• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.243-256
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• 2022

In 1914, Bohr proved that there is an r₀ ∈ (0, 1) such that if a power series ∑^∞_m=0 c_mz^m is convergent in the open unit disc and |∑^∞_m=0 c_mz^m| < 1 then, ∑^∞_m=0 |c_mz^m| < 1 for |z| < r₀. The largest value of such r₀ is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.2
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• pp.173-181
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• 2001

This paper presents an artificial life algorithm which is remarkable in the area of engineering for functions optimization. As artificial life organisms have a sensing system, they can find the resource which they want to find and metabolize. And the characteristics of artificial life are emergence and dynamic interaction with environment. In other words, the micro-interaction with each other in the artificial lifes group results in emergent colonization in the whole system. In this paper, therefore, artificial life algorithm by using above characteristics is employed into functions optimization. The optimizing ability and convergent characteristics of this proposed algorithm is verified by using three test functions. The numerical results also show that the proposed algorithm is superior to genetic algorithms and immune algorithms for the multimodal functions.

• East Asian mathematical journal
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• v.19 no.2
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• pp.241-249
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• 2003

In [11] the feeble continuity is introduced and then the weak and strong forms of feeble(or, equivalently $\alpha$-continuity) continuity are studied. In this note, we introduce a type of function called a slightly $\alpha$-continuous function and study several properties of it

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.121-134
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• 2021

In this paper we introduce the notion of paranormed p-absolutely convergent and paranormed Cesro summable sequences of complex uncertain variables with respect to measure, mean, distribution etc. defined by on Orlicz function. We have established some relationships among these notions as well as with other classes of complex uncertain variables.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.635-644
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• 2004

A method of identifying structural parameters such as stiffness and damping coefficients at interfacial points of vibro-acoustic systems is suggested using an optimization technique. To identify the parameters using a numerical optimization algorithm, cost functions are defined. The cost function should be zero at the correct parameter values. To minimize the cost functions using an optimization technique, a design sensitivity analysis procedure is developed in the framework of the multi-domain FRF-based substructuring method. As a numerical example, a ladder-like structure problem is introduced. With known parameter values and different initial guesses of the parameters, convergence characteristics to the exact value are compared f3r the three cost functions. Investigating the contours of the cost functions, we find the first cost function has the largest convergent region to the correct value. As another practical problem, stiffnesses of engine mounts and bushings in a passenger car are identified. The numerical examples show that the proposed method is efficient and accurate far realistic problems.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.6
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• pp.536-545
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• 2004

A method of identifying structural parameters such as stiffness and damping coefficients at interfacial points of vibro-acoustic systems is suggested using an optimization technique. To identify the parameters using a numerical optimization algorithm, cost functions are defined. The cost function should be zero at the correct parameter values. To minimize the cost functions using an optimization technique, a design sensitivity analysis procedure is developed in the framework of the multi-domain FRF-based substructuring method. As a numerical example, a ladder-like structure problem is introduced. With known parameter values and different initial guesses of the parameters, convergence characteristics to the exact value are compared for the three cost functions. Investigating the contours of the cost functions, we find the first cost function has the largest convergent region to the correct value. As another practical problem, the stiffnesses of engine mounts and bushings in a passenger car are identified. The numerical examples show that the proposed method is efficient and accurate for realistic problems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.501-509
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• 2003

A method of identifying structural parameters such as stiffness and damping coefficients at interfacial points of vibro-acoustic systems is suggested using an optimization technique. To identify the parameters using a numerical optimization algorithm, cost functions are defined. The cost function should be zero at the correct parameter values. To minimize the cost functions using an optimization technique, a design sensitivity analysis procedure is developed in the framework of the multi-domain FRF-based substructuring method. As a numerical example, a ladder-like structure problem is introduced. With known parameter values and different initial guesses of the parameters, convergence characteristics to the exact value are compared for the three cost functions. Investigating the contours of the cost functions, we find the first cost function has the largest convergent region to the correct value. As another practical problem, stiffnesses of engine mounts and bushings in a passenger car are identified. The numerical examples show that the proposed method is efficient and accurate even when applied to realistic problems.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.543-552
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• 2012

In this paper, we will show that if ${\mu}$ is a Borel measure on the unit disk D such that ${\int}_{D}\frac{d{\mu}(z)}{(1-\left|z\right|^2)^{p\alpha}}$ < ${\infty}$ where 0 < ${\alpha},{\rho}$ < ${\infty}$, then a bounded sequence of functions {$f_n$} in the $\alpha$-Bloch space $\mathcal{B}{\alpha}$ has a convergent subsequence in the space $D_p({\mu})$ of analytic functions f on D satisfying $f^{\prime}\;{\in}\;L^p(D,{\mu})$. Also, we will find some conditions such that ${\int}_D\frac{d\mu(z)}{(1-\left|z\right|^2)^p$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.5
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• pp.1066-1073
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• 1993

Using regular finite elements and infinite elements simultaneously, elastic boundary value problems with infinite domain can be analyzed more effectively and accurately. In this paper, two dimensional infinite elements have been formulated by means of applying the derived mapping function to the coordinates and multiplying the regular displacement shape functions by a decay function. Orders(m, n) of the mapping and decay functions are found for the purpose of obtaining the convergent solutions without respect to the various decay lengthes. As a result of numerical tests for an infinite plate with a hole under internal pressure, two sets of function orders are obtained as follows. (a) n=0, m=1.5 (b) n=m=0.65

• Journal of Information Processing Systems
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• v.14 no.2
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• pp.455-468
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• 2018

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.