• BMB Reports
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• v.42 no.9
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• pp.593-598
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• 2009

Cell cycle progression is regulated by both transcriptional and post-transcriptional mechanisms. MicroRNAs (miRNAs) emerge as a new class of small non-coding RNA regulators of cell cycle as recent evidence suggests. It is hypothesized that expression of specific miRNAs oscillates orderly along with cell cycle progression. However, the oscillated expression patterns of many candidate miRNAs have yet to be determined. Here, we describe miRNA expression profiling in double-thymidine synchronized HeLa cells as cell cycle progresses. Twenty-five differentially expressed miRNAs were classified into five groups based on their cell cycle-dependent expression patterns. The cyclic expression of six miRNAs (miR-221, let-7a, miR-21, miR-34a, miR-24, miR-376b) was validated by real-time quantitative RT-PCR (qRT-PCR). These results suggest that specific miRNAs, along with other key factors are required for maintaining and regulating proper cell cycle progression. The study deepens our understanding on cell cycle regulation.

• Journal of the Semiconductor & Display Technology
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• v.18 no.3
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• pp.77-81
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• 2019

Recently, Korea has been making efforts at the government level to overcome the national crisis that Japan's dependency on technology in the semiconductor and display materials sectors has also escaped due to export regulations on three materials carried out by Japan. Therefore, based on the data of the National Science & Technology Information Service (NTIS) operated by the government, we analyze the trend of R & D investment in the display field, thereby improving R & D to improve material technology competitiveness in the future. Let's examine the implications of investment. A total of 5 years of new research and development investment in the field of display was invested as basic research fund for 25%, 15% for applied research, and 53% for development research. In terms of development cost and development period, the basic research showed that the amount of money and the development period were shorter than that of applied research. In other words, the basic research accounted for 25% of the R & D investment and the average R & D period was only 3.2 years. As we can see from the recent development of H fiber carbon fiber, which was recently developed and entered full-scale production, we were able to succeed because of the benefits of government support for 10 years while giving the same material title differently. In order to escape from Japan's technological dependence on semiconductor and display materials in Korea, As such, basic research in the field of materials is only possible when long-term research is conducted.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• Journal of Welding and Joining
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• v.27 no.3
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• pp.67-72
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• 2009

The flux cored arc welding (FCAW) process is one of the most frequently employed and important welding process due to high productivity and excellent workability. The process is performed either as an automated process or as a semi-automatic process. In FCAW process, welding voltage has been considered as a qualitative indication of arc length. But it is necessary to let welding operators know, maintain and manage the arc length directly by estimating and displaying it. In this study, to develop arc length estimation technique, we measured a welding circuit resistance($R_sc$) and then we calculated welding circuit voltage drop($V_sc$). Also, we measured arc peak voltage($V_ap$). By subtracting $V_sc$ from $V_arc$, we can easily calculate net arc voltage drop($V_arc$). Consequently, we suggested arc length estimating equation and basic algorithm by regressive analyzing the relationship between net arc voltage drop($V_arc$) and real arc length(Larc) measured by high speed camera. Therefore, arc length can be predicted by just monitoring welding current and voltage.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.193-200
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• 1994

Let x : $M^{n}$ .rarw. $E^{m}$ be an isometric immersion of a manifold $M^{n}$ into the Euclidean space $E^{m}$ and .DELTA. the Laplacian of $M^{n}$ defined by -div.omicron.grad. The family of such immersions satisfying the condition .DELTA.x = .lambda.x, .lambda..mem.R, is characterized by a well known result ot Takahashi (8]): they are either minimal in $E^{m}$ or minimal in some Euclidean hypersphere. As a generalization of Takahashi's result, many authors ([3,6,7]) studied the hypersurfaces $M^{n}$ in $E^{n+1}$ satisfying .DELTA.x = Ax + b, where A is a square matrix and b is a vector in $E^{n+1}$, and they proved independently that such hypersurfaces are either minimal in $E^{n+1}$ or hyperspheres or spherical cylinders. Since .DELTA.x = -nH, the submanifolds mentioned above satisfy .DELTA.H = .lambda.H or .DELTA.H = AH, where H is the mean curvature vector field of M. And the family of hypersurfaces satisfying .DELTA.H = .lambda.H was explored for some cases in [4]. In this paper, we classify space curves x : R .rarw. $E^{3}$ satisfying .DELTA.x = Ax + b or .DELTA.H = AH, and find conditions for such curves to be equivalent.alent.alent.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.323-329
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• 2022

