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HE NONCOMMUTATIVE ℓ1 - ℓ2 INEQUALITY FOR HILBERT C*-MODULES AND THE EXACT CONSTANT

  • Krishna, K. Mahesh;Johnson, P. Sam
    • Nonlinear Functional Analysis and Applications
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    • 제27권2호
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    • pp.249-259
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    • 2022
  • Let 𝓐 be a unital C*-algebra. Then it follows that $\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}{\leq}\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$, ∀n ∈ ℕ, ∀a1, …, an ∈ 𝓐. By modifications of arguments of Botelho-Andrade, Casazza, Cheng, and Tran given in 2019, for certain n-tuple x = (a1, …, an) ∈ 𝓐n, we give a method to compute a positive element cx in the C*-algebra 𝓐 such that the equality $$\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}=c_x\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$$ holds. We give an application for the integral of Kasparov. We also derive a formula for the exact constant for the continuous ℓ1 - ℓ2 inequality.

두 치환체를 가진 비닐시클로프로판의 시클로펜텐으로의 열적자리 옮김반응 (Thermal Rearrangement of 1,1-Disubstituted 2-Vinylcyclopropanes to 4,4-Disubstituted Cyclopentenes)

  • ;안광덕
    • 대한화학회지
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    • 제22권3호
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    • pp.158-163
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    • 1978
  • 1-위치에 두개의 극성치환체를 가진 2-비닐시클로프로판 1a, 1b, 1c, 1d를 300$^{\circ}C$ 이하로 가열한 결과 4,4-위치에 치환된 대응하는 시클로펜텐 2a, 2b, 2c, 2d로의 자리 옮김반응이 용이하게 일어났다. 시아노기가 치환된 1b는 용매로 희석시켜서 170${\circ}C$로 반응시켰을 때 2b로의 자리옮김이 관찰되었지만, 1c와 1d는 $200^{\circ}C$ 이상의 온도에서 반응이 일어났고, 페닐기가 치환된 1a는 $250{\circ}C$ 이상의 온도에서 반응이 일어났고, 페닐기가 치환된 1a는 250$^{\circ}C$ 에서 용매 사용없이 열반응으로 2a가 생성되었다. 1a의 시클로펜텐으로의 열적 자리옮김반응은 거의 정량적이었지만 1b, 1c, 1d의 경우에는 시클로펜텐외에 상당량의 고분자물질 3이 생성되었다. 1c의 경우에는 시클로펜텐외에 시클로프로판 고리가 열린 디엔 4가 관찰되었다. 두 기가 치환된 시클로프로판 1이 용이하게 시클로펜텐 2로 열적 자리옮김 반응을 하는 이유는 두 극성기가 반응 중간물질인 디라디칼 5를 안정화 시키는 효과로서 설명하였다.

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캔버스 카이트의 유체역학적 특성에 관한 연구 - 2. 삼각형 캔버스 카이트의 특성 - (The hydrodynamic characteristics of the canvas kite - 2. The characteristics of the triangular canvas kite -)

