• Journal of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.899-909
• /
• 2006

Let T be a bounded linear operator on a complex infinite dimensional Hilbert space $\scr{H}$. We say that T is a quasi-class A operator if $T^*\|T^2\|T{\geq}T^*\|T\|^2T$. In this paper we prove that if T is a quasi-class A operator and f is a function analytic on a neigh-borhood or the spectrum or T, then f(T) satisfies Weyl's theorem and f($T^*$) satisfies a-Weyl's theorem.

• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.91-101
• /
• 2008

Let H be a Hilbert space. Assume that $0{\leq}{\alpha}$, ${\beta}{\leq}1$ and r(t) > 0 in I = [0, T]. By means of the fixed point theorem of Leray-Schauder type the existence principles of solutions for two point boundary value problems of the form $\array{(r(t)x^{\prime}(t))^{\prime}+f(t,x(t),r(t)x^{\prime}(t))=0,\;t{\in}I\\x(0)=x(T)=0}$ are established where f satisfies for positive constants a, b and c ${\mid}{f(t,x,y){\mid}{\leq}a{\mid}x{\mid}^{\alpha}+b{\mid}y{\mid}^{\beta}+c\;\;for\;all(t,x,y){\in}I{\times}H{\times}H$.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.1
• /
• pp.13-30
• /
• 2007

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

• Kyungpook Mathematical Journal
• /
• v.27 no.1
• /
• pp.35-41
• /
• 1987

Consider the system (i) x'=Ax. Let ${\Phi}$ be its fundamental matrix solution. If there is w>0 such that A(t+w)-A(t) commutes with ${\Phi}$ for all t, then we call this system a "generalized" Floquet system or a "G. F. system". We show that $A(t+w)-A(t)=B_1$=constant if and only if $A(t)=C+B_1t/w+Q(t)$, Q is periodic of period w>0. For this A(t) We prove that if all eigenvalues of $B_1$ have negative real parts, then the origin is asumptotically stable. We find a growth condition for a continuous D(t) which guarantees that all solutions of z'=[A(t)+D(t)]z are bounded if all solutions of the G. F. system (i) are bounded. Combining the foregoing results yield a class of perturbed G. F. operators all of whose solutions are bounded.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• pp.499-511
• /
• 2015

This paper shows that the solutions to the perturbed dierential system $$y^{\prime}=f(t,y)+{\int}_{t_o}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded property. To show this property, we impose conditions on the perturbed part ${\int}^{t}_{t_o}g(s,y(s))ds+h(t,y(t),Ty(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.14 no.6
• /
• pp.26-30
• /
• 1977

Redundancies in the Calculation of DFT and FFT are analized and new algorithms are proposed which are capable of reducing the machine time by a considerable amount. New extensions of T.D C.F. and T.D.F.T. are given for the discrete case which permit a deeper insights for the techniques of digital signal Proessing i. e. Discrete Fourier Transform, Convolution Sum and Correlation sequences.

• Proceedings of the Korean Reliability Society Conference
• /
• 2000.04a
• /
• pp.185-191
• /
• 2000

A survival variable is a nonnegative random variable X with distribution function F and a survival function (equation omitted)=1－F. This variable is said to be New Better than Used of specified age $t_{0}$ if (equation omitted) for all $\chi$$\geq$0 and a fixed to. We propose the test for $H_{0}$ : (equation omitted) for all $\chi$$\geq$0 against $H_1$：(equation omitted) for all $\chi$$\geq$0 when the specified age $t_{0}$ is unknown but can be estimated from the data when $t_{0}$=${\mu}$, the mean of F, and also when $t_{0}$=$\xi_p$, the pth percentile of F. This test statistic, which is based on a linear function of the order statistics from the sample, is readily applied in the case of small sample. Also, this test statistic is more simple than the test statistic of Ahmad's test statistic (1998). Finally, the performance of this test is presented.

• Journal of electromagnetic engineering and science
• /
• v.13 no.2
• /
• pp.127-133
• /
• 2013

We examined the scaling effects of a number of gate_fingers (N) and gate_widths (w) on the high-frequency characteristics of $0.1-{\mu}m$ metamorphic high-electron-mobility transistors. Functional relationships of the extracted small-signal parameters with total gate widths ($w_t$) of different N were proposed. The cut-off frequency ($f_T$) showed an almost independent relationship with $w_t$; however, the maximum frequency of oscillation ($f_{max}$) exhibited a strong functional relationship of gate-resistance ($R_g$) influenced by both N and $w_t$. A greater $w_t$ produced a higher $f_{max}$; but, to maximize $f_{max}$ at a given $w_t$, to increase N was more efficient than to increase the single gate_width.

• Speech Sciences
• /
• v.13 no.3
• /
• pp.97-105
• /
• 2006

The objective of this study was to analyze the acoustic patterns of Japanese /t/ produced by 40 Korean speakers in order to find an effective method of teaching it to Koreans. The experimental data consisted of 400 /t/ phonemes in word initial or non-initial positions of 10 words. Informants were in their twenties and raised in Daejeon and the surrounding area. Results showed that there were distinctive trends in duration and intensity of the major and non-major groups productions. Both groups pronounced the phoneme longer than the native speakers with more open mouths but with less loudness. The formant analysis showed that F1 values of the Japanese /t/ pronounced by Japanese major group were lower than those of the non-major. Its F2 values by the major group were higher than those of the non-major, which would suggest that the Koreans produced the tongue blade in more frontal position than the native speakers.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1969-1980
• /
• 2017

Let ${\Gamma}$ be a nonzero torsionless commutative cancellative monoid with quotient group ${\langle}{\Gamma}{\rangle}$, $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be a graded integral domain graded by ${\Gamma}$ such that $R_{{\alpha}}{\neq}\{0\}$ for all ${\alpha}{\in}{\Gamma},H$ be the set of nonzero homogeneous elements of R, C(f) be the ideal of R generated by the homogeneous components of $f{\in}R$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. In this paper, we introduce the notion of graded t-almost Dedekind domains. We then show that R is a t-almost Dedekind domain if and only if R is a graded t-almost Dedekind domain and RH is a t-almost Dedekind domains. We also show that if $R=D[{\Gamma}]$ is the monoid domain of ${\Gamma}$ over an integral domain D, then R is a graded t-almost Dedekind domain if and only if D and ${\Gamma}$ are t-almost Dedekind, if and only if $R_{N(H)}$ is an almost Dedekind domain. In particular, if ${\langle}{\Gamma}{\rangle}$ isatisfies the ascending chain condition on its cyclic subgroups, then $R=D[{\Gamma}]$ is a t-almost Dedekind domain if and only if R is a graded t-almost Dedekind domain.