Journal of Mathematics Research, Issue: Vol.12, No.1JMRMon, 17 Feb 2020 10:07:51 +0000Zend_Feed_Writer 2 (http://framework.zend.com)
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jmr@ccsenet.org (Journal of Mathematics Research)Journal of Mathematics ResearchAnalytic Solutions of the Eigenvalues of Mathieu’s EquationMathieu’s eigenvalue problem −y′′(x) + 2e_0 cos(2x)y(x) = λy(x), 0 < x < ℓ is symmetric if cos(2x) = cos(2ℓ − 2x) for ℓ = k0π, k0 ∈ N, and skew-symmetric if cos(2x) = − cos(2ℓ − 2x) for ℓ = π/2. Two typical boundary conditions are considered. When the eigenfunctions are expanded by the orthonormal bases of sine functions or cosine functions, we can derive an n-dimensional matrix eigenvalue problem, endowing with a special structure of the symmetric coefficient matrix A := [a_ij], a_ij = 0 if i + j is an odd integer. Based on it, we can obtain the eigenvalues easily and analytically. When ℓ = k_0π, k_0 ∈ N, we have a_ij = 0 if |i − j| > 2k_0. Besides the diagonal band, A has two off-diagonal bands, and furthermore, a cross band appears when k_0 ≥ 2. The product formula, the recursion formulas of characteristic functions and a fictitious time integration method (FTIM) are developed to find the eigenvalues of Mathieu’s equation.]]>Mon, 16 Dec 2019 06:20:21 +0000
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http://www.ccsenet.org/journal/index.php/jmr/article/view/0/415540Three Positive Solutions for Boundary Value Problem of Fractional q-Differential EquationIn this paper, we study the boundary value problem of a Riemann-Liouville fractional q-difference equation. By applying the Leggett-Williams fixed point theorem and the properties of the Green’s function, three positive solutions are obtained.]]>Fri, 13 Dec 2019 06:49:54 +0000
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41568
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/415680Optimization of Micro-Electrical Discharge Machining Parameters of Ti6AL4V Component: A Mapping StudySat, 01 Feb 2020 05:22:57 +0000
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http://www.ccsenet.org/journal/index.php/jmr/article/view/0/415850New Mathematical model of Retailer-to-Individual Customer Optimal Product Supply Strategies Under False Demand Pattern: Customer Discount ModeSat, 01 Feb 2020 05:26:00 +0000
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41814
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/418140Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded MaterialsA mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).]]>Wed, 15 Jan 2020 03:41:04 +0000
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http://www.ccsenet.org/journal/index.php/jmr/article/view/0/418230Interaction Orientation, Innovative Method and Corporate PerformanceThu, 06 Feb 2020 02:01:08 +0000
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41861
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/418610Barrelled Linearly Topologized Modules Over a Discrete Valuation RingSat, 01 Feb 2020 09:38:52 +0000
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41862
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/418620Determination of Time-Dependent Coefficients in Time-Fractional Diffusion Equations by Variational Iteration MethodSat, 01 Feb 2020 09:40:04 +0000
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41953
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/419530Some Associated Curves of Normal Indicatrix of a Regular CurveSat, 01 Feb 2020 09:40:58 +0000
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http://www.ccsenet.org/journal/index.php/jmr/article/view/0/419540Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 12, No. 1Sat, 01 Feb 2020 09:41:29 +0000
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