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242. The general rigidity result for bundles of A-covelocities and A-jets
- Creator:
- Jiří Tomáš
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, r-jet, bundle functor, Weil functor, Lie group, jet group, B-admissible A-velocity, 13, and 51
- Language:
- English
- Description:
- Let M be an m-dimensional manifold and A = Dr k/I = R⊕NA a Weil algebra of height r. We prove that any A-covelocity TA x f ∈ TA x M, x ∈ M is determined by its values over arbitrary max{widthA,m} regular and under the first jet projection linearly independent elements of TA x M. Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result TA M ≃ T r M without coordinate computations, which improves and generalizes the partial result obtained in Tomáš (2009) from m > k to all cases of m. We also introduce the space JA(M,N) of A-jets and prove its rigidity in the sense of its coincidence with the classical jet space Jr(M,N)., Jiří Tomáš., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
243. The groups of automorphisms of the Witt Wn and Virasoro Lie algebras
- Creator:
- Bavula, Vladimir V.
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, algebra, derivace funkce, mathematics, derivatives (mathematics), group of automorphisms, monomorphism, Lie algebra, Witt algebra, Virasoro algebra, automorphism, locally nilpotent derivation, 13, and 51
- Language:
- English
- Description:
- Let Ln = K[x1±1,..., xn±1] be a Laurent polynomial algebra over a field K of characteristic zero, Wn:= DerK(Ln) the Lie algebra of K-derivations of the algebra Ln, the so-called Witt Lie algebra, and let Vir be the Virasoro Lie algebra which is a 1-dimensional central extension of the Witt Lie algebra. The Lie algebras Wn and Vir are infinite dimen- sional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: AutLie(Vir) \simeq AutLie(W1) \simeq {±1} \simeq K*, and give a short proof that AutLie(Wn) \simeq AutK-alg(Ln) \simeq GLn(Z) \ltimes K*n., Vladimir V. Bavula., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
244. The index for Fredholm elements in a Banach algebra via a trace. II
- Creator:
- Grobler, Jacobus J, Raubenheimer, Heinrich, and Swartz, Andre
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- algebra, mathematics, trace, index, Fredholm element, 13, and 51
- Language:
- English
- Description:
- We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index., Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
245. The L^{2}\bar{\partial } -Cauchy problem on weakly q-pseudoconvex domains in Stein manifolds
- Creator:
- Saber, Sayed
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, \overline \partial operator, q-convex domain, Stein manifold, \overline \partial -Neumann operator, 13, and 51
- Language:
- English
- Description:
- Let X be a Stein manifold of complex dimension n\geqslant 2 and \Omega \Subset X be a relatively compact domain with C^{2} smooth boundary in X. Assume that Ω is a weakly q-pseudoconvex domain in X. The purpose of this paper is to establish sufficient conditions for the closed range of \overline \partial on Ω. Moreover, we study the \overline \partial -problem on Ω. Specifically, we use the modified weight function method to study the weighted \overline \partial -problem with exact support in Ω. Our method relies on the L^{2} -estimates by Hörmander (1965) and by Kohn (1973)., Sayed Saber., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
246. The real symmetric matrices of odd order with a P-set of maximum size
- Creator:
- Du, Zhibin and da Fonseca, Carlos M
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, real symmetric matrix, graph, multiplicity of eigenvalues, P-set, P-vertices, 13, and 51
- Language:
- English
- Description:
- Suppose that A is a real symmetric matrix of order n. Denote by m_{A}(0) the nullity of A. For a nonempty subset α of {1, 2,..., n}, let A(α) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α. When m_{A(\alpha )}(0) = m_{A}(0)+|α|, we call α a P-set of A. It is known that every P-set of A contains at most \left \lfloor n/2 \right \rfloorelements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step to the full characterization of these graphs of odd order, we establish some conditions for such graphs G under which there is a real symmetric matrix A whose graph is G and contains a P-set of size (n − 1)/2., Zhibin Du, Carlos M. da Fonseca., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
247. Thompson's conjecture for the alternating group of degree $2p$ and $2p+1$
- Creator:
- Babai, Azam and Mahmoudifar, Ali
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, finite group, conjugacy class size, simple group, 13, and 51
- Language:
- English
- Description:
- For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N(G) = N(L)$, then $G\cong L$. We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z(G)=1$ and $N(G) = N(A_i)$ is necessarily isomorphic to $A_i$, where $i\in\{2p,2p+1\}$., Azam Babai, Ali Mahmoudifar., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
248. Torsion units for some almost simple groups
- Creator:
- Gildea, Joe
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, integrály, mathematics, integrals, Zassenhaus conjecture, torsion unit, partial augmentation, integral group ring, 13, and 51
- Language:
- English
- Description:
- We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group PSL(2, 11). Additionally we prove that the Prime graph question is true for the automorphism group of the simple group PSL(2, 13)., Joe Gildea., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
249. Two ideals connected with strong right upper porosity at a point
- Creator:
- Bilet, Viktoriia, Dovgoshey, Oleksiy, and Prestin, Jürgen
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, one-side porosity, local strong upper porosity, completely strongly porous set, ideal, 13, and 51
- Language:
- English
- Description:
- Let SP be the set of upper strongly porous at 0 subsets of \mathbb{R}^{+} and let Î(SP) be the intersection of maximal ideals I\subseteq SP. Some characteristic properties of sets E \in Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of \mathbb{R}^{+} is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014)., Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
250. Unicyclic graphs with bicyclic inverses
- Creator:
- Panda, Swarup Kumar
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, adjacency matrix, unicyclic graph, bicyclic graph, inverse graph, perfect matching, 13, and 51
- Language:
- English
- Description:
- A graph is nonsingular if its adjacency matrix $A(G)$ is nonsingular. The inverse of a nonsingular graph $G$ is a graph whose adjacency matrix is similar to $A(G)^{-1}$ via a particular type of similarity. Let $\mathcal{H}$ denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in $\mathcal{H}$ which possess unicyclic inverses. We present a characterization of unicyclic graphs in $\mathcal{H}$ which possess bicyclic inverses., Swarup Kumar Panda., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public