• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.255-265
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• 2016

In this paper, we define and study the delta alpha derivative on time scales. Many basic properties of delta alpha derivative will be obtained.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.455-466
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• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• Korean Journal of Pharmacognosy
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• v.38 no.4
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• pp.327-333
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• 2007

The chemical composition of the volatile constituents from the leaves, stems, and roots of Acanthopanax senticosus growing wild in Mt. Deok-Yu was determined by GC and GC/MS spectrometric analysis with the aid of NBS, Wiley Library and RI indice searches. The major constituents identified were ${\delta}-elemene\;(23.14%),\;{\beta}-elemene\;(5.59%),\;{\gamma}-cadinene\;(5.43%),\;and\;{\alpha}-bergamotene\;(28.54%)$ in the leaves, ${\alpha}-pinene\;(11.50%),\;{\delta}-elemene\;(17.62%),\;{\alpha}-bergamotene\;(27.21%)$, and bicycloheptane derivative (6.38%) in the stems, and ${\alpha}-pinene\;(21.90%)$, and (+)-aromadendrene (3.77%) in the roots.

• Journal of Pharmaceutical Investigation
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• v.31 no.2
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• pp.125-130
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• 2001

Bucillamine is a novel cysteine derivative with two free intramolecular sulfhydryl groups, and has a preventive and therapeutic effect on adjuvant arthritis, suggesting its antirheumatic action. With respect to the effect on the immune system, bucillamine-exerted such immunoregulating actions are to nomalize an excessive reduction or acceleration in immune reaction. It is useful not only in patients with early stage of rheumatoid arthritis (RA) but also in those with active RA retained for more than 10 years. The purpose of the present study was to evaluate the bioequivalence of two bucillamine tablets, $Rimatil^{TM}$ (Chong Kun Dang Pharmaceutical Co., Ltd.) and $Bucilin^{TM}$ (Kuhn Il Pharmaceutical Co., Ltd.), according to the guidelines of Korea Food and Drug Administration (KFDA). Eighteen normal male volunteers, $23.67{\pm}2.09$ years in age and $65.03{\pm}6.73\;kg$ in body weight, were divided into two groups and a randomized $2{\times}2$ cross-over study was employed. After three tablets containing 100 mg of bucillamine per tablet were orally administered, blood was taken at predetermined time intervals and the concentrations of bucillamine in serum were determined using GC/MS with mass selective detector. Pharmacokinetic parameters such as $AUC_t$, $C_{max}\;and\;T_{max}$ were calculated and ANOVA test was utilized for the statistical analysis of the parameters. The results showed that the differences in $AUC_t$, $C_{max}\;and\;T_{max}$ between two tablets were -0.29%, -3.20% and 8.22%, respectively, when calculated against the $Rimatil^{TM}$ tablet. The powers $(1-{\beta})$ for $AUC_t\;and\;C_{max}$ were 84.31 % and 91.16%, respectively. Minimum detectable differences $({\Delta})$ at ${\alpha}=0.10$ and $1-{\beta}=0.8$ were less than 20% (e.g., 18.58% and 16.51% for $AUC_t\;and\;C_{max}$, respectively). The 90% confidence intervals were within ${\pm}20%$ (e.g.,$-12.77{\sim}12.20$ for $AUC_t$ and $-14.30{\sim}7.90$ for $C_{max}$). Two parameters met the criteria of KFDA for bioequivalence, indicating that $Bucilin^{TM}$ tablet is bioequivalent to $Rimatil^{TM}$ tablet.

• Journal of Pharmaceutical Investigation
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• v.31 no.1
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• pp.57-62
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• 2001

Azelastine, a phthalazinone derivative, is an antiallergic agent which demonstrates histamine $H_1-receptor$ antagonist activity and also inhibits histamine release from mast cells following antigen and non-antigen stimuli. Thus, azelastine may be useful in the management of both asthma and allergic disorders. The purpose of the present study was to evaluate the bioequivalence of two azelastine hydrochloride tablets, $Azeptin^{TM}$ (Bu Kwang Pharmaceutical Co., Ltd.) and $Azela^{TM}$ (Kyung Dong Pharmaceutical Co., Ltd.), according to the guidelines of Korea Food and Drug Administration (KFDA). Eighteen normal male volunteers, $22.44{\pm}2.01$ years in age and $61.99{\pm}6.18\;kg$ in body weight, were divided into two groups and a randomized $2{\times}2$ cross-over study was employed. After two tablets containing 1 mg of azelastine hydrochloride per tablet were orally administered, blood was taken at predetermined time intervals and the concentrations of azelastine in serum were determined using HPLC with fluorescence detector. Pharmacokinetic parameters such as $AUC_t$, $C_{max}\;and\;T_{max}$ were calculated and ANOVA test was utilized for the statistical analysis of the parameters. The results showed that the differences in $AUC_t$, $C_{max}\;and\;T_{max}$ between two tablets were -6.45%, -2.60% and -7.14%, respectively, when calculated against the $Azeptin^{TM}$ tablet. The powers $(1-{\beta})$ for $AUC_t\;and\;C_{max}$ were 96.65% and 88.47%, respectively. Minimum detectable differences $({\Delta})$ at ${\alpha}=0.05$ and $1-{\beta}=0.8$ were less than 20% (e.g., 14.40% and 17.65% for $AUC_t\;and\;C_{max}$, respectively). The 90% confidence intervals were within ${\pm}20%$ (e.g., $-14.87{\sim}1.97$ and $-12.92{\sim}7.72$ for $AUC_t\;and\;C_{max}$, respectively). Two parameters met the criteria of KFDA for bioequivalence, indicating that $Azela^{TM]$ tablet is bioequivalent to $Azeptin^{TM}$ tablet.