• Journal of Communications and Networks
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• v.3 no.4
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• pp.361-364
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• 2001

Over an additive abelian group G of order g and for a given positive integer $\lambda$, a generalized Hadamard matrix GH(g, $\lambda$) is defined as a gλ$\times$gλ matrix[h(i, j)], where 1 $\leq i \leqg\lambda and 1 \leqj \leqg\lambda$, such that every element of G appears exactly $\lambd$atimes in the list h($i_1, 1) -h(i_2, 1), h(i_1, 2)-h(i_2, 2), …, h(i_1, g\lambda) -h(i_2, g\lambda), for any i_1\neqi_2$. In this paper, we propose a new method of expanding a GH(g^m, \lambda_1) = B = [B_{ij}] over G^m$ by replacing each of its m-tuple B_{ij} with B_{ij} + GH(g, $\lambda_2) where m = g\lambda_2. We may use g^m/\lambda_1 (not necessarily all distinct) GH(g, \lambda_2$)s for the substitution and the resulting matrix is defined over the group of order g.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.239-248
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• 2021

In this paper we study modules with the W F I⁺-extending property. We prove that if M satisfies the W F I⁺-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I⁺-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M₁ ⊕ M₂ for some semisimple submodule M₁ and Noetherian (respectively, Artinian) submodule M₂. Moreover, we show that if M is a W F I-extending module with pseudo duo, C₂ and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.

• Journal of Plant Biology
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• v.29 no.1
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• pp.53-65
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• 1986

The montane forests of Ulreung Island, Korea, were investigated by the ZM school method. By comparing the montane forests of this island with those of Korean Peninsula and of Japan, a new order, F a g e t a l i a m u l t i n e r v i s, a new alliance, F a l g i o n m u l t i n e r v i s, a new association, H e p a t i c o-F a g e t u m m u l t i n e r v i s and Rhododendron brachycarpum-Pinus parviflora community were recognized. The H e p a t i c o - F a g e t u m m u l t i n e r v i s was further subdivided into four subassociations; Subass. of Sasa kurilensis, Subass. of Rumohra standishii, Subass. of Rhododendron brachycarpum and Subass. of typicum. Each community was described in terms of floristic, structural and environmental features.

• The Korean Journal of Nuclear Medicine
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• v.33 no.6
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• pp.493-501
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• 1999

Purpose: We conducted a comparative study to evaluate the diagnostic values of T1-201, Tc-99m MIBI and I-131 scans in the follow-up assessment after ablative I-131 therapy in differentiated thyroid cancer. Materials and Methods: The study population consisted of 20 patients who underwent surgical removal of thyroid cancer and ablative radioactive iodine therapy, and followed by one or mote times of I-131 retreatments (33 cases). In all patients, T1-201, Tc-99m MIBI, diagnostic and therapeutic I-131 scans were performed and the results were analyzed retrospectively. Also serum thyroglobulin levels were measured in all patients. The final diagnosis of recurrent or metastatic thyroid cancer was determined by clinical, biochemical, radiologic and/or biopsy findings. Results: Positive rates (PR) of Tc-99m MIBI, T1-201, diagnostic and therapeutic I-131 scans in detecting malignant thyroid tissue lesions were 70% (19/27), 54% (15/28), 35% (17/48) and 63% (30/48), respectively. The PR in the group of 20 cases (28 lesions) who underwent concomitant T1-201 and I-131 scans were in the order of therapeutic 131 scan 71%, T1-201 scan 54% and diagnostic I-131 scan 36%. There was no statistically significant difference between T1-201 and diagnostic I-131 scans (p>0.05). In the group of 20 cases (27 lesions) who underwent concomitant Tc-99m MIBI and I-131 scans, the PR were in the order of Tc-99m MIBI scan 70%, I-131 therapeutic scan 52% and I-131 diagnostic scan 33%. The PR of Tc-99m MIBI was significantly higher than that of diagnostic I-131 scan (p<0.05). Conclusion: Tc-99m MIBI scan is superior to diagnostic I-131 scan in detecting recurrent or metastatic thyroid cancer following ablation therapy in patients with differentiated thyroid cancer. T1-201 scan did not showed significantly higher positive rate than diagnostic I-131 scan. Instead of diagnostic I-131 scan before the I-131 retreatment, Tc-99m MIBI scan without discontinuing thyroid hormone replacement would be a prudent and effective approach in the management of these patients.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.483-492
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• 2004

Let : [0, 1] $\times$ [0, $\infty$) $\longrightarrow$ [0, $\infty$) be continuous and a ${\in}$ C([0, 1], [0, $\infty$)),and let ${\xi}_{i}$ $\in$ (0, 1) with 0 < {\xi}$_1$ < ${\xi}_2$ < … < ${\xi}_{m-2}$ < 1, $a_{i}$, $b_{i}$ ${\in}$ [0, $\infty$) with 0 < $\Sigma_{i=1}$ /$^{m-2}$ $a_{i}$ < 1 and $\Sigma_{i=1}$$^{m-2}$ < l. This paper is concerned with the following m-point boundary value problem: $\chi$″(t)＋a(t) (t.$\chi$(t))＝0,t ${\in}$(0,1), $\chi$'(0)＝$\Sigma_{i=1}$ $^{m-2}$ /$b_{i}$$\chi$'(${\xi}_{i}$),$\chi$(1)＝$\Sigma_{i=1}$$^{m-2}$$a_{i}$$\chi$(${\xi}_{i}$). The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively.

• 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.

