One Hat Cyber Team

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\'ed\'b3 \'f1\'ef\'e5\'f6\'b3\'e0\'eb\'b3\'e7\'ee\'e2\'e0\'ed\'ee\'bf \'e2\'f7\'e5\'ed\'ee\'bf \'f0\'e0\'e4\'e8 \'c4\~26.206.01 \'b2\'ed\'f1\'f2\'e8\'f2\'f3\'f2\'f3 \'ec\'e0\'f2\'e5\'ec\'e0\'f2\'e8\'ea\'e8 \'cd\'c0\'cd \'d3\'ea\'f0\'e0\'bf\'ed\'e8 \'e7
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\par 
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\'cd \'d3\'ea\'f0\'e0\'bf\'ed\'e8. 
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\par 
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\'c4\'e6.\~\'f4\'ee\'ed\~\'cd\'e5\'e9\'ec\'e0\'ed, \'cc.\'c3.\~\'ca\'f0\'e5\'e9\'ed, \'de.\'cc.\~\'c1\'e5\'f0\'e5\'e7\'e0\'ed\'f1\'fc\'ea\'e8\'e9, \'b2.\'cc.\~\'c3\'e5\'eb\'fc\'f4\'e0\'ed\'e4, \'c0.\'c3.\~\'ca\'ee\'f1\'f2\'fe\'f7\'e5\'ed\'ea\'ee, \'de.
\'d1.\~C\'e0\'ec\'ee\'e9\'eb\'e5\'ed\'ea\'ee, \'c2.\'cb.\~\'ce\'f1\'f2\'f0\'ee\'e2\'f1\'fc\'ea\'e8\'e9 \'f2\'e0 \'b3\'ed.). }{\lang1049\langfe1049\langnp1049\insrsid10436661 
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\'ef\'f0\'ee \'f1\'f3\'ec\'f3 \'e4\'e2\'ee\'f5 \'e5\'f0\'ec\'b3\'f2\'ee\'e2\'e8\'f5 \'ec\'e0\'f2\'f0\'e8\'f6\'fc). \'c4\'eb\'ff \'e4\'ee\'f1\'eb\'b3\'e4\'e6\'e5\'ed\'ed\'ff \'f6\'b3\'ba\'bf \'e7\'e0\'e4\'e0\'f7\'b3 \'e7\'f0\'f3\'f7\'ed\'ee \'e2\'e8\'ea
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\par }{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'c7 \'b3\'ed\'f8\'ee\'e3\'ee \'e1\'ee\'ea\'f3, \'ee\'ef\'e8\'f1 \'ed\'e5\'f0\'ee\'e7\'ea\'eb\'e0\'e4\'ed\'e8\'f5 \'f2\'e0 \'f8\'f3\'f0\'b3\'e2\'f1\'fc\'ea\'e8\'f5 (brick, \'f2\'f0\'e0\'ed\'e7\'e8\'f2
\'e8\'e2\'ed\'e8\'f5) \'ee\'e1\rquote \'ba\'ea\'f2\'b3\'e2 \'f3 \'ea\'e0\'f2\'e5\'e3\'ee\'f0\'b3\'bf \'f1\'e8\'f1\'f2\'e5\'ec \'ef\'b3\'e4\'ef\'f0\'ee\'f1\'f2\'ee\'f0\'b3\'e2 \'eb\'b3\'ed\'b3\'e9\'ed\'ee\'e3\'ee \'ef\'f0\'ee\'f1\'f2\'ee\'f0\'f3 (\'d8.\~
\'c1\'f0\'e5\'ed\'ed\'e5\'f0 (1967), \'b2.\'cc.\~\'c3\'e5\'eb\'fc\'f4\'e0\'ed\'e4 \'f2\'e0 \'c2.\'ce.\~\'cf\'ee\'ed\'ee\'ec\'e0\'f0\'fc\'ee\'e2 (1971), \'cb.\'ce.\~\'cd\'e0\'e7\'e0\'f0\'ee\'e2\'e0 (1968), \'c2.\~\'c4\'eb\'e0\'e1 \'f2\'e0 \'ca.\~\'d0\'b3
\'ed\'e3\'e5\'eb\'fc (1976), \'cf.\~\'c4\'ee\'ed\'ee\'e2\'e0\'ed \'f2\'e0 \'cc.\~\'d4\'f0\'e5\'e9\'f1\'eb\'e8\'f5 (1973) \'f2\'e0 \'b3\'ed.) \'ef\'ee\'e2\rquote \'ff\'e7\'e0\'ed\'e8\'e9 \'b3\'e7 }{\lang1049\langfe1049\langnp1049\insrsid2313852 *}{
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\'ec\'e8 \'ec\'ee\'e6\'ed\'e0 \'ec\'ee\'e6\'ed\'e0 \'ef\'ee\'e2\rquote \'ff\'e7\'e0\'f2\'e8 \'f1\'e8\'f1\'f2\'e5\'ec\'f3 \'ef\'b3\'e4\'ef\'f0\'ee\'f1\'f2\'ee\'f0\'b3\'e2, \'e1\'e5\'f0\'f3\'f7\'e8 \'ef\'b3\'e4\'ef\'f0\'ee\'f1\'f2\'ee\'f0\'e8 \'ff\'ea \'ee
\'e1\'f0\'e0\'e7\'e8 \'e2\'b3\'e4\'ef\'ee\'e2\'b3\'e4\'ed\'e8\'f5 \'ef\'f0\'ee\'e5\'ea\'f2\'ee\'f0\'b3\'e2). \'d3 \'e4\'e8\'f1\'e5\'f0\'f2\'e0\'f6\'b3\'bf \'e2\'e8\'e2\'f7\'e0\'ba\'f2\'fc\'f1\'ff \'e2\'e7\'e0\'ba\'ec\'ee\'e7\'e2\rquote \'ff\'e7\'ee\'ea 
\'ec\'b3\'e6 \'ed\'e5\'e7\'e2\'b3\'e4\'ed\'e8\'ec\'e8 }{\lang1049\langfe1049\langnp1049\insrsid2313852 *}{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 -\'e7\'ee\'e1\'f0\'e0\'e6\'e5\'ed\'ed\'ff\'ec\'e8 \'f2\'e0\'ea\'e8\'f5 \'e0\'eb\'e3\'e5\'e1\'f0 
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\par {\listtext\pard\plain\fs20\insrsid10436661 \hich\af0\dbch\af0\loch\f0 2.\tab}}{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'c4\'eb\'ff }{\lang1049\langfe1049\langnp1049\insrsid2313852 *}{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 -\'e0
