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

• YAKHAK HOEJI
• /
• v.22 no.4
• /
• pp.238-241
• /
• 1978

A simple and convenient method of detecting N, N-dimethy laniline (D.M.A.) residues in ampicillin trihydrate (A.T.) was established. D.M.A. was extracted by chloroform from the chloroform presaturated N/10-ammonia water solution of A.T. and chromatographed on silica gel G thin layer. Blue spot appeared in 15minutes after spray of 2, 6-dichloroquinonechlorimide solution was compared with the blue spot of reference concomitantly processed. The developing solvent was prepared by mixing equal volume of cyclohexane and chloroform. To quantitate the amount of D.M.A. in A.T., T.L.C. was performed with the Eastmann Chromatogram sheet, then color density was measured by Cosmo Superclick densitometer. The developing solvent at this time was cyclohexane-chlorofonn (3+7) mixture. The peak areas obtained with the amount of D.M.A ranging from 0.05 to 2.0 .mu.g were linear to color density. Better sensitive results would be available with the densitometer equipped with monochromator.

• Journal of the Korean Society of Fisheries and Ocean Technology
• /
• v.9 no.1
• /
• pp.1-18
• /
• 1973

For regulating the depth of midwater trawl nets towed at the optimum constant speed, the changes in the shape of warps caused by adding a weight on an arbitrary point of the warp of catenary shape is studied. The shape of a warp may be approximated by a catenary. The resultant inferences under this assumption were experimented. Accordingly feasibilities for the application of the result of this study to the midwater trawl nets were also discussed. A series of experiments for basic midwater trawl gear models in water tank and a couple of experiments of a commercial scale gears at sea which involve the properly designed depth control devices having a variable attitude horizontal wing were carried out. The results are summarized as follows: 1. According to the dimension analysis the depth y of a midwater trawl net is introduced by $$y=kLf(\frac{W_r}{R_r},\;\frac{W_o}{R_o},\;\frac{W_n}{R_n})$$) where k is a constant, L the warp length, f the function, and $W_r,\;W_o$ and $W_n$ the apparent weights of warp, otter board and the net, respectively, 2. When a boat is towing a body of apparent weight $W_n$ and its drag $D_n$ by means of a warp whose length L and apparent weight $W_r$ per unit length, the depth y of the body is given by the following equation, provided that the shape of a warp is a catenary and drag of the warp is neglected in comparison with the drag of the body: $$y=\frac{1}{W_r}\{\sqrt{{D_n^2}+{(W_n+W_rL)^2}}-\sqrt{{D_n^2+W_n}^2\}$$ 3. The changes ${\Delta}y$ of the depth of the midwater trawl net caused by changing the warp length or adding a weight ${\Delta}W_n$_n to the net, are given by the following equations: $${\Delta}y{\approx}\frac{W_n+W_{r}L}{\sqrt{D_n^2+(W_n+W_{r}L)^2}}{\Delta}L$$ $${\Delta}y{\approx}\frac{1}{W_r}\{\frac{W_n+W_rL}{\sqrt{D_n^2+(W_n+W_{r}L)^2}}-{\frac{W_n}{\sqrt{D_n^2+W_n^2}}\}{\Delta}W_n$$ 4. A change ${\Delta}y$ of the depth of the midwater trawl net by adding a weight $W_s$ to an arbitrary point of the warp takes an equation of the form $${\Delta}y=\frac{1}{W_r}\{(T_{ur}'-T_{ur})-T_u'-T_u)\}$$ Where $$T_{ur}^l=\sqrt{T_u^2+(W_s+W_{r}L)^2+2T_u(W_s+W_{r}L)sin{\theta}_u$$ $$T_{ur}=\sqrt{T_u^2+(W_{r}L)^2+2T_uW_{r}L\;sin{\theta}_u$$ $$T_{u}^l=\sqrt{T_u^2+W_s^2+2T_uW_{s}\;sin{\theta}_u$$ and $T_u$ represents the tension at the point on the warp, ${\theta}_u$ the angle between the direction of $T_u$ and horizontal axis, $T_u^2$ the tension at that point when a weights $W_s$ adds to the point where $T_u$ is acted on. 5. If otter boards were constructed lighter and adequate weights were added at their bottom to stabilize them, even they were the same shapes as those of bottom trawls, they were definitely applicable to the midwater trawl gears as the result of the experiments. 6. As the results of water tank tests the relationship between net height of H cm velocity of v m/sec, and that between hydrodynamic resistance of R kg and the velocity of a model net as shown in figure 6 are respectively given by $$H=8+\frac{10}{0.4+v}$$ $$R=3+9v^2$$ 7. It was found that the cross-wing type depth control devices were more stable in operation than that of the H-wing type as the results of the experiments at sea. 8. The hydrodynamic resistance of the net gear in midwater trawling is so large, and regarded as nearly the drag, that sweeping depth of the gear was very stable in spite of types of the depth control devices. 9. An area of the horizontal wing of the H-wing type depth control device was $1.2{\times}2.4m^2$. A midwater trawl net of 2 ton hydrodynamic resistance was connected to the devices and towed with the velocity of 2.3 kts. Under these conditions the depth change of about 20m of the trawl net was obtained by controlling an angle or attack of $30^{\circ}$.

