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      • KCI등재

        Comparative and Structural Analysis of the Interaction between β-Lactoglobulin type A and B with a New Anticancer Component (2,2'-Bipyridin n-Hexyl Dithiocarbamato Pd(II) Nitrate)

        A. Divsalar,A. A. Saboury*,H. Mansoori-Torshizi,B. Hemmatinejad 대한화학회 2006 Bulletin of the Korean Chemical Society Vol.27 No.11

        The interaction between whey carrier protein b-lactoglobulin type A and B (BLG-A and -B) and 2,2'-bipyridin n-hexyl dithiocarbamato Pd(II) nitrate (BPHDC-Pd(II)), a new heavy metal complex designed for anticancer property, was investigated by fluorescence spectroscopy combined with chemometry and circular dichroism (CD) techniques. A strong fluorescence quenching reaction of BPHDC-Pd(II) to BLG-A and -B was observed. Hence, BPHDC-Pd(II) complex can be bound to both BLG-A and -B, and quench the fluorescence spectra of the proteins. The quenching constant was determined using the modified Stern-Volmer equation. The binding parameters were evaluated by fluorescence quenching method. The results of binding study provided evidences presence of two and three sets of binding sites on the BLG-B and -A, respectively, for BPHDC-Pd(II) complex. Using fluorescence spectroscopy and chemometry, the ability of BLG-A and -B to form an intermediate upon interaction with BPHDC-Pd(II) complex was assessed. CD studies displayed that under influence of different concentrations of BPHDC-Pd(II) complex, the regular secondary structure of BLG-B had no significant changes, whereas for BLG-A a transition from a-helix to b-structure was appeared. The results for both of BLG-A and -B displayed that BPHDC-Pd(II) complex can induce a conformational transition from the native form to an intermediate state with a slightly opened conformation, which is detectable with chemometry analyses.

      • KCI등재

        On the edge -to -vertex detour number of a graph

        A.P. Santhakumaran 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.3

        For two vertices u and v in a graph G=(V,E), The detour distance D(u,v) s the length of a longest, u-v path in G. A u-v path of length D(u,v) is called a u-v detour. For subsets A and B of V, the detour distance D(A,B) is defined as D(A,B)=(formula). A u-v path of length D(A,B) is called an A-B detour joining the sets A, B⊆V where u∈B. A vertex x is said to lie on an A-B detour is a vertex of A-B detour. A set S⊆E is called an detour joining a pair of edges of S. The edge-to-vertex detour number dn2(G) OF G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn2(G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn2(G) = q or dn2(G) = q-1 or dn2(G) = q-2 are characterized.

      • KCI등재

        Lebesgue’s criterion for the Riemann integration with respect to a state on a separable unital C*- algebra

        A. I. Shtern 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.2

        In the paper “Semicontinuous envelopes, Riemann integral, and uniform distribution in C*-algebras” (Funct. Anal. Appl. 29 (4), 268– 275 (1995)(1996)), the author had constructed the Riemann integral with respect to a state on a separable unital C*-algebra A. In particular, the semicontinuous hulls of elements of the enveloping von Neumann algebra A of A were introduced and studied and, for a given state ! on A, a class of selfadjoint elements of the algebra A that are Riemann integrable with respect to the state ω were introduced. It was also proved that this class is the self-adjoint part of a C*-algebra, and relations to the uniform distribution of states of the C*-algebra A with respect to the state ω were indicated. In the present note, we supplement these results by a version of Lebesgue’s criterion for the Riemann integrability of self-adjoint elements of A.

      • KCI등재

        Upper edge-to-vertex detour monophonic number of a graph

        A. P. Santhakumaran,P. Titus,K. Ganesamoorthy 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.2

        For a connected graph G = (V,E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u−v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V , the monophonic distance dm(A,B) is defined as dm(A,B) = min{dm(x, y) : x ∈ A, y ∈ B}. A u−v path of length dm(A, B) is called an A−B detour monophonic path joining the sets A,B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a detour monophonic path joining a pair of edges of S. The edge-to-vertex detour monophonic number dmev(G) of G is the minimum cardinality of its edge-to-vertex detour monophonic sets and any edge-to-vertex detour monophonic set of car- dinality dmev(G) is an edge-to-vertex detour monophonic basis of G. An edge-to-vertex detour monophonic set S in a connected graph G is called a minimal edge-to-vertex detour monophonic set of G if no proper subset of S is an edge-to-vertex detour monophonic set of G. The upper edge-to-vertex detour monophonic number dm+ ev(G) of G is the maxi- mum cardinality of a minimal edge-to-vertex detour monophonic set of G. We determine bounds for it and certain general properties of these concepts are studied. It is shown that for every pair a, b of integers with 2 ≤ a ≤ b, there exists a connected graph G with dmev(G) = a and dm+ ev(G) = b.