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\par {\listtext\pard\plain\fs20\insrsid10436661 \hich\af0\dbch\af0\loch\f0 3.\tab}}{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'ce\'f2\'f0\'e8\'ec\'e0\'ed\'ee \'ed\'e5\'ee\'e1\'f5\'b3\'e4\'ed\'b3 \'f2\'e0 \'e4\'ee\'f1\'f2\'e0\'f2\'ed\'b3 \'f3\'ec
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\par }\pard \qj \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 {\b\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'cf\'f0\'e0\'ea\'f2\'e8\'f7\'ed\'e5 \'e7\'ed\'e0\'f7\'e5\'ed\'ed\'ff \'ee\'e4\'e5\'f0\'e6\'e0\'ed\'e8\'f5 \'f0\'e5\'e7\'f3\'eb\'fc\'f2\'e0\'f2
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\par }{\b\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'ce\'f1\'ee\'e1\'e8\'f1\'f2\'e8\'e9 \'e2\'ed\'e5\'f1\'ee\'ea \'e7\'e4\'ee\'e1\'f3\'e2\'e0\'f7\'e0.}{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661  \'c2\'e8\'e7\'ed\'e0\'f7\'e5\'ed\'ed\'ff 
\'e7\'e0\'e3\'e0\'eb\'fc\'ed\'ee\'e3\'ee \'ef\'eb\'e0\'ed\'f3 \'e4\'ee\'f1\'eb\'b3\'e4\'e6\'e5\'ed\'ed\'ff, \'ef\'ee\'f1\'f2\'e0\'ed\'ee\'e2\'ea\'e0 \'e7\'e0\'e2\'e4\'e0\'ed\'fc \'ed\'e0\'eb\'e5\'e6\'e0\'f2\'fc \'ed\'e0\'f3\'ea\'ee\'e2\'ee\'ec\'f3 \'ea
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\par }{\b\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'c0\'ef\'f0\'ee\'e1\'e0\'f6\'b3\'ff \'f0\'e5\'e7\'f3\'eb\'fc\'f2\'e0\'f2\'b3\'e2 \'e4\'e8\'f1\'e5\'f0\'f2\'e0\'f6\'b3\'bf.}{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661  \'d0\'e5\'e7\'f3
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\'e8 \'e4\'ee\'ea\'f2\'ee\'f0 \'f4.-\'ec. \'ed\'e0\'f3\'ea \'de.\'d1.\~\'d1\'e0\'ec\'ee\'e9\'eb\'e5\'ed\'ea\'ee) \'f2\'e0 \'ed\'e0 \'f2\'e0\'ea\'e8\'f5 \'ea\'ee\'ed\'f4\'e5\'f0\'e5\'ed\'f6\'b3\'ff\'f5 \'b3 \'f8\'ea\'ee\'eb\'e0\'f5: }{
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\par {\listtext\pard\plain\f3\fs20\insrsid10436661 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \qj \li720\ri0\nowidctlpar\faauto\ls8\rin0\lin720\itap0 {\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 VI \'ec\'b3\'e6\'ed\'e0\'f0\'ee\'e4\'ed\'e0 \'ea\'ee\'ed
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\'e5\'ec\'e0\'f2\'e8\'ea\'e8, 20-26 \'f7\'e5\'f0\'e2\'ed\'ff 2005 \'f0.; }{\lang1049\langfe1049\langnp1049\insrsid10436661 
\par {\listtext\pard\plain\f3\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
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\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  On existence of }{\lang1033\langfe1049\langnp1033\insrsid13975535 *}{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 -representations
 of certain algebras related to extended Dynkin graphs // Methods Funct. }{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid13975535 Anal. Topology. \endash  2006. \endash  Vol.\~12, \'b9\~2. \endash  P.\~197\endash 204. }{
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Yulia Moskaleva, Vasyl Ostrovskyi, and Kostyantyn Yusenko. }{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  On quadruples of linearly connected projections and transitive systems of subspaces // Methods Funct. }{
\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 Anal. Topology. \endash  2007. \endash  Vol.\~13, \'b9\~1. \endash  P.\~43 \endash  49. }{\lang1049\langfe1049\langnp1049\insrsid10436661 
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\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  On parameters sets of algebras  when }{\fs20\lang1058\langfe1049\langnp1058\insrsid13975535 \'c3}{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
