# International Journal of Pure Mathematics

**E-**ISSN: 2313-0571

Volume 3, 2016

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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**Volume 3, 2016**

Title of the Paper: **Estimating Volume Tensor by Fakir Probe**

Authors: **Jiří Janáček, Daniel Jirák**

Pages: **62-64**

Abstract: Interactive Fakir method for object volume measurements using virtual spatial grid of lines is used for basic shape analysis evaluating second moment tensor of intersections of the spatial grid with the studied object. The method is applied on developmental study of Pheasant brain.

Title of the Paper: **Characterization of the Three-Bar Linkage System Generated Symmetric and Asymmetric Lemniscate-like Curves**

Authors: **Hee Seok Nam, Gaspar Porta, Hyung Ju Nam**

Pages: **56-61**

Abstract: In this paper, we investigate the characterization of the family of curves generated by three-bar linkage systems. Depending on the location of the marker on the middle rod, symmetric or asymmetric lemniscate-like curves are constructed. An algebraic representation is presented using the distances from the foci as a generalization of the Lemniscate of Bernoulli. It turns out that the corresponding Cartesian equation is of the form of the Hippopede defined as the intersection of a torus and a plane. A geometric construction shows how we can construct a family of symmetric or asymmetric lemniscate-like curves using a circle and a fixed point. It leads to a polar representation. Finally, a parametric representation is given for the completion of the characterization.

Title of the Paper: **A Three-Dimensional Topological Model of Ternary Phase Diagram**

Authors: **Hong Bao, Yingxue Mu**

Pages: **52-55**

Abstract: In order to obtain a visualization of the complex internal structure of ternary phase diagram, the paper realized three-dimensional topology model of the ternary phase diagram with the designed data structure and improved algorithm, under the guidance of relevant theories of computer graphics. The purpose of the model is mainly to analyze the relationship between each phase region of the ternary phase diagram. The model not only obtain isothermal section graph at any temperature, but also extract a particular phase region in which users are interested.

Title of the Paper: **Notes about the Linear Complexity of the Cyclotomic Sequences Order Three and Four over Finite Fields**

Authors: **Vladimir Edemskiy, Nikita Sokolovskiy**

Pages: **46-51**

Abstract: We investigate the linear complexity and the minimal polynomial over the finite fields of the characteristic sequences of cubic and biquadratic residue classes. Also we find the linear complexity and the minimal polynomial of the balanced cyclotomic sequences of order three.

Title of the Paper: **Interiors and Closures of Sets and Applications**

Authors: **Soon-Mo Jung**

Pages: **41-45**

Title of the Paper: **On the m-Term Best Approximation of Functions and Greedy Algorithm**

Authors: **Martin Grigoryan**

Pages: **34-40**

Abstract: It is proved that the trigonometric system possesses the L^1-strong and greedy property. Also it is described the class of Lebesgue integrable functions such that the error between function and m-term best approximant with respect to the trigonometric system has the following behavior - o[1/[(ln^δ) m]], δ>0

Title of the Paper: **Remark on Small Analytic Solutions to the Schrodinger Equation with Cubic Convolution**

Authors: **Hironobu Sasaki**

Pages: **26-33**

Abstract: We consider the Cauchy problem for the Schrödinger equation with cubic convolution in space dimension d ≥ 3. We assume that the interaction potential V belongs to the weak L^d/σ space with 2 ≤ σ < d. We prove that if the initial data ϕ is sufficiently small in the sense of the Sobolev space H^σ/2-1 and either ϕ or its Fourier transform Fϕ satisfies a real-analytic condition, then the solution u(t) is also real-analytic for any t ≠ 0. We also prove that if ϕ and V satisfy some strong condition, then u(t) can be extended to an entire function on Cd for any t ≠0. We remark that no H^σ/2-1 smallness condition is imposed on first and higher order partial derivatives of ϕ and Fϕ.

Title of the Paper: **Some Parametric Inequalities on Strongly Regular Graphs Spectra**

Authors: **Vasco Moço Mano, Luís de Almeida Vieira**

Pages: **20-25**

Abstract: In this work we deal with the problem of finding suitable admissibility conditions for the parameter sets of strongly regular graphs. To address this problem we analyze the regularity of these graphs through the introduction of a parameter and deduce some parametric admissibility conditions. Applying an asymptotic analysis, the conditions obtained enabled us to extract some spectral conclusions over the class of strongly regular graphs.

Title of the Paper: **The Birkhoff Weak Integral of Real Functions with Respect to a Multimeasure**

Authors: **Anca Croitoru, Alina Gavrilut, Alina Iosif**

Pages: **12-19**

Abstract: In this paper we define and study a new Birkhoff type integral (Bw) RA fdμ (called Birkhoff weak) for a real function f with respect to a set multifunction μ taking values in the family of all nonempty subsets of a real Banach space. Some classical properties are presented, such as heredity, monotonicity (relative to the function f, to the set multifunction μ and to the set A), homogeneity (with respect to f and μ) and additivity (relative to f, μ and A). Birkhoff weak integrability properties on atoms are also established.

Title of the Paper: **Using Simulation to Solve the Newsvendor Problem under Parameter Uncertainty**

Authors: **David F. Muñoz, David G. Muñoz**

Pages: **6-11**

Abstract: We discuss the formulation and solution to the newsvendor problem under a Bayesian framework that allows us to incorporate the uncertainty in the parameters of demand modeling (introduced in the process of parameter estimation). We present an example with an analytical solution and use this example to show that a classical approach (without parameter uncertainty) tends to overestimate the expected benefit. Furthermore, we conduct experiments that confirm our results and illustrate the estimation of the optimal order size using stochastic simulation, method that is suggested when model complexity does not allow us to obtain an analytical solution.

Title of the Paper: **On the Local Property of φ-|Α, pn|k Summability of Factored Fourier Series**

Authors: **H. Ozarslan, S. Yildiz**

Pages: **1-5**

Abstract: In this paper, a more general theorem concerning the local property of φ-|Α, pn|k summability of factored Fourier series has been proved. Also some new results have been obtained.