      • SCISCIESCOPUS

        A spick-and-span approach to the immobilization of horseradish peroxidase on Au nanospheres incorporated with a methionine/graphene biomatrix for the determination of endocrine disruptor bisphenol A

        Vilian, A.T. Ezhil,Giribabu, Krishnan,Choe, Sang Rak,Muruganantham, Rethinasabapathy,Lee, Hoomin,Roh, Changhyun,Huh, Yun Suk,Han, Young-Kyu Elsevier Sequoia 2017 Sensors and actuators. B Chemical Vol.251 No.-

        <P><B>Abstract</B></P> <P>In the present study, we employ a straightforward, benign strategy to prepare thiol-functionalized reduced graphene oxide (S-RGO) using methionine as the sulphur source and reducing agent. The immobilization of horseradish peroxidase (HRP) over the AuNPs/S-RGO was developed by incorporating AuNPs on the S-RGO surface. The fabricated HRP/AuNPs/S-RGO electrode exhibits a remarkable decrease in the overpotential and a significantly increased oxidation peak current of bisphenol A (BPA) compared with the bare glassy carbon electrode (GCE) and AuNPs/S-RGO electrode. The biosensor shows an excellent amperometric analytical performance with a low detection limit of 2.6×10<SUP>−12</SUP> M and a linear range from 2.0×10<SUP>−11</SUP> to 1.18×10<SUP>−9</SUP> M, with the response time <2s for BPA. From the results, the apparent Michaelis-Menten constant was calculated as 8.14nM. The HRP/AuNPs/S-RGO biosensor exhibited faster response, adequate storage stability, inexpensive, simple fabrication with disposability, satisfactory reproducibility and repeatability, and outstanding selectivity. Finally, the constructed biosensor was utilized successfully for detecting BPA in tomato juice and milk samples with acceptable results.</P> <P><B>Highlights</B></P> <P> <UL> <LI> HRP/AuNPs/S-RGO biocomposite has been prepared to determine bisphenol A. </LI> <LI> The AuNPs/S-RGO is a promising platform for HRP immobilization. </LI> <LI> The biosensor exhibits excellent stability, reproducibility and high selectivity. </LI> <LI> It exhibits LOD of 2.6×10<SUP>−12</SUP> in a wide linear range from 2.0×10<SUP>−11</SUP> to 1.18×10<SUP>−9</SUP> M. </LI> <LI> It detects bisphenol A in real samples such as tomato juice and milk. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>

