Pairs of eta-quotients with dual weights and their applications

Choi, Dohoon,Kim, Byungchan,Lim, Subong Elsevier 2019 Advances in mathematics Vol.355 No.-

<P><B>Abstract</B></P> <P>Let <I>D</I> be the differential operator defined by D : = 1 2 π i d d z . This induces a map <SUP> D k + 1 </SUP> : M − k ! ( <SUB> Γ 0 </SUB> ( N ) ) → M k + 2 ! ( <SUB> Γ 0 </SUB> ( N ) ) , where M k ! ( <SUB> Γ 0 </SUB> ( N ) ) is the space of weakly holomorphic modular forms of weight <I>k</I> on <SUB> Γ 0 </SUB> ( N ) . The operator <SUP> D k + 1 </SUP> plays important roles in the theory of Eichler-Shimura cohomology and harmonic weak Maass forms. On the other hand, eta-quotients are fundamental objects in the theory of modular forms and partition functions. In this paper, we show that the structure of eta-quotients is very rarely preserved under the map <SUP> D k + 1 </SUP> between dual spaces M − k ! ( <SUB> Γ 0 </SUB> ( N ) ) and M k + 2 ! ( <SUB> Γ 0 </SUB> ( N ) ) . More precisely, we classify dual pairs ( f , <SUP> D k + 1 </SUP> f ) under the map <SUP> D k + 1 </SUP> such that <I>f</I> is an eta-quotient and <SUP> D k + 1 </SUP> f is a non-zero constant multiple of an eta-quotient. When the levels are square-free, we give the complete classification of such pairs. In general, we find a necessary condition for such pairs: the weight of the primitive eta-quotient f ( z ) = η <SUP> ( <SUB> d <SUB> i 1 </SUB> </SUB> z ) <SUB> b 1 </SUB> </SUP> ⋯ η <SUP> ( <SUB> d <SUB> i t </SUB> </SUB> z ) <SUB> b t </SUB> </SUP> is less than or equal to 4 and every prime divisor of each <SUB> d i </SUB> is less than 11. We also give various applications of these classifications. In particular, we find all eta-quotients of weight 2 and square-free level <I>N</I> such that they are in the Eisenstein space for <SUB> Γ 0 </SUB> ( N ) . To prove our main theorems, we use various combinatorial properties of a Latin square matrix whose rows and columns are exactly divisors of <I>N</I>.</P>

$PKC{\eta}$ Regulates the $TGF{\beta}3$-induced Chondrogenic Differentiation of Human Mesenchymal Stem Cell

Ku, Bo Mi,Yune, Young Phil,Lee, Eun Shin,Hah, Young-Sool,Park, Jae Yong,Jeong, Joo Yeon,Lee, Dong Hoon,Cho, Gyeong Jae,Choi, Wan Sung,Kang, Sang Soo The Korean Society of Developmental Biology 2013 발생과 생식 Vol.17 No.4

Transforming growth factor (TGF) family is well known to induce the chondrogenic differentiation of mesenchymal stem cells (MSC). However, the precise signal transduction pathways and underlying factors are not well known. Thus the present study aims to evaluate the possible role of C2 domain in the chondrogenic differentiation of human mesenchymal stem cells. To this end, 145 C2 domains in the adenovirus were individually transfected to hMSC, and morphological changes were examined. Among 145 C2 domains, C2 domain of protein kinase C eta ($PKC{\eta}$) was selected as a possible chondrogenic differentiation factor for hMSC. To confirm this possibility, we treated $TGF{\beta}3$, a well known chondrogenic differentiation factor of hMSC, and examined the increased-expression of glycosaminoglycan (GAG), collagen type II (COL II) as well as $PKC{\eta}$ using PT-PCR, immunocytochemistry and Western blot analysis. To further evaluation of C2 domain of $PKC{\eta}$, we examined morphological changes, expressions of GAG and COL II after transfection of $PKC{\eta}$-C2 domain in hMSC. Overexpression of $PKC{\eta}$-C2 domain induced morphological change and increased GAG and COL II expressions. The present results demonstrate that $PKC{\eta}$ involves in the TGF-${\beta}3$-induced chondrogenic differentiation of hMSC, and C2 domain of $PKC{\eta}$ has important role in this process.

