• Honam Mathematical Journal
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• v.37 no.4
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• pp.505-512
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• 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.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.349-357
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• 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 $f \notin BMOA$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-245
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• 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
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• v.25 no.3
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• pp.390-398
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• 2000

The purpose of this study was to evaluate the apical fitness of non-standardized gutta-percha cones in root canals prepared with rotary Ni-Ti root canal instruments of various tapers and apical tip sizes. Simulated sixty curved root canals of plastic blocks were prepared with crown-down technique using rotary root canal instruments of Maillefer ProFile$^{(R)}$ .04 and .06 taper (Maillefer Instrument SA, Switzerland). Specimens were divided into six groups and prepared as follows: Group 1, prepared up to size 25 of .04 taper ; Group 2, prepared up to size 30 of .04 taper ; Group 3, prepared up to size 35 of .04 taper ; Group 4, prepared up to size 25 of .06 taper ; Group 5, prepared up to size 30 of .06 taper ; Group 6 ; prepared up to size 35 of .06 taper. After cutting off the coronal portion of plastic, blocks perpendicular to the long axis of the canal with the use of a diamond saw, apical 5mm of canal space was analyzed. Prepared apical canal spaces were duplicated using rubber base impression material to evaluate two dimensional total area of apical canal space. Various sized gutta-percha cones were applied in the 5mm-apical canal space, which were size 25, size 30 and size 35 standardized gutta-percha cone, Diadent Dia-Pro ISO-.04$^{TM}$ and .06$^{TM}$(Diadent, Korea), and medium-fine (MF), fine (F), fine-medium (FM) and medium (M) sized non-standardized gutta-percha cones (Diadent, Korea). Coronal excess gutta-percha were cut off with a sharp blade. Photographs of impressed apical canal spaces and gutta-percha cones were taken with a CCD camera under a stereomicroscope and stored in a computer. Areas of the total canal space and gutta-percha cones were calculated using a digitalized image analysing program, CompuScope (Sungjin Multimedia Co., Korea). Ratio of apical fitness was obtained by calculating the area of gutta-percha cone to the total area of the canal space. The data were analysed statistically using One-way Analysis of Variance and Duncan's Multiple Range Test. The results were as follows: 1. In canals prepared up to size 25 ProFile$^{(R)}$ of .04 taper, non-standardized MF and F cones occupied significantly more canal space than Dia-Pro ISO-.04$^{TM}$ or size 25 standardized ones (p<0.05). 2. In canals prepared up to size 30 ProFile$^{(R)}$ of .04 taper, non-standardized F cones occupied significantly more canal space than Dia-Pro ISO-.04$^{TM}$ or size 30 standardized ones (p<0.05), and non-standardized MF cones occupied more canal space than size 30 standardized ones (p<0.05). 3. In canals prepared up to size 35 ProFile$^{(R)}$ of .04 taper, there was no significant difference in canal space occupation among non-standardized MF and F, size 35 standardized, and Dia-Pro ISO-.04$^{TM}$ cones (p>0.05). 4. In canals prepared up to size 25 ProFile$^{(R)}$ of .06 taper, non-standardized MF and F cones occupied significantly more canal space than Dia-Pro ISO-.06$^{TM}$, or size 25 standardized ones (p<0.05), and Dia-Pro ISO-.06$^{TM}$, cones occupied significantly more space than size 25 standardized ones (p<0.05). 5. In canals prepared up to size 30 ProFile$^{(R)}$ of .06 taper, non-standardized FM cones occupied significantly more canal space than Dia-Pro ISO-.06$^{TM}$ or size 30 standardized ones (p<0.05), and non-standardized F cones occupied significantly more canal space than size 30 standardized ones (p<0.05). 6. In canals prepared up to size 35 ProFile$^{(R)}$ of .06 taper, non-standardized M and FM, Dia-Pro ISO-.06$^{TM}$ occupied significantly more canal space than size 35 standardized ones (p<0.05). In summary, in both canals prepared with .04 or .06 taper ProFile$^{(R)}$, non-standardized cones showed better fitness than Dia-Pro ISO$^{TM}$ or standardized ones, which was more characteristic in smaller canals.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.185-202
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• 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
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• v.18 no.1_2
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• pp.339-350
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• 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.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.609-618
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• 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)))$.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.38-46
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• 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.

• Speech Sciences
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• v.14 no.4
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• pp.203-212
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• 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
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• v.13 no.2
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• pp.235-240
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• 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]).