• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.585-604
• /
• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.10A
• /
• pp.1492-1498
• /
• 2000

Pilot symbol aided modulation (PSAM) using the conventional sinc interpolation (CSI) achieves nearly the same BER performance as Caver' optimal Wiener interpolation but with much less complexity. The CSI, however, has to use a non-rectangular window function that is applied to the sinc function to smooth out the abrupt truncation of rectangular window. In this paper, we propose the modified sinc interpolation (MSI). With the weighting factor the MSI scheme with no window has almost the same BER performance as the CSI scheme using window, In addition, if we use the MSI with a window its BER performance gets close to that of the theoretical one. We assume the multicarrier QAM system and an optimal frame structure for performance evaluation.

• Journal of Aquaculture
• /
• v.6 no.1
• /
• pp.1-12
• /
• 1993

Identification of blood cells and their physological functions in the cultured scallop, Patinopecten yessoensis collected from Abashiri Bay, Hokkaido, Japan were studied by electron microscopic structure and histological observations. The physiological function of each blood cell type was studied on the basis of its cytological structure, the lysosome in the blood cell and its phagocytosis. The blood cells were classified as Type I, Type II and Type III. The morphological characteristics of each blood cell type are as follows ; Type I : The cell is oval shaped and its cytoplasm contains comparatively low electron dense materials. The oval nucleus is sometimes ramified into two nuclei. Lumps of tubular smooth endoplasmic reticula and vacuoles are distributed near the nucleus. Type II : The cell appears long and oval shaped, and its cytoplasm contains high electron dense materials. The oval nucleus does not ramify, and large numbers of sac-like smooth endoplasmic reticula and free ribosomes are developed around the nucleus. No vacuoles exist in the cytoplasm Type 1II : The cell is round in shape and the electron density of the cytoplasm is the highest among the three types of cells because of large quantities of rough­surfaced endoplasmic reticula and no vacuoles. Particularly, the nucleus reveals a wheel-like shape owing to lumps of tuberous chromatin. The cells of Type I and II seem to have the role of carrying out phagocytosis on either foreign materials such as bacteria or endogenous old cells and the transport of nutritive materials. The type III cell, which has not been found in any bivalve species of non Pectinidae, may be said to have the function of production and the secretion of protein related to some humoral defense materials.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.5
• /
• pp.2381-2399
• /
• 2019

Traditional recommendation algorithms on Collaborative Filtering (CF) mainly focus on the rating prediction with explicit ratings, and cannot be applied to the top-N recommendation with implicit feedbacks. To tackle this problem, we propose a new collaborative filtering approach namely Maximize MAP with Matrix Factorization (MFMAP). In addition, in order to solve the problem of non-smoothing loss function in learning to rank (LTR) algorithm based on pairwise, we also propose a smooth MAP measure which can be easily implemented by standard optimization approaches. We perform experiments on three different datasets, and the experimental results show that the performance of MFMAP is significantly better than other recommendation approaches.

• Interaction and multiscale mechanics
• /
• v.6 no.2
• /
• pp.137-156
• /
• 2013

In this paper, a meshfree shell adaptive procedure is developed for the applications in the sheet metal forming simulation. The meshfree shell formulation is based on the first-order shear deformable shell theory and utilizes the degenerated continuum and updated Lagrangian approach for the nonlinear analysis. For the sheet metal forming simulation, an h-type adaptivity based on the meshfree background cells is considered and a geometric error indicator is adopted. The enriched nodes in adaptivity are added to the centroids of the adaptive cells and their shape functions are computed using a first-order generalized meshfree (GMF) convex approximation. The GMF convex approximation provides a smooth and non-negative shape function that vanishes at the boundary, thus the enriched nodes have no influence outside the adapted cells and only the shape functions within the adaptive cells need to be re-computed. Based on this concept, a multi-level refinement procedure is developed which does not require the constraint equations to enforce the compatibility. With this approach the adaptive solution maintains the order of meshfree approximation with least computational cost. Two numerical examples are presented to demonstrate the performance of the proposed method in the adaptive shell analysis.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.9
• /
• pp.1314-1319
• /
• 2004

In this study, parameter optimization of micro-static mixer with a cantilever beam was accomplished for maximizing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• Geomechanics and Engineering
• /
• v.11 no.2
• /
• pp.235-252
• /
• 2016

This paper presents a new numerical solution of the ultimate lateral capacity of rectangular piles in clay. The two-dimensional plane strain finite element was employed to determine the limit load of this problem. A rectangular pile is subjected to purely lateral loading along either its major or minor axes. Complete parametric studies were performed for two dimensionless variables including: (1) the aspect ratios of rectangular piles were studied in the full range from plates to square piles loaded along either their major or minor axes; and (2) the adhesion factors between the soil-pile interface were studied in the complete range from smooth surfaces to rough surfaces. It was found that the dimensionless load factor of rectangular piles showed a highly non-linear function with the aspect ratio of piles and a slightly non-linear function with the adhesion factor at the soil-pile interface. In addition, the dimensionless load factor of rectangular piles loaded along the major axis was significantly higher than that loaded along the minor axis until it converged to the same value at square piles. The solutions of finite element analyses were verified with the finite element limit analysis for selected cases. The empirical equation of the dimensionless load factor of rectangular piles was also proposed based on the data of finite element analysis. Because of the plane strain condition of the top view section, results can be only applied to the full-flow failure mechanism around the pile for the prediction of limiting pressure at the deeper length of a very long pile with full tension interface that does not allow any separation at soil-pile interfaces.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.363-447
• /
• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Journal of Biomedical Engineering Research
• /
• v.36 no.5
• /
• pp.211-220
• /
• 2015

Recently, model-based iterative reconstruction (MBIR) has played an important role in transmission tomography by significantly improving the quality of reconstructed images for low-dose scans. MBIR is based on the penalized-likelihood (PL) approach, where the penalty term (also known as the regularizer) stabilizes the unstable likelihood term, thereby suppressing the noise. In this work we further improve MBIR by using a more expressive regularizer which can restore the underlying image more accurately. Here we used a spline regularizer derived from a linear combination of the two-dimensional splines with first- and second-order spatial derivatives and applied it to a non-quadratic convex penalty function. To derive a PL algorithm with the spline regularizer, we used a separable paraboloidal surrogates algorithm for convex optimization. The experimental results demonstrate that our regularization method improves reconstruction accuracy in terms of both regional percentage error and contrast recovery coefficient by restoring smooth edges as well as sharp edges more accurately.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1535-1547
• /
• 2015

A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth vector field ${\xi}$ on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: $$\frac{1}{2}L_{\xi}g+Ric={\lambda}g$$, where $L_{\xi}g$ is the Lie-derivative of the metric tensor g with respect to ${\xi}$, Ric is the Ricci tensor of (M, g) and ${\lambda}$ is a constant. A Ricci soliton (M, g, ${\xi}$, ${\lambda}$) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.