• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.15-33
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• 2024

In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

• 충청수학회지
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• 제27권2호
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• pp.271-276
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• 2014

Recently, Taji [7] and Harms et al. [4] studied the regularized gap function of QVI analogous to that of VI by Fukushima [2]. Discussions are made in a finite dimensional Euclidean space. In this note, an infinite dimensional generalization is considered in the framework of a reflexive Banach space. To do so, we introduce an extended quasi-variational inequality problem (in short, EQVI) and a generalized regularized gap function of EQVI. Then we investigate some basic properties of it. Our results may be regarded as an infinite dimensional extension of corresponding results due to Taji [7].

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.795-812
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• 2013

The merit function arises from the development of the solution methods for the complementarity problems defined over the cone of non negative real vectors and has been well extended to the complementarity problems defined over the symmetric cones. In this paper, we focus on the extension of the merit functions including the gap function, the regularized gap function, the implicit Lagrangian and others to the complementarity problems defined over the nonsymmetric matrix cone. These theoretical results of this paper suggest new solution methods based on unconstrained and/or simply constrained methods to solve the matrix cone complementarity problems (MCCP).

• BMB Reports
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• 제28권4호
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• pp.316-322
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• 1995

The GTPase activating protein (GAP) can function both as a negative regulator and an effector of $p21^{ras}$. Overexpression of GAP in NIH-3T3 cells has been shown to inhibit transformation by ms or src. To investigate the function of GAP in a differentiative system, we overexpressed this protein in the nerve growth factor (NGF)-responsive PC12 cell line. Two-fold overexpression of GAP caused a delay of several days in the onset of NGF- but not FGF-induced neuronal differentiation of PC12 cells. However, the NGF-induced activation or tyrosine phosphorylation of upstream (Trk, PLC-${\gamma}1$, SHC) and downstream (B-Raf and $p44^{mapk/erk1}$) components of $p21^{ras}$, signalling cascade was not altered by GAP overexpression. Therefore, the change of phenotype induced by GAP was probably not due to GAP functioning as a negative regulator of $p21^{ras}$. Rather, we found that NGF-induced tyrosine phosphorylation of SNT, a specific target of neurotrophin-induced tyrosine kinase activity, was inhibited by GAP overexpression. SNT is thought to function upstream or independent of $p21^{ras}$. Thus in PC12 cells, overexpressed GAP may control the rate of neuronal differentiation through a pathway involving SNT rather than the $p21^{ras}$ signalling pathway.

• 충청수학회지
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• 제28권1호
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• pp.145-150
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• 2015

Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.

• 한국결정성장학회지
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• 제16권1호
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• pp.20-24
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• 2006

Iridium-catalyzed carbon nanofilaments were formed on MgO substrate as a function of the gap between the substrate and the plasma using microwave plasma-enhanced chemical vapor deposition method. Under the remote plasma condition, carbon nanofibers were formed on the substrate. Under the adjacent plasma condition, on the other hand, carbon nanotubes-like materials instead of carbon nanofibers could be formed. When the substrate immersed into the plasma, any carbon nanofilaments formation couldn't be observed. During the reaction, the substrate temperatures were measured as a function of the gap. Based on these results, the cause for the different carbon nanofilaments formation according to the gap was discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 춘계학술대회논문집; 부산수산대학교, 10 May 1996
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• pp.95-99
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• 1996

In this paper, we proposed a method to measure the gap between the magnetic pole and the levitated object applying the inductance characteristic which vary according to gap. We made a driving circuit which supply the control input PWM(Pulse Width Modulation) signal and the carrier PWM signal to estimate the gap. Because the inductance is a function of gap, and the current of the carrier signal is a function of the inductance. We investigated the validity of the proposed method through the experimental results.

• Journal of the Optical Society of Korea
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• 제20권5호
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• pp.628-632
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• 2016

We studied experimentally and theoretically the vertical range of the confined electric field in the gap area of metamaterials, which was analyzed for various gap widths using terahertz time-domain spectroscopy. We measured the resonant frequency as a function of the thickness of poly(methyl methacrylate) in the range 0 to 3.2 μm to quantify the effective detection volumes. We found that the effective vertical range of the metamaterial is determined by the size of the gap width. The vertical range was found to decrease as the gap width of the metamaterial decreases, whereas the sensitivity is enhanced as the gap width decreases due to the highly concentrated electric field. Our experimental findings are in good agreement with the finite-difference time-domain simulation results. Finally, a numerical expression was obtained for the vertical range as a function of the gap width. This expression is expected to be very useful for optimizing the sensing efficiency.

• 대한수학회보
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• 제61권2호
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• pp.469-477
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• 2024

For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on the interval [0, 2]. It is known that this invariant of an L-space knot is the Legendre-Fenchel transform (or, convex conjugate) of a certain gap function derived from the Alexander polynomial. To recover an information lost in the Upsilon invariant, Kim and Livingston introduced the secondary Upsilon invariant. In this note, we prove that the secondary Upsilon invariant of an L-space knot is a concave conjugate of a restricted gap function. Also, a similar argument gives an alternative proof of the above fact that the Upsilon invariant of an L-space knot is a convex conjugate of a gap function.

• 한국수학교육학회지시리즈A:수학교육
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• 제37권1호
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• pp.87-99
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• 1998

Mathematics education is very important in future because mathematics is the basis of every study, for example, natural and social science, etc. Our nation wide curriculum has been revised six times since 1948. In 1992, the sixth revision was enforced and we are using the revised textbook now. This study aims at helping of continuous investigation for educational curriculum and textbook, and aims at efficient teaching by preventing unnecessary repetition and excessive gap in real field by analyzing the articulation of Analytics part in school textbook from elementary to high school. This thesis consists of the followings. 1.Investigation of the principles and natures of articulation along with curriculum course and notice the articulation based on the analysing tools. 2.Importance of learning functions. 3.To get the propriety, formation of 8 judging group and classification of content materials in function chapters by the judges based on the analyzing tools. 4.Analysis of presentation method and terminologies in the first concepts, suggestion teaching method to reduce gap and help of understanding on first concepts in the study of function. As a result 'development' consists of 55.8% of the total and it is higher than 'duplication' and 'gap'. To be specific in periods, between elementary school and middle school 'development' takes 64.5% and this shows an acceptable articulation in the period. While 39.4% of 'gap' in articulation between middle school and high school looks high compared with 'gap' between the previous periods. The item suggested with the 'gap' is the 'definition of function', 'value of function', 'parallel translation', 'exponential and logarithmic function'. It is observed that these materials is suddenly appeared in high school.