http://ccsenet.org/journal/index.php/jmr/issue/feedJournal of Mathematics Research2016-08-01T18:11:25-07:00Sophia Wangjmr@ccsenet.orgOpen Journal Systems<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>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>http://ccsenet.org/journal/index.php/jmr/article/view/59341Key Role of Dimensional Analysis Homogeneity in Proving Riemann Hypothesis and Providing Explanations on the Closely Related Gram Points2016-07-31T20:05:11-07:00John Y. C. Tingjycting@hotmail.comRiemann 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 $\frac{1}{2}$.2016-07-25T19:45:33-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/61732The Shift Invariant Discrete Wavelet Transform (SIDWT) with Inflation Time Series Application2016-07-31T20:05:11-07:00Suparti Supartisupartisudargo@yahoo.co.idRezzy Eko Carakasupartisudargo@yahoo.co.idBudi Warsitosupartisudargo@yahoo.co.idHasbi Yasinsupartisudargo@yahoo.co.id<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>2016-07-25T00:00:00-07:00Copyright (c) 2016 Suparti Suparti, Rezzy Eko Caraka, Budi Warsito, Hasbi Yasinhttp://ccsenet.org/journal/index.php/jmr/article/view/60151Computational Algorithms for Solving Spectral/$hp$ Stabilized Incompressible Flow Problems2016-07-31T20:05:11-07:00Rakesh Ranjanantony.tc@gmail.comAnthony Theodore Chronopoulosantony.tc@gmail.comYusheng Fengantony.tc@gmail.comIn 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.2016-07-25T19:45:33-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/60205Useful Numerical Statistics of Some Response Surface Methodology Designs2016-07-31T20:05:12-07:00Iwundu M. P.mary.iwundu@uniport.edu.ng<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>2016-07-25T19:45:33-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/60385Some Fixed Point Theorems in Complete Dislocated Quasi-b-metric Space2016-07-31T20:05:12-07:00Hao Wuwuha90@163.comDingping Wuwdp68@163.comIn 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.2016-07-25T19:45:33-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/60619The Proof for A Convergent Integral and Another Nonzero Integral--Respectively Using the Riemann Zeta Function and the Trigonometric Sums2016-07-31T20:05:12-07:00Hao-Cong Wuwhc87788778@163.comIn 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.2016-07-25T19:45:33-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/61734Finite Element Approximation and Numerical Analysis of Three-dimensional Electrical Impedance Tomography2016-07-31T20:05:12-07:00Yirang Yuanyryuan@sdu.edu.cnJiuping Liyryuan@sdu.edu.cnChangfeng Liyryuan@sdu.edu.cnTongjun Sunyryuan@sdu.edu.cnElectrical 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.2016-07-25T00:00:00-07:00Copyright (c) 2016 Yirang Yuan, Jiuping Li, Changfeng Li, Tongjun Sunhttp://ccsenet.org/journal/index.php/jmr/article/view/61912Multivariate Lagrange Interpolation at Sinc Points Error Estimation and Lebesgue Constant2016-07-31T20:05:12-07:00Maha Youssefmaha.youssef@guc.edu.egHany A. El-Sharkawymaha.youssef@guc.edu.egGerd Baumannmaha.youssef@guc.edu.egThis 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.2016-08-01T00:00:00-07:00Copyright (c) 2016 Maha Youssef, Hany A. El-Sharkawy, Gerd Baumannhttp://ccsenet.org/journal/index.php/jmr/article/view/61746Commutativity of $\Gamma$-Generalized Boolean Semirings with Derivations2016-07-31T20:05:12-07:00Tossatham Makkalafsciutl@ku.ac.thUtsanee Leerawatfsciutl@ku.ac.thIn 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.2016-07-25T00:00:00-07:00Copyright (c) 2016 Tossatham Makkala, Utsanee Leerawathttp://ccsenet.org/journal/index.php/jmr/article/view/61738Solution of a Class of Differential Equation with Variable Coefficients2016-07-31T20:05:12-07:00Huanhuan Xiongxionghuanhuan@163.comYuedan Jinxionghuanhuan@163.comXiangqing Zhaoxionghuanhuan@163.com<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>2016-07-25T00:00:00-07:00Copyright (c) 2016 Huanhuan Xiong, Yuedan Jin, Xiangqing Zhaohttp://ccsenet.org/journal/index.php/jmr/article/view/61772A Double-indexed Functional Hill Process and Applications2016-07-31T20:05:12-07:00Modou Ngomlo@ugb.edu.snGane Samb Lolo@ugb.edu.sn<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>2016-07-27T00:00:00-07:00Copyright (c) 2016 Modou Ngom, Gane Samb Lohttp://ccsenet.org/journal/index.php/jmr/article/view/61739Mathematical Formulation of Laminated Composite Thick Conical Shells2016-08-01T18:11:25-07:00Mohammad Zannonzanno1ms@gmail.comHussam Alrabaiahzanno1ms@gmail.com<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>2016-07-25T00:00:00-07:00Copyright (c) 2016 Mohammad Zannon, Hussam Alrabaiahhttp://ccsenet.org/journal/index.php/jmr/article/view/61741A General Family of Fibonacci-Type Squences2016-07-31T20:05:12-07:00Suriya Nanhongkaifsciutl@ku.ac.thUtsanee Leerawatfsciutl@ku.ac.thIn 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.2016-07-25T00:00:00-07:00Copyright (c) 2016 Suriya Nanhongkai, Utsanee Leerawathttp://ccsenet.org/journal/index.php/jmr/article/view/60086Modelling the Effect of Post-mortem Contact on the Spread of Ebola with Quarantine As an Intervention2016-07-31T20:05:13-07:00Francis T. Odurofrancistoduro@yahoo.co.ukJoseph Baafijbaaafi@aims.edu.ghGeorge Apaaboahgeorge.apaaboah@gmail.comEbola virus disease (EVD) is a severe, often fatal disease in humans and other non-human primates caused by infection with any of the four identified Ebola virus species of the family Filoviridae. This paper develops the SEIR and the SEIHDR epidemic models that investigate the effects of the ante-mortem contact and post-mortem contact on the spread of the disease. The reproduction number of the models are determined. The equilibria and conditions for the existence of the equilibria are also determined. The models are solved numerically and the numerical simulations implemented to elucidate various scenarios. The results of the models are then compared to WHO data of confirmed cases for the 2014 Ebola outbreak in Liberia. It is observed