  • 배봉성;배재현;안희춘;이주희;신정욱
    • 수산해양기술연구
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    • 제40권3호
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    • pp.206-213
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    • 2004
  • 종횡비, 다각형 모양에 따른 평판과 범포의 유체역학적 특성을 규명하고자 직사각형, 사다리꼴 모양으로 모형 평판과 범포를 제작하고 회류수조에서 양 ${\cdot}$ 항력 실험을 수행하였다. 그 결과를 요약하면 다음과 같다. 1. 삼각형 평판의 경우, 종횡비가 1 이하인 모형에서는 38${\sim}$42$^{\circ}$에서 최대 $C_L$이 1.23${\sim}$1.32, 1.5 이상인 모형에서는 20${\sim}$50$^{\circ}$에서 $C_L$이 약 0.85 전후였다. 역삼각형 평판의 경우, 종횡비가 1 이하인 모형에서는 영가가 36${\sim}$38$^{\circ}$에서 최대 $C_L$이 1.46${\sim}$1.56, 1.5 이상인 모형에서는 22${\sim}$26$^{\circ}$에서 1.05${\sim}$1.21 정도였다. 같은 삼각형 평판 모형에서는 전자의 모형이 후자보다 $C_L$이 작게, 양항비도 작게 나타났다. 2. 삼각형 범포의 경우, 종횡비가 1 이하인 모형에서는 영각 46${\sim}$48$^{\circ}$에서 최대 $C_L$이 1.67${\sim}$1.77, 1.5 이상인 모형에서는 20${\sim}$50$^{\circ}$에서 $C_L$이 약 1.1 전후였다. 역삼각형 범포의 경우, 종횡비가 1 이하인 모형에서는 영각 28${\sim}$32$^{\circ}$에서 최대 $C_L$이 1.44${\sim}$1.68, 1.5 이상인 모형에서는 18${\sim}$24$^{\circ}$에서 10.3${\sim}$1.18 정도였다. 같은 삼각형 범포 모형에서는 전자의 모형이 후자보다 $C_L$은 크게, 양항비는 작게 나타났다. 3. 모형에서 물의 유체력을 많이 받을 수 있는 곳에서 만곡꼭지점이 만들어지며, 삼각형 모형에서는 종횡비가 클수록, 역삼각형 모형에서는 작을수록 만곡꼭지점의 위치도 컸다. 4. 만곡도는 전 모형에서 종횡비가 클수록 컸으며, 삼각형 모형에서는 영각이 클수록 컸고 역삼각형 모형에서는 작을수록 컸다.

A NEW MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND KLOOSTERMAN SUMS

  • Han, Di;Zhang, Wenpeng
    • 대한수학회보
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    • 제52권1호
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    • pp.35-43
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    • 2015
  • Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

수서 환경독성 평가와 어류 Cytochrome P450 1A (CYP1A) 유전자 (Assessment of Toxic Effects in Aquatic Environment and the Fish Cytochrome P450 1A(CYP1A) Gene)

  • 윤석주;김일찬;윤용달;이재성
    • 환경생물
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    • 제21권1호
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    • pp.1-7
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    • 2003
  • CYP1A 유전자는 cytochrome P450 약물대사효소에 속하며 다이옥신 등의 내분비계 장애물질에 의해 농도 의존적으로 유도되어 환경오염물질에 의해 유도되는 특성을 이용하여 환경오염물질에 대해 반응하는 생물체의 유전자 발현 변화뿐만 아니라 이를 토대로 특정지역의 환경오염에 관한 정보를 얻을 수 있다. 본 논문에서는 수서환경오염과 관련하여 CYP1A유전자의 유용성을 다각도로 논의하였다.

Development of a Screening System for Plant Defense-Inducing Agent using Transgenic Tobacco Plant with PR-1a Promoter and GUS Gene

  • Oh, Sang-Keun;Lee, Seon-Woo;Kwon, Suk-Yoon;Choi, Do-Il
    • The Plant Pathology Journal
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    • 제21권3호
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    • pp.288-292
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    • 2005
  • Pathogenesis-related protein-1a (PR-1a) is strongly induced in tobacco plants by pathogen attack, exogenous salicylic acid (SA) application and by other developmental processes. In order to develop a rapid screening system for the selection of plant defense-inducing compounds originated from various sources, we have transformed tobacco Samsun NN plants with a chimeric construct consisting of GUS $(\beta-glucuronidase)$. In the $T_1$ generation, three transgenic lines having stable GUS expression were selected for further promoter analysis. Using GUS histochemical assay, we observed strong GUS induction driven by PR-1a promoter in PR1a-GUS transgenic tobacco leaves in response to the exogenous application of SA or benzol (1,2,3) thiadiazole-7-carbothioic acid S-methyl ester (BTH), a SA­derivative compound. In addition, GUS expression was maintained locally or systemically in PR1a-GUS transgenic line $\#5\;T_2$ generation) until after 3 days when they were treated with same chemicals. Our results suggested that the PR1a-GUS reporter gene system in tobacco plants may be applicable for the large-scale screening of defense-inducing substances.

