• Communications for Statistical Applications and Methods
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• 제19권5호
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• pp.655-662
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• 2012

Classification is an important research field in pattern recognition with high-dimensional predictors. The support vector machine(SVM) is a penalized feature selector and classifier. It is based on the hinge loss function, the non-convex penalty function, and the smoothly clipped absolute deviation(SCAD) suggested by Fan and Li (2001). We developed the algorithm for the multiclass SVM with the SCAD penalty function using the local quadratic approximation. For multiclass problems we compared the performance of the SVM with the $L_1$, $L_2$ penalty functions and the developed method.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.713-723
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• 2009

The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.

• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.1-12
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• 2013

The purpose of the present paper is to obtain some subordination- and superordination-preserving properties for multivalent function associated the differintegral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich type theorem for the integral operator is also considered.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

• 호남수학학술지
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• 제43권4호
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• pp.627-639
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• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• 제어로봇시스템학회논문지
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• 제14권7호
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• pp.615-623
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• 2008

This paper proposes an $H_{\infty}$ controller design method for Takagi-Sugeno (T-S) fuzzy systems using a fuzzy basis-function-dependent Lyapunov function. Sufficient conditions for the guaranteed $H_{\infty}$ performance of the T-S fuzzy control system are given in terms of linear matrix inequalities (LMIs). These LMI conditions are further used for a convex optimization problem in which the $H_{\infty}-norm$ of the closed-loop system is to be minimized. To facilitate the basis-function-dependent Lyapunov function approach and thus improve the closed-loop system performance, additional decision variables are introduced in the optimization problem, which provide an additional degree-of-freedom and thus can enlarge the solution space of the problem. Numerical examples show the effectiveness of the proposed method.

• 한국방사선학회논문지
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• 제16권7호
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• pp.975-984
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• 2022

선형 탐촉자는 탐촉자의 길이만큼의 관심 영역을 갖기 때문에 장비에 탑재된 virtual convex 기능을 사용하여 관심 영역을 확장 시킬 수 있다. 하지만 관심 시각 영역의 변화에 따라 초음파 음속 방향의 변화로 인해 화질에 영향을 미칠 것으로 생각되어 이를 객관적으로 확인하고자 하였다. 본 연구를 위해 초음파 정도 관리용 팬텀의 영상 평가와 SNR·CNR을 측정하였다. 그 결과 팬텀 영상 평가에서는 두 영상 모두 기능적 분해능, 회색조 및 동적 범위에서 모두 구조물 식별이 가능했다. 하지만 구조물의 크기와 형태 재현성에는 Standard 영상이 우수한 것을 확인할 수 있었다. SNR·CNR 평가결과, 특정 위치의 구조물을 제외하고는 대부분이 Trapezoidal 영상의 SNR·CNR이 낮았다. 또한, 통계 분석 그래프를 통해 낭성 구조물의 크기가 작아질수록 깊이별 SNR과 CNR이 감소하는 것을 추가로 확인할 수 있었다. 본 연구를 통해 기능사용이 넓은 관심 시각 영역을 제공하는 장점이 있으나 화질에 영향을 준다는 것을 확인할 수 있었으며 Virtual Convex 기능사용 시 검사자는 이를 적절한 상황에 사용하고 질 높은 영상 획득과 장비의 이해도와 숙련도 향상을 위해 다양한 연구를 해야 할 것으로 판단된다.

• 호남수학학술지
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• 제44권1호
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• 대한수학회보
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• 제30권2호
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• pp.171-177
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• 1993

In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권2호
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• pp.15-21
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• 2004

A Conjugate Gradiant (CG) method is proposed for unconstained optimization which is invariant to a nonlinear scaling of a strictly convex quadratic function. The technique has the same properties as the classical CG-method when applied to a quadratic function. The algorithm derived here is based on a logarithmic model and is compared to the standard CG method of Fletcher and Reeves [3]. Numerical results are encouraging and indicate that nonlinear scaling is promising and deserves further investigation.