• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.881-887
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• 1995

Let f be a measurable function on the unit ball B in $C^n$, then we define a maximal function $M_p(f), 1 \leq p < \infty$, by $$ M_p(f)(\zeta ) = \sup_{\delta > 0}(\frac{1}{\sigma(\beta(\zeta, \delta))} \int_{T(\beta(\zeta, \delta))} $\mid$f(z)$\mid$^p \frac{d\nu(z)}{(1-$\mid$z$\mid$^n})^{1/p} $$ where $\sigma$ denotes the surface area measure on S, the boundary of B, and $T(\beta(\zeta, \delta))$ denotes the tent over the ball $\beta(\zeta, \delta)$. We prove that the maximal operator $M_p$ belongs to the Muckenhoupt class $A_1$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.8C
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• pp.756-764
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• 2003

We investigate a probabilistic public key cryptosystem proposed by Paillier. It is based on the discrete logarithmic function and the messages are calculated from the modular product of two those functions, one of which has a fixed value depending on a given public key. The improvement is achieved by a good choice for the public key so that it is possible to get efficient schemes without losing the onewayness and semantic security. Also we suggest the method to get the public key for our schemes.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.289-304
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• 2021

In this paper, we establish several geometric characterizations focusing on the relationship between the squared norm of the second fundamental form and the warping function of SCR-lightlike warped product submanifolds in an indefinite Kaehler manifold. In particular, we find an estimate for the squared norm of the second fundamental form h in terms of the Hessian of the warping function λ for SCR-lightlike warped product submanifolds of an indefinite complex space form. Consequently, we derive an optimal inequality, namely $${\parallel}h{\parallel}^2{\geq}2q\{{\Delta}(ln{\lambda})+{\parallel}{\nabla}(ln{\lambda}){\parallel}^2+\frac{c}{2}p\}$$, for SCR-lightlike warped product submanifolds in an indefinite complex space form. We also provide one non-trivial example for this class of warped products in an indefinite Kaehler manifold.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.6
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• pp.646-650
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• 2014

In this paper, in order to avoid the deterioration of the pattern classification performance which results from the curse of dimensionality, we propose a new feature selection method. The newly proposed feature selection method is based on Fuzzy C-Means clustering algorithm which analyzes the data points to divide them into several clusters and the concept of a function with fuzzy numbers. When it comes to the concept of a function where independent variables are fuzzy numbers and a dependent variable is a label of class, a fuzzy number should be related to the only one class label. Therefore, a good feature is a independent variable of a function with fuzzy numbers. Under this assumption, we calculate the goodness of each feature to pattern classification problem. Finally, in order to evaluate the classification ability of the proposed pattern classifier, the machine learning data sets are used.

• BMB Reports
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• v.45 no.8
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• pp.464-469
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• 2012

Endothelial cells (ECs) apoptosis induced by oxidized low-density lipoprotein (ox-LDL) is thought to play a critical role in atherosclerosis. MicroRNAs (miRNAs) are a class of noncoding RNAs that posttranscriptionally regulate the expression of genes involved in diverse cell functions, including differentiation, growth, proliferation, and apoptosis. MiRNA let-7 family is known to be involved in the regulation of cell apoptosis. However, the function of let-7 in ox-LDL induced ECs apoptosis and atherosclerosis is still unknown. Here, we show that let-7c expression was markedly up-regulated in ox-LDL induced apoptotic human umbilical cord vein endothelial cells (HUVECs). Let-7c over-expression enhanced apoptosis in ECs whereas inhibition of let-7c could partly alleviate apoptotic cell death mediated by ox-LDL. Searching for how let-7c affected apoptosis, we discovered that antiapoptotic protein Bcl-xl was a direct target of let-7c in ECs. Our data suggest that let-7c contributes to endothelial apoptosis through suppression of Bcl-xl.

• BMB Reports
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• v.56 no.3
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• pp.172-177
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• 2023

BEST family is a class of Ca²⁺-activated Cl- channels evolutionary well conserved from bacteria to human. The human BEST paralogs (BEST1-BEST4) share significant amino acid sequence homology in the N-terminal region, which forms the transmembrane helicases and contains the direct calcium-binding site, Ca²⁺-clasp. But the cytosolic C-terminal region is less conserved in the paralogs. Interestingly, this domain-specific sequence conservation is also found in the BEST1 orthologs. However, the functional role of the C-terminal region in the BEST channels is still poorly understood. Thus, we aimed to understand the functional role of the C-terminal region in the human and mouse BEST1 channels by using electrophysiological recordings. We found that the calcium-dependent activation of BEST1 channels can be modulated by the C-terminal region. The C-terminal deletion hBEST1 reduced the Ca²⁺-dependent current activation and the hBEST1-mBEST1 chimera showed a significantly reduced calcium sensitivity to hBEST1 in the HEK293 cells. And the C-terminal domain could regulate cellular expression and plasma membrane targeting of BEST1 channels. Our results can provide a basis for understanding the C-terminal roles in the structure-function of BEST family proteins.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Proceedings of the Plant Resources Society of Korea Conference
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• 2003.04a
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• pp.123-123
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• 2003

In order to study gene expression transcribted during the embryo development, we constructed a cDNA library of embryogenic callus induced from cotylendon of Korean ginseng and generated expressed sequence tags (ESTs) of 3,359 clones randomly selected. The ESTs could be clustered into 1,910 (59.1%) non-redundant groups. Similarity search of the non-redundant ESTs against public non-redundant databases of both protein and DNA indicated that 2,217 groups show similarity to genes of known function. These ESTs clones were divided into eighteen categories depending upon gene function. Most abundant transcripts were ribosomal protein small subunit 28kDa(40), tumor-related protein(35), metallothionein (31), small heat-shock protein class 18.6K(24), and cyclophilin(20). There are no useful informations of gene expression during the embryo development in Korean ginseng. These results could help to understand the embryo development in Korean ginseng.