• 호남수학학술지
• /
• 제37권4호
• /
• pp.505-512
• /
• 2015

In this note we find the upper bound for ${\rho}(u^n,M)=\int_{0}^{T}\int_{0}^{{\mid}u(t){\mid}^n}p(s)dsdt$ and show that $F(y)=y^n$ is $m_{\phi}^M$-Bochner integrable on $C(\mathcal{O} _M)$ for $0{\leq}t{\leq}T$ when $\int_{\mathcal{O}_M}{\parallel}u_0{\parallel}_M^nd{\phi}(u_0)$ is finite.

• 대한수학회논문집
• /
• 제11권2호
• /
• pp.349-357
• /
• 1996

Using a special property of Bloch functions with Hardmard gaps and using the geometric properties of the self maps of the unit disc, we give a way of constructing explicit examples of Bloch functions f whose derivative is in $H^p$ (0 < p < 1) but $f \notin BMOA$.

• 대한수학회보
• /
• 제48권2호
• /
• pp.223-245
• /
• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Restorative Dentistry and Endodontics
• /
• 제25권3호
• /
• pp.390-398
• /
• 2000

근관형성을 위해 표준화된 근관형성기구에 비해 taper가 큰 기구들이 사용되고 있으며 이를 이용하여 형성된 근관은 taper가 큰 근관의 모양을 갖는다. 근관충전방법에 있어 근관의 크기에 적합한 1차적 gutta-percha cone을 선택할 필요가 있다. 본 연구에서는 .04 및 .06 taper의 전동화일로 형성된 근관에 열연화충전법을 위해 가장 적합한 1차 cone을 선택하기 위한 지침 마련의 목적으로, 근단공의 크기와 근관의 taper에 따른 gutta-percha cone의 근단부 근관 내 적 합도를 평가하였다. ProFile$^{(R)}$ .04 taper와 .06 taper를 이용하여 Crown down 방법으로 60개의 모형근관을 형성하였다. 표준화 gutta-percha cone, Dia-Pro ISO-.04$^{TM}$ 및 .06 gutta-percha cone, MF, F, FM 및 M 크기의 비표준화 gutta-percha cone의 근관 내 적합도는 치근단 5mm의 근관면적에 대한 gutta-percha cone의 점유 면적비(%)로 하였다. .04 taper, 25번 크기의 근관에서는 F, MF 크기의 비표준화 cone이 표준화 cone과 Dia-Pro 180-.04$^{TM}$ 보다 우수한 근관적합도를 나타내었고(p<0.05), 30번 크기의 근관에서는 F, Dia-Pro ISO-.04$^{TM}$, FM 크기의 gutta-percha cone 모두 표준화 cone보다 우수한 근관적합도를 나타내었으나(p<0.05), 35번 크기의 근관에서는 모든 gutta-percha cone 사이에 유의한 차이를 나타내지 않았다(p>0.05) .06 taper, 25번 크기의 근관에서는 사용된 비표준화 cone 모두가 표준화 cone, Dia-Pro ISO-.06$^{TM}$ 보다 나은 근관적합도를 나타내었고(P<0.05), 30번 크기의 근관에서는 표준화 cone을 제외한 나머지 gutta-percha cone에서 유의한 차이를 발견할 수 없었다. 35번 크기의 근관에는 M 크기의 비표준화 cone이 가장 우수한 근관적합도를 보이고 있는 것으로 나타났으며, FM과 Dia-Pro ISO-.06$^{TM}$ 사이에서는 유의한 차이가 나타나지 않았다(p>0.05).

• 대한수학회논문집
• /
• 제34권1호
• /
• pp.185-202
• /
• 2019

In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.339-350
• /
• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• 대한수학회지
• /
• 제31권4호
• /
• pp.609-618
• /
• 1994

F. Rhodes [2] introduced the fundamental group $\sigma(X, x_0, G)$ of a transformation group (X,G) as a generalization of the fundamental group $\pi_1(X, x_0)$ of a topological space X and showed a sufficient condition for $\sigma(X, x_0, G)$ to be isomorphic to $\pi_1(X, x_0) \times G$, that is, if (G,G) admits a family of preferred paths at e, $\sigma(X, x_0, G)$ is isomorphic to $\pi_1(X, x_0) \times G$. B.J.Jiang [1] introduced the Jiang subgroup $J(f, x_0)$ of the fundamental group of X which depends on f and showed a condition to be $J(f, x_0)$ = Z(f_\pi(\pi_1(X, x_0)), \pi_1(X, f(x_0)))$.

• 호남수학학술지
• /
• 제46권1호
• /
• pp.38-46
• /
• 2024

Let X, Y be Banach spaces, S_X and S_Y be the unit sphere of X and Y, respectively. Let f₀ : S_X → S_Y be ε-isometry for some ε ≥ 0. In this paper, we show that there is an extension f : X → Y of f₀ such that f is linear.

• 음성과학
• /
• 제14권4호
• /
• pp.203-212
• /
• 2007

This study was to compare some acoustic characteristics of vowels produced by children with cochlear implant (CI) and the children with normal hearing. 20 subjects under ten years old were further classified into two groups (one group of CI children under four years old and the other group of CI children over four years old). For the normal hearing group, 20 subjects are participated in the experiment. Some acoustic parameters including fundamental frequency (F0) and formant frequencies (F1, F2) were measured in the two groups according to the age of cochlear implant operation. For the CI group, three comer vowels (/a/, /i/, /u/) were recorded five times in isolation and analyzed with Multi-Speech (Kay Elemetrics, model 3700), and two independent t-tests on their formant data were conducted using SPSS 11.5. The result showed that the implanted group over four years had a significant difference in F0 and F1 comparing with the implanted group under four years of age as well as the normal hearing group. Those values of the children with the implanted group under four years old were closer to those of the children with the normal hearing. As to the F2, there was no significant difference among implanted groups. However, it was shown that the vowel space for the implanted groups regardless the operation age indicated much smaller than that for the normal hearing children. This acoustic results suggest that CI surgery would be much more effective if it is done under the age of four years old.

• Kyungpook Mathematical Journal
• /
• 제13권2호
• /
• pp.235-240
• /
• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).