible Navier-Stokes equations. The first approach concerns the application of a scalable preconditioner namely the element by element LU preconditioner, while the second concerns the application of Newton-Krylov (NK) methods for solving non-linear problems. We obtain good agreement with benchmark results on standard CFD problems for various Reynolds numbers. We solve the Kovasznay flow and flow past a cylinder at Re-$100$ with this approach. We also utilize the Newton-Krylov algorithm to solve (in parallel) important model problems such as flow past a circular obstacle in a Newtonian flow field, three dimensional driven cavity, flow past a three dimensional cylinder with different immersion lengths. We explore the scalability and robustness of the formulations for both approaches and obtain very good speedup. Effective implementations of these procedures demonstrate for relatively coarse macro-meshes<br />the power of higher order methods in obtaining highly accurate results in CFD. While the procedures adopted in the paper have been explored in the past the novelty lies with applications with higher order methods which have been known to be computationally intensive.Rakesh RanjanAnthony Theodore ChronopoulosYusheng Feng
Copyright (c) 2016 Journal of Mathematics Research
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2016-07-252016-07-25842110.5539/jmr.v8n4p21Useful Numerical Statistics of Some Response Surface Methodology Designs
http://ccsenet.org/journal/index.php/jmr/article/view/60205
<p>Useful numerical evaluations associated with three categories of Response Surface Methodology designs are presented with respect to five commonly encountered alphabetic optimality criteria. The first-order Plackett-Burman designs and the Factorial designs are examined for the main effects models and the complete first-order models respectively. The second-order Central Composite Designs are examined for second-order models. The A-, D-, E-, G- and T-optimality criteria are employed as commonly encountered optimality criteria summarizing how good the experimental designs are. Relationships among the optimality criteria are pointed out with regards to the designs and the models. Generally the designs do not show uniform preferences in terms of the considered optimality criteria. However, one interesting finding is that central composite designs defined on cubes and hypercubes with unit axial distances are uniformly preferred in terms of E-optimality and G-optimality criteria.</p>Iwundu M. P.
Copyright (c) 2016 Journal of Mathematics Research
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2016-07-252016-07-25844010.5539/jmr.v8n4p40Some Fixed Point Theorems in Complete Dislocated Quasi-b-metric Space
http://ccsenet.org/journal/index.php/jmr/article/view/60385
In this paper, we main introduced some concepts and Ciric cyclic fixed point theorem in the complete dislocated quasi-b-metric space. We also can improve some fixed point theorems by Ciric cyclic fixed point theorem such as Kannan cyclic fixed point theorem. It is consist with [Klin-Eam. C, 2016]. Our results for such space consist with the metric space. And our theorems generalization and extend some results in the literature.Hao WuDingping Wu
Copyright (c) 2016 Journal of Mathematics Research
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2016-07-252016-07-25846810.5539/jmr.v8n4p68The Proof for A Convergent Integral and Another Nonzero Integral--Respectively Using the Riemann Zeta Function and the Trigonometric Sums
http://ccsenet.org/journal/index.php/jmr/article/view/60619
In this paper, there are the applications of the main inequalities, and show how to use the analytic properties of the Zeta function and the Laplace transform to prove the convergence of the desired integral. In addition, show how to use the trigonometric sums and the mathematical induction with the method of infinite descent to prove the non-zero value of another integral. In this way, we can obtain the important proofs concerning the Riemann Zeta function and the sum of two primes.Hao-Cong Wu
Copyright (c) 2016 Journal of Mathematics Research
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2016-07-252016-07-25847410.5539/jmr.v8n4p74Finite Element Approximation and Numerical Analysis of Three-dimensional Electrical Impedance Tomography
http://ccsenet.org/journal/index.php/jmr/article/view/61734
Electrical impedance tomography is solved by solving an inverse problem of elliptic equation, and a new numerical method or a new technique is argued to consider finite element (such as normal element and mixed element) in this paper on three dimensional region. Introducing different perturbations to boundary restrictions and using different spacial steps, the authors obtain numerical solutions and give comparison with exact solutions. Numerical data show that numerical solution can approximate exact solution well as spacial step taken small and the approximation of Neumann boundary condition is more stable than that of Dirichlet case.<br />For Newton iterations on finite element method, a large-scaled system of massive linear equations is solved in each iteration, thus the computation is quite expensive. So two techniques are argued in the first half of this paper. Firstly, the invariance property of quasi-element stiffness matrix is used in the iterations and a type of special current model is introduced. Then the minimum number of direct problems solved is considered. Later a local conservative numerical approximation, low order mixed element (block-centered method) is presented in the latter part and the positive semi-definiteness and the existence of its solution are proved. Computational formula of error functional Jacobi matrix is derived and the least direct problems in each iteration are solved by using the symmetry of algorithm and a special current basis. This method has been applied successfully in actual numerical simulation of three-dimensional electrical impedance tomography.Yirang YuanJiuping LiChangfeng LiTongjun Sun