Group Size And Measure Of Group-Level Properties

Kim,Kyoung-Su,Kim In-Sook,Jun,Gyung-Ju,Yang,Dong-Min 한국인적자원관리학회 2009 인적자원관리연구 Vol.16 No.4

Bliese와 Halverson(1998)은 집단수준의 효과를 분석하는데 있어서 기존에 사용되어 온 eta-squared 보다는 eta-squared 값이 사용되어야만 한다는 것을 주장하였다 그러나 이들이 제시한 수정된 eta-squared 접근은 다음과 같은 한계점을 가지게 되는 바 첫째, 이 접근법은 개인수준의 데이터를 집단 수준의 데이터로 만드는데 있어서의 정당성을 제공하는 기준을 구체적으로 제시하고 있지 못하다는 것을 들 수 있고, 둘째, 이 접근법은 또한 집단 내 효과를 용인하고 분석하는 기준을 제공하고 있지 못하다는 점을 들 수 있다 본 논문에서는 이러한 한계점을 극복할 수 있는 몇 가지의 대안을 제시하고 있으며, 이와 더불어 개인수준의 데이터를 집단 수준으로 만드는 것에 대한 정당성을 위한 또 하나의 추가적인 절차를 제시하였다 Bliese and Halverson(1998) argue that corrected eta-squared, rather than eta-squared, should be used for analyzing group-level effects However, their proposed corrected eta-squared approach has the following limitations (1) it fails to specify a criterion for justifying the aggregation of individual-level data to the group level and (2) it fails to specify a criterion for analyzing and allowing for within-group effects In this paper, we suggest several alternatives that overcome these limitations We suggest an additional procedure for justifying the aggregation of individual-level data to the group level

${\eta}_T$ Pairing 알고리즘의 효율적인 하드웨어 구현

이동건,이철희,최두호,김철수,최은영,김호원,Lee, Dong-Geoon,Lee, Chul-Hee,Choi, Doo-Ho,Kim, Chul-Su,Choi, Eun-Young,Kim, Ho-Won 한국정보보호학회 2010 정보보호학회논문지 Vol.20 No.1

최근 무선 센서 네트워크 보안 분야에서는 키 교환을 위한 부가적인 통신이 필요 없이 통신 엔터티 상호간에 암호화를 수행할 수 있는 페어링 암호가 주목받고 있다. 본 논문에서는 이러한 페어링 암호의 한 종류인 ${\eta}_T$ 페어링에 대한 효율적인 하드웨어 구현을 제시한다. 이를 위해 병렬 처리 및 레지스터/자원의 최적화에 기반한 ${\eta}_T$ 페어링 알고리즘에 대한 효율적인 하드웨어 구조를 제안하며, 제안한 구조를 GF($2^{239}$) 상에서 FPGA로 구현한 결과를 나타낸다. 제안한 구조는 기존의 구현 결과에 비해 Area Time Product에 있어 15% 나은 결과를 가진다. Recently in the field of the wireless sensor network, many researchers are attracted to pairing cryptography since it has ability to distribute keys without additive communication. In this paper, we propose efficient hardware implementation of ${\eta}_T$ pairing which is one of various pairing scheme. we suggest efficient hardware architecture of ${\eta}_T$ pairing based on parallel processing and register/resource optimization, and then we present the result of our FPGA implementation over GF($2^{239}$). Our implementation gives 15% better result than others in Area Time Product.

Power reduction for recovery of a FinFET by electrothermal annealing

Han, Joon-Kyu,Park, Jun-Young,Choi, Yang-Kyu Elsevier 2019 Solid-state electronics Vol.151 No.-

<P><B>Abstract</B></P> <P>A strategy of reducing the power consumption to cure gate dielectric damage by electrothermal annealing (ETA) is proposed. A tri-gate FinFET was fabricated to demonstrate the damage curing by the ETA. Localized Joule heat induced by high current flowing through dual gate electrodes successfully annealed the damaged gate dielectric. Furthermore, a design methodology to save power consumption during the ETA was explored. Electrical measurements and simulations were performed considering scaling-down and material engineering points of view. This work contributes to improving the reliability of the FinFET by developing the ETA approach with reduced power consumption.</P> <P><B>Highlights</B></P> <P> <UL> <LI> An oxide damage of a tri-gate FinFET was cured nearly to the pristine state by ETA. </LI> <LI> A design methodology to save power consumption during ETA was explored. </LI> <LI> The power consumption of ETA was reduced by scaling-down and material optimization. </LI> </UL> </P>

한국 요석 환자의 Eta-1/Osteopontin 유전자 다형성 분석

김태형,이소연,정우현,오승영,문영태,김경도,김영선,이미경,김혜련,명순철 대한비뇨의학회 2008 Investigative and Clinical Urology Vol.49 No.1

