• 제어로봇시스템학회:학술대회논문집
• /
• 1995.10a
• /
• pp.332-335
• /
• 1995

A simple and effective method for improving Euclidean norm condition number for chemical processing system is presented. The singular value sensitivities of Freudenberg et al. (1982) is used to estimate the behavior of singular values of process transfer function matrix when design parameter is changed, then the condition number can be calculated straightforwardly. The method requires explicit dependencies of each transfer function matrix elements on design parameters. These dependencies can be obtained either by symbolic differentiation in the form of explicit function of design parameters, or by numerical perturbation studies for units with large and complicated models. Gerschgorin-type lower bound for minimum singular value is introduced to detect the large divergencies near singular point due to linearity of sensitivities. The case studies are performed to show the efficiency of the proposed method.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1994.10a
• /
• pp.223-228
• /
• 1994

A new velocity formulation technique, which contains the advantage of UBET and the shape function of FEM, is proposed. In the proposed technique, a shape function is used to improve the unreasonableness of elemental partition and to solve the difficulty of velocity-field determination. In order to verify the effectiveness of this rechnique, T-shaped forging processes are simulated. The results are compared with these obtained by experimental measurements in T-shaped forging. In T-shaped forging, good agreements between theory and experiment are also confined.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.3
• /
• pp.189-202
• /
• 2009

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.3
• /
• pp.861-869
• /
• 2006

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, the problem of determining optimal burn-in time for a system which performs given mission is considered. It is assumed that the given mission time is not a fixed constant but a random variable which follows an exponential distribution. Assuming that the underlying lifetime distribution of a system has an eventually increasing failure rate function, an upper bound for the optimal burn-in time which maximizes the probability of performing given mission is derived. The obtained result is also applied to an illustrative example.

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.521-534
• /
• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• Korean Journal of Mathematics
• /
• v.27 no.4
• /
• pp.1027-1041
• /
• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.579-588
• /
• 2005

In this paper we study the asymptotics for the energy density in the self-dual Chern-Simons CP(1) model. When the sequence of corresponding multivortex solutions converges to the topological limit, we show that the field configurations saturating the energy bound converges to the limit function. Also, we show that the energy density tends to be concentrated at the vortices and antivortices as the Chern-Simons coupling constant $\kappa$ goes to zero.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.10 no.1
• /
• pp.31-40
• /
• 1985

When an economy has institutional price constraints the relationship between market prices and shadow prices is not yet fully investigated. A pure consumption economy is considered where market prices guide the consumption behavior and shadow prices measure the social value of resources. In this case we show that if the utility function is additively separable there exists a complementarity relation between the difference of the market price and the shadow price and the difference of the market price and the regulated upper (or lower) bound.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1635-1646
• /
• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• Review of KIISC
• /
• v.2 no.4
• /
• pp.30-36
• /
• 1992

이 논문에서 우리는 여러 가지 분할 항등식을 유도했고 제한된 분할에 관한 새로운 항등식을 증명하고, 분할의 기본적인 이론과 분할함수(Partition Number Function)가 다항식 함수가 아니라는 것을 보이며, n 의 분할의 수 p(n)에 대한 하계(Lower Bound)를 얻기 위해 Stirling의 n ! 에 대한 근사값을 소개한다. 그리고 Hardy-Ramanujan 공식, Euler 항등식과 p(n) 의 순환식을 유도하며, 그리고 $d_m$(n)이n을m개의 부분으로 분할하는 분할의 수를 나타낼 때 우리는 $d_m$(n)에 관한 일반적인 공식을 p(n)과 함께 행렬식의 형태로 표현한다.