• International Journal of Control, Automation, and Systems
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• 제6권6호
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• pp.960-967
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• 2008

This paper shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system.

• 한국정밀공학회지
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• 제8권3호
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• pp.93-104
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• 1991

Limit analysis is based on the duality theorem which equates the least upper bound to the greatest lower bound. In this study, limit analysis of axisymmetric forming problem with workhardening materials is formulated by minimizing the upper bound functional and finite element program is developed for forward estrusion. Limit loads, velocity and flow line fields are directly obtained under various process conditions and deformation characteristics such as strains, strain rates and grid distortion are obtained from the optimum velocity components by numerical calculation. The experimental observation was carried out for extrusion and compared with computed results. The good agreement between theoretical and experimental results is shown that the developed programming is very effective for the analysis of axisymmetric extrusion.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권6호
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• pp.2074-2093
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• 2022

RSA is known as one of the best techniques for securing secret information across an unsecured network. The private key which is one of private parameters is the aim for attackers. However, it is exceedingly impossible to derive this value without disclosing all unknown parameters. In fact, many methods to recover the private key were proposed, the performance of each algorithm is acceptable for the different cases. For example, Wiener's attack is extremely efficient when the private key is very small. On the other hand, Fermat's factoring can quickly break RSA when the difference between two large prime factors of the modulus is relatively small. In general, if all private parameters are not disclosed, attackers will be able to confirm that the private key is unquestionably inside the scope [3, n - 2], where n is the modulus. However, this scope has already been reduced by increasing the greatest lower bound to [d_il, n - 2], where d_il ≥ 3. The aim of this paper is to decrease the least upper bound to narrow the scope that the private key will remain within this boundary. After finishing the proposed method, the new scope of the private key can be allocated as [d_il, d_ir], where d_ir ≤ n - 2. In fact, if the private key is extremely close to the new greatest lower bound, it can be retrieved quickly by performing a brute force attack, in which d_ir is decreased until it is equal to the private key. The experimental results indicate that the proposed method is extremely effective when the difference between prime factors is close to each other and one of two following requirement holds: the first condition is that the multiplier of Euler totient function is very close to the public key's small value whereas the second condition is that the public key should be large whenever the multiplier is far enough.

• 대한수학회지
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• 제39권4호
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• pp.593-609
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• 2002

The order of speciality of an ample invertible Sheaf L on a curve is the least integer m so that $L^{ m}$ is nonspecial. There is a reasonable upper bound of the order of speciality for a simple invertible sheaf in terms of its degree and projective dimension. We study the case where it reaches the upper bound. Moreover we for mulate Castelnuovo's genus bound involving the order of speciality.ality.

• 대한수학회논문집
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• 제33권2호
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• pp.631-638
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• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• 충청수학회지
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• 제25권4호
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• pp.687-689
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• 2012

We find an upper bound on the least positive exponent of a nonzero Fourier coefficient for a modular form with a nonzero constant term for ${\Gamma}_0(N)$ under certain conditions where N is a prime number $p$ or $2p$.

• 대한수학회지
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• 제56권4호
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• International Journal of Control, Automation, and Systems
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• 제6권2호
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• pp.269-277
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• 2008

This paper proposes a necessary and sufficient condition of convergence in the $L_2$-norm sense for a feedback-based iterative learning control (ILC) system including a multi-input multi-output (MIMO) linear time-invariant (LTI) plant. It is shown that the convergence conditions for a nominal plant and an uncertain plant are equal to the nominal performance condition and the robust performance condition in the feedback control theory, respectively. Moreover, no additional effort is required to design an iterative learning controller because the performance weighting matrix is used as an iterative learning controller. By proving that the least upper bound of the $L_2$-norm of the remaining tracking error is less than that of the initial tracking error, this paper shows that the iterative learning controller combined with the feedback controller is more effective to reduce the tracking error than only the feedback controller. The validity of the proposed method is verified through computer simulations.

• 대한수학회보
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• 제59권1호
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• pp.167-177
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• 2022

A vertex v of a graph G = (V, E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is called a double vertex-edge dominating set if every edge of E is ve-dominated by at least two vertices of S. The minimum cardinality of a double vertex-edge dominating set of G is the double vertex-edge domination number γ_dve(G). In this paper, we provide an upper bound on the double vertex-edge domination number of trees in terms of the order n, the number of leaves and support vertices, and we characterize the trees attaining the upper bound. Finally, we design a polynomial time algorithm for computing the value of γ_dve(T) for any trees. This gives an answer of an open problem posed in [4].

• 한국정보과학회논문지:소프트웨어및응용
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• 제37권1호
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• pp.60-73
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• 2010

본 연구의 목적은 한국어 수분류사 체계를 설정하고, 수분류사와 공기명사 간 의미관계 정보를 제공하는 한국어 수분류사 어휘의미망 "KorLexClas 1.5"의 정보구조와 구축방식을 소개하는 데 있다. KorLex 명사, 동사, 형용사, 부사가 영어 워드넷(Princeton WordNet)을 기반으로 참고구축 방식으로 개발된 것에 비해, KorLexClas 1.0버전과 이를 확장한 1.5버전은 직접구축 방식으로 개발하였다는 점에서, 수분류사의 계층구조와 언어단위 간 의미관계 설정은 매우 방대한 시간과 정교한 구축 방식을 요구한다. 따라서 작업의 효율성을 기함과 동시에, 구축된 어휘의미망의 신뢰성 및 확장성을 높이기 위해, (1) 다양한 기구축 언어자원을 활용하되 상호 검증하는 절차를 거치고, (2) 부분문장 분석방법을 이용하여, 수분류사 및 공기명사 목록을 확장하며, (3) 언어학적 준거를 기준으로 수분류사의 계층구조를 설정하고, (4) 수분류사와 공기명사 간 의미관계 정보를 제공하되 확장성을 확보하기 위해, KorLexNoun 1.5에 '최하위 공통상 위노드(LUB : Least Upper Bound)'를 설정하는 방식을 택한다. 이러한 특성을 가진 KorLexClas 1.5는 기계번역을 비롯한 한국어정보처리의 제 분야에 응용될 수 있다.