• 한국생물공학회:학술대회논문집
• /
• 2001.11a
• /
• pp.646-647
• /
• 2001

The enzymatic synthesis of conjugates of lysine and aspartic acid with D-glucose was studied. Optimase M-440 showed the very poor regioselectivity in the transesterification of $N{\alpha}$,$N'{\varepsilon}-di-t-Boc-L-Lys-OTFE$ and N-t-Boc-L-Asp-diOTFE with D-glucose. The acylation of glycosidic -OH and primary -OH of D-glucose occurred. However, Optimase M-440 catalyzed only the acylation of primary -OH group in the transesterification of $N{\alpha}$,$N'{\varepsilon}-di-t-Boc-L-Lys-OTFE$ and N-t-Boc-L-Asp-diOTFE with ${\alpha}-$ and ${\beta}-methylglucopyranoside$ in high yields without any other transesterification. Optimase M-440 also discriminated carboxyl groups of N-t-Boc-L-Asp-diOTFE.

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.35C no.5
• /
• pp.11-16
• /
• 1998

We analyze the software reliability growth models for the specified period from the viewpoint of theory of differential equations. we defien a genralized form of reliability growth models as follws: dN(t)/dt = b(t)f(N(t)), Where N(t) is the number of remaining faults and b(t) is the failure rate per software fault at time t. We show that the well-known three software reliability growth models - Goel - Okumoto, s-shaped, and Musa-Okumoto model- are special cases of the generalized form. We, also, extend the generalized form into an extended form being dN(t)/dt = b(t, .gamma.)f(N(t)), The genneralized form can be obtained if the distribution of failures is given. The extended form can be used to describe a software reliabilit growth model having weibull density function as a fault exposure rate. As an application of the generalized form, we classify three mentioned models according to the forms of b(t) and f(N(t)). Also, we present a case study applying the generalized form.

• Journal of the Korean Mathematical Society
• /
• v.41 no.5
• /
• pp.773-793
• /
• 2004

We consider a system of particles with locations { $X_{i}$ $^{n}$ (t):t$\geq$0,i＝1,…,n} in $R^{d}$ , time-varying weights { $A_{i}$ $^{n}$ (t) : t $\geq$0,i ＝ 1,…,n} and weighted empirical measure processes $V^{n}$ (t)＝1/n$\Sigma$$_{i=1}$$^{n}$ $A_{i}$ $^{n}$ (t)$\delta$ $X_{i}$ $^{n}$ (t), where $\delta$$_{x}$ is the Dirac measure. It is known that there exists the limit of { $V_{n}$ } in the week* topology on M( $R^{d}$ ) under suitable conditions. If { $X_{i}$ $^{n}$ , $A_{i}$ $^{n}$ , $V^{n}$ } satisfies some diffusion equations, applying Ito formula, we prove a central limit type theorem for the empirical process { $V^{n}$ }, i.e., we consider the convergence of the processes η$_{t}$ $^{n}$ ≡ n( $V^{n}$ -V). Besides, we study a characterization of its limit.t.

