• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.475-484
• /
• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

• Journal of applied mathematics & informatics
• /
• v.41 no.2
• /
• pp.273-286
• /
• 2023

In this paper we show that if T ∈ L(X) and S ∈ L(X) is a Riesz operator commuting with T and X_S(F) ∈ Lat(S), where F = {0} or F ⊆ ℂ ⧵ {0} is closed then T|X_S(F) and T|X_T(F) + S|X_S(F) share the local spectral properties such as SVEP, Dunford's property (C), Bishop's property (𝛽), decomopsition property (𝛿) and decomposability. As a corollary, if T ∈ L(X) and Q ∈ L(X) is a quasinilpotent operator commuting with T then T is Riesz if and only if T + Q is Riesz. We also study some spectral properties of Riesz operators acting on Banach spaces. We show that if T, S ∈ L(X) such that TS = ST, and Y ∈ Lat(S) is a hyperinvarinat subspace of X for which 𝜎(S|Y ) = {0} then 𝜎_*(T|Y + S|Y ) = 𝜎_*(T|Y ) for 𝜎_* ∈ {𝜎, 𝜎_loc, 𝜎_sur, 𝜎_ap}. Finally, we show that if T ∈ L(X) and S ∈ L(Y ) on the Banach spaces X and Y and T is similar to S then T is Riesz if and only if S is Riesz.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1027-1040
• /
• 2012

The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.

• Kyungpook Mathematical Journal
• /
• v.55 no.3
• /
• pp.507-514
• /
• 2015

Let D be an integral domain, t be the so-called t-operation on D, and S be a (not necessarily saturated) multiplicative subset of D. In this paper, we study the Nagata ring of S-Noetherian domains and locally S-Noetherian domains. We also investigate the t-Nagata ring of t-locally S-Noetherian domains. In fact, we show that if S is an anti-archimedean subset of D, then D is an S-Noetherian domain (respectively, locally S-Noetherian domain) if and only if the Nagata ring $D[X]_N$ is an S-Noetherian domain (respectively, locally S-Noetherian domain). We also prove that if S is an anti-archimedean subset of D, then D is a t-locally S-Noetherian domain if and only if the polynomial ring D[X] is a t-locally S-Noetherian domain, if and only if the t-Nagata ring $D[X]_{N_v}$ is a t-locally S-Noetherian domain.

• Proceedings of the Technology Innovation Conference
• /
• 2005.06a
• /
• pp.140-158
• /
• 2005

Science & Technology (S&T) is the most important thing to attain competitiveness in the 21st century. Our traditional S&T policies have been focused on hardware infra structure. But, we should consider soft infra of S&T to enhance welfare development of S&T personnel. S&T should be had a correct understanding method of the creation for S&T culture. It implies that S&T policy in the 21st century should consider non-material factors which include social, human, environment and culture. Under this background. This paper defines the concept of welfare of S&T personnel. Also this paper deals with the change of S&T policy of Korea and analyzes the characteristic of each phase. This paper argues that all actors (for example S&T personnel, corporate using S&T, public) should participate in the process of S&T innovation since the 21st century is the generation of popularization of S&T. The purpose of this paper is to suggest a few methods of welfare improvement of S&T personnel to reinforce soft infra structure of S&T.

• Proceedings of the Korea Technology Innovation Society Conference
• /
• 2005.05a
• /
• pp.95-110
• /
• 2005

Science & Technology(S&T) is the most important thing to attain competitiveness in the 21st century, Our traditional S&T policies have been focused on hardware infra structure. we should consider software of S&T to enhance effectiveness. S&T should be had a correct understanding method of the creation for S&T culture. It implies that S&T policy in the 21st century should consider nonmaterial factors which include social, human, environmental and culture. Under this background, The purpose of this paper is to seek new S&T policy in the 21st century. Therefor this paper deals with how we can prepare for the future S&T policy and classify the change of S&T policy of Korea and analyze the characteristic of each phase. This paper argues that all actors (for example, S&T personnel, corporate using S&T, general public) should participate in the process of S&T innovation since the 21st century is the generation of the general public S&T. Also this paper presented the expanded S&T policy Right S&T policy could leads to diffuse right S&T culture. Diffusing S&T culture could accomplish expanded S&T policy which was considered phases of culture and welfare.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.763-775
• /
• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.41 no.3
• /
• pp.253-260
• /
• 1992

In this study, the dielectric, structural and electrical properties of Pb(ZnS11/3TNbS12/3T)OS13T-BaTiOS13T-PbTiOS13T system ceramics were investigated with respect to the variation of YS12TOS13T addition amount. As the YS12TOS13T addition amount is increased, the resistivity at 100$^{\circ}C$ and the resonant/antiresonant frequencies and the frequency constant are slowly increased, and the grain growth is restrained until 0.4 wt% YS12TOS13T addition amount but continuously increased with the addition amount more than 0.4 wt% YS12TOS13T. As the YS12TOS13T addition amount is increased, the density, the diffuseness of dielectric constant and the induced polarization are increased until 0.4 wt% YS12TOS13T addition.

• Proceedings of the Korean Radioactive Waste Society Conference
• /
• 2017.10a
• /
• pp.185-186
• /
• 2017

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.41 no.6
• /
• pp.687-693
• /
• 1992

To improve dielectric, piezoelectric and temperature stability in 0.50Pb(SnS11/2TSbS11/2T)OS13T - 0.35PbTiOS13T - 0.60PbZrOS13T + 0.4[wt%]MnOS12T piezoelectric ceramics which is used for surface acoustic wave devices, CrS12TOS13T was added and the specimens were fabricated by Hot Press method, and their characteristics were measured with CrS12TOS13T addition. From the results, in the specimen added by 0.2[wt%]CrS12TOS13T, dielectric constant and mechanical quality factor were 380 and 2307, respectively, and it was suited for surface acoustic wave device and the temperature coefficient of the resonant frequency in the specimen added by 0.4[wt%]CrS12TOS13T was the least value of 74.96[ppm/$^{\circ}C$].