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LIE IDEALS IN THE UPPER TRIANGULAR OPERATOR ALGEBRA ALG𝓛

  • LEE, SANG KI;KANG, JOO HO
    • Journal of applied mathematics & informatics
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    • v.36 no.3_4
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    • pp.237-244
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    • 2018
  • Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

IDEALS IN THE UPPER TRIANGULAR OPERATOR ALGEBRA ALG𝓛

  • Lee, Sang Ki;Kang, Joo Ho
    • Honam Mathematical Journal
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    • v.39 no.1
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    • pp.93-100
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    • 2017
  • Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

Polarographic Behavior of Cadmium (II) and Copper (II) Complexes of 1,5-Diphenylcarbohydrazide in Dimethylsulfoxide (디메틸술폭시드 속에서 1,5-디페닐카르보히드라지드의 카드뮴 (II) 및 구리 (II) 착물에 대한 폴라로그래피적 거동)

  • Chil-Nam Choe
    • Journal of the Korean Chemical Society
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    • v.30 no.1
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    • pp.51-56
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    • 1986
  • Polarographic behavior of cadmium(II) and copper (II) complexes of 1,5-diphenylcarbohydrazide in dimethylsulfoxide have been investigated by the DC polarography. The reduction processes are estimated as follows; Cd(II)${\cdot}$DPH Complex$\frac{e^-}{(E_{\frac{1}{2}}=-0.12V)}$${\to}$Cd(I)${\cdot}$DPH Complex. Cd(I)${\cdot}$DPH Complex$\frac{e^-}{(E_{\frac{1}{2}}=-0.74V)}$${\to}$Cd(Hg) + nDPH. Cu(II)${\cdot}$DPH Complex$\frac{e^-}{(E_{\frac{1}{2}}=-0.44V)}$${\to}$Cu(I)${\cdot}$DPH Complex. Cu(I)${\cdot}$DPH Complex$\frac{e^-}{(E_{\frac{1}{2}}=-0.84V)}$${\to}$Cu(Hg) + nDPH. The limiting currents of all reduction wave are irreversible. The number of ligand and the dissociation constant for Cu(I)${\cdot}$1.5-diphenylcarbohydrazide complex were found to be 2 and 5.12 ${\times}10^{-8}$, respectively. All reduction waves of complexes are irreversible. Based on the experimental results, the polarographic reductions of complexes in dimethylsulfoxide solution occurred in two one-electron steps.

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Molecular Biological Species Identification of Imported Groupers(Epinephelus moara ♀×E. lanceolatus ♂) (수입산 바리과(Family Serranidae) 잡종 어류(Epinephelus moara ♀×E. lanceolatus ♂)의 분자생물학적 판별)

  • Kim, Yong Hwi;Park, Jong Yeon;Kim, Jae Hoon;Bang, In-Chul
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.53 no.4
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    • pp.566-571
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    • 2020
  • To classify a presumed hybrid of imported grouper species acquired from the National Fishery Products Quality Management Service, maternal and paternal lines were identified based on partial sequencing of mitochondrial cytochrome c oxidase 1 (co1) and nuclear recombination activation gene 1 (rag1) genes. The matrilineal species was identified as Epinephleus moara by a partial (760 bp) co1 sequence. Ambiguous sequences with base pairs belonging to E. moara or E. lanceolatus were found in a total of 15 different base pairs in the partial 1,159 bp of the rag1 gene, and the patrilineal species was found to be E. lanceolatus. Therefore, all of the groupers examined in the study were identified to be hybrids of E. moara and E. lanceolatus. In addition, a fast and convenient method using random amplification of polymorphic DNA (RAPD) was established for hybrid discrimination. Hybrids between E. moara ♀ and E. lanceolatus ♂ were identified through specific bands of 387 bp and 433 bp in PRIMER 6.

Single Nucleotide Polymorphism in Cytochrome P450 2E1 among Korean Patients on Warfarin Therapy

  • Han, Dong-Hoon;Lee, Min-Jeon;Kim, Jeong-Hee;Lee, Suk-Hyang
    • Biomolecules & Therapeutics
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    • v.14 no.4
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    • pp.189-193
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    • 2006
  • This study was designed to assess the distribution of cytochrome P450 2E1 (CYP2E1) polymorphism among Korean patients on warfarin therapy. CYP2E1 polymorphism was analyzed at 5' flanking region of CYP2E1 gene using restriction fragment length polymorphism method. Patient characteristics including the measured internal normalized ratio (INR) were also evaluated. Based on the warfarin dose and the bleeding cases, the patients were grouped as the regular dose control, the regular dose bleeding, the low dose control, and the low dose bleeding. Total 96 patients were evaluated for both Pst I and Rsa I loci of the CYP2E1 gene and the results showed that both loci were tightly linked. Thirty-three patients(34.4%) were heterozygotes and 4 patients(4.2%) were homozygote. There was no significant difference in patient characteristics in the dose and bleeding case groups. CYP2E1 polymorphism showed a little difference among the groups but was not statistically significant, however, lower INR value was observed in homozygote genotype groups. It was also revealed that genotype allele frequencies of CYP2E1 in Korean was close to other Asian groups but was significantly different from other Caucasian and African-American populations.

