• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.77-95
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• 2012

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.

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

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1453-1467
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• 2007

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$(E_1)\;[p(t)|x#(t)|^{\alpha}sgn\;x#(t)]#+q(t)|x(\tau(t)|^{\alpha}sgn\;x(\tau(t))=0$$. $$(E_2),\;(E_3)\;and\;(E_4)\;where\;0<{\alpha}$$ and $${\tau}(t){\leq}t,\;{\tau}#(t)>0,\;{\tau}(t){\rightarrow}{\infty}\;as\;t{\rightarrow}{\infty}$$. In this paper we improve some previous results.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.701-707
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• 1998

An operator $T{\in} {{\mathcal L}(H)}$ is generalized k-quasihyponormal if there exist a constant M>0 such that $T^{\ast k}[M^2(T-z)^{\ast}(T-z)-(T-z)(T-z)^{\ast}]T^k{\geq}0$ for some integer $k{\geq}0$ and all $Z{\in} {\mathbf C}$. In this paper, we show that it T is a generalized k-quasihyponormal operator with the property $0{\not\in}{\sigma}(T)$, then T is subscalar of order 2. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum has interior in C.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.631-638
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• 1996

The parabolic free boundary problem with Puschino dynamics is given by (see in [3]) $$ (1) { \upsilon_t = D\upsilon_{xx} - (c_1 + b)\upsilon + c_1 H(x - s(t)) for (x,t) \in \Omega^- \cup \Omega^+, { \upsilon_x(0,t) = 0 = \upsilon_x(1,t) for t > 0, { \upsilon(x,0) = \upsilon_0(x) for 0 \leq x \leq 1, { \tau\frac{dt}{ds} = C)\upsilon(s(t),t)) for t > 0, { s(0) = s_0, 0 < s_0 < 1, $$ where $\upsilon(x,t)$ and $\upsilon_x(x,t)$ are assumed continuous in $\Omega = (0,1) \times (0, \infty)$.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.199-209
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• 2013

In this paper, we study the oscillation problem of the following higher-order neutral differential equation with positive and negative coefficients and mixed arguments $$z^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$, where $t{\geq}t_0$, $z(t)=x(t)-p(t)x(t-{\tau})$ with $p(t)$ > 0, ${\beta}&gt;1&gt;{\alpha}&gt;0$, ${\tau}$, ${\sigma}_1$ and ${\sigma}_2$ are real numbers. Without imposing any restriction on ${\tau}$, we establish several oscillation criteria for the above equation in two cases: (i) $q_1(t){\leq}0$, $q_2(t)&gt;0$, ${\sigma}_1{\geq}0$ and ${\sigma}_2{\leq}{\tau}$; (ii) $q_1(t){\geq}0$, $q_2(t)&lt;0$, ${\sigma}_1{\geq}{\tau}$ and ${\sigma}_2{\leq}0$. As an interesting application, our results can also be applied to the following higher-order differential equation with positive and negative coefficients and mixed arguments $$x^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$. Two numerical examples are also given to illustrate the main results.

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

• Journal of the East Asian Society of Dietary Life
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• v.21 no.4
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• pp.499-505
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• 2011

The purpose of this research was to study the characteristics of Hanwoo (Korean native cattle) beef fed without mugwort (T0) and Hanwoo beef fed with mugwort (T1) during storage at$3{\pm}1^{\circ}C$ for 50 days. During cold storage, $a^*$ and $b^*$ value of meat color for T1 decreased slowly compared to those of T0, there was significant difference between T0 and T1 after 40 days (p<0.01). The shear force value of T0 and T1 decreased (p<0.001), and the drip loss and cooking loss of T0 and T1 increased (p<0.05). However, there was no significant difference between T0 and T1. During refrigeration period, the volatile basic nitrogen contents of T1 slowly increased compared to T0, there was significant difference between T0 and T1 after 50 days (p<0.01). The total plat count and thiobarbituric acid value of T1 slowly increased compared to T0, and there was significant difference between T0 and T1 after 30 days (p<0.01). Further, the decrease of the antioxidant activity of T1 was delayed, there was significant difference between T0 and T1 after 40 days (p<0.05). There was no significant difference of taste, juiciness, or tenderness of cooked meat between T0 and T1. The aroma and palatability of cooked meat for T1 fed with mugwort were significantly superior than those of T0 at day 30 after storage (p<0.05).

• Journal of Aquaculture
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• v.11 no.2
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• pp.183-191
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• 1998

To substitute fromzed and freeze-dried food for live food in the development of the artificial seedling production of bivalve larvae, the dietary value of live T. suecica was compared with those of freeze-dried T. suecica, frozed T. suecica, live T. suecica (50%)+frozen T. suecica (50%), and live T. suecica (50%)+freeze-dried T. suecica (50%) in the rearing of oyster (Crassotrea gigas) and hen clam (Mactra chinensis) larvae, and manila clam (Tapes philipninarum) spats. Oyster larvae fed live T. suecica showed the highest growth (shell hight $231.9^{\mu}$m) and survival rate (72.6%) and those fed freeze-dried T. suecica showed the lowest growth (shell height $168.9^{\mu}$m) and survival rate (35.3%). However, in the hen clam larvae, there were not significantly different among diet group in growth and survival rate. The small spats of manila clam fed live t. suecica or live T. suecica (50%)+freeze-dried T. suecica (50%) showed higher growth and survival rate than those fed other diet group. In the case of large spats of manila clam, live T. suecica and live T. suecica (50%)+frozen T. suecica (50%) showed better growht. But, survival rates were not different among diet groups. Dietary valuse of frozen and dried T. suecica were different on species and growth stage, and frozen and freeze-dried T. suecica can be partially used as substitute food for T. suecica live T. succica in shellfish hatchery.

• Progress in Medical Physics
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• v.10 no.3
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• pp.125-131
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• 1999

T$_1$/T$_2$ weighted images are being used to give the characteristic contrast among the various tissues and the norma;/abnormal tissues. Abnormalities in tissues, in general, accompany the biochemical changes and eventually structural ones in which results in the change in T$_1$ and T$_2$ relaxation times of water protons. It has been suggested that the mapping of T$_1$/T$_2$ values may serve as a possible tool for the quantitative evaluation of the degree of abnormality. On reconstructing T$_1$/T$_2$ maps(or any other MR parametric map), only corresponding variables are to be varied, such as TE for T$_2$, TI or TR for T$_1$ and b-factor for diffusion images. But often the receiver gain is taken for the optimal usage of A/D converter, so that the set of the image data has different receiver gain. It must be corrected before any attempt to reconstruct the maps. Here we developed method of correcting receiver gain variation effect, using the standard deviation of noise on individual image. The resultant T$_1$ and T$_2$ values were very comparable to the other reported values.