Let $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ be a polynomial of degree n and $p^{\prime}(z)$ its derivative. If $\max\limits_{{\mid}z{\mid}=r}{\mid}p(z){\mid}$ is denoted by M(p, r). If p(z) has all its zeros on |z| = k, k ≤ 1, then it was shown by Govil [3] that $$M(p^{\prime},\;1){\leq}\frac{n}{k^n+k^{n-1}}M(p,\;1)$$. In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.783-800
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• 2002

Let B denote the unit ball in $C^n$, and ν the normalized Lebesgue measure on B. For $\alpha$ > -1, define $dv_\alpha$(z) ＝ $c_\alpha$$(1-\midz\mid^2)^{\alpha}$dν(z), z $\in$ B. Here $c_\alpha$ is a positive constant such that $v_\alpha$(B) ＝ 1. Let H(B) denote the space of all holomorphic functions in B. For $p\geq1$, define the Bergman-Privalov space $(AN)^{p}(v_\alpha)$ by $(AN)^{p}(v_\alpha)$ = ${f\inH(B)$ : $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function $f\inH(B)$ is in $(AN)^{p}$$(v_\alpha)$ if and only if $(1+\midf\mid)^{-2}{log(1+\midf\mid)}^{p-2}\mid\nablaf\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case 1＜p＜$\infty$, or $(1+\midf\mid)^{-2}\midf\mid^{-1}\mid{\nabla}f\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case p ＝ 1, where $nabla$f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.693-715
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• 2024

Let n ∈ ℕ, n ≥ 2. An element (x₁, . . . , x_n) ∈ Eⁿ is called a norming point of T ∈ 𝓛(ⁿE) if ||x₁|| = ··· = ||x_n|| = 1 and |T(x₁, . . . , x_n)| = ||T||, where 𝓛(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ 𝓛(ⁿE), we define Norm(T) = {(x₁, . . . , x_n) ∈ Eⁿ : (x₁, . . . , x_n) is a norming point of T}. Norm(T) is called the norming set of T. Let $0{\leq}{\theta}{\leq}{\frac{{\pi}}{4}}$ and ${\ell}^2_{{\infty},{\theta}}={\mathbb{R}}^2$ with the rotated supremum norm $${\parallel}(x,y){\parallel}_{({\infty},{\theta})}={\max}\{{\mid}x\;cos\;{\theta}+y\;sin\;{\theta}{\mid},\;{\mid}x\;sin\;{\theta}-y\;cos\;{\theta}|\}$$. In this paper, we characterize the norming set of T ∈ 𝓛(ⁿℓ²_(∞,θ)). Using this result, we completely describe the norming set of T ∈ 𝓛_s(ⁿℓ²_(∞,θ)) for n = 3, 4, 5, where 𝓛_s(ⁿℓ²_(∞,θ)) denotes the space of all continuous symmetric n-linear forms on ℓ²_(∞,θ). We generalizes the results from [9] for n = 3 and ${\theta}={\frac{{\pi}}{4}}$.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.445-506
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• 2013

Let ${\sigma}_s(N)$ denote the sum of the s-th power of the positive divisors of N and ${\sigma}_{s,r}(N;m)={\sum_{d{\mid}N\\d{\equiv}r\;mod\;m}}\;d^s$ with $N,m,r,s,d{\in}\mathbb{Z}$, $d,s$ > 0 and $r{\geq}0$. In a celebrated paper [33], Ramanuja proved $\sum_{k=1}^{N-1}{\sigma}_1(k){\sigma}_1(N-k)=\frac{5}{12}{\sigma}_3(N)+\frac{1}{12}{\sigma}_1(N)-\frac{6}{12}N{\sigma}_1(N)$ using elementary arguments. The coefficients' relation in this identity ($\frac{5}{12}+\frac{1}{12}-\frac{6}{12}=0$) motivated us to write this article. In this article, we found the convolution sums $\sum_{k&lt;N/m}{\sigma}_{1,i}(dk;2){\sigma}_{1,j}(N-mk;2)$ for odd and even divisor functions with $i,j=0,1$, $m=1,2,4$, and $d{\mid}m$. If N is an odd positive integer, $i,j=0,1$, $m=1,2,4$, $s=0,1,2$, and $d{\mid}m{\mid}2^s$, then there exist $u,a,b,c{\in}\mathbb{Z}$ satisfying $\sum_{k& lt;2^sN/m}{\sigma}_{1,i}(dk;2){\sigma}_{1,j}(2^sN-mk;2)=\frac{1}{u}[a{\sigma}_3(N)+bN{\sigma}_1(N)+c{\sigma}_1(N)]$ with $a+b+c=0$ and ($u,a,b,c$) = 1(Theorem 1.1). We also give an elementary problem (O) and solve special cases of them in (O) (Corollary 3.27).