Field Studios of In-situ Aerobic Cometabolism of Chlorinated Aliphatic Hydrocarbons

  • Semprini, Lewts
    • 한국지하수토양환경학회:학술대회논문집
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    • 한국지하수토양환경학회 2004년도 총회 및 춘계학술발표회
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    • pp.3-4
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    • 2004
  • Results will be presented from two field studies that evaluated the in-situ treatment of chlorinated aliphatic hydrocarbons (CAHs) using aerobic cometabolism. In the first study, a cometabolic air sparging (CAS) demonstration was conducted at McClellan Air Force Base (AFB), California, to treat chlorinated aliphatic hydrocarbons (CAHs) in groundwater using propane as the cometabolic substrate. A propane-biostimulated zone was sparged with a propane/air mixture and a control zone was sparged with air alone. Propane-utilizers were effectively stimulated in the saturated zone with repeated intermediate sparging of propane and air. Propane delivery, however, was not uniform, with propane mainly observed in down-gradient observation wells. Trichloroethene (TCE), cis-1, 2-dichloroethene (c-DCE), and dissolved oxygen (DO) concentration levels decreased in proportion with propane usage, with c-DCE decreasing more rapidly than TCE. The more rapid removal of c-DCE indicated biotransformation and not just physical removal by stripping. Propane utilization rates and rates of CAH removal slowed after three to four months of repeated propane additions, which coincided with tile depletion of nitrogen (as nitrate). Ammonia was then added to the propane/air mixture as a nitrogen source. After a six-month period between propane additions, rapid propane-utilization was observed. Nitrate was present due to groundwater flow into the treatment zone and/or by the oxidation of tile previously injected ammonia. In the propane-stimulated zone, c-DCE concentrations decreased below tile detection limit (1 $\mu$g/L), and TCE concentrations ranged from less than 5 $\mu$g/L to 30 $\mu$g/L, representing removals of 90 to 97%. In the air sparged control zone, TCE was removed at only two monitoring locations nearest the sparge-well, to concentrations of 15 $\mu$g/L and 60 $\mu$g/L. The responses indicate that stripping as well as biological treatment were responsible for the removal of contaminants in the biostimulated zone, with biostimulation enhancing removals to lower contaminant levels. As part of that study bacterial population shifts that occurred in the groundwater during CAS and air sparging control were evaluated by length heterogeneity polymerase chain reaction (LH-PCR) fragment analysis. The results showed that an organism(5) that had a fragment size of 385 base pairs (385 bp) was positively correlated with propane removal rates. The 385 bp fragment consisted of up to 83% of the total fragments in the analysis when propane removal rates peaked. A 16S rRNA clone library made from the bacteria sampled in propane sparged groundwater included clones of a TM7 division bacterium that had a 385bp LH-PCR fragment; no other bacterial species with this fragment size were detected. Both propane removal rates and the 385bp LH-PCR fragment decreased as nitrate levels in the groundwater decreased. In the second study the potential for bioaugmentation of a butane culture was evaluated in a series of field tests conducted at the Moffett Field Air Station in California. A butane-utilizing mixed culture that was effective in transforming 1, 1-dichloroethene (1, 1-DCE), 1, 1, 1-trichloroethane (1, 1, 1-TCA), and 1, 1-dichloroethane (1, 1-DCA) was added to the saturated