The Alcohol-inducible form of Cytochrome P450 (CYP 2E1): Role In Toxicology and Regulation of Expression

  • Novak, Raymond F.;Woodcroft, Kimberley J.
    • Archives of Pharmacal Research
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    • v.23 no.4
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    • pp.267-282
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    • 2000
  • Cytochrome P45O (CYP) 2E1 catalyzes the metabolism of a wide variety of therapeutic agents, procarcinogens, and low molecular weight solvents. CYP2E1-catalyzed metabolism may cause toxicity or DNA damage through the production of toxic metabolites, oxygen radicals, and lipid peroxidation. CYP2E1 also plays a role in the metabolism of endogenous compounds including fatty acids and ketone bodies. The regulation of CYP2E1 expression is complex, and involves transcriptional, post-transcriptional, translational, and post-translational mechanisms. CYP2E1 is transcriptionally activated in the first few hours after birth. Xenobiotic inducers elevate CYP2E1 protein levels through both increased translational efficiency and stabilization of the protein from degradation, which appears to occur primarily through ubiquitination and proteasomal degradation. CYP2E1 mRNA and protein levels are altered in response to pathophysiologic conditions by hormones including insulin, glucagon, growth hormone, and leptin, and growth factors including epidermal growth factor and hepatocyte growth factor, providing evidence that CYP2E1 expression is under tight homeostatic control.

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17 beta-Estradiol Increases Peak of $\textrm{Ca}^{2+}$ Current in Mouse Early Embryo (에스트로겐이 생쥐 초기배의 $\textrm{Ca}^{2+}$ 전류에 미치는 영향)

  • 강다원;신용원;김은심;홍성근;한재희
    • Journal of Embryo Transfer
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    • v.16 no.2
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    • pp.79-89
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    • 2001
  • Steroid hormones control the expression of many cellular regulators, and a role thor estrogen in mouse oocytes has been well documented. The preovulatory $E_2$increment is generally accepted as the endocrine process regulating induction of in vivo oocyte maturation To address whether the activity of the T-type $Ca^{2+}$ channel is altered by 17 beta-estradiol ( $E_2$), we examined the actions of $E_2$on the calcium channel of mouse oocytes and early embryos. Oocrtes were collected from the oviduct of mice treated with pregnant mare's serum gonadotropin (PMSG) and human choronic gonadotropin (hCG). Whole cell voltage clamp technique and confocal microscopy were used to examine that $E_2$increase intracellular $Ca^{2+}$ concentration ([C $a^{2+}$]$_{i}$ ) via voltage dependent $Ca^{2+}$ channel (VDC) and estrogen receptor (FSR), and $E_2$concentration by the use of radioimmunoassay (RIA) were examined in mouse. The results obtained were as follows: The peak of $Ca^{2+}$ current induced by $E_2$increased 122% to 1.50$\pm$0.03 nA from 1.23$\pm$0.21 nA (n=15) in the presence of 5 mM extracellular $Ca^{2+}$ concentration ([C $a^{2+}$]$_{o}$ ). The increased $Ca^{2+}$ current was temporally associated with $Ca^{2+}$ transients. The intracellular $Ca^{2+}$ level increased 207%~30 s following the addition of 1${\mu}{\textrm}{m}$ $E_2$(relative fluorescence intensity: 836.4$\pm$131.2 for control, n=10, 1736.4$\pm$192.0 in the presence of $E_2$, n=10). $E_2$increased amplitude of $Ca^{2+}$ current and [C $a^{2+}$]$_{i}$ . $E_2$-induced $Ca^{2+}$ current and $E_2$concentration in blood were showed difference on the stage of embryo. These results suggest that $E_2$modulate $Ca^{2+}$ channel to increase $Ca^{2+}$ influx.$Ca^{2+}$ influx.