• 한국생물공학회:학술대회논문집
• /
• 2003.04a
• /
• pp.343-347
• /
• 2003

Power of loess ball on nitrogen and phosphorous removal in wastewater treatment were investigated. flow line A ( anaerobic${\rightarrow}$oxic${\rightarrow}$anoxic(organic source methanol)${\rightarrow}$p-absorption) showed the results of T-P 0.5, T-N 1.0, and COD 10ppm bellow, and flow line B ( oxic${\rightarrow}$anoxic, organic source: methanol${\rightarrow}$p-absorption) showed the results of T-P 0.3, T-N 5.0, and COD 15 ppm bellow. flow line C ( anaerobic${\rightarrow}$oxic${\rightarrow}$anoxic, organic source: wastewater ${\rightarrow}$ p-absorption) showed the results of T-P 0.6, T-N 10, and COD 15 ppm bellow, and flow line D ( oxic${\rightarrow}$anoxic, organic source: methanol${\rightarrow}$p-absorption) showed the results of T-P 1, T-N 8m, and COD 20 ppm bellow. So the results of these experiments showed the probability of loess ball in wastewater treatment.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.63-78
• /
• 1999

Let $\mu$(x) be an increasing function on the real line with finite moments of all oeders. We show that for any linear operator T on the space of polynomials and any interger n $\geq$ 0, there is a constant $\gamma n(T)\geq0$, independent of p(x), such that $\parallel T_p\parallel\leq\gamma n(T)\parallel P\parallel$, for any polynomial p(x) of degree $\leq$ n, where We find a formular for the best possible value $\Gamma_n(T)\;of\;\gamma n(T)$ and estimations for $\Gamma_n(T)$. We also give several illustrating examples when T is a differentiation or a difference operator and $d\mu$(x) is an orthogonalizing measure for classical or discrete orthogonal polynomials.

• Journal of Life Science
• /
• v.19 no.6
• /
• pp.765-769
• /
• 2009

Recent studies have reported that the distribution of HPV-16 sequence variation differs geographically, and more specifically that HPV-16 E6/E7 intratypic variants might carry a high risk for development of ICC (invasive cervical cancer) and CIN (cervical intraepithelial neoplasia) in a given population. To investigate the genetic diversities of HPV-16 E6/E7 oncogene by region, we collected nineteen HPV-16 isolates from sexually high-risk women in Busan, and analyzed the HPV-16 E6/E7 coding regions (nt 34 to 880) with HPV-16 E6/E7 specific PCR amplification. At the nucleotide levet eleven variants of the E6 genes and nine variants of the E7 genes were identified as follows: E6 T178G (n=l1), E6 T178A (n=l), E6 T350G (n=3), E6 A442C (n=2), E6 AI04T, E6 All1G, E6 C116T, E6 G145T, E6 T183G, E6 C335T, E6 G522C and E7 A647G (n=12), E7 A645C, E7 A777C, E7 G663A, E7 T732C, E7 T760C, E7 A775T, E7 T789C and E7 T795G, respectively. At the amino acid levet the isolated HPV-16 E6 and E7 genes showed eleven E6 variants: E6 D25E (n=12), E6 L83V (n=4), E6 E113D (n=2), E6 MIL, E6 Q3R, E6 P5S, E6 Q14H, E6 D25N, E6 127R, E6 H78Y, E6 C140S and three E7 variants: N29S (n=12), L28F, T72S. HPV16 E6 L83V, the dominant variant in the Caucasian population, showed relatively low frequencies in our study population. We elucidated that the dominant HPV-16 E6/E7 variants were HPV-16 E6 D25E (63.2%) and HPV-16 E7 N29S (63.2%), which were phylogenetically included in Asian lineage. Further study is needed to evaluate the risk of cervical cancer related HPV-16 E6/E7 intratypic variants in the Korean population.

• Journal of Ocean Engineering and Technology
• /
• v.7 no.2
• /
• pp.131-140
• /
• 1993

To study the corrosion fatigue begavior of T.M.C.P. steel, the rotary bending fatigue test with the change of concentration of NaCl solution was carried out. Fatigue life in the corrosion environment is decreased markedly in comparision with that in the air. Fatigue limit in the air was about 225 MPa. In case of 3.5% NaCl solution fatigue life could be expressed as .sigma./sub f/=10,392 * (N/sub f/)/sup -o.2923 . According to the paris's rule, crack growth rates could be expressed as da/dN=2.62.*10/sup -7/ .DELTA. K/sup 1.09/(3.5% NaCl solution), da/dN=1.95 *10/sup -7 .DELTA. K/sup 1.05/(1% NaCl solution), da/dN=2.62 * 10/sup -7/.DELTA./sup 0.72/(0.01% NaCl solution) with da/dN expressed in mm/cycle and .DELTA.K in MPa.GAMMA.m. The crack growth rate in the corrosion environment was highest under 3.5% NaCl solution.