• Journal of the Chungcheong Mathematical Society
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• v.17 no.2
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• pp.169-190
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• 2004

Let r, s be nonzero real numbers. Let X, Y be vector spaces. It is shown that if a mapping f : $X{\rightarrow}Y$ satisfies f(0) = 0, and $$sf(\frac{x+y{\pm}z}{r})+f(x)+f(y){\pm}f(z)=sf(\frac{x+y}{r})+sf(\frac{y{\pm}z}{r})+sf(\frac{x{\pm}z}{r})$$, or $$sf(\frac{x+y{\pm}y}{r})+f(x)+f(y){\pm}f(z)=f(x+y)+f(y{\pm}z)+f(x{\pm}z)$$ for all x, y, $z{\in}X$, then there exist an additive mapping A : $X{\rightarrow}Y$ and a quadratic mapping Q : $X{\rightarrow}Y$ such that f(x) = A(x) + Q(x) for all $x{\in}X$. Furthermore, we prove the Cauchy-Rassias stability of the functional equations as given above.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.387-397
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• 2018

In this paper, a general closed-form solution for evaluating the dynamic behavior of a Timoshenko beam on elastic foundation under a moving harmonic line load is formulated in the frequency-wavenumber domain and in a moving coordinate system. It is found that the characteristic equation is quartic with real coefficients only, and its poles can be presented explicitly. This enables the substitution of these poles into Cauchy's residue theorem, leading to the general closed-form solution. The solution can be reduced to seven existing closed-form solutions to different sub-problems and a new closed-form solution to the subproblem of a Timoshenko beam on an elastic foundation subjected to a moving quasi-static line load. Two examples are included to verify the solution.

• Journal of Ocean Engineering and Technology
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• v.19 no.5 s.66
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• pp.78-82
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• 2005

The motion response results of a submerged submarine section in waves are presented. The numerical method is based on Cauchy's integral and 3 degrees-of-freedom motions of submarine sections are calculated in two dimensions, in regular waves. The fully nonlinear free surface and body boundary conditions are applied to the present problem, and the viscous effects on the submarine are modeled by Morison's formulas. The motions of submarine sections in beam sea are directly simulated and the effects of wave frequency, snorkel depth, and bridge are discussed.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.101-108
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• 2008

In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr$\"{o}$dinger equation: $iu_t\;+\;{\Delta}u\;+\;{\mid}u{\mid}^{\alpha}u\;+\;a{\Sigma}_i^d\;u_{x_ix_ix_ix_i}$ = 0, where a is real constant, 1 $\leq$ d < n is a integer is a positive constant, and x = $(x_1,x_2,\cdots,x_n)\;\in\;R^n$. For some admissible ${\alpha}$ we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.113-124
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• 2005

For a Tychonoff space X, C(X) is a Riesz-space. It is well known that C(X) is order-Cauchy complete if and only if X is a quasi~F space and that if X is a compact space and QF(X) is a minimal quasi-F cover of X, then the order- Cauchy completion of C(X) is isomorphic to C(QF(X)). In this paper, we investigate motivations and historical backgrounds of the definition for quasi-spaces and the construction for minimal quasi-F covers.

• Journal of the Korean Mathematical Society
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• v.31 no.2
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• pp.245-254
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• 1994

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.155-165
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• 2012

In this paper, we have studied some fixed point theorems on complete G-metric spaces.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.91-121
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• 2014

Let X and Y be vector spaces. It is shown that a mapping $f:X{\rightarrow}Y$ satisfies the functional equation ${\ddag}$ $$2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^jx_j}{2d})-2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^{j+1}x_j}{2d})=2\sum_{j=2}^{2d}(-1)^jf(x_j)$$ if and only if the mapping $f:X{\rightarrow}Y$ is additive, and prove the Cauchy-Rassias stability of the functional equation (${\ddag}$) in Banach modules over a unital $C^*$-algebra, and in Poisson Banach modules over a unital Poisson $C^*$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras. As an application, we show that every almost homomorphism $h:\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h(d^nuy)=h(d^nu)h(y)$ or $h(d^nu{\circ}y)=h(d^nu){\circ}h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and n = 0, 1, 2, ${\cdots}$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras, and of Lie $JC^*$-algebra derivations in Lie $JC^*$-algebras.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.12
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• pp.3011-3016
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• 2015

Representing protein three-dimensional structure by concatenating a sequence of protein fragments gives an efficient application in analysis, modeling, search, and prediction of protein structures. This paper investigated the effective combination of distance measures, which can exploit large protein structure database, in order to construct a protein fragment library representing native protein structures accurately. Clustering method was used to construct a protein fragment library. Initial clustering stage used inter alpha-carbon distance having low time complexity, and cluster extension stage used the combination of inter alpha-carbon distance, Binet-Cauchy distance, and root mean square deviation. Protein fragment library was constructed by leveraging large protein structure database using the proposed combination of distance measures. This library gives low root mean square deviation in the experiments representing protein structures with protein fragments.

• Journal of Korean Society of Disaster and Security
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• v.6 no.3
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• pp.1-8
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• 2013

Based on random vibration theory, a procedure for calculating the dynamic response of the tall building to time-dependent random excitation is developed. In this paper, the fluctuating along- wind load is assumed as time-dependent random process described by the time-independent random process with deterministic function during a short duration of time. By deterministic function A(t)=1-exp($-{\beta}t$), the absolute value square of oscillatory function is represented from author's studies. The time-dependent random response spectral density is represented by using the absolute value square of oscillatory function and equivalent wind load spectrum of Solari. Especially, dynamic mean square response of the tall building subjected to fluctuating wind loads was derived as analysis function by the Cauchy's Integral Formula and Residue Theorem. As analysis examples, there were compared the numerical integral analytic results with the analysis fun. results by dynamic properties of the tall uilding.