• Journal of the Korean Society for Precision Engineering
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• v.9 no.3
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• pp.140-148
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• 1992

The effect of mechanical, properties in the plastic zone near the crack-tip was investigated, under various controlled loading conditions, i.e., ${\Delta}K$ increasing, ${\Delta}K$ decreasing, and single overload test. For both ${\Delta}K$ decreasing test and ${\Delta}K$ increasing test with constant stress ratio, it is found that the ratio of material constant m'( ${\Delta}K$ decreasing test) to material constant m( ${\Delta}K$ increasing test) is larger than 1 for n<0.1, and it is equal to 1 for 0.10.2. A modified crack growth rate equation based on Forman's equation which applied stable region of fatigue crack propagation in ${\Delta}K$ decreasing test is proposed. Within the limit of this single overload test, an empirical relation between among the retardation ratio (Nd/ $N^{*}$), the strain hardening exponent (n) and the percent peak load (%PL) has been established.established.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1131-1145
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• 2012

The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with p-Laplacian type operators $$\{({\alpha}(t,x^{\Delta}(t)))^{\Delta}-a(t){\phi}_p(x^{\sigma}(t))+f({\sigma}(t),x^{\sigma}(t))=0,\;{\Delta}-a.e.\;t{\in}I\\x^{\sigma}(0)=0,\\{\beta}_1x^{\sigma}(1)+{\beta}_2x^{\Delta}({\sigma}(1))=0,$$ where ${\beta}_1$, ${\beta}_2$ > 0, $I=[0,1]^{k^2}$, ${\alpha}({\cdot},x({\cdot}))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.

• East Asian mathematical journal
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• v.34 no.5
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• pp.643-649
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• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.

• Bulletin of the Korean Chemical Society
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• v.8 no.1
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• pp.31-39
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• 1987

By using a complete rate constant($k_e$) which treats a solvent (water) as a reactant, and a conventional rate constant($k_c$), which ignores the solvent in describing the rate, the parameters ${\Delta}V^{\neq}_s,\;{\Delta}H^{\neq}_s\;and\;{\Delta}S^{\neq}_s$ were introduced. These quantities represent the volume change, the enthalpy change, and the entropy change accompanying the electrostriction which occurs when solvent molecules condense on the activated complex. The authors measured the rates of the solvolysis of benzoyl chloride in water-acetone mixtures at $15^{\circ}$ to $30^{\circ}C$ and 1 bar to 2500 bars. Applying the authors' theory to the experimental results, the parameters, ${\Delta}V^{\neq}_s,\;{\Delta}H^{\neq}_s\;and\;{\Delta}S^{\neq}_s$ were evaluated, and it was found that they are all negative, indicating that water dipoles condense on the activated complex. They also proposed the following equations: ${\Delta}H^{\neq}_c\;=\;{\Delta}H^{\neq}_e\;+\;{\Delta}H^{\neq}_s\;and\; {\Delta}S^{\neq}_c\;=\;{\Delta}S^{\neq}_e\;+{\Delta}S^{\neq}_s\;,\;where\;{\Delta}H^{\neq}_c\;and\;{\Delta}H^{\neq}_c\;and\;{\Delta}S^{\neq}_s $are the activation enthalpy change and the activation entropy change for the conventional reaction rate, respectively, and ${\Delta}H^{\neq}_e$ and ${\Delta}S^{\neq}_e$ are the corresponding quantities for the complete reaction rate. The authors proposed that for the $SN_1$ type, all the quantities, ${\Delta}V^{\neq}_s,\;{\Delta}S^{\neq}_s\;,{\Delta}H^{\neq}_s\;and\;{\Delta}S^{\neq}_s$ are comparatively large, and for the $SN_2$ type, these quantities are smaller than for the $SN_1$ type, and occasionally the case ${\Delta}S^{\neq}_e$ < 0 occurs. Using these criteria, the authors concluded that at high temperature, high pressure and for a high water content solvent, the SN_1$ type mechanism predominates whereas in the reversed case the $SN_2$M type predominates.

• East Asian mathematical journal
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• v.33 no.5
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• pp.571-585
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• 2017

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigen vectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we showed that a 2-type surface M in $E^3$ satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle},{\rangle}$ is the usual inner product in $E^3$, then M is an open part of a circular cylinder. Also we showed that if a quadric hypersurface M in a Euclidean space satisfies ${\langle}{\Delta}x,x{\rangle}=c$ for a constant c, then it is one of a minimal quadric hypersurface, a genaralized cone, a hypersphere, and a spherical cylinder.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.225-231
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• 1999

