• Communications of the Korean Mathematical Society
• /
• v.21 no.2
• /
• pp.293-320
• /
• 2006

Using calculus inequalities and embedding theorems in $R^1$, we establish $W^1_2$-estimates for the solutions of prey-predator population model with cross-diffusion and self-diffusion terms. Two cases are considered; (i) $d_1\;=\;d_2,\;{\alpha}_{12}\;=\;{\alpha}_{21}\;=\;0$, and (ii) $0\;<\;{\alpha}_{21}\;<\;8_{\alpha}_{11},\;0\;<\;{\alpha}_{12}\;<\;8_{\alpha}_{22}$. It is proved that solutions are bounded uniformly pointwise, and that the uniform bounds remain independent of the growth of the diffusion coefficient in the system. Also, convergence results are obtained when $t\;{\to}\;{\infty}$ via suitable Liapunov functionals.

• Kyungpook Mathematical Journal
• /
• v.59 no.3
• /
• pp.465-480
• /
• 2019

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K^{\varphi}_wf)_{w>0}$. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in $C({\mathbb{R}})$, the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$ for the family $(K^{\varphi}_wf)_{w>0}$. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.239-263
• /
• 2019

The $Calder{\acute{o}}n$-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity $a({\xi},x_1,x^{\prime})$ is assumed to be only measurable in one spatial variable $x_1$ and has locally small BMO semi-norm in the other spatial variables x', uniformly in ${\xi}$ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.595-619
• /
• 2022

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1305-1315
• /
• 2022

Let u be a function on a connected finite graph G = (V, E). We consider the mean field equation (1) $-{\Delta}u={\rho}\({\frac{he^u}{\int_Vhe^ud{\mu}}}-{\frac{1}{{\mid}V{\mid}}}\),$ where ∆ is 𝜇-Laplacian on the graph, 𝜌 ∈ ℝ\{0}, h : V → ℝ⁺ is a function satisfying min_x∈V h(x) > 0. Following Sun and Wang [15], we use the method of Brouwer degree to prove the existence of solutions to the mean field equation (1). Firstly, we prove the compactness result and conclude that every solution to the equation (1) is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation (1), say $$d_{{\rho},h}=\{{-1,\;{\rho}>0, \atop 1,\;{\rho}<0.}$$ Consequently, the equation (1) has at least one solution due to the Brouwer degree d_𝜌,h ≠ 0.

• Proceedings of the Korean Vacuum Society Conference
• /
• 2012.08a
• /
• pp.166-166
• /
• 2012

We examined the distribution of Co ions of ferromagnetic n-type Zn(1-x)Co(x)O semiconducting films with the Co concentrations of 0.03~0.07 using x-ray absorption fine structure (XAFS) measurements at the Co and Zn K edges. Extended XAFS (EXAFS) revealed that Co ions mainly occupied the zinc sites of the films. X-ray absorption near edge structure (XANES) spectra demonstrated that the pre-edge peak of the Co K edge was substantially affected by the second neighboring Co ions at the zinc sites due to hybridizing of the Co 4p conduction electrons with the Co 3d bounded electrons. From XANES and EXAFS analysis using ab initio calculations, we found that Co ions uniformly occupied the zinc sites of the Zn (0.93) Co (0.07)O film, whereas the Co ions of the Zn (0.97) Co (0.03)O and Zn (0.95) Co (0.05)O films were substituted at localized zinc sites. The ferromagnetic properties of the Zn (0.93) Co(0.07)O film could be induced by direct interaction between the magnetic dipoles of the Co ions with a mean distance of 4.3 A or by Co 4p electron mediation.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.37 no.1
• /
• pp.1-9
• /
• 2000

In this paper, we design a robust output feedback controller for robot manipulators with bounded parametric uncertainties using high-gain observer. The proposed control scheme with integral action improves tracking error due to limit of the robust feedback gains. High-gain observer is used to solve the noise problem with the joint velocity measurement. This controller avoids the limitation on the variation of unknown parameters and guarantees the uniformly ultimate boundedness of the closed-loop system. The performance of the proposed method is demonstrated by simulation on a 2-link manipulator.

