• Title/Summary/Keyword: Gordon

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EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR KLEIN-GORDON-MAXWELL SYSTEM WITH A PARAMETER

  • Che, Guofeng;Chen, Haibo
    • Journal of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.1015-1030
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    • 2017
  • This paper is concerned with the following Klein-Gordon-Maxwell system: $$\{-{\Delta}u+{\lambda}V(x)u-(2{\omega}+{\phi}){\phi}u=f(x,u),\;x{\in}\mathbb{R}^3,\\{\Delta}{\phi}=({\omega}+{\phi})u^2,\;x{\in}\mathbb{R}^3$$ where ${\omega}$ > 0 is a constant and ${\lambda}$ is the parameter. Under some suitable assumptions on V (x) and f(x, u), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition.

PRECONDITIONED SPECTRAL COLLOCATION METHOD ON CURVED ELEMENT DOMAINS USING THE GORDON-HALL TRANSFORMATION

  • Kim, Sang Dong;Hessari, Peyman;Shin, Byeong-Chun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.595-612
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    • 2014
  • The spectral collocation method for a second order elliptic boundary value problem on a domain ${\Omega}$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] ${\times}$ [0, h], h > 0. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

GLOBAL WEAK SOLUTIONS FOR THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM IN TWO DIMENSIONS

  • Xiao, Meixia;Zhang, Xianwen
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.591-598
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    • 2018
  • This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

General Theorem for Explicit Evaluations and Reciprocity Theorems for Ramanujan-Göllnitz-Gordon Continued Fraction

  • SAIKIA, NIPEN
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.983-996
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    • 2015
  • In the paper A new parameter for Ramanujan's theta-functions and explicit values, Arab J. Math. Sc., 18 (2012), 105-119, Saikia studied the parameter $A_{k,n}$ involving Ramanujan's theta-functions ${\phi}(q)$ and ${\psi}(q)$ for any positive real numbers k and n and applied it to find explicit values of ${\psi}(q)$. As more application to the parameter $A_{k,n}$, in this paper we prove a new general theorem for explicit evaluation of Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction K(q) in terms of the parameter $A_{k,n}$ and give examples. We also find some new explicit values of the parameter $A_{k,n}$ and offer reciprocity theorems for the continued fraction K(q).

OPTIMAL ERROR ESTIMATE OF A DECOUPLED CONSERVATIVE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE KLEIN-GORDON-SCHRÖDINGER EQUATIONS

  • YANG, HE
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.24 no.1
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    • pp.39-78
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    • 2020
  • In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.

The Environmental Impact of Tall vs Small: A Comparative Study

  • Drew, Christopher;Nova, Katrina Fernandez;Fanning, Keara
    • International Journal of High-Rise Buildings
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    • v.4 no.2
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    • pp.109-116
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    • 2015
  • The concept of vertical living has been hailed as a solution to control fast growth and urbanization of cities worldwide. As super tall residential projects become more common and sustainability considerations become more necessary, their efficiency has been called into question. How do vertical residential developments compare with suburban homes? What are the environmental advantages and disadvantages of vertical communities? Is there a middle ground? We present the results from an AS+GG study that compares the environmental performance of different housing typologies ranging from a 215 supertall building to single family residences, including several scales in between. Our samples comprise 2,000 residential units per type and include the infrastructure needed to support them. We analyzed land use, energy use, and lifecycle carbon emissions for each typology. The results show that different typologies perform better depending on the parameter being assessed. We discuss these findings; assess overall performance, and present conclusions.

Numerical solution for nonlinear klein-gordon equation by bollocation method with respect to spectral method

  • Lee, In-Jung
    • Journal of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.541-551
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    • 1995
  • The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

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LORENTZIAN SURFACES WITH CONSTANT CURVATURES AND TRANSFORMATIONS IN THE 3-DIMENSIONAL LORENTZIAN SPACE

  • Park, Joon-Sang
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.41-61
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    • 2008
  • We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

Molecular Spinless Energies of the Morse Potential Energy Model

  • Jia, Chun-Sheng;Cao, Si-Yi
    • Bulletin of the Korean Chemical Society
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    • v.34 no.11
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    • pp.3425-3428
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    • 2013
  • We solve the Klein-Gordon equation with the Morse empirical potential energy model. The bound state energy equation has been obtained in terms of the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $X^1{\sum}^+$ state of ScI molecule have been computed by using the Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.