Let Mf(x) be the Hardy-Littlewood maximal function on $\mathbb{R}^n$. Let $\Phi$ and $\Psi$ be functions satisfying $\Phi$(t) = ${\int^t}_0$a(s)ds and $\Psi(t)$ = ${\int^t}_0$b(s)ds, where a(s) and b(s) are positive continuous such that ${\int^\infty}_0\frac{a(s)}{s}ds$ = $\infty$ and b(s) is quasi-increasing. We show that if there exists a constant $c_1$ so that ${\int^s}_0\frac{a(t)}{t}dt\;c_1b(c_1s)$ for all $s\geq0$, then there exists a constant $c_1$ such that(0.1) $\int_{\mathbb{R^{n}}$ $\Phi(Mf(x))dx\;\leq\;c_2$ $\int_\mathbb{R^{n}}$$\Psi(c_2\midf(x)\mid)dx$ for all $f\epsilonL^1(R^n_$. Conversely, if there exists a constant $c_2$ satisfying the condition (0.1), then there exists a constant $c_1$ so that ${\int^s}_\delta\frac{a(t)}{t}dt=;\leq\;c_1b(c_1s$ for all $\delta$ > 0 and $s\geq\delta$.

• Journal of the Korean Chemical Society
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• v.18 no.5
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• pp.320-328
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• 1974

It is unable to derive the standard emf ($E^{\circ}$) of the cell at high pressure from the conventional method. However, when the concept of the complete equilibrium constant($K{\circ})$) is available to the conventional Nernst equation, it is possible to get the standard emf of the cell at high pressure(complete Nernst equation). Moreover, the other thermodynamic properties, such as the net change of solvation number(k), the compressibility of solvent(${\beta}$), ionization constant(K), the standard free energy change(${\Delta}G^{\circ}$), the standard enthalpy change(${\Delta}H^{\circ}$) and the standard entropy change (${\Delta}S^{\circ}$) of the cell reaction at equilibrium state have been also obtained. In this experiment, the emf of the cell; 12.5 % Cd(Hg)│$CdSO_4(3.105{\times}10^{-3}M),\;Hg_2SO_4│Hg$ have bee measured at temperature from 20 to $35^{\circ}C$ and at pressures from 1 to 2500 atms. The emf of the cell increased with increasing pressure at constant temperature, and did with increasing temperature at constant pressure. The net change of solvation number(k) of the cell reaction was 41.96 at $25^{\circ}C$, and kept constant value with pressure, while, K and ${\Delta}S^{\circ}$ increased with pressure, but whereas ${\Delta}G^{\circ}$ and ${\Delta}H^{\circ}$ decreased. Since the standard emf of the cell at high pressure can be calculated from the complete Nernst equation, the theory of chemical equilibrium could be developed with at high pressure as well as at the atmosphere.

• International Union of Geodesy and Geophysics Korean Journal of Geophysical Research
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• v.21 no.1
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• pp.17-30
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• 1993

The basic processes responsible for the generation of oceanic fronts were reviewed. In particular the process of a shelf sea front produced by tidal stirring was identified from the one dimensional model of the water column in the coastal area, which incorporates the microscale process for the formation of a tidal front. Also a new criterion to predict its location was suggested. The time evolutions of the distributions of density and turbulent kinetic energy calculated from the model show that the criterion for the formation of a thermocline can be predicted as $R{\delta}^4$~ constant for large $\delta$ ($\delta$＞0.5), but the dependence on $\delta$ decreases as $\delta$ goes to O, where $R=H^4Q/{K_b}^3$,{\;}{\delta}=1-Do/H$, Q is the buoyancy flux at the surface, $K_b$ is the eddy diffusivity maintained at the bottom and Do is the depth of a thermocline in the absence of bottom mixing. The depth of a thermocline was found to decrease as the bottom mixing increases for a given value of Do. The results were interpreted in comparison with the previous studies.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• Journal of Photoscience
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• v.12 no.3
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• pp.113-117
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• 2005

Spectroscopic investigations on the interaction of gabapentin (GBP) with bovine serum albumin (BSA) were reported. The association constant of GBP-BSA system was determined at different temperatures (298, 302, 306 and 311 K) based on the fluorescence quenching results. The GBP was found to quench the fluorescence of BSA through static mechanism. Thermodynamic parameters, the standard enthalpy change, $({\Delta}H^o)$ and the standard entropy change $({\Delta}S^o)$ were observed to be $-9.61{\pm}0.008\;kJ\;mol^{-1}$ and $3.58{\pm}0.011\;Jmol^{-1}K{-1}$ respectively. These indicated that the hydrophobic and electrostatic forces played a role in the interaction of GBP with BSA. The negative value of ${\Delta}G^o$ revealed that the binding reaction is spontaneous. The circular dichroism studies indicated the conformational changes in BSA upon interaction with GBP. The effect of some metal ions on the binding constant was also investigated.