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
Tento článek se věnuje historickému kontextu vzniku a přijetí teorému Cauchyho-Kowalevské a teorému Noetherové, dvou jedinečných výsledků, které zásadně ovlivnily moderní matematiku i matematickou a teoretickou fyziku. Autorkami těchto teorémů jsou dvě ženy, Sofie Kowalevská a Emmy Noetherová, které si v době, kdy ženy jen stěží dosahovaly vyššího vzdělání, svým talentem, houževnatostí a úsilím dokázaly vybojovat místo ve vědeckém světě a navždy se zapsaly do historie přírodních věd., The article covers the historical context ot the establishment and recognition of the Cauchy-Kowalevsky theorem and Noether theorem, two unique research results, which have essentially influenced modern mathematics, and mathematical and theoretical physics. The authors of theorems are two women, Sofie Kowalevsky and Emmy Noether who in a time when women barely reached higher education, achieved positions in the scientific world and forever influenced the history of natural sciences., Eliška Beránková., and Obsahuje bibliografii
The aim of this article is to sketch a certain method of indirect reconstruction of the process by which mathematics as a deductive discipline emerged in ancient Greece. We try out this method in a reconstruction of Thales' mathematics, but the main aim for which this method has been developed is the work of Pythagoras. We consider the process of the emergence of mathematics as a process of the constitution of a new language in the framework of which one can carry out deductive proofs. Therefore we base the method of indirect reconstruction of the emergence of mathematics on the theoretical findings in the book L. Kvasz: Vedecká revolúcia ako lingvistická událosť (The Scientific Revolution as a linguistic event, Prague, Filosofia 2013)., Ladislav Kvasz., and Obsahuje poznámky a bibliografii
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 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