• Journal of the Korean Ceramic Society
• /
• v.29 no.12
• /
• pp.926-934
• /
• 1992

Uniform diamond films in a few $\textrm{mm}^2$ size and locally isolated diamond single crystals in size of 60 $\mu\textrm{m}$ were synthesized on Si-wafer and Al2O3 substrate by the method of acetylene flame. The effects of substrate temperature and flow ratio of oxygen to acetylene on the morphology of deposited diamond were investigated. According to the observations of growth behavior of diamond on Si substrate with respect to substrate surface pretreatment and flow ratio, it was shown that well faceted diamonds could grow uniformly when flow ratio was above 0.9 and substrates were densely scratched. With increasing substrates temperature, the crystal morphology changes from octahedron bounded by only {111} plane below 850$^{\circ}C$ to cubo-octahedron with almost equal development of {111} and {100} plane in the temperature range of 850∼950$^{\circ}C$. Between 950∼1050$^{\circ}C$, the {111} faces become rough and concave. Above 1050$^{\circ}C$, new crystallites begin to grow on concave {111} surface and overall morphology looks like cubo-octahedron with degenerated {111} faces. These changes of morphology can be understood in terms of the different growth mode of each crystallographic plane with respect to the substrate temperature and supersaturation. And the observed phenomena on {111} planes can be related to the face instability and twin generation.

• Journal of Electrical Engineering and Technology
• /
• v.12 no.6
• /
• pp.2365-2377
• /
• 2017

This paper addresses two interrelated problems concerning the tracking control of pod propulsion unmanned surface vessel (USV), namely, the modeling of pod propulsion USV, and tracking controller design. First, based on MMG modeling theory, the model of pod propulsion USV is derived. Furthermore, a practical adaptive neural tracking controller is proposed by backstepping technique, neural network approximation and adaptive method. Meanwhile, unlike some existing tracking methods for surface vessel whose control algorithms suffer from "explosion of complexity", a novel neural shunting model is introduced to solve the problem. Using a Lyapunov functional, it is proven that all error signals in the system are uniformly ultimately bounded. The advantages of the paper are that first, the underactuated characteristic of pod propulsion USV is proved; second, the neural shunting model is used to solve the problem of "explosion of complexity", and this is a combination of knowledge in the field of biology and engineering; third, the developed controller is able to capture the uncertainties without the exact information of hydrodynamic damping structure and the sea disturbances. Numerical examples have been given to illustrate the performance and effectiveness of the proposed scheme.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.111-127
• /
• 2005

Let B and S be the unit ball and the unit sphere in $\mathbb{C}^n$, respectively. Let ${\sigma}$ be the normalized Lebesgue measure on S. Define the Privalov spaces $N^P(B)\;(1\;<\;p\;<\;{\infty})$ by $$N^P(B)\;=\;\{\;f\;{\in}\;H(B) : \sup_{0 where H(B) is the space of all holomorphic functions in B. Let ${\varphi}$ be a holomorphic self-map of B. Let ${\mu}$ denote the pull-back measure ${\sigma}o({\varphi}^{\ast})^{-1}$. In this paper, we prove that the composition operator $C_{\varphi}$ is metrically bounded on $N^P$(B) if and only if ${\mu}(S(\zeta,\delta)){\le}C{\delta}^n$ for some constant C and $C_{\varphi}$ is metrically compact on $N^P(B)$ if and only if ${\mu}(S(\zeta,\delta))=o({\delta}^n)$ as ${\delta}\;{\downarrow}\;0$ uniformly in ${\zeta}\;\in\;S. Our results are an analogous results for Mac Cluer's Carleson-measure criterion for the boundedness or compactness of $C_{\varphi}$ on the Hardy spaces $H^P(B)$.