On some problems of the statistical theory of partitions with application to characters of the symmetric group. I

1977 ◽  
Vol 29 (3-4) ◽  
pp. 361-379 ◽  
Author(s):  
M. Szalay ◽  
P. Turán
Keyword(s):  
Statistical Theory ◽  
Symmetric Group ◽  
Group I

scholarly journals Hetero‐oligomeric CPN60 resembles highly symmetric group‐I chaperonin structure revealed by Cryo‐EM

2019 ◽  
Vol 98 (5) ◽  
pp. 798-812 ◽  
Author(s):  
Qian Zhao ◽  
Xiang Zhang ◽  
Frederik Sommer ◽  
Na Ta ◽  
Ning Wang ◽  
...  
Keyword(s):  
Symmetric Group ◽  
Group I

scholarly journals Certain Unitary Representations of the Infinite Symmetric Group, I

1987 ◽  
Vol 105 ◽  
pp. 121-128 ◽  
Author(s):  
Nobuaki Obata
Keyword(s):  
Symmetric Group ◽  
Regular Representation ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Type I ◽  
Discrete Topology ◽  
Type Ii ◽  
Infinite Symmetric Group ◽  
Von Neumann ◽  
Group I

Let X be the set of all natural numbers and let be the group of all finite permutations of X. The group equipped with the discrete topology, is called the infinite symmetric group. It was discussed in F. J. Murray and J. von Neumann as a concrete example of an ICC-group, which is a discrete group with infinite conjugacy classes. It is proved that the regular representation of an ICC-group is a factor representation of type II1. The infinite symmetric group is, therefore, a group not of type I. This may be the reason why its unitary representations have not been investigated satisfactorily. In fact, only few results are known. For instance, all indecomposable central positive definite functions on , which are related to factor representations of type IIl, were given by E. Thoma. Later on, A. M. Vershik and S. V. Kerov obtained the same result by a different method in and gave a realization of the representations of type II1 in. Concerning irreducible representations, A. Lieberman and G. I. Ol’shanskii obtained a characterization of a certain family of countably many irreducible representations by introducing a particular topology in However, irreducible representations have been studied not so actively as factor representations.

scholarly journals Hetero-oligomeric CPN60 resembles highly symmetric group I chaperonin structure revealed by Cryo-EM

2018 ◽  
Author(s):  
Qian Zhao ◽  
Xiang Zhang ◽  
Frederik Sommer ◽  
Na Ta ◽  
Ning Wang ◽  
...  
Keyword(s):  
Symmetric Group ◽  
Chlamydomonas Reinhardtii ◽  
Surface Properties ◽  
Growth Condition ◽  
Model System ◽  
Uneven Distribution ◽  
E Coli ◽  
Group I ◽  
Key Enzyme

AbstractThe chloroplast chaperonin system is indispensable for the biogenesis of Rubisco, the key enzyme in photosynthesis. Using Chlamydomonas reinhardtii as the model system, we revealed that chloroplast chaperonin is consisted of CPN60α, CPN60β1, and CPN60β2, and co-chaperonin is composed of three subunits CPN20, CPN11 and CPN23 in vivo. CPN20 homo-oligomers and all possible other chloroplast co-chaperonin hetero-oligomers are functional, but only CPN11/20/23-CPN60αβ1β2 pair can fully replace GroES/GroEL in E. coli at stringent growth condition. Endogenous CPN60 was purified and its stoichiometry was determined to be 6:2:6 for CPN60α:CPN60β1:CPN60β2. The cryo-EM structures of endogenous CPN60αβ1β2/ADP and CPN60αβ1β2/co-chaperonin/ADP were solved at resolutions of 4.06 Å and 3.82Å, respectively. In both hetero-oligomeric complexes the chaperonin subunits within each ring are highly symmetric. The chloroplast co-chaperonin CPN11/20/23 formed seven GroES-like domains through hetero-oligomerization which symmetrically interact with CPN60αβ1β2. Our structures also reveal an uneven distribution of roof-like structures in the dome-shaped CPN11/20/23 and potentially diversified surface properties in the folding cavity of CPN60αβ1β2 that might enable the chloroplast chaperonin system to assist in the folding of specific substrates.

scholarly journals The Standard Representation of the Symmetric Group Sn over the Ring of Integers

2016 ◽  
Vol 3 (5) ◽  
pp. 126-127
Author(s):  
Kunle Adegoke ◽  
Olawanle Layeni ◽  
Rauf Giwa ◽  
Gbenga Olunloyo
Keyword(s):  
Symmetric Group ◽  
Standard Representation ◽  
Ring Of Integers ◽  
Group I

Ultrastructural Lesions Produced by Alcohol and Sucrose in the Heart and Liver of C57BL Mice

1970 ◽  
Vol 28 ◽  
pp. 208-209
Author(s):  
K.K. SEKHRI ◽  
C.S. ALEXANDER ◽  
H.T. NAGASAWA
Keyword(s):  
Osmium Tetroxide ◽  
Male Mice ◽  
Alcohol Group ◽  
Group Iii ◽  
Group I ◽  
C57bl Mice ◽  
Group Ii

C57BL male mice (Jackson Lab., Bar Harbor, Maine) weighing about 18 gms were randomly divided into three groups: group I was fed sweetened liquid alcohol diet (modified Schenkl) in which 36% of the calories were derived from alcohol; group II was maintained on a similar diet but alcohol was isocalorically substituted by sucrose; group III was fed regular mouse chow ad lib for five months. Liver and heart tissues were fixed in 2.5% cacodylate buffered glutaraldehyde, post-fixed in 2% osmium tetroxide and embedded in Epon-araldite.

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