• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.887-902
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• 2023

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y²] + [x², f(y)] on a 𝜌-complete convex modular *-algebra χ_𝜌 by using ∆₂-condition via convex modular 𝜌.

• 한국군사과학기술학회지
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• 제14권2호
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• pp.313-320
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• 2011

SPH(Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique that is useful as an alternative numerical analysis method used to analyze high deformation problems as well as astrophysical and cosmological problems. In SPH, all points within the support of the kernel are taken as neighbours. The accuracy of the SHP is highly influenced by the method for choosing neighbours from all particle points considered. Typically a linked-list method or tree search method has been used as an effective tool because of its conceptual simplicity, but these methods have some liability in anisotropy situations. In this study, convex hull algorithm is presented as an improved method to eliminate this artifact. A convex hull is the smallest convex set that contains a certain set of points or a polygon. The selected candidate neighbours set are mapped into the new space by an inverse square mapping, and extract a convex hull. The neighbours are selected from the shell of the convex hull. These algorithms are proved by Fortran programs. The programs are expected to use as a searching algorithm in the future SPH program.

• International Journal of Aeronautical and Space Sciences
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• 제4권2호
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• pp.9-16
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• 2003

Piezoelectric materials are widely used to construct smart or adaptive structures. Although extensive efforts have been devoted to the analysis of piezoelectric materials in recent years, most researches have been conducted by assuming that the material properties are fixed and have no uncertainties. Intrinsically, material properties have a certain amount of scatter and such uncertainties can affect the performance of component. In this paper, the convex modeling is used to consider such uncertainties in calculating the crack extension force of piezoelectric material and the results are compared with the one obtained via the Monte Carlo simulation. Numerical results show that crack extension forces increase when uncertainties considered, which indicates that such uncertainties should not be ignored for reliable lifetime prediction. Also, the results obtained by the convex modeling and the Monte Carlo simulation show good agreement, which demonstrates the effectiveness of the convex modeling.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• 전기의세계
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• 제22권3호
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• pp.13-24
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• 1973

In this report, as a method to solve the problems on impulse insulation coordination in ribbon core transformer owing to it's BIL stepping up, new design to alter winding distribution of multiple-layer concentric winding to Convex type winding is proposed. The main focus of this method is to settle the weakness of axial direction insulation strength and as a result of theoretical analysis through experiment of model transformers, the following conclusions are obtained; (a) As the electric loadings in a design which increases by strengthenning axial direction insulation endurance in presently avarilable transformers owing to it's BIL stepping up can be restricted in Convex type winding, reasonable design will be suited to the transformer with higher BIL. (b) Convex type winding is a very improved insulation design in respect of insulation coordination because it has shield plate effect to even impulse oscillation. (c) There is a disadvantage to cause leakage flux to increase in Convex type winding, however, the constancy of electric loadings in a design in spite of BIL stepping up restricts the increase of leakage flux to some extent.

• 한국지능시스템학회논문지
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• 제18권1호
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• pp.145-149
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• 2008

The similarity measure is constructed for non-convex fuzzy membership function using well known Hamming distance measure. Comparison with convex fuzzy membership function is carried out, furthermore characteristic analysis for non-convex function are also illustrated. Proposed similarity measure is proved and the usefulness is verified through example. In example, usefulness of proposed similarity is pointed out.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.123-134
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• 2023

Since Knaster, Kuratowski, and Mazurkiewicz established their KKM theorem in 1929, it was first applied to topological vector spaces mainly by Fan and Granas. Later it was extended to convex spaces by Lassonde and to extensions of c-spaces by Horvath. In 1992, such study was called the KKM theory by ourselves. Then the theory was extended to generalized convex spaces or G-convex spaces. Motivated by such spaces, there have appeared several particular types of artificial spaces. In 2006 we introduced abstract convex spaces which contain all existing spaces appeared in the KKM theory. Later in 2014-2020, Khahn and Quan introduced "topologically based existence theorems" and the so-called KKM structure. In the present paper, we show that their structure is a particular type of already known KKM spaces.

• Interaction and multiscale mechanics
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• 제2권2호
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• 한국음향학회지
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• 제21권7호
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• pp.592-599
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• 2002

본 연구에서는 상용 유한요소 해석 프로그램인 PZflex를 이용하여 초음파 탐촉자를 설계하고 이에 따라 제작하였다. 제작된 탐촉자는 복부 진단용에 적합한 크기와 형태로 중심 주파수 5 ㎒에 128개의 압전 소자가 곡면상에 1차원 배열된 컨벡스 (convex)형이며 두 층의 음향정합층, 하나의 후면층 그리고 각 압전소자 간의 커프로 구성된다. 제작된 탐촉자의 성능을 평가하여 설계치의 타당성을 검증하였으며, 등가회로 해석법에 의한 결과와 비교하여 유한 요소 해석법에 의한 설계법의 우수성을 확인하였다