Purpose: Osteopontin(OPN) is one of the major non-collagenous bone matrix proteins produced by osteoblasts and osteolclasts, and it is also involved in the pathogenesis of urolithiasis. Single nucleotide polymorphisms(SNPs), as a tool for searching for the genetic markers of disease, have a large role in investigating the genetic markers of complex human diseases. The aim of this study is to investigate the association with this SNP at position nucleotide 9250(C→T) in the OPN gene and the susceptibility to urolithiasis. We also compared the allele frequency of Koreans with those of Americans and Japanese. Materials and Methods: A total of 161 urolithiasis patients and 104 healthy controls were studied. The SNPs located at position 9520 in the OPN gene were genotyped using restriction fragment length polymorphism(RFLP). The wild-type sequence contains a C while the polymorphism variant is a T(C→T), which results in the appearance of an Alu I restriction site. Results: The gene frequencies of C/C, C/T and T/T at position 9250 on the Eta-1/osteopontin gene in urolithiasis patients were 10.6%, 36.6% and 52.8%, respectively, compared with 6.7%, 27.9% and 65.8%, respectively, in the controls(p>0.05). The allele frequencies of C and T at this position in the urolithiasis patients were 28.9 and 72.1, respectively, whereas those in the controls were 20.7 and 79.3, respectively,(p<0.05). The allele frequencies found in the present study were compared with those coding SNPs described in the USA database; 60 and 39(USA) vs 20.7 and 79.3 (Korea), respectively(p<0.05). Conclusions: Those findings suggest there is no association of with Eta-1/osteopontin genetic polymorphism, but the allele frequencies were significantly associated with urolithiasis patients. We also observed difference of allele frequencies in our controls and in the USA controls and these differences may be caused by a difference in the incidence of urolithiasis patients between the two countries. (Korean J Urol 2008;49:55-59) Purpose: Osteopontin(OPN) is one of the major non-collagenous bone matrix proteins produced by osteoblasts and osteolclasts, and it is also involved in the pathogenesis of urolithiasis. Single nucleotide polymorphisms(SNPs), as a tool for searching for the genetic markers of disease, have a large role in investigating the genetic markers of complex human diseases. The aim of this study is to investigate the association with this SNP at position nucleotide 9250(C→T) in the OPN gene and the susceptibility to urolithiasis. We also compared the allele frequency of Koreans with those of Americans and Japanese. Materials and Methods: A total of 161 urolithiasis patients and 104 healthy controls were studied. The SNPs located at position 9520 in the OPN gene were genotyped using restriction fragment length polymorphism(RFLP). The wild-type sequence contains a C while the polymorphism variant is a T(C→T), which results in the appearance of an Alu I restriction site. Results: The gene frequencies of C/C, C/T and T/T at position 9250 on the Eta-1/osteopontin gene in urolithiasis patients were 10.6%, 36.6% and 52.8%, respectively, compared with 6.7%, 27.9% and 65.8%, respectively, in the controls(p>0.05). The allele frequencies of C and T at this position in the urolithiasis patients were 28.9 and 72.1, respectively, whereas those in the controls were 20.7 and 79.3, respectively,(p<0.05). The allele frequencies found in the present study were compared with those coding SNPs described in the USA database; 60 and 39(USA) vs 20.7 and 79.3 (Korea), respectively(p<0.05). Conclusions: Those findings suggest there is no association of with Eta-1/osteopontin genetic polymorphism, but the allele frequencies were significantly associated with urolithiasis patients. We also observed difference of allele frequencies in our controls and in the USA controls and these differences may be caused by a difference in the incidence of urolithiasis patients between the two countries. (Korean J Urol 2008;49:55-59)

A NOTE ON THE θ₃(0, τ)

Kim, Daeyeoul,Jeon, Hyeong-Gon The Kangwon-Kyungki Mathematical Society 1998 한국수학논문집 Vol.6 No.1

Let ${\eta}(\tau)=q^{1/24}\prod_{n=1}^{\infty}(1-q^n)$, where $q=e^{2{\pi}i{\tau}}$ and ${\tau}{\in}\mathbb{C}$. Then the transformation $$g(\tau)={\rho}\frac{\{\eta(\frac{\tau+1}{2})\eta(\frac{\tau+2}{2})\}^{16}}{\eta(\tau)^{24}}({\bar{{\rho}}{\eta}}(\frac{\tau+1}{2})^8+{\eta}(\frac{\tau+2}{2})^8)^2$$ is holomorphic for Im ${\tau}$ > 0, and has the property $$g(\tau+1)=g(\tau),\;g(-\frac{1}{\tau})={\tau}^{12}g(\tau)$$. (Theorem)