      • 화이트헤드의 유기체 철학과 쿼크

        임진아 ( Jin A Yim ) 한국화이트헤드학회 2013 화이트헤드 연구 Vol.26 No.-

        궁극적 물질은 무엇이며, 그 물질의 성질에 대해 연구하는 분야는 물리학 중에서도 소립자물리학의 연구영역이다. 소립자물리학이 궁극적 요소에 대한 사유에는 궁극적 요소는 물질이며, 파동이 아닌 입자적 특성을 가진 그 무엇이 아니겠는가 하는 가정이 전제되어 있다. 20세기 초반, 플랑크의 에너지 양자가설로 인해 촉발된 물리학의 혁명은 물리학이 연구하는 대상인 물질 그 자체에 대한 관점의 전환을 요구했다. 파동과 입자는 양립할 수 없는 물질의 양태이다. 그러나 물질의 이중성으로 잘 알려져 있듯이 파동은 입자의 성질을, 입자는 파동의 성질을 가지고 있다는 것이 드러났다. 또한 극미의 세계에서는 매우 많은 숫자의 소립자가 발견되었으나, 현재 물리학자들은 양성자와 중성자와 같은 핵자를 만드는 근본적인 물질로 간주하는 쿼크 및 전자를 이 세계를 구성하는 가장 근원적인 입자들로 생각 한다.이 글은 두 가지의 목적을 가지고 있다. 첫 번째, 20세기에 양자역학에서 시작된 물질의 이중성으로부터 쿼크가 가진 성질을 통해 전통적인 물질관에 대해 비판하고자 한다. 두 번째, 현재까지도 명쾌한 해답이 제시되지 않고 있는 물질의 이중성 및 쿼크의 실체성에 대한 의문을 화이트헤드의 유기체철학의 관점으로 고찰해보고자 한다. The ultimate matter is what , and an field to study for the property of the material is study are of the particle physics. The ultimate element is matter in the reason for the ultimate element particle physics, And it is to a prerequisite a home doing whether it is the what with the property of the particle that is not wave motion. The prompted physical revolution required the change over of the point of view for material itself which was the object which physics studied(grand prix) by Energy Quantum hypothesis of initial, Planck in the 20th century. Wave motion and a particle are appearance of the materials which they cannot balance. However, it appeared in the wave motion that the particle had a nature of the wave motion with the nature of the particle to be known for the duality of the material well. In addition, the elementary particle of a great many numbers was discovered in the particle physical world, but current physicists think about quark to consider to be a basic material making the nuclear particle which seems to be a neutron with a positive child and an electron with root-like particles to frame this world. This essay consider as two kinds of purposes. It thinks first to think to criticize it for outlook on traditional material through the nature that quark has from the duality of the material which began in quantum mechanics in the 20th century. It thinks to consider a shrug for the second, duality of the material that the answer that is clear to date is not shown and substantiality of the quark at a point of view of the organized body philosophy of A. N. Whitehead.

      • A형 간염의 자연항체와 예방접종을 통한 항체 생성률의 역가 비교분석

        권원현,김경화,조경아,문기춘,김정인,이인원,Kwon, Won Hyun,Kim, Kyung Hwa,Cho, Kyung A,Moon, Ki Choon,Kim, Jung In,Lee, In Won 대한핵의학기술학회 2013 핵의학 기술 Vol.17 No.2