that the SEIHDR model agrees better with the data than the SEIR model. Moreover, a new model, the SEIQDR model (a modification of the SEIHDR Model) is formulated which incorporates quarantine as an intervention. Again, this SEIQDR model is compared to the WHO data of confirmed cases for the 2014 Ebola outbreak in Liberia. The results of the SEIQDR model is found to agree better than those of the other models especially in respect of the latter stages of the disease outbreak. Finally, the effect of vaccination on both the SEIHDR and the SEIQDR models is investigated. Different rates of vaccination using numerical simulations in order to predict the effect of vaccination on the infected individuals over time is also discussed. The SEIQDR model with vaccination indicates a lower threshold which should not be less than 25\% as compared to the SEIHDR model for which vaccination should not be less than 65\%. It is observed that vaccination as an additional strategy helps to control the disease more effectively.2016-07-31T19:54:12-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/60236On Dynamical Systems for Transport Logistic and Communications2016-07-31T20:05:13-07:00Alexander P. Buslaevapal2006@yandex.ruAlexander G. Tatashevapal2006@yandex.ruIn this paper a discrete dynamical system is considered . There is a dial with $N$ positions (vertices) and $M$ particles. Particles are located in vertices. Each particle moves, at every time unit, in accordance with its plan. The plan is logistics, given through a real number which belongs to the segment $[0,1].$ The number is represented in positional numeral system with base $N$ equal to the number of vertices. A competition takes place if particles must move in opposite directions simultaneously. A rule of competition resolution is given. Systems characteristics are investigated for sets of rational and irrational plans. Some algebraic constructions are introduced for this purpose. Probabilistic analogues (random walks) are also considered.2016-07-31T20:04:01-07:00Copyright (c) 2016 Journal of Mathematics Researchhttp://ccsenet.org/journal/index.php/jmr/article/view/61914A Location Problem of Obstacles in Population Dynamics2016-07-31T20:10:33-07:00Sidy Lylysidyly@gmail.comFulgence Mansallysidyly@gmail.comDiaraf Secklysidyly@gmail.comMoussa Baldelysidyly@gmail.comThe aim of this paper is to determine the optimal locations where Fish Aggregating Devices (F.A.D) or artificial traps must be placed in a given place of the sea and to preverse resources. Our work focuses on two parts: the first one is the study of static optimization problem with a functional taking into account the distance between the sites or F.A.D and the second one is devoted to solving an optimization problem with constraints expressed in classical model of fishery: Lagrange's method and Pontryagin's maximum principle the main mathematical tools to get characterization results of the location of artificial traps.2016-08-01T00:00:00-07:00Copyright (c) 2016 Sidy Ly, Fulgence Mansal, Diaraf Seck, Moussa Baldehttp://ccsenet.org/journal/index.php/jmr/article/view/61915Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 8, No. 42016-07-31T20:33:41-07:00Sophia Wangjmr@ccsenet.org<div><p><em>Journal of Mathematics Research</em> wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.</p><p>Many authors, regardless of whether <em>Journal of Mathematics Research</em> publishes their work, appreciate the helpful feedback provided by the reviewers.</p><p><strong>Reviewers for Volume 8, Number 4</strong></p><p><strong> </strong></p></div><strong><br clear="all" /> </strong><p><span style="font-family: Times New Roman; font-size: medium;">Abdelaziz Mennouni</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Alberto Simoes</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Ali Berkol</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Antonio Boccuto</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Arman Aghili</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Cecília Rosa</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Chung-Chuan Chen</span></p><p><span style="font-family: Times New Roman; font-size: medium;">David Bartl</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Dimple Chalishajar</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Eric José Avila</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Hari M. Srivastava</span></p><p><span style="font-family: Times New Roman; font-size: medium;">K.V.L.N.ACHARYULU</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Khalil Ezzinbi</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Kuldeep Narain Mathur</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Li Wang</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Michael Wohlgenannt</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Mohammad Sajid</span></p><p><span style="font-family: Times New Roman; font-size: medium;">N. V. Ramana Murty</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Ömür DEVECİ</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Pengcheng Xiao</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Philip Philipoff</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Prof.Maria Alessandra Ragusa</span></p><p><span style="font-family: Times New Roman; font-size: medium;">R. Roopkumar</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Roberto S. Costas-Santos</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Rosalio G. Artes</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Saima Anis</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Sanjib Kumar Datta</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Selcuk Koyuncu</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Sergiy Koshkin</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Sreedhara Rao Gunakala</span></p><p><span style="font-family: Times New Roman; font-size: medium;">Vishnu Narayan Mishra</span></p>2016-08-01T00:00:00-07:00Copyright (c) 2016 Sophia Wang