Let a \subseteq \mathbb{C} [x1, ..., xn] be a monomial ideal andJ(a^{c}) the multiplier ideal of a with coefficient c. Then J(a^{c}) is also a monomial ideal of \mathbb{C} [x1, ..., xn], and the equality J(a^{c}) = a implies that 0 < c < n + 1. We mainly discuss the problem when J (a) = a or J({a^{n = 1 - \varepsilon }}) = a for all 0 < ε < 1. It is proved that if J (a) = a then a is principal, and if J({a^{n = 1 - \varepsilon }}) = a holds for all 0 < ε < 1 then a = (x1, ..., xn). One global result is also obtained. Let ã be the ideal sheaf on \mathbb{P}^{n-1} associated with a. Then it is proved that the equality J (ã) = ã implies that ã is principal., Cheng Gong, Zhongming Tang., and Obsahuje seznam literatury
Let \Omega \subset {{\Bbb C}^n} be a bounded, simply connected \mathbb{C} -convex domain. Let \alpha \in \mathbb{Z}_{+}^{n} and let f be a function on Ω which is separately {C^{2{\alpha _j} - 1}} -smooth with respect to zj (by which we mean jointly {C^{2{\alpha _j} - 1}} -smooth with respect to Rezj, Imzj). If f is α-analytic on Ω\f−1(0), then f is α-analytic on Ω. The result is well-known for the case a_{i}=1, 1\leqslant i\leqslant n even when f a priori is only known to be continuous., Abtin Daghighi, Frank Wikström., and Obsahuje seznam literatury
We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results., Lihua You, Yujie Shu, Xiao-Dong Zhang., and Obsahuje seznam literatury
We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on p and on the symmetric part of a gradient of u, namely, it is represented by a stress tensor T (Du, p):= v(p, |D|2)D which satisfies r-growth condition with r \in (1, 2]. In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in the paper Caffarelli, Peral (1998)., Václav Mácha., and Obsahuje seznam literatury
The imbalance of an edge e = {u, v} in a graph is defined as i(e) = |d(u)−d(v)|, where d(·) is the vertex degree. The irregularity I(G) of G is then defined as the sum of imbalances over all edges of G. This concept was introduced by Albertson who proved that I(G)\leqslant 4n^{3}/27 (where n = |V(G)|) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves the Laplacian spectral radius λ., Felix Goldberg., and Obsahuje seznam literatury
Fiedler and Markham (1994) proved {\left( {\frac{{\det \hat H}}{k}} \right)^k} \geqslant \det H, where H = (H_{ij})_{i,j}^{n}_{=1} is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and \hat H = \left( {tr{H_{ij}}} \right)_{i,j = 1}^n. We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove \det \left( {{I_n} + \hat H} \right) \geqslant \det {\left( {{I_{nk}} + kH} \right)^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}}}., Minghua Lin., and Obsahuje seznam literatury
The paper studies applications of C*-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4. In conclusion, we consider two numerical examples illustrating our main results., Igor Nikolaev., and Obsahuje seznam literatury