Let G be a graph of order n and λ(G) the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. One of the main results of the paper is the following theorem Let k \geqslant 2,
n \geqslant k^{3} + k + 4, and let G be a graph of order n, with minimum degree δ(G) \geqslant k. If \lambda \left( G \right) \geqslant n - k - 1, then G has a Hamiltonian cycle, unless G=K_{1}\vee (K_{n-k-1}+K_{k}) or G=K_{k}\vee
(K_{n-2k}+\bar{K}_{k})., Vladimir Nikiforov., and Obsahuje seznam literatury
Let G be a finite group and H a subgroup. Denote by D(G;H) (or D(G)) the crossed product of C(G) and \mathbb{C}H (or \mathbb{C}G) with respect to the adjoint action of the latter on the former. Consider the algebra \left \langle D(G), e\right \rangle generated by D(G) and e, where we regard E as an idempotent operator e on D(G) for a certain conditional expectation E of D(G) onto D(G; H). Let us call \left \langle D(G), e\right \rangle the basic construction from the conditional expectation E: D(G) → D(G; H). The paper constructs a crossed product algebra C(G/H ×G) \rtimes \mathbb{C}G, and proves that there is an algebra isomorphism between \left \langle D(G), e\right \rangle and C(G/H×G) \rtimes \mathbb{C} G., Qiaoling Xin, Lining Jiang, Zhenhua Ma., and Obsahuje seznam literatury
We investigate the Bergman kernel function for the intersection of two complex ellipsoids {(z,w1,w2) 2 Cn+2 : |z1|2+. . .+|zn|2+|w1|q
<1, |z1|2+. . .+|zn|2+|w2|r < 1}. We also compute the kernel function for {(z1,w1,w2) 2 C3 : |z1|2/n + |w1|q < 1, |z1|2/n + |w2|r < 1} and show deflation type identity between these two domains. Moreover in the case that q = r = 2 we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem., Tomasz Beberok., and Seznam literatury
The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed., Sen Ming, Han Yang, Zili Chen, Ls Yong., and Obsahuje bibliografii
We compute the central heights of the full stability groups S of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such S proved recently by Casolo & Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for ascending series the central height can be any ordinal number., Bertram A. F. Wehrfritz., and Obsahuje seznam literatury
A digraph is associated with a finite group by utilizing the power map f: G → G defined by f(x) = xkfor all x \in G, where k is a fixed natural number. It is denoted by γG(n, k). In this paper, the generalized quaternion and 2-groups are stud- ied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2-group are determined for a 2-group to be a generalized quaternion group. Further, the classification of two generated 2-groups as abelian or non-abelian in terms of semi-regularity of the power digraphs is completed., Uzma Ahmad, Muqadas Moeen., and Obsahuje seznam literatury
Let $\Delta$ be a pure simplicial complex on the vertex set $[n]=\{1,\ldots,n\}$ and $I_\Delta$ its Stanley-Reisner ideal in the polynomial ring $S=K[x_1,\ldots,x_n]$. We show that $\Delta$ is a matroid (complete intersection) if and only if $S/I_\Delta^{(m)}$ ($S/I_\Delta^m$) is clean for all $m\in\mathbb{N}$ and this is equivalent to saying that $S/I_\Delta^{(m)}$ ($S/I_\Delta^m$, respectively) is Cohen-Macaulay for all $m\in\mathbb{N}$. By this result, we show that there exists a monomial ideal $I$ with (pretty) cleanness property while $S/I^m$ or $S/I^{(m)}$ is not (pretty) clean for all integer $m\geq3$. If $\dim(\Delta)=1$, we also prove that $S/I_\Delta^{(2)}$ ($S/I_\Delta^2$) is clean if and only if $S/I_\Delta^{(2)}$ ($S/I_\Delta^2$, respectively) is Cohen-Macaulay., Somayeh Bandari, Ali Soleyman Jahan., and Obsahuje bibliografické odkazy
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
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
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