• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1753-1757
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• 2015

In this note we obtain a unique continuation result for the differential inequality ${\mid}\bar{\partial}u{\mid}{\leq}{\mid}Vu{\mid}$, where $\bar{\partial}=(i{\partial}_y+{\partial}_x)/2$ denotes the Cauchy-Riemann operator and V (x, y) is a function in $L^2(\mathbb{R}^2)$.

• Korean Journal of Health Education and Promotion
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• v.23 no.2
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• pp.109-119
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• 2006

Objectives: A number of studies in economically developed countries have shown occurrence of stroke and cardiovascular disease to be inversely related to socioeconomic class. The purpose of this study is to investigate socioeconomic differentials in stroke and cardiovascular disease mortality in Korea. Methods: Two data from two sources, registry data from National Health Insurance Corporation and death certification data from National Statistics Office, were used to calculate mortality rate for five socioeconomic classes. Poisson regression analysis was used to calculate relative indices of inequality as a measure of mortality differentials between socioeconomic classes. Results: For males, graded socioeconomic differentials in mortality were observed with higher mortality rates related to lower socioeconomic class for intracerebral hemorrhage, cerebral infarct, hypertension, ischemic heart disease, myocardial infarct, and arrhythmia. The relative index of inequality for stroke and cardiovascular disease was 1.61(95% CI=1.54-1.68). For females, these differentials were observed for arrhythmia and intracerebral hemorrhage. The relative index of inequality was 1.06(95% CI=1.02-1.11). Conclusions: This socioeconomic differential in mortality, consistent with the results of other studies performed in economically developed countries suggest that Socioeconomic class can influence mortality regardless of the developmental stage of the country.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.43-55
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• 2011

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.819-835
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• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.427-435
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• 2007

The existence theorem and continuous dependence property in $"L^2"$ sense for solutions of backward stochastic differential equation (shortly BSDE) with Lipschitz coefficients were respectively established by Pardoux-Peng and Peng in [1,2], Mao and Cao generalized the Pardoux-Peng's existence and uniqueness theorem to BSDE with non-Lipschitz coefficients in [3,4]. The present paper generalizes the Peng's continuous dependence property in $"L^2"$ sense to BSDE with Mao and Cao's conditions. Furthermore, this paper investigates the continuous dependence property in "almost surely" sense for BSDE with Mao and Cao's conditions, based on the comparison with the classical mathematical expectation.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1409-1426
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• 2020

Let 𝒜_n be the class of analytic functions f(z) of the form f(z) = z + ∑^∞_k=n+1 α_kz^k, n ∈ ℕ defined on the open unit disk 𝔻, and let $${\Omega}_n:=\{f{\in}{\mathcal{A}}_n:\|zf^{\prime}(z)-f(z)\|<{\frac{1}{2}},\;z{\in}{\mathbb{D}}\}$$. In this paper, we make use of differential subordination technique to obtain sufficient conditions for the class Ω_n. Writing Ω := Ω₁, we obtain inclusion properties of Ω with respect to functions which map 𝔻 onto certain parabolic regions and as a consequence, establish a relation connecting the parabolic starlike class 𝒮_P and the uniformly starlike UST. Various radius problems for the class Ω are considered and the sharpness of the radii estimates is obtained analytically besides graphical illustrations.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.559-581
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• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.967-982
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• 2023

The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.335-335
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• 2000

Applications such as unmanned aerial vehicles (UAVs), autonomous underwater vehicles (AUVs) and the time varying nature of their navigation, guidance and control systems motivate an integrated approach to trajectory general ion and trajectory tracking for autonomous vehicles. In this paper, an experimental testbed was designed for studying this integrated trajectory control approach. In this paper we apply the separating approach to an autonomous nonlinear vehicle system. A new linear matrix inequality based H$_{\infty}$ control technique for periodic time-varying systems is applied to the role of trajectory tracking. Trajectory general ion is accomplished by exploit ing the differential flatness property of the vehicle system; this at lows product ion of desired feasible nominal or reference trajectories from certain ″flat'system outputs. Simulation and experimental results are presented showing stable tracking of a periodic circular trajectory.