A Quantitative Risk Assessment for Public Commercial Unmanned Aerial Systems

See Yeon Kim(김시연),Alfonsus Julanto Endharta(엔드하르타 알폰수스 주란토),Jongwoon Kim(김종운) 한국산학기술학회 2021 한국산학기술학회논문지 Vol.22 No.9

본 연구에서는 상업용 무인 항공 시스템(UAS, Unmanned Aircraft System) 운용 시 안전과 관련된 위험요인의 위험도 추정을 위한 문제 수목 분석에 기초한 정량적 위험도 평가 방법을 제안하였다. 문제 수목 분석의 기본은 결함 수목 분석(FTA, Fault Tree Analysis)과 사건 수목 분석(ETA, Event Tree Analysis)이다. UAS의 추락사고는 안전과 관련된 위험사건의 예로 본 논문에서 사용되었으며 추락을 발생시킬 수 있는 위험요인 중 하나의 위험요인의 원인을 나열하였다. 발생확률은 FTA를 통해 도출되며, 사고 결과는 ETA를 통해 분석된다. 무인 항공 시스템에서 발생할 수 있는 사고의 위험도 평가를 위한 절차를 제안하였으며, 운용 단계에서 운용하기 전에 사전 비행 위험도 평가 시 적용할 수 있다. UAS 통신 끊김(LOC, Loss of Communication)으로 인한 추락 사고가 예로 사용된다. UAS의 LOC은 추진 시스템 고장 또는 오작동, 날씨, 바람, 바람 전단 또는 난류, 차량 성능 저하 상태 및 전자파 간섭(EMI, electromagnetic interference)에 의해 발생할 수 있습니다. ETA에 대한 시나리오를 선정하고 사고의 치명도 또는 리스크를 분석한다. This study proposes a quantitative risk-assessment method based on problem tree analysis to estimate the safety-related hazard risk in the operation of a commercial unmanned aerial system (UAS). The basis of the problem tree analysis is Fault Tree Analysis (FTA) and Event Tree Analysis (ETA). A crash accident of a UAS was used as an example of a safety-related hazard, and the possible causes of the crash were listed. The occurrence probabilities were derived through FTA, while the consequences of the accident were analyzed through ETA. The risk of the crash accident was assessed, and the general procedure can be considered in a pre-flight risk assessment before operation. A crash accident due to aircraft loss of communication (LOC) was used as an illustration. Aircraft LOC can be caused by propulsion-system failure or malfunction, weather, wind, wind shear or turbulence, vehicle degradation, and electromagnetic interference (EMI). The scenarios for ETA were arranged, and the accident criticality was analyzed.

성능위주설계를 위한 ETA 기법 활용 고찰

김학범(Kim, H.B.),이수경(Lee, S.K.),송동우(Song, D.W.),김기성(Kim, K.S.),김종훈(Kim, J.H.) 한국화재소방학회 2011 한국화재소방학회 학술대회 논문집 Vol.2011 No.추계

본 연구에서는 소방시설의 성능위주의설계를 수행하기 위하여 ETA(Event Tree Analysis) 기법을 적용하는 방안을 고찰하였다. ETA기법에서는 화재시나리오를 사건(Event)의 인과관계로 된 각 단계의 사건으로 구성한다. 본 연구에서는 ETA에서 구성된 시나리오에 따른 심각도를 화재시뮬레이션과 피난 시뮬레이션을 통한 수행으로 사망자수를 도출하는 방안을 적용하였고, 각 시나리오의 빈도(확률)은 FTA(Fault Tree Analysis) 기법을 적용하여 분기 확률을 도출하도록 하였다. ETA에서 도출한 사망자수와 빈도를 이용하여 F-N 커브를 작성하여 위험도를 평가하여 소방설계의 보완 및 대책을 수립하는 방안을 제시하였다.

HYBRID-TYPE SET-VALUED VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACES

Lee, Byung-Soo,Khan, Mohd. Firdosh,Salahuddin, Salahuddin The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we introduce a relaxed hybrid-type$\eta$-f-${\alpha}$-pseudomo-notonicity. By using the KKM-technique, we establish some existence results for set-valued variational-like inequalities with $\eta-f-\alpha$-pseudomonotone, relaxed $\eta-f-\alpha$-pseudomonotone, Fan-KKM Theorem.