• 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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• East Asian mathematical journal
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• v.31 no.1
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• pp.127-134
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• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.601-618
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• 2000

Let (and $g^*$) be the space of regular test (and generalized, resp.) white noise functions. The integral kernel operators acting on and transformation groups of operators on are studied, and then every integral kernel operator acting on can be extended to continuous linear operator on $g^*$. The existence and uniqueness of solutions of Cauchy problems associated with certain integral kernel operators with intial data in $g^*$ are investigated.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.357-369
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• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• Journal of Ocean Engineering and Technology
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• v.14 no.1
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• pp.1-5
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• 2000

A numerical analysis for wave motion in the shallow water is presented. The method is based on potential theory. The fully nonlinear free surface boundary condition is assumed in an inner domain and this solution is matched along an assumed common boundary to a linear solution in outer domain. In two-dimensional problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.109-115
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.789-797
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• 2020

By considering a certain univalent function in the open unit disk 𝕌, that maps 𝕌 onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We determine the coefficient bounds for functions in this new class. Relevant connections of some of the results obtained with those in earlier works are also provided.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.387-400
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• 2009

We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.