• 대한수학회지
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• 제42권3호
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• pp.485-498
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• 2005

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.

• 대한수학회논문집
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• 제21권2호
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• pp.237-251
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• 2006

In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.

• 호남수학학술지
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• 제44권3호
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• pp.325-338
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• 2022

In this paper, a new identity is given. On the basis of this identity, we establish some new estimates of Milne's quadrature rule, for functions whose first derivative is s-convex. We discuss the cases where the derivatives are bounded as well as Lipschitzian. Some illustrative applications are given.

• 충청수학회지
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• 제23권4호
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• pp.657-661
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• 2010

We study a singular function which we call a generalized cylinder convex(concave) function induced from different generalized dyadic expansion systems on the unit interval. We show that the generalized cylinder convex(concave)function is a singular function and the length of its graph is 2. Using a local dimension set in the unit interval, we give some characterization of the distribution set using its derivative, which leads to that this singular function is nowhere differentiable in the sense of topological magnitude.

• 품질경영학회지
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• 제46권3호
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• pp.425-440
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• 2018

Purpose: This study is aimed at developing of the flex resistance testing process at low temperature with the waterproof fabric to suit the military environment, and is designed to fit for the purpose of the waterproof materials in order to optimize the test method by finding out matters to improve from existing the test method and through previous studies. Methods: The test method, which has been applied to flex resistance of existing water-repellent materials, was improved and consequently, differentiated test results could be obtained according to the test temperature, sample size, and flexing method. Results: The testing of the total of 8 samples revealed that performance of the military requirement could hardly be met just by presenting the materials or 2~3 layers when the quality criteria for high functional water repellent fabrics were applied. PTFE(Polytetrafluoroethylene) is preferred to PU(Polyurethane) to be used in the extremely low-temperature environment, but durability under the low-temperature environment may be varied depending on film thickness or laminating technique even if the materials of waterproof films are identical. Therefore, in addition to the material or texture, the test method capable of reflecting durability under the low-temperature environment shall be suggested, and the newly designed test method proposed in this study was shown to suggest differentiated quality criteria by the material. Conclusion: The water resistance measurement and the test method following flex resistance with expanded range of flex will enable the differentiable test of the samples according to the number of repetition. This study is meaningful in that it suggests a differentiable test method capable of establishing a basis of deciding suitable material when selecting military goods made of water repellent material by properly improving the test method.

• 한국컴퓨터그래픽스학회논문지
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• 제25권3호
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• pp.133-142
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• 2019

물리기반 캐릭터 애니메이션에서 궤적 최적화(trajectory optimization) 기법은 캐릭터 동작에 대한 시스템 동역학 모델(system dynamics model)에 기반하여 가까운 최적의 미래 상태를 예측하여 캐릭터의 동작을 자동적으로 생성하는데 널리 사용되어 왔다. 캐릭터와 환경 간의 접촉 현상을 강체 충돌로 다루는 경우 일반적으로 시스템 동역학 모델은 그 수식이 닫힌 형식(closed form)으로 유도되지 못하고 미분이 불가능하다. 따라서 최근까지 많은 연구자들이 접촉 완화(contact smoothing) 기법을 통해 시스템 동역학의 수치적 미분에 기반한 효율적인 궤적 최적화 기법을 발표해 왔다. 하지만 수치적 미분 정보는 분석적 미분과 달리 부정확하기 때문에 궤적 최적화의 안정성에 영향을 미칠 수 있다. 이 문제를 해결하기 위해 본 논문에서는 접촉 완화 모델에 대한 근사화를 통해 시스템 동역학을 분석적으로 미분하여 닫힌 형식의 도함수를 유도하고, 이를 기반으로 사용자의 온라인 입력에 따라 예제 데이터 없이 이족 캐릭터의 동작을 안정적으로 생성하는 예측 제어 기법(model predictive control (MPC))을 제안한다.

• 대한수학회보
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• 제50권1호
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• 충청수학회지
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• 제4권1호
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• pp.61-69
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• 1991

By $C^{(1)}$[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by $${\parallel}f{\parallel}=\sup_{x{\in}[0,1]}({\mid}f(x){\mid}+{\mid}f^{\prime}(x){\mid})\text{ for }f{\in}C^{(1)}$$. By A we denote the sub algebra of $C^{(1)}$ defined by $$A=\{f{\in}C^{(1)}:f(0)=f(1)\text{ and }f^{\prime}(0)=f^{\prime}(1)\}$$. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1] onto itself.

• 대한수학회지
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• 제38권3호
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• pp.683-695
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• 2001

In this paper we are concerned with theoretical properties of gap functions for the extended variational inequality problem (EVI) in a general Banach space. We will present a correction of a recent result of Chen et. al. without assuming the convexity of the given function Ω. Using this correction, we will discuss the continuity and the differentiability of a gap function, and compute its gradient formula under tow particular situations in a general Banach space. Our results can be regarded as infinite dimensional generalizations of the well-known results of Fukushima, and Zhu and Marcotte with soem modifications.

• 호남수학학술지
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• 제28권1호
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• pp.125-133
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• 2006

We investigate the approximation order to a function in $L_p$[-1, 1] for $0{\leq}p<{\infty}$ by generalized translation networks. In most papers related to neural network approximation, sigmoidal functions are adapted as an activation function. In our research, we choose an infinitely many times continuously differentiable function as an activation function. Using the integral modulus of continuity and the divided difference formula, we get the approximation order to a function in $L_p$[-1, 1].