        2008년부터 A형 간염 환자들이 급속히 증가하고 본원에 내원하여 건진을 받는 대부분의 수검자들이 A형 간염(IgG) 항체 생성 유무에 관심이 많아지며 검사 건수가 증가하였다. 그에 따라 항체 검사결과가 cut-off값에 걸리는 검체가 많아져 원인을 분석하였더니 대부분 A형 간염 예방접종을 한 수검자들이었다. 이에 저자들은 건강증진센터에서 설문조사를 통하여 자연면역을 획득한 수검자들 그룹과 본원에서 A형 간염 예방접종(1차, 2차)을 실시한 직원들 그룹으로 나누어 검사를 시행하였고 cut-off값을 기준으로 항체 생성률과 그에 대한 역가를 비교하고 진단검사의학과와 핵의학과에서 사용하는 진단 시약간에 항체 생성률과 그에 대한 역가를 비교해 보고자 했고, 2012년 8월 한 달 동안 건진 수검자 185명을 설문조사하여 자연면역을 획득한 119명과 본원에서 예방 접종을 실시한 직원들을 대상으로 1차 접종자 53명, 2차 접종자 59명으로 대상을 분류했다. 항체 생성률은 cut-off값 1을 기준했을 때 0.90-1.10 (${\pm}$), 0.60-0.89 (1+), 0.30-0.59 (2+), 0.01-0.29 (3+)로 나누어 역가를 비교하고, 같은 기준으로 제조사별 백신 접종 후 항체 생성률에 대한 역가를 비교평가 해 보았다. 그 결과, 건진 수검자 중 자연 면역을 획득한 수검자는 cut-off값 1을 기준했을 때, 0.90-1.10 (${\pm}$)가 0%, 0.60-0.89 (1+)가 0%, 0.30-0.59 (2+)가 4.2%, 0.01-0.29 (3+)가 96%로 역가가 <0.60 ($${\geq_-}2+$$)가 100%였다. 그리고 예방접종을 실시한 직원들의 항체 생성률은 1차 접종자 중 ${\pm}$가 59.1%, 1+가 18.1%, 2+가 18.1%, 3+가 4.6%로 총 45.3%였고, 역가는 $${\geq_-}$$ 0.60 ($${\leq_-}1+$$)가 77.3%였다. 2차 접종자의 항체 생성률은 ${\pm}$가 1.9%, 1+가 15.4%, 2+가 36.54%, 3+가 46.2%로 총 88.1%였고 역가는 <0.60 ($${\geq_-}2+$$) 82.7%가 였다. 또한 제조사별로 비교 하였을 때 1차 접종자의 항체 생성률은 BNIBT 20.8% (${\pm}24.5%$), GB 15.7% (${\pm}7.8%$), RIAKEY 94.3% (${\pm}3.8%$), ROCHE 83% (${\pm}0%$), Abbot 73.1% (${\pm}5.8%$)였고, 2차 접종자의 항체 생성률은 BNIBT 86.4% (${\pm}1.7%$), GB 88.5% (${\pm}1.9%$), RIAKEY 100% (${\pm}0%$), ROCHE 98.3% (${\pm}0%$), Abbot 98.2% (${\pm}0%$)였다. 즉 자연면역 항체가 예방접종에 의한 항체보다 역가가 높다는 것을 알 수 있었고, 1차 접종 후 보다는 2차 접종 후 검사를 시행했을 때 항체 생성률과 역가가 대부분 높아짐을 알 수 있었다. 따라서 결과 보고시 negative, index (${\pm}$), weak positive (1+), positive (2+), strong positive (3+)로 역가를 나누어 보고를 하거나 결과값에 index값을 같이 적어서 결과를 상세히 보고한다면 과거결과와 비교도 가능할 것이다. 또 제조사별 비교 시 1차 예방접종 후의 항체 생성률과 역가에서 시약간에 많은 차이를 보이고 있었고, 매년 예방 접종률이 높아지고 있는 시점에서 이러한 차이를 줄이기 위해서 각 제조사들은 민감도나 재현성에 더 주의를 기울여야 하겠고, 자연면역항체와 예방접종을 통한 항체간에 생길 수 있는 미지의 차이를 감안하여 검사자들이 사용하는 시약을 신뢰할 수 있도록 더 연구하고 개발해야 할 것이다. Purpose: Since 2008, hepatitis A patients was rapidly increasing. So, Most of the health checkup examinees were interested in whether hepatitis A antibody was a lot. thereby The number of tests was increasing. In recent years, Antibody test results in the range of cut-off values were increased. According to the cause analysis, most examinees had a hepatitis A vaccine. This study was conducted to classify hepatitis A antibody as natural antibody and antibody after vaccination and compared the titer for seroconversion rate based on cut-off values. Materials and Methods: For a month in August 2012, First, We surveyed 185 health examinees and classified 119 health examinees who had acquired natural antibody. Second, for employees who were inoculated against hepatitis at our hospital, We classified into 53 primary inoculators and 59 secondary inculators. when the standard of cut-off value was 1, The seroconversion rate was compared the titer divided by 0.90-1.10 (${\pm}$), 0.60-0,89 (1+), 0.30-0.59 (2+), 0.01-0.29 (3+) and we compared the titer for seroconversion rate by each manufacturer after vaccination. Results: When the standard of cut-off value was 1, the titer of 119 health examinees who had acquired natural antibody was 0.90-1.10 (${\pm}$): 0%, 0.60-0.89 (1+): 0%, 0.30-0.59 (2+): 4.2%, 0.01-0.29 (3+): 96% and the titer of <0.60 ($${\geq_-}2+$$) was 100%. The titer of 53 primary inoculators was 0.90-1.10 (${\pm}:59.1%$), 0.60-0.89 (1+): 18.1%, 0.30-0.59 (2+): 18.1%, 0.01-0.29 (3+): 4.6% and the seroconversion rate was 45.3%. The titer of $${\geq_-}0.60$$ ($${\leq_-}1+$$) was 77.3%. The titer of 59 secondary inoculators was 0.90-1.10 (${\pm}:1.9%$), 0.60-0.89 (1+): 15.4%, 0.30-0.59 (2+): 36.54%, 0.01-0.29 (3+): 46.2% and the seroconversion rate was 88.1%. The titer of <0.60 ($${\geq_-}2+$$) was 82.7%. When we compared the titer for seroconversion rate by each manufacturer after vaccination, the seroconversion rate of 53 primary inoculators was BNIBT: 20.8% (${\pm}:24.5%$), GB: 15.7% (${\pm}:7.8%$), RIAKEY: 94.3% (${\pm}:3.8%$), ROCHE: 83% (${\pm}:0%$), ABBOTT: 73.1% (${\pm}:5.8%$) and the seroconversion rate of 59 secondary inoculators was BNIBT : 86.4% (${\pm}:1.7%$), GB: 88.5% (${\pm}:1.9%$), RIAKEY: 100% (${\pm}:0%$), ROCHE: 98.3% (${\pm}:0%$), ABBOTT: 98.2% (${\pm}:0%$). Conclusion: The study show that the titer of natural immune antibodies is higher than the titer of vaccination and the titer of secondary inoculation is mainly higher than the titer of primary inoculation. Consequently, if we know the titer of hepatitis A antibodies, it will help to give resullt reports. And then, when we compared the titer and the seroconversion rate by each manufacturer, There was a very distinct difference. As the test subjects inoculate against hepatitis A (HAV), it is considered BNIBT, GB will occur false negative rate and RIAKEY, ROCHE, ABOTT will occur false positive rate.

