• International Journal of Control, Automation, and Systems
• /
• v.6 no.6
• /
• pp.960-967
• /
• 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.

• Journal of the Korean Society for Precision Engineering
• /
• v.8 no.3
• /
• pp.93-104
• /
• 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)
• /
• v.16 no.6
• /
• pp.2074-2093
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.593-609
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.631-638
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.4
• /
• pp.687-689
• /
• 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 $2p$.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.1001-1016
• /
• 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
• /
• v.6 no.2
• /
• pp.269-277
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.167-177
• /
• 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].

• Journal of KIISE:Software and Applications
• /
• v.37 no.1
• /
• pp.60-73
• /
• 2010

This paper aims to describe KorLexClas 1.5 which provides us with a very large list of Korean numeral classifiers, and with the co-occurring noun categories that select each numeral classifier. Differently from KorLex of other POS, of which the structure depends largely on their reference model (Princeton WordNet), KorLexClas 1.0 and its extended version 1.5 adopt a direct building method. They demand a considerable time and expert knowledge to establish the hierarchies of numeral classifiers and the relationships between lexical items. For the efficiency of construction as well as the reliability of KorLexClas 1.5, we use following processes: (1) to use various language resources while their cross-checking for the selection of classifier candidates; (2) to extend the list of numeral classifiers by using a shallow parsing techniques; (3) to set up the hierarchies of the numeral classifiers based on the previous linguistic studies; and (4) to determine LUB(Least Upper Bound) of the numeral classifiers in KorLexNoun 1.5. The last process provides the open list of the co-occurring nouns for KorLexClas 1.5 with the extensibility. KorLexClas 1.5 is expected to be used in a variety of NLP applications, including MT.