• Bulletin of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1567-1605
• /
• 2023

Let d ∈ ℕ and α ∈ (0, min{2, d}). For any a ∈ [a^*, ∞), the fractional Schrödinger operator 𝓛_a is defined by 𝓛_a := (-Δ)^α/2 + a|x|^-α, where $a^*:={\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}(d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with 𝓛_a and two-weight norm estimates for several square functions associated with 𝓛_a.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.35-59
• /
• 2006

In this paper, we generalized the results of [23, 26], and get the results of the condition number of the W-weighted Drazin-inverse solution of linear system W AW\chi=b, where A is an $m{\times}n$ rank-deficient matrix and the index of A W is $k_1$, the index of W A is $k_2$, b is a real vector of size n in the range of $(WA)^{k_2}$, $\chi$ is a real vector of size m in the range of $(AW)^{k_1}$. Let $\alpha$ and $\beta$ be two positive real numbers, when we consider the weighted Frobenius norm $\|[{\alpha}W\;AW,\;{\beta}b]\|$(equation omitted) on the data we get the formula of condition number of the W-weighted Drazin-inverse solution of linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.13.2-13
• /
• 2003

We propose some properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses versus on with loss function.

• Journal of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.733-763
• /
• 2006

We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.40-45
• /
• 1991

This paper deals with the design of feedback controllers which minimize the $H^{\infty}$-norm of the weighted sensitivity function. Using the Lagrange multiplier method and the Nevanlinna-Pick interpolation theory, an algorithm which stabilizes a plant and makes the output to track the reference signal is proposed..

• Journal of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.613-624
• /
• 2000

We characterize a condition for M to be of weak type ($\Phi$1, $\Phi$2) in terms of Orlicz norms.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.833-842
• /
• 2011

We prove that Toeplitz operators with symbols in RW are bounded and we calculate some upper bounds of the norm of these Toeplitz operators. We also analyze n-th derivative of Toeplitz operators and get some local estimates.

• Journal of the Korean Society for Precision Engineering
• /
• v.25 no.2
• /
• pp.72-79
• /
• 2008

In the redundant actuation system which has more actuators than a system's mobility, there are various method to determine actuated torques because those are not determined uniquely. This paper presents a torque distribution method using weighted-pseudoinverse to optimize the maximum torque of various actuated inputs of the redundant system. The various weighting factor of weighted-pseudoinverse is studied to reduce maximum actuated torque. This method is experimentally applied to 3RRR parallel robot, which shows that presented method can efficiently reduce the maximum actuated torque.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.39 no.1
• /
• pp.33-41
• /
• 2002

In this paper, we present a frequency weighted model reduction using LMIs for minimizing the H$\infty$ weighted model error compared with the methods of frequency weighted balanced truncation and frequency weighted Hankel norm approximation. The proposed algorithm, its form is equal to the sufficient condition of performance preserving controller approximation, is based on an iterative two-step LMI scheme induced from bound real lemma. So, it can be applied to the problem of the performance preserving controller approximation. The controller reduction is useful in a practical control design and ensures its easy implementation and high reliability The validity of the proposed algorithm is shown through numerical examples. Additionaly, we extend the proposed algorithm to performance preserving controller approximation by applying to the HIMAT(highly maneuverable aircraft technology) system.

• Journal of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.203-224
• /
• 2014

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.