• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.653-657
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• 2014

Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that $$Ext^i{_R}(R/I,H^t{_{I,J}}(M))$$ is finitely generated for i = 0, 1 where t=inf{$i{\in}\mathbb{N}_0:H^2{_{I,J}}(M)$ is not finitely generated}. Also, we prove that $H^i{_{I+J}}(H^t{_{I,J}}(M))$ is Artinian when dim(R/I + J) = 0 and i = 0, 1.

• Clinical and Experimental Pediatrics
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• v.52 no.10
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• pp.1140-1146
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• 2009

Purpose:The pathophysiology of magnesium, the second highest common compound in humans, is still unclear, especially in preterm babies. We accessed the association between total magnesium (tMg), ionized Mg (iMg), and gestational age (GA) and that between serum magnesium (sMg) and intraventricular hemorrhage (IVH) in preterm babies. Methods:In all, 119 inborn preterm infants admitted between July 2006 and February 2008 were divided into the IVH group (19) and the control group (100) and were prospectively analyzed. TMg, iMg, pH, total calcium (tCa), and ionized Ca (iCa) levels were determined immediately after delivery or within 3 hours after birth, and their correlation with GA were investigated. Results:TMg was not correlated with GA, tCa, iCa, and pH. IMg was correlated with tMg (r=0.288, P=0.002) and iCa (r=0.212, P=0.021); however, it was not correlated with GA and pH. Mean GA and birth weight were significantly lower (P=0.002) and smaller (P=0.030) in the IVH group. Mean sMg was higher in the IVH group ($2.5{\pm}0.9mg/dL$) than in the control group ($2.1{\pm}0.6mg/dL$) (P=0.021). SMg was a risk factor even after logistic regression analysis (OR, 2.798; 95% C.I., 1.265-6.192; P=0.011). Conclusion:In less than 37-week-old preterm babies, tMg and iMg were similar, regardless of GA. High sMg may be a risk factor for IVH in premature babies, regardless of their exposure to antenatal magnesium.

• Nuclear Engineering and Technology
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• v.7 no.2
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• pp.127-133
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• 1975

For isotopic exchange labelling of 3,5,3'-triiodothyronine (T$_3$) and thyroxine (T$_4$) with radioiodide in the presence of molecular iodine, T$_3$:I$_2$ or T$_4$:I$_2$ molar ratios, pH, and reaction time are. considered to be important factors. A modified labelling and separation method is proposed in present paper, by which T$_3$-$^{125}$ I and T$_4$-$^{125}$ I can be obtained with the mean labelling yields of 45%, and 50%, respectively. The whole reaction products can be separated by adoption of thin-layer chromatography technique using silica gel plate and the solvent system composd of chloroform, methanol and ammonia.

• The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
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• v.20 no.2 s.33
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• pp.171-178
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• 2007

Objective : The aim of this study was to evaluate Yangdorak and D.I.T.I. for analysis of Symptom-complexes. Method : This study was selected 26 acne patients in Dongshin University Oriental Medical Hospital. We used Yangdorak (SME5800N, Sord Medicom Co., Korea) and D.I.T.I. (Digital Infrared Thermal Imaging 256, Dorex Inc, Orange CA, USA) and investigated the results of Yangdorak and D.I.T.I.. We made a comparison according to Deficiency or Excess(虛實) of acne patients. Result : In comparing Yangdorak results according to Deficiency or Excess(虛實) of acne patients, Triple-energizer(三焦), Intestine(大腸), Liver(肝), Stomach(胃) meridian in Excess group are higher than Deficiency group, and Kidney(腎) meridian in Deficiency group are lower than Excess group. D.I.T.I. reveald hyperthemia of face and chest on acne patients. The temperature of face and chest on Excess group is higher than Deficiency group. There is no statistically significant value compared with data of other group.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1341-1352
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• 2016

Let R be a commutative Noetherian ring, ${\Phi}$ a system of ideals of R and $I{\in}{\Phi}$. In this paper among other things we prove that if M is finitely generated and $t{\in}\mathbb{N}$ such that the R-module $H^i_{\Phi}(M)$ is $FD_{{\leq}1}$ (or weakly Laskerian) for all i < t, then $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all i < t and for any $FD_{{\leq}0}$ (or minimax) submodule N of $H^t_{\Phi}(M)$, the R-modules $Hom_R(R/I,H^t_{\Phi}(M)/N)$ and $Ext^1_R(R/I,H^t_{\Phi}(M)/N)$ are finitely generated. Also it is shown that if cd I = 1 or $dimM/IM{\leq}1$ (e.g., $dim\;R/I{\leq}1$) for all $I{\in}{\Phi}$, then the local cohomology module $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all $i{\geq}0$. These generalize the main results of Aghapournahr and Bahmanpour [2], Bahmanpour and Naghipour [6, 7]. Also we study cominimaxness and weakly cofiniteness of local cohomology modules with respect to a system of ideals.

• Journal of the Korean Ceramic Society
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• v.41 no.5
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• pp.401-405
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• 2004

Undoped SrB $i_2$T $a_2$O$_{9}$, donor-doped Sr$_{0.99}$B $i_2$(Ta$_{0.99}$W$_{0.01}$)$_2$O$_{9}$ and acceptor-doped SrB $i_2$(Ta$_{0.99}$Ti$_{0.01}$)$_2$O$_{8.99$ ceramics were prepared and their microstructure, ferroelectric P-E hysteresis and Curie temperature were investigated. Grain size did not influence P-E hysteresis curve in undoped SrB $i_2$T $a_2$O$_{9}$ ceramics. Donor-Doped Sr$_{0.99}$B $i_2$(Ta$_{0.99}$W$_{0.01}$)$_2$O$_{9}$ ceramics showed more saturated P-E hysteresis curve with larger remanent polarization (P$_{r}$) than undoped SrB $i_2$T $a_2$O$_{9}$ ceramics while acceptor-doped SrB $i_2$(Ta$_{0.99}$Ti$_{0.01}$)$_2$O$_{8.99}$ ceramics led to a pinched P-E hysteresis loop. Larger polarization in donor-doped Sr$_{0.99}$B $i_2$(Ta$_{0.99}$W$_{0.01}$)$_2$O$_{9}$ ceramics resulted from easier domain wall motion by Sr-vacancies.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.319-326
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• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.