• Korean Journal of Mathematics
• /
• v.24 no.3
• /
• pp.545-565
• /
• 2016

In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: $$T_{\lambda}(f;x)={\large\int_{\Omega}}K_{\lambda}(t,x,f(t))dt,\;x{\in}{\Psi},\;{\lambda}{\in}{\Lambda}$$, where ${\Psi}$ = and ${\Omega}$ = stand for arbitrary closed, semi-closed or open bounded intervals in ${\mathbb{R}}$ or these set notations denote $\mathbb{R}$, and ${\Lambda}$ is a set of non-negative numbers, to the function $f{\in}L_{p,{\omega}}({\Omega})$, where $L_{p,{\omega}}({\Omega})$ denotes the space of all measurable functions f for which $\|{\frac{f}{\omega}}\|^p$ (1 ${\leq}$ p < ${\infty}$) is integrable on ${\Omega}$, and ${\omega}:{\mathbb{R}}{\rightarrow}\mathbb{R}^+$ is a weight function satisfying some conditions.

• The Korean Journal of Pain
• /
• v.20 no.1
• /
• pp.8-14
• /
• 2007

Background: Anticonvulsants and antidepressants are adjuvant analgesic drugs that are used widely for treating chronic neuropathic pain syndromes. The combined analgesic effect of gabapentin and milnacipran was investigated with a rat neuropathic pain model. Methods: The rat neuropathic pain model was made by ligating the spinal nerves (L5 and L6). An intrathecal catheter was inserted into the subarachnoid space. Tactile allodynia was tested with the up-down method using von Frey hair. We determined the antiallodynic effect of intraperitoneal (I.P.) and intrathecal (I.T.) gabapentin. The combined effect of I.P. gabapentin (50 mg/kg) and milnacipran (0, 10 and 30 mg/kg) was investigated. Results: Intraperitoneal and intrathecal administration of gabapentin increased the threshold for tactile allodynia (the ED50 was 60.6 mg/kg and $45.5{\mu}g$, respectively). Co-administration of I.P. milnacipran increased the antiallodynic effect of I.P. gabapentin in a dose-dependent fashion. Conclusion: The combined administration of milnacipran and gabapentin may increase the total analgesic effect during treatment of neuropathic pain.

• Journal of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.235-254
• /
• 2022

Let ℍⁿ be the Heisenberg group and Q = 2n + 2 be its homogeneous dimension. Let 𝓛 = -∆_ℍⁿ + V be the Schrödinger operator on ℍⁿ, where ∆_ℍⁿ is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class $B_{q_1}$ for q₁ ≥ Q/2. Let H^p_𝓛(ℍⁿ) be the Hardy space associated with the Schrödinger operator 𝓛 for Q/(Q+𝛿₀) < p ≤ 1, where 𝛿₀ = min{1, 2 - Q/q₁}. In this paper, we consider the Hardy type estimates for the operator T_𝛼 = V^𝛼(-∆_ℍⁿ + V )^-𝛼, and the commutator [b, T_𝛼], where 0 < 𝛼 < Q/2. We prove that T_𝛼 is bounded from H^p_𝓛(ℍⁿ) into L^p(ℍⁿ). Suppose that b ∈ BMO^𝜃_𝓛(ℍⁿ), which is larger than BMO(ℍⁿ). We show that the commutator [b, T_𝛼] is bounded from H¹_𝓛(ℍⁿ) into weak L¹(ℍⁿ).

• Journal of The Korean Astronomical Society
• /
• v.39 no.2
• /
• pp.41-50
• /
• 2006

We present the results of new multi-color CCD photometry for the contact binary XZ Leo, together with reasonable explanations for the period and light variations. Six new times of minimum light have been determined. A period study with all available timings confirms Qian's (2001) finding that the O-C residuals have varied secularly according to $dP/dt\;=\;+8.20{\times}10^{-8}\;d\;yr^{-l}$. This trend could be interpreted as a conservative mass transfer from the less massive cool secondary to the more massive hot primary in the system with a mass flow rate of about $5.37{\times}10^{-8}\;M_{\odot}\;yr^{-l}$. By simultaneous analysis of our light curves and the previously published radial-velocity data, a consistent set of light and velocity parameters for XZ Leo is obtained. The small differences between the observed and theoretical light curves are modelled by a blue third light and by a hot spot near the neck of the primary component. Our period study does not support the tertiary light but the hot region which may be formed by gas streams from the cool secondary. The solution indicates that XZ Leo is a deep contact binary with the values of q=0.343, $i=78^{\circ}.8$, ${\Delta}(T_1-T_2)=126\;K$, and f=33.6 %, differing much from those of Niarchos et al. (1994). Absolute parameters of XZ Leo are determined as follows: $M_1=1.84\;M_{\odot},\;M_2=0.63\;M_{\odot},\;R_1=1.75\;R_{\odot},\;R_2=1.10\;R_{\odot},\;L_1=7.19\;L_{\odot},\;and\;L_2=2.66\;L_{\odot}$.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
• /
• v.19 no.1
• /
• pp.105-121
• /
• 1989

