• Journal of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.397-406
• /
• 2004

For a Boolean rank-l matrix $A\;=\;ab^{t}$, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-l matrices.

• The Korean Journal of Pain
• /
• v.24 no.2
• /
• pp.74-80
• /
• 2011

Background: Lidocaine patch (L5P) has demonstrated short-term efficacy in treating both acute surgical pain and chronic neuropathic pain with tolerable side effects. Percutaneous endoscopic lumbar discectomy (PELD) is the mainstay of minimally invasive spine surgery (MISS). Sufficient analgesia during PELD surgery makes the patient consider it real MISS. This study was performed to evaluate the efficacy and adverse effects of lidocaine patch in patients who underwent PELD under local anesthesia. Methods: L5P (L group) or placebo (P group) was randomly applied on the skin of the back covering the anticipated path of the working channel before 1 hour of surgery in 100 patients who underwent a single level PELD at L4-L5. Efficacy of the lidocaine patch was assessed by patient's numeric rating scale (NRS) of pain at each stage during the surgery and by a 5-scale grading of the satisfaction with the anesthesia of the operator and patients after surgery. Results: Mean NRS scores at the stages of needle insertion, skin incision, serial dilation and insertion of working channel, and subcutaneous suture were significantly lower in the L group than the P group. Postoperative operator's and patients' satisfaction scores were also significantly higher in L group than in the P group. There were subtle adverse effects in both groups. Conclusions: L5P provided better pain relief during PELD, especially at the stage of needle insertion, skin incision, serial dilation and insertion of working channel, and subcutaneous suture. It also provided higher patient and operator postoperative satisfaction, with only subtle adverse effects.

• Communications of the Korean Mathematical Society
• /
• v.18 no.3
• /
• pp.485-490
• /
• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i=y_i$ , for i, = 1,2,…,n. In this article, we investigate compact interpolation problems in tridiagonal algebra : Given vectors x and y in a Hilbert space, when is there a compact operator A in a tridiagonal algebra such that Ax = y?

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.787-798
• /
• 2018

For $1{\leq}p{\leq}{\infty}$, let $H^p$ be the usual Hardy space on the unit circle. When ${\alpha}$ and ${\beta}$ are bounded functions, a singular integral operator $S_{{\alpha},{\beta}}$ is defined as the following: $S_{{\alpha},{\beta}}(f+{\bar{g}})={\alpha}f+{\beta}{\bar{g}}(f{\in}H^p,\;g{\in}zH^p)$. When p = 2, we study the hyponormality of $S_{{\alpha},{\beta}}$ when ${\alpha}$ and ${\beta}$ are some special functions.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.337-345
• /
• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• Communications of the Korean Mathematical Society
• /
• v.29 no.1
• /
• pp.205-212
• /
• 2014

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The L-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small ${\varepsilon}$ > 0. An example is presented to illustrate the efficiency of the obtained results.

• Journal of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.425-443
• /
• 2010

We investigate the Schr$\ddot{o}$dinger type operator $H_2\;=\;(-\Delta_{\mathbb{H}^n})^2+V^2$ on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sublaplacian and the nonnegative potential V belongs to the reverse H$\ddot{o}$lder class $B_q$ for $q\geq\frac{Q}{2}$, where Q is the homogeneous dimension of $\mathbb{H}^n$. We shall establish the estimates of the fundamental solution for the operator $H_2$ and obtain the $L^p$ estimates for the operator $\nabla^4_{\mathbb{H}^n}H^{-1}_2$, where $\nabla_{\mathbb{H}^n}$ is the gradient operator on $\mathbb{H}^n$.

• Honam Mathematical Journal
• /
• v.33 no.1
• /
• pp.115-120
• /
• 2011

Given vectors x and y in a separable complex Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following : Let Alg$\cal{L}$ be a tridiagonal algebra on a separable complex Hilbert space H and let x = ($x_i$) and y = ($y_i$) be vectors in H. Then the following are equivalent: (1) There exists an invertible operator A = ($a_{kj}$) in Alg$\cal{L}$ such that Ax = y. (2) There exist bounded sequences $\{{\alpha}_n\}$ and $\{{{\beta}}_n\}$ in $\mathbb{C}$ such that for all $k\in\mathbb{N}$, ${\alpha}_{2k-1}\neq0,\;{\beta}_{2k-1}=\frac{1}{{\alpha}_{2k-1}},\;{\beta}_{2k}=\frac{\alpha_{2k}}{{\alpha}_{2k-1}\alpha_{2k+1}}$ and $$y_1={\alpha}_1x_1+{\alpha}_2x_2$$ $$y_{2k}={\alpha}_{4k-1}x_{2k}$$ $$y_{2k+1}={\alpha}_{4k}x_{2k}+{\alpha}_{4k+1}x_{2k+1}+{\alpha}_{4k+2}x_{2k+2}$$.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.337-353
• /
• 1994

Let H be a Schrodinger operator in $L^2$(R) H =(equation omitted) ＋ V(x), with supp V ⊂ [-R, R]. A number $z_{0}$ / in the lower half-plane is called a resonance for H if for all $\phi$ with compact support 〈$\phi$, $(H - z)^{-l}$ $\phi$〉 has an analytic continuation from the upper half-plane to a part of the lower half-plane with a pole at z = $z_{0}$ . Thus a resonance is a sort of generalization of an eigenvalue. For Im k > 0, ($H - k^2$)$^{-1}$ is an integral operator with kernel, given by Green's function(omitted)

• The Pure and Applied Mathematics
• /
• v.5 no.1
• /
• pp.17-21
• /
• 1998

In [5], Zhu introduces a bounded operator T from $L^{\infty}$(D) into Bloch space B. In this paper, we will consider the generalized Bloch spaces $B_{q}$ and find bounded operator from $L^{\infty}$(D) into $B_{q}$.