      • KCI등재

        Genetic Variation of SCN5A in Korean Patients with Sick Sinus Syndrome

        Young-Soo Lee,Michael A Olaopa,정병천,이상희,신동구,박형섭,조용근,한상미,이명훈,김윤년 대한심장학회 2016 Korean Circulation Journal Vol.46 No.1

        Background and Objectives: Due to recent studies that have shown an association between the genetic variation of SCN5A and sick sinus syndrome (SSS), we sought to determine if a similar correlation existed in Korean patients with SSS. Subjects and Methods: We enrolled 30 patients with SSS who showed a sinus pause (longer than 3.0 s) in Holter monitoring, in addition to 80 controls. All exons including the putative splicing sites of the SCN5A gene were amplified by polymerase chain reaction and sequenced either directly or following subcloning. Wild-type and single nucleotide polymorphisms were expressed in human embryonic kidney cells, and the peak sodium current (INa) was analyzed using the whole-cell patch-clamp technique. Results: A total of 9 genetic variations were identified: 7 variations (G87A-A29A, IVS9-3C>A, A1673G-H558R, G3823A-D1275N, T5457C-D1819D, T5963G-L1988R, and C5129T-S1710L) had been previously reported, and 2 variants (A3075T-E1025D and T4847A-F1616Y) were novel; the potential structural effects of F1616Y were analyzed in a three-dimensional model of the SCN5A domain. Patch-clamp studies at room temperature demonstrated that the peak INa was significantly increased by 140% in HEK cells transfected with F1616Y comparedwith wild-type (-335.13 pA/pF±24.04, n=8 vs. -139.95 pA/pF±23.76, n=7, respectively). Furthermore, the voltage dependency of theactivation and steady-state inactivation of F1616Y were leftward-shifted compared with wild-type (Vh activation=-55.36 mv±0.22, n=8 vs. Vh activation=-44.21 mV±0.17, n=7; respectively; Vh inactivation=-104.47 mV±0.21, n=7 vs. Vh inactivation=-84.89 mV±0.09, n=12, respectively). Conclusion: F1616Y may be associated with SSS.