The author analysed tomograms and submento-vertex radiograms of 90 temporomandibular joints from 45 asymptomatic young adults. 15 had Angle class Ⅰ malocclusion, 15 classⅡ and 15 class Ⅲ. Corrected lateral tomograms were obtained in three condylar positions; centric occlusion, centric relation and 1 inch mouth opening. The condylar angulation, depth of cut, joint spaces were analysed in each radiogram. The obtained results were as follows; 1. The mean condylar angulation in Angle class Ⅰ, Ⅱ, Ⅲ group was 17.55±5.51° 13.33±8.85° 16.25±6.60° respectively, and there was no significant difference in each group. The mean condylar angulation of right side (16.62±7.23°) was larger than left side (14.80±7.33°). 2. The mean depth of cut in Angle class Ⅰ, Ⅱ, Ⅲ group was 8.13±1.61㎝, 3.05±3.80㎝, 7.75±2.19㎝, respectively. Angle class Ⅰ and class Ⅱ group revealed significant difference in measurement (p<0.0l). 3. The mean height of articular fossa in Angle class Ⅰ, Ⅱ, Ⅲ group was 8.67±3.06㎜, 9.61±2.57㎜, 8.93±2.83㎜, respectively. And the mean width of articular fossa was 19.90±2.80㎜, 19.48±3.83㎜, 20.36±4.82㎜, respectively. 4. The mean height and width of condylar head was 5.11±1.16㎜, 11.20±2.26㎜, respectively. 5. In centric occlusion, the superior joint space was the largest (3.42±1.42㎜), followed by anterior joint space (2.94±1.95㎜) and the posterior joint space (2.64±1.19㎜. In centric relation, the anterior joint space was the largest (3.86±2.17㎜), followed by the superior joint space (3.64±3.68㎜) and the posterior joint space (1.18±0.77㎜). 6. The displaced measurement from centric relation to centric occlusion was 1.10±1.04㎜ anteriorly and 0.24±0.97㎜ inferiorly. In 1 inch mouth opening state, the condylar head displaced posteroinferiorly (2.49±2.49㎜ posteriorly, 1.17±1.34㎜ inferiorly) from the apex of articular eminence. And Angle class Ⅰ and Ⅱ group, Angle class Ⅱ and Ⅲ group revealed significant difference in posterior measurement, respectively (p<0.01).

• The Korean Journal of Physiology and Pharmacology
• /
• v.13 no.6
• /
• pp.491-496
• /
• 2009

Skeletal muscle atrophy is a common phenomenon during the prolonged muscle disuse caused by cast immobilization, extended aging states, bed rest, space flight, or other factors. However, the cellular mechanisms of the atrophic process are poorly understood. In this study, we investigated the involvement of mitogen-activated protein kinase (MAPK) in the expression of muscle-specific RING finger 1 (MuRF1) during atrophy of the rat gastrocnemius muscle. Histological analysis revealed that cast immobilization induced the atrophy of the gastrocnemius muscle, with diminution of muscle weight and cross-sectional area after 14 days. Cast immobilization significantly elevated the expression of MuRF1 and the phosphorylation of p38 MAPK. The starvation of L6 rat skeletal myoblasts under serum-free conditions induced the phosphorylation of p38 MAPK and the characteristics typical of cast-immobilized gastrocnemius muscle. The expression of MuRF1 was also elevated in serum-starved L6 myoblasts, but was significantly attenuated by SB203580, an inhibitor of p38 MAPK. Changes in the sizes of L6 myoblasts in response to starvation were also reversed by their transfection with MuRF1 small interfering RNA or treatment with SB203580. From these results, we suggest that the expression of MuRF1 in cast-immobilized atrophy is regulated by p38 MAPK in rat gastrocnemius muscles.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1531-1548
• /
• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Journal of Microbiology and Biotechnology
• /
• v.1 no.4
• /
• pp.251-255
• /
• 1991

A 16 kilobase (kb) HindIII fragment of alkalophilic Bacillus sp. YC-335 containing a gene for xylanase synthesis was inserted at the HindIII site of pBR322 and cloned in Escherichia coli HB101. After subcloning of recombinant plasmid pYS52, the 1.5 kb fragment was found to code for xylanase activity, and the hybrid plasmid was named pYS55. The DNA insert of the plasmid was subjected to restriction enzyme mapping, which showed that pYS55 had single site for PuvII and SstI in the 1.5 kb insert fragment. Southern hybridization analysis revealed that the cloned gene was hybridized with chromosomal DNA from alkalophilic Bacillus sp. YC-335. About 64% of the enzyme activity was observed in the extracellular and periplasmic space of E. coli HB10l carrying pYS55.

• Bulletin of the Korean Chemical Society
• /
• v.13 no.5
• /
• pp.491-498
• /
• 1992

Chelating triphosphines were applied to freeze the fluxionality and to minimize the number of isomers found in the monophosphine analogues and this technique was proved to be useful. RuH(NO)$P_3$($P_3$; Cyttp, ttp and etp) complexes were characterized to have similar trigonal bipyramidal structures with linear NO groups. Cyttp prefers to have a meridional geometry while etp prefers a facial one and ttp complexes are mixture of these two isomers. The crystal structure of RuH(NO)(Cyttp) has been determined to have a distorted trigonal bipyramidal structure with a linear NO in the equatorial plane. The crystals are orthorhombic, space group $P_{nma}$, with unit cell dimensions a = 16.356(2), b = 20.474(2), c = 10.915(l) ${\AA}$, V = 3655 ${\AA}^3$, Z = 4, R = 0.035 and $R_w$ = 0.034 for the 2900 intensities with $F_o^2 >3{\sigma}(F_o^2)$ and the 208 variables.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.1025-1050
• /
• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.