• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.271-287
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• 2022

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant Ω_X(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of Ω_X(α) and γ_X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.61-78
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• 2023

In this paper, we introduce two new geometric constants related to the heights of triangles: ∆_H(X) and ∆_h(X, I). We also propose two new geometric constants, ∆_m(X) and ∆_M(X), related to the midlines of equilateral triangles, and discuss the relation between the heights and midlines in equilateral triangles. We give estimates for these geometric constants in terms of other geometric parameters, and the geometric constants are used to discuss geometric properties such as uniform non-squareness, uniform normal structure, and the fixed point property.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1757-1764
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• 1997

The geometric and elastic models based on the unit cell have been proposed to predict the geometric characteristics and the engineering constants of plain and satin woven composites. In the geometric model, length and inclined angle of the yarn crimp and the fiber volume fraction of woven composites have been predicted. In the elastic model, the coordinate transformation has been utilized to transform the elastic constants of the yarn crimp to those of woven composites, and the effective elastic constants have been determined from the volume averaging of the constituent materials. Good correlations between the model predictions and the experimental results of carbon/epoxy and glass/epoxy woven composites have been observed. Based on the model, the effect of various geometric parameters and materials on the three-dimensional elastic properties of woven composites can be identified.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1569-1575
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• 2019

In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for $L^1$ and $L^{\infty}$ spaces.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.305-310
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• 1998

In this paper, we introduce the conditions that the P-process has the intensity function which it is a standard form of gamma distribution. And we show that the transformed geometric Poisson process which the intensity function is a standard form of gamma distribution is a alternative sign P-process

• 연구논문집
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• s.23
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• pp.45-56
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• 1993

In order to acquire more comprehensive understanding of textile composites, the processing-microstructure-performance relationships for a variety of material systems, reinforcing schemes and processing technologies should be established. In this paper, emphasis is placed on the integrated analysis of three-dimensional (3-D) 2-step braided composites. The analysis includes the geometric model of unit cells, identification of key process parameters and processing windows due to limiting geometries of yarn jamming, and prediction of elastic constants of the composite. The coordinate transformation and averaging of stiffness and compliance constants are utilized in the prediction of elastic constants. Since there are several types of unit cells in the thickness and width directions of the composites, characterization of mechanical properties is based upon the macro-cell, which occupies the entire cross-section and the unit pitch length of the sample. The performance map demonstrates that a wide range of elastic properties can be achieved by varying the geometric and process parameters.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.199-223
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• 2023

We introduce the constants E[t, X], C_NJ[X] and J[t, X] to describe the asymmetry of the norm. They can be seen as the skew version of the Gao's parameter, von Neumann-Jordan constant and Milman's moduli, respectively. We establish basic properties of these constants, relating them other well known constants, and use these properties to calculate the constants for specific spaces. We then use these constants to study Hilbert spaces, uniformly non-square spaces and their normal structures. With the Banach-Mazur distance, we use them to study isomorphic Banach spaces.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.455-468
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• 1996

Certain analytic behavior of geometric objects defined on a Riemannian manifold depends on some very crude properties of the manifold. Some of those crude invariants are the volume growth rate, isoperimetric constants, and the likes. However, these crude invariants sometimes exercise surprising control over the analytic behavior.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.631-644
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• 2021

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds $$\frac{{\partial}u}{{\partial}t}={\Delta}u+a(x,t)u^p+b(x,t)u^q$$ where, 0 < p, q < 1 are real constants and a(x, t) and b(x, t) are functions which are C² in the x-variable and C¹ in the t-variable. We shall get an interesting Harnack inequality as an application.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.38-41
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• 2001

A new 2-D braided textile metal matrix composite was developed and characterized. The constituent materials consist of PAN type carbon fiber as reinforcements and pure aluminum as matrices. The braided preforms of different braider yarn angles were fabricated. For a fixed bundle size of 12K, three braider yarn angles was selected: $30^{\circ}$, $45^{\circ}$, and $60^{\circ}$. The braided preforms were infiltrated with pure Al by vacuum assisted squeeze casting. Through the investigation of melt pressing methods and the effects of process parameters such as applied pressure, and pouring temperature, the optimal process conditions were identified as follows: applied pressure of 60MPa, pouring temperature of $800^{\circ}C$. Using the measured geometric parameters, 3-D engineering constants of metal matrix composites have been determined from the elastic model, which utilizes the coordinate transformation and the averaging of stiffened and compliance constants based upon the volume of each reinforcement and matrix material.