• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1275-1289
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• 1996

The plane elasticity problem of collinear cracks in a layered medium is investigated. The medium is modeled as bonded structure constituted from a surface layer and a semi-infinite substrate. Along the bond line between the two dissimilar homegeneous constituents, it is assumed that as interfacial zone having the functionally graded, nonhomogeneous elastic modulus exists. The layered medium contains three collinear cracks, one in each constituent material oriented perpendicular to the nominal interfaces. The stiffness matrix formulation is utilized and a set of homogeneous conditions relevant to the given problem is readily satisfied. The proposed mixed boundary value problem is then represented in the form of a system of integral equations with Cauchy-type singular kernels. The stress intensity factors are defined from the crack-tip stress fields possessing the standard square-root singular behavior. The resulting values of stress intensity factors mainly address the interactions among the cracks for various crack sizes and material combinations.

• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.419-429
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• 2005

This paper considers eigenstructure assignment in high-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically very simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effect of the proposed approaches.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.483-494
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• 2017

In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: $$T_{\lambda}(f;x)={\int_a^b}{\sum^n_{m=1}}f^m(t)K_{{\lambda},m}(x,t)dt,\;{\lambda}{\in}{\Lambda},\;x{\in}(a,b)$$, where ${\Lambda}$ is an index set consisting of the non-negative real numbers, and $n{\geq}1$ is a finite natural number, at ${\mu}$-generalized Lebesgue points of integrable function $f{\in}L_1(a,b)$. Here, $f^m$ denotes m-th power of the function f and (a, b) stands for arbitrary bounded interval in ${\mathbb{R}}$ or ${\mathbb{R}}$ itself. We also handled the indicated problem under the assumption $f{\in}L_1({\mathbb{R}})$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1615-1623
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• 2014

Let $G{\leq}S_n$ and ${\chi}$ be any nonzero complex valued function on G. We first study the irreducibility of the generalized matrix polynomial $d^G_{\chi}(X)$, where $X=(x_{ij})$ is an n-by-n matrix whose entries are $n^2$ commuting independent indeterminates over $\mathbb{C}$. In particular, we show that if $\mathcal{X}$ is an irreducible character of G, then $d^G_{\chi}(X)$ is an irreducible polynomial, where either $G=S_n$ or $G=A_n$ and $n{\neq}2$. We then give a necessary and sufficient condition for the equality of two generalized matrix functions on the set of the so-called ${\chi}$-singular (${\chi}$-nonsingular) matrices.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.593-604
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• 2018

Recently, a new version of expansiveness which is closely attached to some certain weak version of hyperbolicity was given for $C^1$ vector fields as following: a $C^1$ vector field X will be called rescaling expansive on a compact invariant set ${\Lambda}$ of X if for any ${\epsilon}$ > 0 there is ${\delta}$ > 0 such that, for any $x,\;y{\in}{\Lambda}$ and any time reparametrization ${\theta}:{\mathbb{R}}{\rightarrow}{\mathbb{R}}$, if $d({\varphi}_t(x),\,{\varphi}_{{\theta}(t)}(y)){\leq}{\delta}{\parallel}X({\varphi}_t(x)){\parallel}$ for all $t{\in}{\mathbb{R}}$, then ${\varphi}_{{\theta}(t)}(y){\in}{\varphi}_{(-{\epsilon},{\epsilon})}({\varphi}_t(x))$ for all $t{\in}{\mathbb{R}}$. In this paper, some equivalent definitions for rescaled expansiveness are given.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.471-478
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• 2006

In this paper we prove that if AX=b is a partial sign-solvable linear system with A being sign non-singular matrix and if ${\alpha}=\{j:\;x_j\;is\;sign-determined\;by\; Ax=b\}, then $A_{\alpha}X_{\alpha}=b_{\alpha}$ is a sign-solvable linear system, where $A_{\alpha}$ denotes the submatrix of A occupying rows and columns in o and xo and be are subvectors of x and b whose components lie in ${\alpha}$. For a sign non-singular matrix A, let $A_l,\;...,A_{\kappa}$ be the fully indecomposable components of A and let ${\alpha}_i$ denote the set of row numbers of $A_r,\;r=1,\;...,\;k$. We also show that if $A_x=b$ is a partial sign-solvable linear system, then, for $r=1,\;...,\;k$, if one of the components of xor is a fixed zero solution of Ax=b, then so are all the components of x_{{\alpha}r}$.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.359-369
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• 2000

Let X be an integral Gorenstein projective curve with g:=pa(X) $\geq$ 3. Call $G^r_d$ (X,**) the set of all pairs (L,V) with L$\epsilon$Pic(X), deg(L) = d, V $\subseteq$ H^0$(X,L), dim(V) =r+1 and V spanning L. Assume the existence of integers d, r with 1 $\leq$ r$\leq$ d $\leq$ g-1 such that there exists an irreducible component, , of $G^r_d$(X,**) with dim($\Gamma$) $\geq$ d - 2r and such that the general L$\geq$$\Gamma$ is spanned at every point of Sing(X). Here we prove that dim( ) = d-2r and X is hyperelliptic.

• Bulletin of the Korean Chemical Society
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• v.24 no.7
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• pp.971-974
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• 2003

By utilizing singular value decomposition (SVD) and shift averaged Harr wavelet transform (WT) with a set of Daubechies wavelet coefficients (1/2, -1/2), a method that can simultaneously eliminate an unwanted large solvent peak and noise peaks from NMR data has been developed. Noise elimination was accomplished by shift-averaging the time domain NMR data after a large solvent peak was suppressed by SVD. The algorithms took advantage of the WT, giving excellent results for the noise elimination in the Gaussian type NMR spectral lines of NMR data pretreated with SVD, providing superb results in the adjustment of phase and magnitude of the spectrum. SVD and shift averaged Haar wavelet methods were quantitatively evaluated in terms of threshold values and signal to noise (S/N) ratio values.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.412-417
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• 1998

This paper provides accurate flexural vibration solutions for thick (Mindlin) sectorial plates. A Ritz method is employed which incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of Mindlin “corner functions". These corner functions model the singular vibratory moments and shear forces, which simultaneously exist at the vertex of corner angle exceeding 180$^{\circ}$. The first set guarantees convergence to the exact frequencies as sufficient terms are taken. The second set represents the corner singularities, and accelerates convergence substantially. Numerical results are obtained for completely free sectorial plates. Accurate frequencies are presented for a wide spectrum of vertex angles (90$^{\circ}$, 180$^{\circ}$, 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 35 5$^{\circ}$,and 359$^{\circ}$)and thickness ratios.tios.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.355-362
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• 2009

In this paper, we present a framework for managing group behaviors in multi-agent swarm systems. The framework explores the benefits by dynamic associations with the proposed artificial potential functions to realize complex swarming behaviors. A key development is the introduction of a set of flocking by dynamic association (DA) algorithms that effectively deal with a host of swarming issues such as cooperation for fast migration to a target, flexible and agile formation, and inter-agent collision avoidance. In particular, the DA algorithms employ a so-called systematic singular association (SSA) rule for fast migration to a target and compact formation through inter-agent interaction. The resulting algorithms enjoy two important interrelated benefits. First, the SSA rule greatly reduces time-consuming for migration and satisfies low possibility that agents may be lost. Secondly, the SSA is advantageous for practical implementations, since it considers for agents even the case that a target is blocked by obstacles. Extensive simulation presents to illustrate the viability and effectiveness of the proposed framework.