• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.75-85
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• 2005

In this paper, the visco-Da-Rios equation; (0.1) ($$\frac{{\partial}{\gamma}}{{\partial}t}=\frac{{\partial}{\gamma}}{{\partial}s}{\bigwedge}\frac{D}{ds}\frac{{\partial}{\gamma}}{{\partial}s}+{\nu}\frac{{\partial}{\gamma}}{{\partial}s}$$) is investigated on 3-dimensional complete orientable Riemannian manifolds. The global existence of solution is discussed by trans-forming (0.1) into a cubic nonlinear Schrodinger equation for complete orient able Riemannian 3-manifolds of constant curvature.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.333-346
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• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.665-674
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• 2015

Lack of a general matrix formula hampers implementation of the semi-partial correlation, also known as part correlation, to the higher-order coefficient. This is because the higher-order semi-partial correlation calculation using a recursive formula requires an enormous number of recursive calculations to obtain the correlation coefficients. To resolve this difficulty, we derive a general matrix formula of the semi-partial correlation for fast computation. The semi-partial correlations are then implemented on an R package ppcor along with the partial correlation. Owing to the general matrix formulas, users can readily calculate the coefficients of both partial and semi-partial correlations without computational burden. The package ppcor further provides users with the level of the statistical significance with its test statistic.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.109-116
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• 1997

In the present paper we consider an abstract partial dif-ferential equation of the form $\frac{\partial^2u}{{\partial}t^2}-\frac{\partial^2u}{{\partial}x^2}+A(x.t)u=f(x, t)$, where ${A(x, t):(x, t){\epsilon}\bar{G} }$ is a family of linear closed operators and $G=GU{\partial}G$, G is a suitable bounded region in the (x, t)-plane with bound-are ${\partial}G$. It is assumed that u is given on the boundary ${\partial}G$. The objective of this paper is to study the considered Dirichlet problem for a wide class of operators $A(x, t)$. A Dirichlet problem for non-elliptic partial differential equations of higher orders is also considerde.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.205-209
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• 2005

In this paper we discuss on the uniquenss of the solution of partial differential equations: (1) $${\frac{{\partial}w}{{\partial}{\bar{z}}}}=F(z,\;w,\;{\frac{{\partial}w}{{\partial}z}}}+G(z,\;w.{\bar{w})$$ in the sobolev space $W_{1,p}(D)$.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.361-374
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• 2009

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.859-872
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• 2008

In this paper, the problem of partial asymptotic stabilization of nonlinear control cascaded systems with integrators is considered. Unfortunately, many controllable control systems present an anomaly, which is the non complete stabilization via continuous pure-state feedback. This is due to Brockett necessary condition. In order to cope with this difficulty we propose in this work the partial asymptotic stabilization. For a given motion of a dynamical system, say x(t,$x_0,t_0$)=(y(t,$y_0,t_0$),z(t,$z_0,t_0$)), the partial stabilization is the qualitative behavior of the y-component of the motion(i.e., the asymptotic stabilization of the motion with respect to y) and the z-component converges, relative to the initial vector x($t_0$)=$x_0$=($y_0,z_0$). In this work we present new results for the adding integrators for partial asymptotic stabilization. Two applications are given to illustrate our theoretical result. The first problem treated is the partial attitude control of the rigid spacecraft with two controls. The second problem treated is the partial orientation of the underactuated ship.

• Journal of Power Electronics
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• v.19 no.6
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• pp.1566-1574
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• 2019

Maximum power point tracking (MPPT) under the partial shading condition is a challenging research topic for photovoltaic systems. Shaded photo-voltaic module result in complex peak patterns on the power versus voltage curve which can misguide classical MPPT algorithms. Thus, various kinds of global MPPT algorithms have been studied. These have typically consisted of partial shading detection, global peak search and MPPT. The conventional partial shading detection algorithm aims to detect all of the occurrences of partial shading. This results in excessive execution of global peak searches and discontinuous operation of the MPPT. This in turn, reduces the achievable power for the PV module. Based on a theoretical investigation of power verse voltage curve patterns under various partial shading conditions, it is realized that not all the occurrences of partial shadings require a global peak search. Thus, an intelligent partial shading detection algorithm that provides exact identification of global peak search necessity is essential for the efficient utilization of solar energy resources. This paper presents a new partial shading determinant algorithm utilizing adaptive threshold levels. Conventional methods tend to be too sensitive to sharp shading patterns but insensitive to smooth patterns. However, the proposed algorithm always shows superb performance, regardless of the partial shading patterns.

• Clinics in Shoulder and Elbow
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• v.26 no.4
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• pp.366-372
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• 2023

Background: There is minimal literature on the morphology of partial distal biceps tendon (DBT) tears. We sought to investigate tear morphology by retrospectively reviewing 3-Tesla magnetic resonance imaging (3T MRI) scans of elbows with partial DBT tears and to propose a basic classification system. Methods: 3T MRI scans of elbows with partial DBT tears were retrospectively reviewed by two experienced observers. Basic demographic data were collected. Tear morphology was recorded including type, presence of retraction (>5 mm), and presence of discrete long-head and short-head tendons at the DBT insertion. Results: For analysis, 44 3T MRI scans of 44 elbows with partial DBT tears were included. There were 9 isolated long-head tears (20%), 13 isolated short-head tears (30%), 2 complete long-head tears with a partial short-head tear (5%), 5 complete short-head tears with a partial long-head tear (11%), and 15 peel-off tears (34%). Retraction was seen in 5 or 44 partial tears (11%), and 13 of the 44 DBTs were bifid tendons at the insertion (30%). Conclusions: Partial DBT tears can be classified into five sub-types: long-head isolated tears, short-head isolated tears, complete long-head tears with partial short-head involvement, complete short-head tears with partial long-head involvement, and peel-off tears. Classification of tears may have implications for operative and non-operative management. Level of evidence: III.