• East Asian mathematical journal
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• 제29권3호
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• pp.349-353
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• 2013

In this paper, we study equations over nilpotent groups of class 2. We show that there are some overgroups which contains solutions of equations with exponent sum 1 over nilpotent groups of class 2. As known, equations over a field has a solution in an extension field which contains a copy of the given field. But it is not easy to find that a solution of equations over groups. In many cases, even if equations over groups has a solution, the overgroup is not concrete but very Here we find the concrete overgroups in case of nilpotent groups.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.517-522
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• 2006

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability of the multi-additive functional equation $f(x1+x2,y1+y2,z1+z2)={\Sigma}_{1{\le}i,j,k{\le}2}\;f(x1,yj,zk)$.

• 대한수학회보
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• 제34권4호
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• pp.561-571
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• 1997

The general (continuous) solution and the asymptotic behaviors of the unbounded solution of the functional equation $f(x + y)^2 = af(x)f(y) + bf(x)^2 + cf(y)^2$ and the Hyers-Ulam stability of that functional equation for the case when a = 2 and b = c = 1 shall be investigated.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.513-519
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Jensen's functional equation $$2f(\frac{x_1+y_1}{2},\;\cdots,\;\frac{x_n+y_n}{2})=f(x_1,\;\cdots,\;x_n)+f(y_1,\;\cdots,\;y_n)$$. The function f given by $f(x_1,\;\cdots,\;x_n)=a_1x_1+{\cdots}+a_nx_n+b$ is a solution of the above functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.103-110
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• 2008

In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form $f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$ is a solution of the above functional equation.

• Biomolecules & Therapeutics
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• 제4권2호
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• pp.154-161
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• 1996

General pharmacological properties of LB-00014, an erythropoietin which was produced by recombinant DNA technique in Biotech Research Institute, LG Chemical Ltd. were examined. The administration of LB-00014 (60, 600, 6000 IU/kg, iv) in mice had no effect in general behavior and central nervous system, and no influences on normal body temperature, writhing syndromes induced by 0.7% acetic acid solution and chemoshock produced by strychnine and pentetrazole solution. LB-00014 (60, 600, 6000 IU/kg, iv) given to anesthetized rabbits showed no effect on blood pressure of carotid artery and respiration rates, and it did not influence the responses produced by injection of acetylcholine or epinephme. The administration of LB-00014 (601, 600, 6000 IU/kg, iv) in rats had no effect on the plasma prothrombin time, activated partial thromboplastin time and hemolytic action. The platelet aggregation induced by collagen in human plasma was not influenced by LB-00014 (10, 100, 1000 lU/kg, iv). It showed no direct effect at 100 and 1000IU/m1 in isolated stomach fundus and uterus of rats and ileum of guinea-pig, and it also had no inhibition of contraction produced by acetylcholine, oxytocin, serotonin and histamine in the above-mentioned preparations. It did not influence gastric secretion, pH and acid output at 6000 IU/kg, iv in rats, but showed a significant increase in intestinal propulsion of mice at 6000 IU/kg, iv. Its administration (60, 600, 6000 lU/kg, iv) caused no effect on urine and electrolyte excretion in rats. These results indicate that LB-00014 does not exsert any of serious pharmacological effects.

• Corrosion Science and Technology
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• 제20권6호
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• pp.367-372
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• 2021

The effect of carbon addition on the general corrosion behavior of high-chromium cast iron (HCCI) was studied by a scanning electron microscope with energy dispersive spectroscopy (SEM-EDS) or electron back-scattered diffraction (EBSD), or electrochemical polarization techniques in 0.1 mol dm^-3 H₂SO₄ + 0.05 mol dm^-3 HCl at room temperature. The addition of 2.1-2.8 wt% carbon to HCCI increased the fraction of eutectic austenite and eutectic carbide phases, while that of HCCI decreased the fraction of the primary austenitic phase. Potentiostatic polarization of the HCCI at -0.35 V_SSCE or 0.0 V_SSCE resulted in preferential general corrosion of the primary austenitic or eutectic austenitic phases, respectively. The decrease in corrosion current density and the shift in noble corrosion potential direction with increasing carbon content in the HCCI indicated that the fraction and the chemical composition of austenitic (primary and eutectic) and carbide phases were strongly related to the general corrosion behavior of the HCCI.

• 한국경영과학회지
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• 제18권2호
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• pp.147-156
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• 1993

Recently a new concept of shadow prices, called average shadow price, has been developed. This paper provides a dual problem and the corresponding duality theorems justifying this new shadow price. The general duality framework is used. As an important secondary result, a new reduced class of price function, the pp. h.-class, has been developed for the general duality theory. This should be distinguished from other known reductions achieved in some specific areas of mathematical programming, in that it sustains the strong duality property in all the mathematical programs. The new general dual problem suggested with this pp. h.-class provides, as an optimal solution, the average shadow prices.

• 경영과학
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• 제33권1호
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• pp.77-87
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• 2016

I study optimal consumption and investment choices of an infinitely-lived economic agent with a general time-separable von Neumann-Morgenstern utility under general borrowing constraints against future labor income. An explicit solution is provided by the dynamic programming method. It is shown that the optimal consumption and risky investment decrease as the borrowing constraints become stronger.

• 대한수학회지
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• 제58권6호
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• pp.1433-1448
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• 2021

In the present work, we investigate a viscoelastic equation involving a logarithmic nonlinear source term. After proving the existence of solutions, we establish a general decay estimate of the solution using energy estimates and theory of convex functions. This result extends and complements some previous results of [9, 21].