• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제30권3호
• /
• pp.337-345
• /
• 2023

Different versions of the boundary Schwarz lemma for the 𝒩 (𝜌) class are discussed in this study. Also, for the function g(z) = z+b₂z²+b₃z³+... defined in the unit disc D such that g ∈ 𝒩 (𝜌), we estimate a modulus of the angular derivative of g(z) function at the boundary point 1 ∈ 𝜕D with g'(1) = 1 + 𝜎 (1 - 𝜌), where ${\rho}={\frac{1}{n}}{\sum\limits_{i=1}^{n}}g(c_i)={\frac{g^{\prime}(c_1)+g^{\prime}(c_2)+{\ldots}+g^{\prime}(c_n)}{n}}{\in}g^{\prime}(D)$ and 𝜌≠1, 𝜎 > 1 and c₁, c₂, ..., c_n ∈ 𝜕D. That is, we shall give an estimate below |g"(1)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z ≠ 0. Estimating is made by using the arithmetic average of n different derivatives g'(c₁), g'(c₂), ..., g'(c_n).

• 대한수학회지
• /
• 제48권2호
• /
• pp.397-420
• /
• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• 마이크로전자및패키징학회지
• /
• 제22권4호
• /
• pp.91-98
• /
• 2015

신축성 전자패키징에 응용하기 위해 강성도가 서로 다른 polydimethylsiloxane 탄성고분자인 Sylgard 184와 Dragon Skin 10을 사용하여 섬(island) 구조가 삽입된 강성도 국부변환 신축성 기판을 형성한 후, 강성도 국부변환부의 폭에 따른 기판의 탄성계수를 분석하였다. 기판 기지로는 탄성계수가 0.09 MPa인 Dragon Skin 10을 사용하였으며, 기판 기지 내에 삽입되는 강성도 국부변환부는 탄성계수가 2.15 MPa인 Sylgard 184로 형성하였다. 신축성 기판의 형상은 길이 6.5 cm, 두께 0.4 cm, 폭 2.5 cm이었으며, 중앙부에 길이 4 cm, 두께 0.2 cm, 폭 0.5~1.5 cm인 강성도 국부변환부를 삽입하였다. 폭 0.5 cm의 Sylgard 184를 Dragon Skin 10에 삽입함에 따라 기판의 탄성계수가 0.09 MPa에서 0.16 MPa로 증가하였다. Sylgard 184의 폭을 1.0 cm 및 1.5 cm으로 증가시킴에 따라 기판의 탄성계수가 0.18 MPa와 0.2 MPa로 증가하였으며, Sylgard 184 강성도 국부변환부의 폭에 따른 기판 탄성계수의 변화는 등변형률의 Voigt 구조와 등응력의 Reuss 구조를 조합하여 예측한 값과 잘 일치하였다.

• Structural Engineering and Mechanics
• /
• 제88권6호
• /
• pp.589-598
• /
• 2023

This article addresses the quasi-static analysis of time-dependent honeycomb sandwich plates with various geometrical properties based on the bending analysis of elastic honeycomb sandwich plates employing a time function with three unknown coefficients. The novel point of the developed method is that the responses of viscoelastic honeycomb sandwich plates under static transversal loads are clearly formulated in the space and time domains with very low computational costs. The mechanical properties of the sandwich plates are supposed to be elastic for the faces and viscoelastic honeycomb cells for the core. The Boltzmann superposition integral with the constant bulk modulus is used for modeling the viscoelastic material. The shear effect is expressed using the first-order shear deformation theory. The displacement field is predicted by the product of a determinate geometrical function and an indeterminate time function. The simple HP cloud mesh-free method is utilized for discretizing the equations in the space domain. Two coefficients of the time function are extracted by answering the equilibrium equation at two asymptotic times. And the last coefficient is easily determined by solving the first-order linear equation. Numerical results are presented to consider the effects of geometrical properties on the displacement history of viscoelastic honeycomb sandwich plates.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제27권4호
• /
• pp.157-169
• /
• 2020

In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.1027-1041
• /
• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
• /
• pp.263-266
• /
• 2000

본 논문에서는 복잡한 카오스 신호를 발생시키는 HVPM(hyperchaotic volume preserving maps) 모델과 HVPM 모델의 구현회로를 제안한다. 랜덤한 카오스 신호를 발생시키기 위하여 3차원 이산시간(discrete-time) 연산과 비선형 사상(maps)으로 모듈러(modulus) 함수를 이용하여 하이퍼카오스 신호를 발생시킨다. 그리고 HVPM 모델은 여러 가지 시스템 파라미터들을 변화시키면 다양한 카오스 신호를 발생시킬 수 있으며, 출력되는 카오스 신호는 비주기성을 갖게 된다. 이러한 특징을 갖는 HVPM 모델의 회로 구현을 위하여 2단 N형의 함수를 CMOS와 선형 연산증폭기 및 비교기를 이용하여 보드상에서 구현하여, 다양한 하이퍼카오스 신호를 확인할 수 있었다.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제24권3호
• /
• pp.129-145
• /
• 2017

In this paper, we establish lower estimates for the modulus of the non-tangential derivative of the holomorphic functionf(z) at the boundary of the unit disc. Also, we shall give an estimate below |f''(b)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_0{\neq}0$.

• Korean Journal of Mathematics
• /
• 제22권2호
• /
• pp.307-315
• /
• 2014

We investigate an approximation order of a continuous $2{\pi}$-periodic function by periodic neural networks. By using the De La Vall$\acute{e}$e Poussin sum and the modulus of continuity, we obtain a degree of approximation by periodic neural networks.

• Journal of Ship and Ocean Technology
• /
• 제1권1호
• /
• pp.48-56
• /
• 1997

This paper deals with the energy dissipation of ductile metal plate due to cutting. By using nondimensional analysis, we present that the dissipation energy of tearing behaviour can be formulated as a function of slenderness ratio expressed by cutting length, yield stress, plate thickness and elastic modulus. The validity of the proposed formula for Al-alloy, copper and mild steel is demonstrated by comparing the proposed formula with experimental results, which are shown in good agreements except for thick mild steel plate.