• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.165-714
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• 2007

The basis number of a graph G is the least positive integer $k$ such that G has a $k$-fold basis. In this paper, we prove that the basis number of the cartesian product of a path with a circular ladder, a M$\ddot{o}$bius ladder and path with a net is exactly 3. This improves the upper bound of the basis number of these graphs for a general theorem on the cartesian product of graphs obtained by Ali and Marougi, see [2]. Also, by this general result, the cartesian product of a theta graph with a M$\ddot{o}$bius ladder is at most 5. But in section 3 we prove that it is at most 4.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.3
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• pp.139-145
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• 2001

In this paper, we consider the H$_2$(or guaranteed cost control) and H$_{\infty}$ controller design methods for singular(or descriptor) systems with input time delay. Also, a mixed H$_2$and H$_{\infty}$ controller design algorithm is treated by combination of the proposed H$_2$and H$_{\infty}$ controller design method. The sufficient conditions for the existence of controllers and controller design methods are introduced at each Lemma and Theorem. Furthermore, we present optimization problems to get the upper bound of performance measures. The proposed methods are checked by examples.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.371-373
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• 1992

This note proposes a novel robust adaptive control algorithm for systems with unknown disturbances by introducing an additional term in the control input. This additional term is easily implementable by estimating the upper bound of the unknown disturbances. By this term, the output error can be made to be uniformly ultimately bounded in a desired region via Lyapunov second stability theorem when the relative degree of system is one.

• Magazine of the Korea Concrete Institute
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• v.10 no.1
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• pp.109-118
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• 1998

전단거동에 의해 지배되는 고강도 철근콘크리트 춤이 큰 보의 전단역학적 거동 및 전단강도특성을 고려한 이론식을 제시하고자 소성이론에 근거한 극한해석에서 상계치정리를 이용하여 이론적 전개를 하였으며, 고강도 R/C춤이 큰 보의 전단응력에 영향을 미치는 콘크리트 압축강도, 수직전단보강근 및 수평잔단보강근의 보강효과를 고려한 이론식을 제시하였으며, 수평철근 즉 주인장철근 및 수평전단보강근의 장부작용을 고려하였다. 실험결과와 비교할 때 제안식은 수직잔단보강근의 전단보강효과를 과대평가하고있으며, 수평전단보강근의 효과를 적절하게 평가하고 있음을 나타내었다. 또 전단스팬비가 0.5, 0.85인 경우에는 제안식에 의한 값이 다소 낮게 나타내, 전단스팬비가 낮은 경우는 다소 과소평가하는 것으로 나타났다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.677-682
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• 1985

극치해석적인 상계정리를 기초로 하여, 평면변형 인발에서 발생하는 내부결함(central bursting)을 예측하기 위해 중심에서 공동(voids)을 가진 금속에 대해 비례흐름(proportional flow)과 내부결 함의 흐름을 비교하여 해석하였다. 이 결함을 촉진시키는 공정조건에 대한 판정식(criterion)을 변형경화 금속에 대해 유도하였다. 공동을 가진 금속은 공동들을 축소시키기 위해 정상적인 재 료(sound material)의 흐름과 동일 방법으로 흐를 수 있으며, 경우에 따라서는 내부결함을 확장 하기 위해 흐를 수도 있다. 본 연구에서는 다이의 경사각, 단면감소율 및 마찰 등의 어떤 공정 변수 영역에서 중심축 상에 많은 공동을 가진 변형경화 금속에서도 내부결함이 발생할 수 있다는 것이다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.33-40
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• 1998

Although a structural analysis based on e linear elastic theory yields good results for deformations and stresses produced by working loads, it fails to assess the teal load-carrying of the plates on the verge of yielding. In case of a limit analysis of plates, the yield line theory is widely used on the basis of the upper bound theorem and theoretically it overestimates the strength of the plate. There is, therefore, a general need for analytical methods of predicting the inelastic behavior and load-carrying capacities of plate subjected to arbitrary loadings and boundary conditions. The $\rho$-version of finite element method has been presented for determining the accurate limit load of plates. The numerical results by $\rho$-version model compares with the results obtained by the h-version software ADINA as well as with the available analytical solutions in literatures.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.35-44
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• 1994

In this paper we study exponential growth of Betti numbers over artinian local rings. By the Change of Tor Formula the results in the paper extend to the asymptotic behavior of Betti numbers over Cohen-Macaulay local rings. Using the length function of an artinian ring we calculate an upper bound for the number of generators of modules, this is then used to maximize the number of generators of sygyzy modules. Finally, applying a filtration of an ideal, which we call a Loewy series of an ideal, we derive an invariant B(R) of an artinian local ring R, such that if B(R)>1, then the sequence $b^{R}$$_{i}$ (M) of Betti numbers is strictly increasing and has strong exponential growth for any finitely generated non-free R-module M (Theorem 2.7).).

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.1967-1969
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• 2001

This paper deals with the design of observer-based $H_{\infty}$ controller for linear time-delay systems. By adapting the model transformation and Lyapunov theorem, we presents a sufficient condition which meets the prescribed $H_{\infty}$ norm upper bound from the exogenous disturbances to the measured outputs. The conditions are expressed in terms of coupled two matrix inequalities, and the $H_{\infty}$ controller and the observer are obtained by checking the feasibility of two matrix inequalities. Finally, we shows the usefulness of our result by an example.

• Transactions of Materials Processing
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• v.23 no.3
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• pp.139-144
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• 2014

In the current study, we present a new model for predicting width spread of a slab with a dog-bone shaped cross section during rolling in the roughing train of a hot strip mill. The approach is based on the extremum principle for a rigid plastic material and a three dimensional admissible velocity field. The upper bound theorem is used for calculating the width spread of the slab. The prediction accuracy of the proposed model is examined through comparison with the predictions from 3-D finite element (FE) process simulations.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.181-195
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• 2000

A two-step procedure for the application of non linear constrained programming to the limit analysis of rigid brick-block systems with no-tension and frictional interface is implemented and applied to various masonry structures. In the first step, a linear problem of programming, obtained by applying the upper bound theorem of limit analysis to systems of blocks interacting through no-tension and dilatant interfaces, is solved. The solution of this linear program is then employed as initial guess for a non linear and non convex problem of programming, obtained applying both the 'mechanism' and the 'equilibrium' approaches to the same block system with no-tension and frictional interfaces. The optimiser used is based on the sequential quadratic programming. The gradients of the constraints required are provided directly in symbolic form. In this way the program easily converges to the optimal solution even for systems with many degrees of freedom. Various numerical analyses showed that the procedure allows a reliable investigation of the ultimate behaviour of jointed structures, such as stone masonry structures, under statical load conditions.