• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.489-509
• /
• 2024

In this paper, let q ∈ (0, 1]. We establish the boundedness of intrinsic g-functions from the Hardy-Lorentz spaces with variable exponent H^p(·),q(ℝⁿ) into Lorentz spaces with variable exponent L^p(·),q(ℝⁿ). Then, for any q ∈ (0, 1], via some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of H^p(·),q(ℝⁿ) in terms of wavelets.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.363-447
• /
• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.3
• /
• pp.475-496
• /
• 2021

The main aim is to define a new class of generalized h-variational inequality problems and its generalized h-variational inequality problems. We define the class of h-𝜂-invex set, h-𝜂-invex function and H-pseudospace. Existence of the solution of the problems are established in H-pseudospace with the help of H-KKM mapping theorem and HC_*-condition of 𝜂 associated with the function h.

• Proceedings of the KIEE Conference
• /
• 2004.11c
• /
• pp.729-731
• /
• 2004

This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.247-260
• /
• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.29B no.3
• /
• pp.16-24
• /
• 1992

In this paper, we solve the problem of designing a robust optimal controller which minimizes the H$\infty$-norm of the mixed sensitivity function matrix for linear multivariable systems. For a given minimized value, ${\gamma}$>o, an algorithm of finding all stabilizing controllers, such that the H$\infty$-norm of the mixed sensitivity function matrix is less than ${\gamma}$, is developed. The proposed algorithm, which is based on the model-matching and the interpolation theory, can be used for the H$\infty$-optimization problem.

• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.31A no.8
• /
• pp.72-79
• /
• 1994

In this paper semi empirical models are presented for the hot electron induced threshold voltage shift(${\Delta}V_{t}$) and effective channel shortening length (${\Delta}L_{H}$) in degraded PMOSFET. Trapped electron charges in gate oxide are calculated from the well known gate current model and ΔLS1HT is calculated by using trapped electron charges. (${\Delta}L_{H}$) is a function of gate stress voltage such as threshold voltage shift and degradation of drain current. From the correlation between (${\Delta}L_{H}$) has a logarithmic function of stress time. From the measured results, (${\Delta}V_{t}$) and (${\Delta}L_{H}$) are function of initial gate current and device channel length.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.20 no.7
• /
• pp.611-614
• /
• 2007

The changes in the work $function({\Phi}_w)$ in the MgO protective layers after $plasma(Ar,\;H_2)$ treatment have been studied using ${\Upsilon}-focused$ ion beam $({\Upsilon}-FIB)$ system. The ${\Phi}_w$ was determined as follows: Ar-plasma $treatment({\Phi}_w=4.52eV)$, $H_2-plasma$ $treatment({\Phi}_w=5.65eV)$, and non-plasma $treatment({\Phi}_w=4.64eV)$. The results indicated that the H-plasma could not make any effective physical etching due to the small masses of hydrogen atoms and molecules while the hydration of H-plasma could grow some contaminating materials on the surface of MgO.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.10 no.10
• /
• pp.1796-1803
• /
• 2006

This Paper describes a systematic method for designing the $H_{\infty}$ controller for the inverted pendulum which is a nonlinear and single-input double-outputs system. In particular, the open-loop system is conbined with a pre-filter to shape the open-loop transfer function for the sensitivity function ind the complementary sensitivity function to be kept the desirable frequency characteristics. Consequently, the loop shaping technique of the open-loop transfer function reduces the impacts of the model uncertainties, measurement noises and exogenous disterbances on the dynamic characteristics of the inverted pendulum. The results of simulation and experiment show the efficiency of the proposed control method comparing with conventional PID control method.

• The Korean Journal of Physiology and Pharmacology
• /
• v.26 no.5
• /
• pp.325-333
• /
• 2022

Heart failure (HF) has become one of the severe public health problems. The detailed role of mitochondrial function in HF was still unclear. Benzoylaconine (BAC) is a traditional Chinese medicine, but its role in HF still needs to be explored. In this study, oxygen-glucose deprivation and reperfusion (OGD/R) was executed to mimic the injury of H9C2 cells in HF. The viability of H9C2 cells was assessed via MTT assay. OGD/R treatment markedly decreased the viability of H9C2 cells, but BAC treatment evidently increased the viability of OGD/R-treated H9C2 cells. The apoptosis of H9C2 was enhanced by OGD/R treatment but suppressed by BAC treatment. The mitochondrial membrane potential was evaluated via JC-1 assay. BAC improved the mitochondrial function and suppressed oxidative stress in OGD/R-treated H9C2 cells. Moreover, Western blot analysis revealed that the protein expression of p-AMPK and PGC-1α were reduced in OGD/R-treated H9C2 cells, which was reversed by BAC. Rescue assays indicated that AMPK attenuation reversed the BAC-mediated protective effect on OGD/R-treated cardiomyocytes. Moreover, BAC alleviated myocardial injury in vivo. In a word, BAC modulated the mitochondrial function in OGD/R-induced cardiomyocyte injury by activation of the AMPK/PGC-1 axis. The findings might provide support for the application of BAC in the treatment of HF.