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A Variable Latency Newton-Raphson's Floating Point Number Reciprocal Computation (가변 시간 뉴톤-랍손 부동소수점 역수 계산기)

  • Kim Sung-Gi;Cho Gyeong-Yeon
    • The KIPS Transactions:PartA
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    • v.12A no.2 s.92
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    • pp.95-102
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    • 2005
  • The Newton-Raphson iterative algorithm for finding a floating point reciprocal which is widely used for a floating point division, calculates the reciprocal by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the reciprocal of a floating point number F, the algorithm repeats the following operations: '$'X_{i+1}=X=X_i*(2-e_r-F*X_i),\;i\in\{0,\;1,\;2,...n-1\}'$ with the initial value $'X_0=\frac{1}{F}{\pm}e_0'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 27 for the single precision floating point, and 57 for the double precision floating point. Let $'X_i=\frac{1}{F}+e_i{'}$, these is $'X_{i+1}=\frac{1}{F}-e_{i+1},\;where\;{'}e_{i+1}, is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to $'\frac{1}{F}{'}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables $(X_0=\frac{1}{F}{\pm}e_0)$ with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal unit. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia scientific computing, etc.

Echinostoma mekongi n. sp. (Digenea: Echinostomatidae) from Riparian People along the Mekong River in Cambodia

  • Cho, Jaeeun;Jung, Bong-Kwang;Chang, Taehee;Sohn, Woon-Mok;Sinuon, Muth;Chai, Jong-Yil
    • Parasites, Hosts and Diseases
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    • v.58 no.4
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    • pp.431-443
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    • 2020
  • Echinostoma mekongi n. sp. (Digenea: Echinostomatidae) is described based on adult flukes collected from humans residing along the Mekong River in Cambodia. Total 256 flukes were collected from the diarrheic stool of 6 echinostome egg positive villagers in Kratie and Takeo Province after praziquantel treatment and purging. Adults of the new species were 9.0-13.1 (av. 11.3) mm in length and 1.3-2.5 (1.9) mm in maximum width and characterized by having a head collar armed with 37 collar spines (dorsal spines arranged in 2 alternative rows), including 5 end group spines. The eggs in feces and worm uterus were 98-132 (117) ㎛ long and 62-90 (75) ㎛ wide. These morphological features closely resembled those of Echinostoma revolutum, E. miyagawai, and several other 37-collar-spined Echinostoma species. However, sequencing of the nuclear ITS (ITS1-5.8S rRNA-ITS2) and 2 mitochondrial genes, cox1 and nad1, revealed unique features distinct from E. revolutum and also from other 37-collar-spined Echinostoma group available in GenBank (E. bolschewense, E. caproni, E. cinetorchis, E. deserticum, E. miyagawai, E. nasincovae, E. novaezealandense, E. paraensei, E. paraulum, E. robustum, E. trivolvis, and Echinostoma sp. IG). Thus, we assigned our flukes as a new species, E. mekongi. The new species revealed marked variation in the morphology of testes (globular or lobulated), and smaller head collar, collar spines, oral and ventral suckers, and cirrus sac compared to E. revolutum and E. miyagawai. Epidemiological studies regarding the geographical distribution and its life history, including the source of human infections, remain to be performed.

Performance Analysis of Assisted-Galileo Signal Acquisition Under Weak Signal Environment (약 신호 환경에서의 Assisted-Galileo 신호 획득 성능 분석)

  • Lim, Jeong-Min;Park, Ji-Won;Sung, Tae-Kyung
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.7
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    • pp.646-652
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    • 2013
  • EU's Galileo project is a market-based GNSS (Global Navigation Satellite System) that is under development. It is expected that Galileo will provide the positioning services based on new technologies in 2020s. Because Galileo E1 signal for OS (Open Service) shares the same center frequency with GPS L1 C/A signal, CBOC (Composite Binary Offset Carrier) modulation scheme is used in the E1 signal to guarantee interoperability between two systems. With E1 signal consisting of a data channel and a pilot channel at the same frequency band, there exist several options in designing signal acquisition for Assisted-Galileo receivers. Furthermore, compared to SNR worksheet of Assisted-GPS, some factors should be examined in Assisted-Galileo due to different correlation profile and code length of E1 signal. This paper presents SNR worksheets of Galileo E1 signals in E1-B and E1-C channel. Three implementation losses that are quite different from GPS are mainly analyzed in establishing SNR worksheets. In the worksheet, hybrid long integration of 1.5s is considered to acquire weak signal less than -150dBm. Simulation results show that the final SNR of E1-B signal with -150dBm is 19.4dB and that of E1-C signal is 25.2dB. Comparison of relative computation shows that E1-B channel is more profitable to acquire the strongest signal in weak signal environment. With information from the first satellite signal acquisition, fast acquisition of the weak signal around -155dBm can be performed with E1-C signal in the subsequent satellites.