Copyright (c) 2016 Yirang Yuan, Jiuping Li, Changfeng Li, Tongjun Sun
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2016-07-252016-07-25849910.5539/jmr.v8n4p99Multivariate Lagrange Interpolation at Sinc Points Error Estimation and Lebesgue Constant
http://ccsenet.org/journal/index.php/jmr/article/view/61735
This paper gives an explicit construction of multivariate Lagrange interpolation at Sinc points. A nested operator formula for Lagrange interpolation over an m-dimensional region is introduced. For the nested Lagrange interpolation, a proof of the upper bound of the error is given showing that the error has an exponentially decaying behavior. For the uniform convergence the growth of the associated norms of the interpolation operator, i.e., the Lebesgue constant has to be taken into consideration. It turns out that this growth is of logarithmic nature O((log n)^m). We compare the obtained Lebesgue constant bound with other well known bounds for Lebesgue constants using different set of points.Maha Youssef YoussefHany A. El-SharkawyGerd Baumann
Copyright (c) 2016 Maha Youssef Youssef, Hany A. El-Sharkawy, Gerd Baumann
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2016-07-252016-07-258411810.5539/jmr.v8n4p118Commutativity of $\Gamma$-Generalized Boolean Semirings with Derivations
http://ccsenet.org/journal/index.php/jmr/article/view/61746
In this paper the notion of derivations on $\Gamma$-generalized Boolean semiring are established, namely $\Gamma$-$(f, g)$ derivation and $\Gamma$-$(f, g)$ generalized derivation. We also investigate the commutativity of prime $\Gamma$-generalized Boolean semiring admitting $\Gamma$-$(f, g)$ derivation and $\Gamma$-$(f, g)$ generalized derivation satisfying some conditions.Tossatham MakkalaUtsanee Leerawat
Copyright (c) 2016 Tossatham Makkala, Utsanee Leerawat
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2016-07-252016-07-258413210.5539/jmr.v8n4p132Solution of a Class of Differential Equation with Variable Coefficients
http://ccsenet.org/journal/index.php/jmr/article/view/61738
<p>In this paper, we obtain the formula of solution to the initial value problem for a hyperbolic partial differential equation with variable coefficient which is the modification of the famous D’ Alembert formula.</p>Huanhuan XiongYuedan JinXiangqing Zhao
Copyright (c) 2016 Huanhuan Xiong, Yuedan Jin, Xiangqing Zhao
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2016-07-252016-07-258414010.5539/jmr.v8n4p140A Double-indexed Functional Hill Process and Applications
http://ccsenet.org/journal/index.php/jmr/article/view/61772
<div>Let $X_{1,n} \leq .... \leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (\textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the sequence of stochastic processes</div><div> </div><div>\begin{equation}<br />T_{n}(f,s)=\sum_{j=1}^{j=k}f(j)\left( \log X_{n-j+1,n}-\log<br />X_{n-j,n}\right)^{s} , \label{fme}<br />\end{equation}</div><div> </div><div>indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}%^{\ast}\longmapsto \mathbb{R}_{+}$ and $s \in ]0,+\infty[$ and where $k=k(n)$ satisfies</div><div> </div><div>\begin{equation*}<br />1\leq k\leq n,k/n\rightarrow 0\text{ as }n\rightarrow \infty .<br />\end{equation*}</div><div> </div><div>We show that this is a stochastic process whose margins generate estimators of the extreme value index when $F$ is in the extreme domain of attraction. We focus in this paper on its finite-dimension asymptotic law and provide a class of new estimators of the extreme value index whose performances are compared to analogous ones. The results are next particularized for one explicit class $\mathcal{F}$.</div>Modou NgomGane Samb Lo
Copyright (c) 2016 Modou Ngom, Gane Samb Lo
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2016-07-272016-07-278414410.5539/jmr.v8n4p144Mathematical Formulation of Laminated Composite Thick Conical Shells
http://ccsenet.org/journal/index.php/jmr/article/view/61739
<span lang="EN-US">The </span><span lang="EN-US">mathematical formulation</span><span lang="EN-US">of thick conical shells using third order shear deformation of thick shell theory are presented. The equations of motion are obtained using Hamilton’s principle. For present analysis, we consider shell's system transverse normal stress, rotary inertia and shear deformation.</span>Mohammad ZannonHussam Alrabaiah
Copyright (c) 2016 Mohammad Zannon, Hussam Alrabaiah
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2016-07-252016-07-258416610.5539/jmr.v8n4p166A General Family of Fibonacci-Type Squences
http://ccsenet.org/journal/index.php/jmr/article/view/61741
In this work, we introduce a further generalization of the Fibonacci-type sequence, namely, generalized Fibonacci-type sequence. We also provide the general solution of nonhomogeneous generalized Fibonacci-type sequence, which can be expressed in terms of the Fibonacci-type numbers.Suriya NanhongkaiUtsanee Leerawat
Copyright (c) 2016 Suriya Nanhongkai, Utsanee Leerawat
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2016-07-252016-07-258417210.5539/jmr.v8n4p172