• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.83-99
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• 2022

In this paper, we extend some previous works by Liu et al. on the existence of transcendental entire solutions of differential-difference equations of Fermat type. In addition, we also present a precise description of the associated entire solutions.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.29-38
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• 2016

For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.1
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• pp.77-91
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• 2007

In this paper, we present a symbiotic evolutionary algorithm for multi-objective optimization. The goal in multi-objective evolutionary algorithms (MOEAs) is to find a set of well-distributed solutions close to the true Pareto optimal solutions. Most of the existing MOEAs operate one population that consists of individuals representing the entire solution to the problem. The proposed algorithm has a two-leveled structure. The structure is intended to improve the capability of searching diverse and food solutions. At the lower level there exist several populations, each of which represents a partial solution to the entire problem, and at the upper level there is one population whose individuals represent the entire solutions to the problem. The parallel search with partial solutions at the lower level and the Integrated search with entire solutions at the upper level are carried out simultaneously. The performance of the proposed algorithm is compared with those of the existing algorithms in terms of convergence and diversity. The optimization problems with continuous variables and discrete variables are used as test-bed problems. The experimental results confirm the effectiveness of the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1011-1016
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• 2011

In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equation on $R^N$. we obtained the results under different suitable conditions on the locally H$\"{o}$lder continuous nonlinearity f(x, u), we needn't any mono-tonicity condition about the nonlinearity.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.127-135
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• 1998

Let ${\rho}(A)$ and ${\rho}(B)$ denote the orders of entire functions $A(z)$ and $B(z)$ respectively. Suppose that ${\rho}(A)$ > 1 and 0 < ${\rho}(B){\leq}\frac{1}{2}$, and that ${\rho}$(A) is not an integer. Then it is shown that every nonconstant solution $f$ of $f^{{\prime}{\prime}}+A(z)f^{\prime}+B(z)f=0$ is of infinite order if all the zeros of $A(z)$ lie in a certain angular sector depending on its genus. In addition, we investigate some growth properties of $A(z)$.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.105-114
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• 2005

In this paper we investigate the growth of finite order solutions of the differential equation $f^{(k)}\;+\;A_{k-1}(Z)f^{(k-l)}\;+\;{\cdots}\;+\;A_1(z)f^{\prime}\;+\;A_0(z)f\;=\;F(z)$, where $A_0(z),\;{\cdots}\;,\;A_{k-1}(Z)\;and\;F(z)\;{\neq}\;0$ are entire functions. We find conditions on the coefficients which will guarantees the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. We also estimate the lower bounds of order of solutions if one of the coefficient is dominant in the sense that has larger order than any other coefficients.

• Journal of the Korean Professional Engineers Association
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• v.41 no.3
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• pp.45-49
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• 2008

Considering domestic situation such as economical crisis, $CO_2$ exhaust amount limit based on the Climatic Change Convention, sky-rocketed oil prices. 97% of energy import from abroad, and import sum reaching up to 20% of entire import, we need to invest new recycle energy and future energy development at a full blast.

• Journal of Powder Materials
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• v.16 no.5
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• pp.351-357
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• 2009

A two-step recovery method was developed to produce copper powders from copper chloride waste solution as byproducts of MoO$_3$ leaching process. The first step consisted of replacing noble copper ions with external Fe$^{3+}$ ions which were formed by dissolving iron scraps in the copper chloride waste solution. The replaced copper ions were subsequently precipitated as copper powders. The second step was cementation of entire solution mixture to separate (pure) copper powders from aqueous solution of iron chloride. Cementation process variables of temperature, time, and added amount of iron scraps were optimized by using design of experiment method and individual effects on yield and efficiency of copper powder recovery were investigated. Copper powders thus obtained from cementation process were further characterized using various analytical tools such as XRD, SEM-EDS and laser diffraction and scattering methods.Cementation process necessitated further purification of recovered copper powders and centrifugal separation method was employed, which successfully yielded copper powders of more than 99% purity and average 1$\sim$2$\mu$m in size.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.798-802
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• 2010

The integration of GIS and fuzzy MCDA(Multi-Criteria Decision Analysis) allows the engineer to determine the preferred alternative for each spatial location in the study area. The next step is to recommend to the final decision makers a single flood management alternative for the entire region. Note that if the study area is large, it might be possible to use the kind of information to recommend different alternatives for different portions of the region. However, for this study it is assumed that only a single alternative will be used. In this study, a "cost of uniformity" metric is proposed that allows decision makers to compute the impact of selecting a single alternative for the entire floodplain. This metric represents the increase in the average distance metric value as compared to the spatially diverse solution from the MCDA and GIS analysis. The results could be applied to any region of the floodplain as desired. Whether the decision makers decide to apply these calculations to the entire floodplain or to specific important regions within the floodplain, an analysis of the increases in the cost of uniformity provides an integrated way for the decision maker to rank the alternatives. This should provide an improvement in their engineering analysis.