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\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid13975535 . "Algebraic versus analytic representations". \endash  }{\fs20\lang1049\langfe1049\langnp1049\insrsid10436661 \'ca\'e8\'bf\'e2}{
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Yulia Moskaleva, Vasyl Ostrovskyi, and Kostyantyn Yusenko.}{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  On quadruples of linearly connected projections and transitive systems of subspaces // }{
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\par }{\b\fs20\lang1033\langfe1049\langnp1033\insrsid13975535 
\par }{\b\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 Yusenko K.A. The structure theorems for }{\lang1033\langfe1049\langnp1033\insrsid13975535 *}{\b\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
-algebras generated by the families of projections}{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 .\~\emdash  Manuscript. }{\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
\par }{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 Thesis for the degree of candidate of physical and mathematical sciences by speciality 01.01.01\~\emdash 
 mathematical analysis. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 2007. }{\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
\par }{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 0.2cm The thesis is devoted to the subsequent development of the }{\lang1033\langfe1049\langnp1033\insrsid13975535 *}{
\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 -algebras connected with star-shaped graphs. Such algebras arise as th}{\fs20\lang1033\langfe1049\langnp1033\insrsid13975535 e generalization of well-known H.Wey}{
\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 l\rquote s problem about the sum of two hermitian matrices. In work we investigate the case when the star-shaped graph is the extended Dynkin graph. For the case }{\pard\plain 
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}}}{\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  we got the full description of the parameters set for which the algebra has a }{\lang1033\langfe1049\langnp1033\insrsid13975535 *}{
\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 -representation. We also found the condition under which there exist one-to-one correspondence between irreducible representations and 
transitive systems of subspaces. For other extended Dynkin graphs we investigate the structure properties of the parameters set for which the corresponding algebras have }{\lang1033\langfe1049\langnp1033\insrsid13975535 *}{
\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 -representations. Given the condition under which such sets are infinite. }{\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
\par }\pard \qj \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 {\b\i\fs20\lang1033\langfe1049\langnp1033\insrsid13975535 
\par }{\b\i\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 Key words:}{\i\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  }{\lang1033\langfe1049\langnp1033\insrsid13975535 *}{
\i\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 -algebras, representation theory, projections, operators, systems of subspaces, transitive and indecomposable systems, Dynkin graphs, Coxeter functors.}{
\fs20\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852  }{\lang1033\langfe1049\langnp1033\insrsid10436661\charrsid2313852 
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