• 호남수학학술지
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• 제34권2호
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.123-134
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• 2023

Since Knaster, Kuratowski, and Mazurkiewicz established their KKM theorem in 1929, it was first applied to topological vector spaces mainly by Fan and Granas. Later it was extended to convex spaces by Lassonde and to extensions of c-spaces by Horvath. In 1992, such study was called the KKM theory by ourselves. Then the theory was extended to generalized convex spaces or G-convex spaces. Motivated by such spaces, there have appeared several particular types of artificial spaces. In 2006 we introduced abstract convex spaces which contain all existing spaces appeared in the KKM theory. Later in 2014-2020, Khahn and Quan introduced "topologically based existence theorems" and the so-called KKM structure. In the present paper, we show that their structure is a particular type of already known KKM spaces.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 하계종합학술대회논문집
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• pp.46-49
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• 1998

In this paper, we introduce the notion of intelligent communication by introducing a novel intelligent receiver model. This receiver is continually evolving and learns and improves in performance as it compiles its experience over time. In digital communication context, in a typical training mode, it jearns the concept of "1" as is deteriorated by arbitrary (not necessarily additive as is typically assumed) disturbance and /or modulation. After learning "1", in test mode, it classifies the received signal "1" and "0" almost completely. The intelligent receiver as implemented is grounded on the recently introduced Stochastic Morphological Sampling Theorem(SMST), a distribution-free result which gives theoretical bounds on the sample complexity(training size) needed for the required performance parameters such as accuracy($\varepsilon$) and confidence($\delta$). Based on this theorem, we demonstrate --almost irrespective of channel and modulation model-- the number of samples needed to learn the concept of "1" is not too "large" and the resulting universal receiver structure, that corresponding to classical Nearest Neighbor rule in Pattern Recognition Theory, is trivial. We check the surprising efficiency and validity of this model through some simple simulations. and validity of this model through some simple simulations.

• 전자공학회논문지SC
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• 제48권6호
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• pp.8-14
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• 2011

본 연구에서는 불확실 단일 입력 시스템의 경우에 대하여 Utkin 정리의 증명을 제시한다. 소위 두가지의 대각화 방법(Diagonalization Method)이라 불리는 Utkin 정리의 두 변환 방법에 대한 불변 정리를 비교적으로 분명히 증명한다. 슬라이딩모드의 수식 즉 슬라이딩 면은 두가지 대각화 변환에 대하여 변화 없고 두 인가된 제어입력은 같은 이득을 갖는다. 두가지 대각화 방법에 의하여 같은 결과를 얻는다. 설계 예와 시뮬레이션 연구를 통하여 제안된 결과의 효용성을 입증한다.

• Advances in Computational Design
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• 제8권2호
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• pp.133-145
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• 2023

Scaling and similitude large scale structural member to small scale model is considered the most important matter for the experimental tests because of the difficulty in controlling, lack of capacities and expenses, furthermore that most of MSc and PhD students suffering from choosing the suitable specimen before starting their experimental study. The current study adopts to take large scale slab with opening as a case study of structural member where the slab is squared with central squared opening, the boundary condition is fixed from all sides, the load represents by four concentrated force in four corners of opening, as well as, the study adopts Buckingham theorem which has been used for scaling, all the parameters of the problem have been formed in dimensionless groups, the main groups have been connected by a relations, those relations are represented by force, maximum stress and maximum displacement. Finite element method by ANSYS R18.1 has been used for analyzing and forming relations for the large scale member. Prediction analysis has been computed for three small scale models by depending on the formed relations of the large scale member. It is found that Buckingham theorem is considered suitable way for creating relations among the parameters for any structural problem then making similitude and scaling the large scale members to small scale members. Finally, verification between the prediction and theoretical results has been done, it is observed that the maximum deviation between them is not more than 2.4%.

• 대한수학회보
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• 제46권3호
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• pp.447-461
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• 2009

In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ satisfying the condition that the structure Jacobi operator $R_{\xi}$ commutes with the 3-structure tensors ${\phi}_i$, i = 1, 2, 3.

• 대한수학회지
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• 제30권1호
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• pp.173-183
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• 1993

• 대한수학회논문집
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• 제9권4호
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• pp.897-903
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• 1994

In this paper we characterize the distributions with $L^p$-growth. Moreover, we give a much simpler structure theorem than already known so far.

• Structural Engineering and Mechanics
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• 제25권1호
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• pp.107-126
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• 2007

The problem related to the computation of bounds on plastic deformations for structures in plastic shakedown condition (alternating plasticity) is studied. In particular, reference is made to structures discretized by finite elements constituted by elastic perfectly plastic material and subjected to a special combination of fixed and cyclic loads. The load history is known during the steady-state phase, but it is unknown during the previous transient phase; so, as a consequence, it is not possible to know the complete elastic plastic structural response. The interest is therefore focused on the computation of bounds on suitable measures of the plastic strain which characterizes just the first transient phase of the structural response, whatever the real load history is applied. A suitable structural model is introduced, useful to describe the elastic plastic behaviour of the structure in the relevant shakedown conditions. A special bounding theorem based on a perturbation method is proposed and proved. Such theorem allows us to compute bounds on any chosen measure of the relevant plastic deformation occurring at the end of the transient phase for the structure in plastic shakedown; it represents a generalization of analogous bounding theorems related to the elastic shakedown. Some numerical applications devoted to a plane steel structure are effected and discussed.

• ETRI Journal
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• 제21권3호
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• pp.41-48
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• 1999

We have calculated differential reflection coefficient for isolated well structure of micro-scale, etched on dielectric surface. The differential reflection coefficient is computed using Green's second integral theorem. The purpose of our computation is to find a class of well profiles which give maximal diffusive scattering. To have such a maximal effect, we have concluded that the waist radius of Gaussian beam and its wavelength should be comparable to the well width and that well depth has to be larger than a wavelength. Exact calculation of differential reflection coefficients of dielectric surface with isolated structure on it may be used for the examination of dielectric surfaces and also in making simple but efficient diffuser.