• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.93-102
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• 1997

Let C be a nonempty closed convex subset of a Banach space E and let $T_1, \cdots, T_N$ be nonexpansive mappings from C into itself (recall that a mapping $T : C \longrightarrow C$ is nonexpansive if $\left\$\mid$ Tx - Ty \right\$\mid$ \leq \left\$\mid$ x - y \right\$\mid$$ for all $x, y \in C$). We consider the fixed point problem for nonexpansive mappings : find a common fixed point, i.e., find a point in $\cap_{i=1}^N Fix(T_i)$, where $Fix(T_i) := {x \in C : x = T_i x}$ denotes the set of fixed points of $T_i$.

• The Korean Journal of Nuclear Medicine
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• v.33 no.6
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• pp.493-501
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• 1999

Purpose: We conducted a comparative study to evaluate the diagnostic values of T1-201, Tc-99m MIBI and I-131 scans in the follow-up assessment after ablative I-131 therapy in differentiated thyroid cancer. Materials and Methods: The study population consisted of 20 patients who underwent surgical removal of thyroid cancer and ablative radioactive iodine therapy, and followed by one or mote times of I-131 retreatments (33 cases). In all patients, T1-201, Tc-99m MIBI, diagnostic and therapeutic I-131 scans were performed and the results were analyzed retrospectively. Also serum thyroglobulin levels were measured in all patients. The final diagnosis of recurrent or metastatic thyroid cancer was determined by clinical, biochemical, radiologic and/or biopsy findings. Results: Positive rates (PR) of Tc-99m MIBI, T1-201, diagnostic and therapeutic I-131 scans in detecting malignant thyroid tissue lesions were 70% (19/27), 54% (15/28), 35% (17/48) and 63% (30/48), respectively. The PR in the group of 20 cases (28 lesions) who underwent concomitant T1-201 and I-131 scans were in the order of therapeutic 131 scan 71%, T1-201 scan 54% and diagnostic I-131 scan 36%. There was no statistically significant difference between T1-201 and diagnostic I-131 scans (p>0.05). In the group of 20 cases (27 lesions) who underwent concomitant Tc-99m MIBI and I-131 scans, the PR were in the order of Tc-99m MIBI scan 70%, I-131 therapeutic scan 52% and I-131 diagnostic scan 33%. The PR of Tc-99m MIBI was significantly higher than that of diagnostic I-131 scan (p<0.05). Conclusion: Tc-99m MIBI scan is superior to diagnostic I-131 scan in detecting recurrent or metastatic thyroid cancer following ablation therapy in patients with differentiated thyroid cancer. T1-201 scan did not showed significantly higher positive rate than diagnostic I-131 scan. Instead of diagnostic I-131 scan before the I-131 retreatment, Tc-99m MIBI scan without discontinuing thyroid hormone replacement would be a prudent and effective approach in the management of these patients.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.695-701
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• 2016

Let I and J be two ideals of a commutative Noetherian ring R and M, N be two non-zero finitely generated R-modules. Let t be a non-negative integer such that $H^i_{I,J}(N)$ is (I, J)-minimax for all i < t. It is shown that the generalized local cohomology module $H^i_{I,J}(M,N)$ is (I, J)-Cofinite minimax for all i < t. Also, we prove that the R-module $Ext^j_R(R/I,H^i_{I,J}(N))$ is finitely generated for all $i{\leq}t$ and j = 0, 1.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.100-109
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• 1983

Let ${X_i}$ be a process with stationary and independent increments whose log characteristic function is expressed as $ibut-2^{-1}\sigma^2u^2t+t\int_{{0 }^c}{(exp(iux)-1-iux(i+x^2)^{-1})dv(x)}$. Our main result is taht $x^2(\int_{\y\>x}{dv(y)})/(\int_{$\mid$y$\mid$\leqx}{y^2dv(y)+\sigma^2}) \to 1$ as $x \to 0 (resp. x \to \infty)$ is necessary, and sufficient for ${X-i}$ to have ${A_t}$ and ${B_t}$ such that $(X_t-A_t)/B_t \to^D n(0,1)$ as $t \to 0 (resp. t \to \infty)$.

• Journal of Korean Medicine for Obesity Research
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• v.20 no.2
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• pp.109-121
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• 2020

Objectives: Tanshinone I is a bioactive constituent in Salvia miltiorrhiza. At present, the anti-obesity effect and mechanism of tanshinone I are not fully understood. Here we investigated the effect of tanshinone I on lipid accumulation in 3T3-L1 preadipocytes and zebrafish. Methods: Lipid accumulation and triglyceride (TG) content in 3T3-L1 cells were determined by Oil Red O staining and AdipoRed assay, respectively. The expression and phosphorylation levels of adipogenic/lipogenic proteins in 3T3-L1 cells were evaluated by Western blotting. The messenger RNA (mRNA) expression levels of adipogenic/lipogenic markers and leptin in 3T3-L1 cells were measured by reverse transcription polymerase chain reaction (RT-PCR). Lipid accumulation in zebrafish was assessed by LipidGreen2 staining. Results: Tanshinone I at 5 μM largely blocked lipid accumulation and reduced TG content in differentiating 3T3-L1 cells. Furthermore, tanshinone I decreased the expression of CCAAT/enhancer-binding protein-α (C/EBP-α), peroxisome proliferator-activated receptor-γ (PPAR-γ), fatty acid synthase (FAS), acetyl CoA carboxylase (ACC), and perilipin A but also the phosphorylation of signal transducer and activator of transcription-3 (STAT-3) in differentiating 3T3-L1 cells. In addition, tanshinone I increased the phosphorylation of adenosine 3',5'-cyclic monophosphate (cAMP)-activated protein kinase (AMPK) while decreased the intracellular adenosine triphosphate (ATP) content with no change in the phosphorylation and expression of liver kinase-B1 in differentiating 3T3-L1 cells. Importantly, tanshinone I also reduced the extent of lipid deposit formation in developing zebrafish. Conclusions: These findings demonstrate that tanshinone I has strong anti-adipogenic effects on 3T3-L1 cells and reduces adiposity in zebrafish, and these anti-adipogenic effect in 3T3-L1 cells are mediated through control of C/EBP-α, PPAR-γ, STAT-3, FAS, ACC, perilipin A, and AMPK.

• The Korean Journal of Nuclear Medicine
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• v.24 no.1
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• pp.87-92
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• 1990

T1-201 and I-131 scintigraphy were performed to visualize malignant lesions postoperatively in 26 patients with well-differentiated thyroid cancer. Anyone of uptake index and retention index was higher in malignant lesions than that in benign lesions. T1-201 scintigraphy showed uptake ininflammatory tissues. T1-201 concentration was observed in fourteen patients and six of them had malignant lesions, while I-131 concentration was observed in six patients and all had malignant lesions. In sensitivity, combination of T1-201 and I-131 scintigraphy is higher than I-131 or T1-201 scintigraphy only. In postoperative patients with well-differentiated thyroid cancer, it may be useful that T1-201 scintigraphy will be performed simultaneously with I-131 scintigraphy for detecting recurrence.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.167-177
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• 1992

In this paper, we investigate the limiting distribution of $M_n = max (X_1, X-2, \cdots, X_n)$ in the infinite moving average process ${X_t = \sum c_i Z_{t-i}}$ generated from i.i.d. negative binomial variables $Z_i$'s. While no limit result is possible, nonetheless asymptotic bounds are derived. We also present the tail behavior of $X_t$, i.e., weighted sum of i.i.d. random variables. This continues a study made by Rootzen (1986) for discrete innovation sequences.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.231-244
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• 2005

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.387-391
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• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.