• Journal of the Korean Statistical Society
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• 제1권1호
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• pp.18-24
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• 1973

Study on convexity has been improved in many statistical fields, such as linear programming, stochastic inverntory problems and decision theory. In proof of main theorem in Section 3, M. Loeve already proved this theorem with the $r$-th absolute moments on page 160 in [1]. Main consideration is given to prove this theorem using convex theorems with the generalized $t$-th mean when some convex properties hold on a real linear vector space $R_N$, which satisfies all properties of finite dimensional Hilbert space. Throughout this paper $\b{x}_j, \b{y}_j$ where $j = 1,2,......,k,.....,N$, denotes the vectors on $R_N$, and $C_N$ also denotes a subspace of $R_N$.

• Bulletin of the Korean Mathematical Society
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• 제33권1호
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• pp.97-106
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• 1996

The study of surface in a Euclidean space whose Gauss map G satisfies the condition : \DeltaG = AG(*)$ for some matrix A was studied by C. Baikoussis, D. E. Blair, B. Y. Chen, F. Dillen, L. Verstraelen ([1]1, [2], [7]) and so on.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1125-1134
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• 2017

In this paper, we present a new multilevel in space and energy diffusion (MSED) method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1) a grey (one-group) diffusion equation used to efficiently converge the fission source and eigenvalue, (2) a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3) a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

• Journal of the Korean Mathematical Society
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• 제54권2호
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• pp.381-397
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• 2017

In this paper, we study surfaces in 3-dimensional Minkowski space in terms of certain type of their Gauss map. We give several results on these surfaces whose Gauss map G satisfies ${\square}G=f(G+C)$ for a smooth function f and a constant vector C, where ${\square}$ denotes the ChengYau operator. In particular, we obtain classification theorems on the rotational surfaces in ${\mathbb{E}}^3_1$ with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.

• Bulletin of the Korean Mathematical Society
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• 제48권3호
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Honam Mathematical Journal
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• 제38권2호
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• pp.269-277
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• 2016

In a paper of S. H. Choi [2], the author studied the derivations of a restricted Weyl Type non-associative algebra, and determined a 1-dimensional vector space of derivations. We describe all the derivations of this algebra and prove that they form a 3-dimensional Lie algebra.

• Journal of computational fluids engineering
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• 제8권3호
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• pp.21-31
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• 2003

A non-dissipative and very accurate one-dimensional upwind leapfrog method is extended to higher-order and multi-dimensional advection and acoustic equations. The higher-order versions are developed by extending the stencils in space and time. The schemes are then successfully applied to the classical test cases for advection and acoustics.

• Communications of the Korean Mathematical Society
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• 제34권1호
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• pp.287-301
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• 2019

In this paper we study monotonicity the first eigenvalue for a class of (p, q)-Laplace operator acting on the space of functions on a closed Riemannian manifold. We find the first variation formula for the first eigenvalue of a class of (p, q)-Laplacians on a closed Riemannian manifold evolving by the Ricci-Bourguignon flow and show that the first eigenvalue on a closed Riemannian manifold along the Ricci-Bourguignon flow is increasing provided some conditions. At the end of paper, we find some applications in 2-dimensional and 3-dimensional manifolds.

• International Journal of Aeronautical and Space Sciences
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• 제12권3호
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• pp.288-295
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• 2011

This paper addresses minimum-fuel, two-dimensional trajectory optimization for a soft lunar landing from a parking orbit to a desired landing site. The landing site is usually not considered when performing trajectory optimization so that the landing problem can be handled. However, for precise trajectories for landing at a desired site to be designed, the landing site has to be considered as the terminal constraint. To convert the trajectory optimization problem into a parameter optimization problem, a pseudospectral method was used, and C code for feasible sequential quadratic programming was used as a numerical solver. To check the reliability of the results obtained, a feasibility check was performed.

• Analytical Science and Technology
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• 제20권4호
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• pp.355-360
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• 2007

The title complex, $(C_3H_{12}N_2)[\{Cd(H_2O)(C_6H_5O_7)\}_2]{\cdot}6H_2O$, I, has been prepared and its structure characterized by FT-IR, EDS, elemental analysis, ICP-AES, and X-ray single crystallography. It is triclinic system, $P{\bar{1}}$ space group with a = 10.236(2), b = 11.318(2), c = $13.198(2){\AA}$, ${\alpha}=77.95(1)^{\circ}$, ${\beta}=68.10(1)^{\circ}$, ${\gamma}=78.12(1)^{\circ}$, V = $1373.5(3){\AA}^3$, Z = 2. Complex I has constituted by protonated 1,3-diaminopropane cations, citrate coordinated cadmium(II) anions, and free water molecules. The central cadmium atoms have a capped trigonal prism geometry by seven coordination with six oxygen atoms of three different citrate ligands and one water molecule. Citrate ligands are bridged to three different cadmium atoms. Each cadmium atom is linked by carboxylate and hydroxyl groups of citrate ligand to construct an one-dimensional ladder-type assembly structure. The polymeric crystal structure is stabilized by three-dimensional networks of the intermolecular O-H${\cdots}$O and N-H${\cdots}$O hydrogen-bonding interaction.