      • KCI등재

        초등학교 축구선수의 성격타입(A/B), 정신력과 운동몰입의 구조적 관계

        김인수(Kim In-Soo),최정아(Choi Jeang-a) 한국체육교육학회 2016 한국체육교육학회지 Vol.20 No.4

        이 연구는 초등학교 축구선수의 A/B 타입 성격과 정신력, 운동몰입 간에 어떤 인과관계가 있는지를 밝힘으로써 초등학교 축구선수의 경기력 향상에 도움을 주고자 수행되었다. 이러한 연구목적을 달성하기 위해 G광역시와 J도에 소재한 초등학교 축구선수로 등록된 236명과 중학교 축구 선수 110명을 대상으로 A/B 타입 성격척도, 정신력 척도, 운동몰입척도를 사용하여 집단 간 t-test 및 공변량 구조분석을 실시하였다. 변인 간의 구조적 관계분석을 위해 A/B 타입 성격을 외생변인으로 하고, 정신력과 운동몰입을 내생변인으로 한 구조모델을 설정하고 검증하였으며 그 결과 첫째, A/B 타입 성격 간 비교에서A 타입 성격소유자가 B타입 성격소유자에 비해 정신력과 운동몰입이 높은 것으로 나타났다. 입상경력유무집단 간 비교에서 입상경력이 있는 선수는 그렇지 못한 선수에 비해 A 타입 성격, 정신력, 운동몰입이 높았다. 초등학교 축구선수와 중학교 축구선수 간 비교에서는 성격타입, 정신력, 운동몰입에 차이가 없었다. 둘째, 변인 간 상관분석을 실기한 결과 A/B 타입 성격, 정신력, 운동몰입 간에는 서로 유의한(p<.01) 상관이 있었다. 셋째, 변인 간 구조관계를 분석한 결과 완전매개모형이 적합한 것으로 나타났고, A/B 타입 성격을 외생변인으로 하고 정신력과 운동몰입을 내생변인으로 한 구조모형은 이론모델로서 양호한 것으로 나타났으며(χ2=20.13, df=7, Q=2.88, RMR=.01, GFI=.97, TLI=.94, NFI=.96, CFI=.97, RMSEA=.08) 세부 구조경로에서는 A/B타입 성격 → 정신력, 정신력 → 운동몰입의 경로가 유의한(p<.01) 것으로 나타났다. 이를 요약하면 초등학교 축구선수의 경우 A타입 성격 성향이 강할수록 정신력과 운동몰입 수준이 높으며 지방대회 3위 이상의 입상경력을 가진 선수는 그렇지 않는 선수에 비해 A 타입 성격 성향이 강하고, 정신력과 운동몰입 수준이 높다. 또한, A/B 성격 성향은 정신력과 밀접한 관련이 있으며 정신력은 운동몰입과 인과관계가 있는 것으로 나타나 초등학교 축구선수의 운동몰입 수준을 증가시키기 위해서는 정신력의 강화가 필요함을 제시해 주고 있다. Purpose: The Purpose of this study was to define structural relation among A/B type behavior pattern, mental toughness, and sport commitment of elementary school soccer players. Methods: This study set up a structural relation model which was composed of exogenous variables as A/B type behavior pattern and endogenous variables were mental toughness, and sport commitment of soccer players. The participants were 236 elementary school and 110 middle school soccer players who lived in G city and J province. This study used A/B type behavior pattern scale, Mental toughness scale and commitment scale. Results: In analysis of t-test, A type players show higher mental toughness and sport commitment than those of B type. The players who had experienced more 3rd place in province soccer competition show higher A type behavior pattern, mental toughness, and behavioral commitment than those of the others. There were no differences between elementary school players and middle school players in A/B type behavior pattern, mental toughness and sport commitment. In analysis of correlation, there were significant relations between A/B type behavior pattern, mental toughness and sport commitment. In analysis structure equation, this model can be used as theoretical model because general indexes were proved(χ2=20.13, df=7, Q=2.88, RMR=.01, GFI=.97, TLI=.94, NFI=.96, CFI=.97, RMSEA=.08). In analysis details index, there were significant paths of A/B type behavior pattern → mental toughness, mental toughness → sport commitment. Conclusion: In this study define there are causal relationships among A/B type behavior pattern, mental toughness and sport commitment. To approve sport commitment of elementary school soccer players, players kept up A type behavior pattern and make strong mental toughness.

      • Van der Waerden's continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko's conjecture

        A. I. Shtern 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.2

        As was proved by van der Waerden in 1933, every finite-dimensional locally bounded representation of a semisimple compact Lie group is continuous. In this paper, with the help of an earlier result of the author claiming that the van der Waerden theorem holds for any connected semisimple Lie group, it is proved that every locally bounded finite-dimensional representation of a connected Lie group is continuous on the commutator subgroup of the group; moreover, it turns out that a connected Lie group satis¯es the assertion of the van der Waerden theorem (i.e., all locally bounded finite-dimensional representations of the group are continuous) if and only if the group is perfect (i.e., coincides with the commutator subgroup). Thus, for perfect connected linear Lie groups, the structure of (totally) bounded sets de¯nes the topology, and any boundedness-preserving group isomorphism of a perfect connected linear Lie group onto another perfect connected linear Lie group is automatically continuous. To study this phenomenon, the notion of discontinuity group of a locally bounded finite-dimensional representation of a topological group is introduced and studied. The notion of local boundedness of a representation is naturally related to the notion of point oscillation (at the identity element of the group) introduced by the author in 2002. According to a conjecture expressed by A. S. Mishchenko, the finite-dimensional representations of Lie groups can take only three possible values for the (reasonably defined) point oscillation, namely, 0, 2, and 1. We prove the validity of the conjecture. As a corollary, we prove that the class of connected Lie groups for which the point oscillation of a finite-dimensional representation can take only two values, 0 and 1, is the very class of perfect connected Lie groups. Related open problems are indicated.

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