zone at the test site. This mixture of contaminants was evaluated since they are often present as together as the result of 1, 1, 1-TCA contamination and the abiotic and biotic transformation of 1, 1, 1-TCA to 1, 1-DCE and 1, 1-DCA. Model simulations were performed prior to the initiation of the field study. The simulations were performed with a transport code that included processes for in-situ cometabolism, including microbial growth and decay, substrate and oxygen utilization, and the cometabolism of dual contaminants (1, 1-DCE and 1, 1, 1-TCA). Based on the results of detailed kinetic studies with the culture, cometabolic transformation kinetics were incorporated that butane mixed-inhibition on 1, 1-DCE and 1, 1, 1-TCA transformation, and competitive inhibition of 1, 1-DCE and 1, 1, 1-TCA on butane utilization. A transformation capacity term was also included in the model formation that results in cell loss due to contaminant transformation. Parameters for the model simulations were determined independently in kinetic studies with the butane-utilizing culture and through batch microcosm tests with groundwater and aquifer solids from the field test zone with the butane-utilizing culture added. In microcosm tests, the model simulated well the repetitive utilization of butane and cometabolism of 1.1, 1-TCA and 1, 1-DCE, as well as the transformation of 1, 1-DCE as it was repeatedly transformed at increased aqueous concentrations. Model simulations were then performed under the transport conditions of the field test to explore the effects of the bioaugmentation dose and the response of the system to tile biostimulation with alternating pulses of dissolved butane and oxygen in the presence of 1, 1-DCE (50 $\mu$g/L) and 1, 1, 1-TCA (250 $\mu$g/L). A uniform aquifer bioaugmentation dose of 0.5 mg/L of cells resulted in complete utilization of the butane 2-meters downgradient of the injection well within 200-hrs of bioaugmentation and butane addition. 1, 1-DCE was much more rapidly transformed than 1, 1, 1-TCA, and efficient 1, 1, 1-TCA removal occurred only after 1, 1-DCE and butane were decreased in concentration. The simulations demonstrated the strong inhibition of both 1, 1-DCE and butane on 1, 1, 1-TCA transformation, and the more rapid 1, 1-DCE transformation kinetics. Results of tile field demonstration indicated that bioaugmentation was successfully implemented; however it was difficult to maintain effective treatment for long periods of time (50 days or more). The demonstration showed that the bioaugmented experimental leg effectively transformed 1, 1-DCE and 1, 1-DCA, and was somewhat effective in transforming 1, 1, 1-TCA. The indigenous experimental leg treated in the same way as the bioaugmented leg was much less effective in treating the contaminant mixture. The best operating performance was achieved in the bioaugmented leg with about over 90%, 80%, 60 % removal for 1, 1-DCE, 1, 1-DCA, and 1, 1, 1-TCA, respectively. Molecular methods were used to track and enumerate the bioaugmented culture in the test zone. Real Time PCR analysis was used to on enumerate the bioaugmented culture. The results show higher numbers of the bioaugmented microorganisms were present in the treatment zone groundwater when the contaminants were being effective transformed. A decrease in these numbers was associated with a reduction in treatment performance. The results of the field tests indicated that although bioaugmentation can be successfully implemented, competition for the growth substrate (butane) by the indigenous microorganisms likely lead to the decrease in long-term performance.