• The Korean Journal of Zoology
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• v.39 no.1
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• pp.115-121
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• 1996

To investigate gestational profiles in gene expression of placental lactogen I fpL4), PL-lI and Pit-1, RNA samples were extracted from the placentas of pregnant day 12 to 20 at 2 day intervals. Northern blots showed changes in gene expression of PL4, - 11 and Pit-i. Sizes of PL-l and -II mRNA were changed and amounts of PL-I, -H and Pit-1 mRNA increased during progress of gestation. To examine the effect of estrogen on the gene expression of PL-I, -Il and Pit-1, pregnant female rats were ovariectomized (OVX) and daily injected with estradiol (OVX + E). OVX markedly lowered the amount of PL4 and 41 mRNA, and shifted niRNA size from 1 kb to i 3 kb in PL-l mRNA and 0.6 kb to i kb in PL-ll mRNA, respectively. OVX had no effect on the mRNA size of Pit-1, but markedly attenuated Pit-1 mRNA level. Estrogen injection reversed the effect of OVX on the size-shift but not on the amount of PL4 and -Il mRNA. Replacement of E partially recovered OVX-induced inhibition of Pit-i mRNA level. Present results suggest that estrogen may play a pivotal role on the gene expression of PL-l and -Il such as alternative RNA splicing and/or polyadenylation, and Pit-1 may be involved in the gene expression of PL-l and 41 by estrogen.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1505-1519
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• 2017

Assume that M is an R-module where R is a commutative ring. A proper submodule N of M is called a weakly 2-absorbing primary submodule of M if $0{\neq}abm{\in}N$ for any $a,b{\in}R$ and $m{\in}M$, then $ab{\in}(N:M)$ or $am{\in}M-rad(N)$ or $bm{\in}M-rad(N)$. In this paper, we extended the concept of weakly 2-absorbing primary ideals of commutative rings to weakly 2-absorbing primary submodules of modules. Among many results, we show that if N is a weakly 2-absorbing primary submodule of M and it satisfies certain condition $0{\neq}I_1I_2K{\subseteq}N$ for some ideals $I_1$, $I_2$ of R and submodule K of M, then $I_1I_2{\subseteq}(N:M)$ or $I_1K{\subseteq}M-rad(N)$ or $I_2K{\subseteq}M-rad(N)$.

• The Korean Journal of Nuclear Medicine
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• v.34 no.4
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• pp.285-293
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• 2000

Purpose: A prospective comparison was made between imaging with Tc-99m pertechnetate (Tc-99m) and Ioine-131 (I-131) for the detection of residual and metastatic tissue after total thyroidectomy in patients with well-differentiated thyroid carcinoma. Materials and Methods: Initially our patients had imaging with Tc-99m, followed by I-131 within 3 days. The study included 21 patients who had ablation with high dose of I-131 ranging from 100 mCi to 150 mCi. Planar and pinhole images were acquired for both Tc-99m and I-131. Diagnostic images of Tc-99m and I-131 were compared with post-therapy images. Degree of uptake on Tc-99m and I-131 images was scored by four point scale and compared. Results: The results of the Tc-99m study were: 16 of 19 studies (84%) were positive on simple planar images, but 19 of 20 studies (95%) were positive on pinhole images. Conventional I-131 diagnostic imaging on the other hand showed that all studies (100%) were positive on both planar and pinhole images. There was a significant difference in degree of uptake between Tc-99m and I-131 planar images (p<0.05). Only one case of Tc-99m scintigraphy was negative on both planar and pinhole studies (false negative). There was no distant metastasis on the therapeutic I-131 images. Conclusion: Tc-99m scan using pinhole in certain clinical situations is an alternative to the I-131 scan in detecting thyroid or lymph node metastasis prior to the first ablative treatment after thyroidectomy for well-differentiated thyroid carcinoma.

• The Korean Journal of Nuclear Medicine
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• v.37 no.2
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• pp.120-127
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• 2003

Purpose: To evaluate diagnostic sensitivity of nuclear imaging in the detection of residual thyroid tissue and metastatic lesion, we have compared neck scintigrams with Tc-99m pertechnetate (Tc-99m scan) and high dose I-131 iodide (I-131 scan) in patients with differentiated thyroid cancer. Subjects and Methods: One hundred thirty-five thyroidectomized patients for differentiated thyroid cancer were enrolled in this study. Twenty-three had a previous history of radioiodine therapy. Planar and pin-hole images of anterior neck with Tc-99m were acquired at 20 minutes after injection, followed by I-131 scan three days after high-dose radioiodine therapy within 7 days interval. Patients were asked to discontinue thyroid hormone replacement more than 4 weeks. Results: All subjects were in hypothyroid state. Seventy out of 135 patients (51.9%) showed concordant findings between Tc-99m and I-131 scans. I-131 scan showed higher number of uptake foci in all of 65 patients showing discordant finding. Tc-99m scan showed no thyroid bed uptake in 34 patients, whereas 23 of them (67.6%) showed bed uptake in I-131 scan. Tc-99m scan did not show any uptake in thyroid bed in 11 of 112 patients without previous history of radioiodine therapy, but 9 of them showed bed uptake in I-131 scan. Tc-99m scan showed no bed uptake in all of the 23 patients with previous history of radioiodine therapy, in contrast 14 of them (60.9%) showed bed uptake in I-131 scan. Conclusion: These results suggest that Tc-99m scan has poor detectability for residual thyroid tissue or metastatic lesion in thyroidectomized differentiated thyroid cancer patients, compared to high dose I-131 therapy scan. Tc-99m scan could not detect any remnant tissue or metastatic lesion in patients with previous history of radioiodine treatment, especially.