• 대한수학회논문집
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• 제12권4호
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• pp.1039-1064
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• 1997

Existence and Uniqueness for Volterra equations (VE) with a weak regularity assumption on A, the relative closedness of A are investigaed by means of the Laplace transform theory. Also, (VE) are studied by means of the method of convoluted solution operator families.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.227-235
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• 2004

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.

• 열처리공학회지
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• 제36권6호
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• pp.389-395
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• 2023

Damping capacities of Mg-2.5%Al and Mg-2.5%Zn (in atomic) solid solutions were comparatively investigated in order to clarify the influence of solutionized Al and Zn elements on the damping characteristics of Mg. In this study, solid solutions with similar grain size were obtained by solution treatment at 678 K for different times (24 h for Mg-2.5%Al and 36 h for Mg-2.5%Zn), followed by water quenching at RT. The Mg-2.5%Al and Mg-2.5%Zn solid solutions showed similar damping capacities in the strain-amplitude independent region of 1 × 10^-6 ~ 1 × 10^-5 and in the strain-amplitude dependent region below 6 × 10^-4, over which the Mg-2.5%Zn solid solution possessed better damping capacity than the Mg-2.5%Al solid solution. The damping tendencies depending on strain-amplitude for the two solid solutions were analyzed and discussed in terms of similar length between weak pinning points (solutes) and different solute/dislocation interaction forces in Granato-Lücke model.

• Bulletin of the Korean Chemical Society
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• 제34권12호
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• pp.3591-3596
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• 2013

The enantioselective aza-Morita Baylis Hillman reaction of nitroalkene and N-tosylimine catalyzed by thiourea-tertiary amine has been investigated using density functional theory. Enantioselectivity is dominated by the cooperative effect of non-covalent and weak covalent interactions imposed by different units of catalyst. As Lewis base, the tertiary amine unit activates nitroalkene via weak covalent bond. The weak covalent interaction orients the reaction in a major path with smaller variations of this bond. The aromatic ring unit activates N-tosylimine via ${\pi}-{\pi}$ stacking. The non-covalent interaction selects the major path with smaller changes of the efficient packing areas. Thiourea unit donates more compact H-bonded network for species of the major path. The calculated ee value in xylene solution phase (97.6%) is much higher than that in N,N-Dimethylformamide (27.2%). Our conclusion is also supported by NBO analysis.

• 대한수학회보
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• 제57권4호
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• pp.1003-1031
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• 2020

We consider the following Dirichlet initial boundary value problem with a gradient absorption and a nonlocal source $$\frac{{\partial}u}{{\partial}t}-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)={\lambda}u^k{\displaystyle\smashmargin{2}{\int\nolimits_{\Omega}}}u^sdx-{\mu}u^l{\mid}{\nabla}u{\mid}^q$$ in a bounded domain Ω ⊂ ℝ^N, where p > 1, the parameters k, s, l, q, λ > 0 and µ ≥ 0. Firstly, we establish local existence for weak solutions; the aim of this part is to prove a crucial priori estimate on |∇u|. Then, we give appropriate conditions in order to have existence and uniqueness or nonexistence of a global solution in time. Finally, depending on the choices of the initial data, ranges of the coefficients and exponents and measure of the domain, we show that the non-negative global weak solution, when it exists, must extinct after a finite time.

• 대한수학회보
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• 제51권2호
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• pp.479-499
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• 2014

In this paper, we propose new iteration methods for finding a common point of the solution set of a pseudomonotone equilibrium problem and the solution set of a monotone equilibrium problem. The methods are based on both the extragradient-type method and the viscosity approximation method. We obtain weak convergence theorems for the sequences generated by these methods in a real Hilbert space.

• 대한수학회지
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• 제44권3호
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• pp.585-603
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• 2007

The author studies the local $H\ddot{o}lder$ convergence of the solution to an evolution equation of p-Ginzburg-Landau type, to the heat flow of the p-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

• 대한화장품학회지
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• 제13권1호
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• pp.29-35
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• 1987

Purely synthesized L-ascorbic acid 2 phosphate Mg salt (1 AsA PMg) improved the weak point of ascorbic acid which is easily decomposed in water solution. This compound is hydrolyzed with phosphatase of skin to corresponding ascorbic acid giving Vitamine C activities. The buffer solution of potassium acetate 0.5% and citric acid 0.005% and the sodium sulfite respectively showed good stabilizing effect of the AsA PMg solution. Compared to the other ascorbic acid derivatives the good solubility of AsA PMg gives broad application to cosmetic field.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1419-1432
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• 2023

In this study, we take into account interval-valued vector optimization problems (IVOP) and obtain their relationships to interval vector variational inequalities (IVVI) of Stampacchia and Minty kind in aspects of convexificators, as well as the (IVOP) LU-efficient solution under the LU-convexity assumption. Additionally, we examine the weak version of the (IVVI) of the Stampacchia and Minty kind and determine the relationships between them and the weakly LU-efficient solution of the (IVOP). The results of this study improve and generalizes certain earlier results from the literature.

• 대한수학회보
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• 제35권3호
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• pp.485-490
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• 1998

We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.