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Statistical Inference for an Arithmetic Process

  • Francis, Leung Kit-Nam
    • Industrial Engineering and Management Systems
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    • 제1권1호
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    • pp.87-92
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    • 2002
  • A stochastic process {$A_n$, n = 1, 2, ...} is an arithmetic process (AP) if there exists some real number, d, so that {$A_n$ + (n-1)d, n =1, 2, ...} is a renewal process (RP). AP is a stochastically monotonic process and can be used for modeling a point process, i.e. point events occurring in a haphazard way in time (or space), especially with a trend. For example, the vents may be failures arising from a deteriorating machine; and such a series of failures id distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for an AP, similar to those for a geometric process (GP) proposed by Lam (1992). Two statistics are suggested for testing whether a given process is an AP. If this is so, we can estimate the parameters d, ${\mu}_{A1}$ and ${\sigma}^{2}_{A1}$ of the AP based on the techniques of simple linear regression, where ${\mu}_{A1}$ and ${\sigma}^2_{A1}$ are the mean and variance of the first random variable $A_1$ respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

Relationship between the Expression of Forkhead box M1 (FoxM1) and $p27^{kip1}$ in Non-Small Cell Lung Cancers

  • ;;;;;노미숙
    • 대한의생명과학회지
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    • 제14권4호
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    • pp.243-248
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    • 2008
  • The Forkhead box M1 (FoxM1) has been shown to regulate transcription of cell cycle genes essential for $G_1$-S and $G_2$-M progression, including $p27^{kip1}$. The $p27^{kip1}$ gene is a member of the universal cyclin-dependent kinase inhibitor family. Immunohistochemical studies for FoxM1 and $p27^{kip1}$ were performed in 154 lung cancers (69 squamous cell carcinomas (SCC) and 85 adenocarcinomas (ADC)). Immunoreactivity for FoxM1 and $p27^{kip1}$ were found in 79 (51.3%) and 49 (31.8%) out of 154 cases, respectively. Forty-six (58.2%) of the 79 cases with a positive FoxM1 immunoreactivity showed a negative $p27^{kip1}$ expression in 154 lung cancers. According to histologic type, 22 (53.7%) of the 41 SCC cases with a positive FoxM1 immunoreactivity showed a negative $p27^{kip1}$ expression and 24 (63.2%) of the 38 ADC cases with a positive FoxM1 immunoreactivity showed a negative $p27^{kip1}$ expression. The expression of $p27^{kip1}$ was significantly higher in the SCC than in the ADC (P=0.050). There were no significant associations between the FoxM1 and $p27^{kip1}$ expressions and other clinicopathologic factors. These findings suggest that FoxM1 overexpression may diminish the expression of $p27^{kip1}$ protein in lung cancers. Further studies are needed to define the relation between FoxM1 and $p27^{kip1}$ for examining the mechanisms of tissue-specific FoxM1 expression.

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p.R72P, PIN3 Ins16bp Polymorphisms of TP53 and CCR5Δ32 in North Indian Breast Cancer Patients

  • Guleria, Kamlesh;Sharma, Sarika;Manjari, Mridu;Uppal, Manjit Singh;Singh, Neeti Rajan;Sambyal, Vasudha
    • Asian Pacific Journal of Cancer Prevention
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    • 제13권7호
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    • pp.3305-3311
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    • 2012
  • Background: The present study aimed to find the prognostic implications of two polymorphisms in TP53 (p.R72P, PIN3 Ins16bp) and one in CCR5 ($CCR5{\Delta}32$) in sporadic breast cancer patients. Methods: DNA samples of 80 breast cancer patients and 80 age and gender matched unrelated healthy control individuals from Punjab, North West India were analyzed. Results: For p.R72P, the genotype frequency was 13.8% (RR), 58.8% (RP), 27.5% (PP) in patients and 33.9% (RR), 40.0% (RP), 26.5% (PP) in controls. For PIN3 Ins16bp, the genotype frequencies were 53.75% (A1A1), 37.5% (A1A2), 8.75% (A2A2) in patients and 66.3% (A1A1), 31.3% (A1A2), 2.5% (A2A2) in controls. Only 4 (5%) breast cancer patients were heterozygous for $CCR5{\Delta}32$ deletion. Common RR-A1A1-WT/WT genotype was lower while RP-A1A2-WT/WT genotype was higher in patients as compared to controls. RP-A1A1-WT/WT genotype was significantly higher in patients as compared to control individuals (p = 0.008). Conclusion: Though a clear association of any particular genotype with sporadic breast cancer or stage was not apparent, the results of present study were suggestive that sporadic breast cancer patients with RR-A1A1-WT/WT genotype might have a better response to chemotherapy, thus improving their chances of survival.