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841.
842.
Armin Rainer 《Mathematische Nachrichten》2009,282(12):1623-1636
We study the regularity of the roots of complex monic polynomials P (t) of fixed degree depending smoothly on a real parameter t. We prove that each continuous parameterization of the roots of a generic C∞ curve P (t) (which always exists) is locally absolutely continuous. Generic means that no two of the continuously chosen roots meet of infinite order of flatness. Simple examples show that one cannot expect a better regularity than absolute continuity. This result will follow from the proposition that for any t0 there exists a positive integer N such that t ? P (t0 ± (t – t0)N ) admits smooth parameterizations of its roots near t0. We show that Cn curves P (t) (where n = deg P) admit differentiable roots if and only if the order of contact of the roots is ≥ 1. We give applications to the perturbation theory of normal matrices and unbounded normal operators with compact resolvents and common domain of definition: The eigenvalues and eigenvectors of a generic C∞ curve of such operators can be arranged locally in an absolutely continuous way (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
843.
Jean-Luc Chabert 《代数通讯》2015,43(1):309-324
We first globalize some recent results about polynomials whose divided differences are integer-valued on subsets of discrete valuation domains. This allows us to describe explicit computations, in particular for polynomials which are integer-valued on the prime numbers. Then, we specialize other recent results about integer-valued polynomials on triangular matrices to matrices whose coefficients are in some subsets, and in particular, when the coefficients are primes. 相似文献
844.
The nature of this paper is a practical application of a proper time‐series methodology to evaluate policy impacts when there is uncertainty about the data being difference‐stationary (DS) or trend‐stationary (TS). We use this methodology to examine the trend behavior of two air pollutants, nitrogen oxides (NOX) and volatile organic compounds (VOC). In particular, we concentrate on answering two questions. First, were there breaks in the trends of NOX and VOC emissions around the same time environmental policies such as the Clean Air Act Amendments (CAAA) of 1970 were passed? And second, accounting for possible breaks are the US emissions of NOX and VOC TS or DS? Our empirical results show a clear evidence of a trend shift in NOX and VOC emissions at the time the CAAA of 1970 were passed, implying that this policy has been effective in reducing air pollution emissions, as well as additional breaks that correspond to other events and environmental policies before and after 1970. The unit root tests indicate that NOX are DS irrespective of the number of breaks in the trend whereas results for VOC emissions depend on the number of breaks assumed. 相似文献
845.
Hugh Thomas 《Discrete Mathematics》2006,306(21):2711-2723
The usual, or type An, Tamari lattice is a partial order on , the triangulations of an (n+3)-gon. We define a partial order on , the set of centrally symmetric triangulations of a (2n+2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the An Tamari lattice, and therefore that it deserves to be considered the Bn Tamari lattice. We also define a bijection between and the noncrossing partitions of type Bn defined by Reiner. 相似文献
846.
Let (R, 𝔪) be a Noetherian Gorenstein local ring and I be a principal ideal of R. In this article we show that the Bass numbers of the R-modules R/I n take constant values for large n. 相似文献
847.
848.
The Kumjian–Pask algebra KP(Λ) is a graded algebra associated to a higher-rank graph Λ and is a generalization of the Leavitt path algebra of a directed graph. We analyze the minimal left ideals of KP(Λ), and identify its socle as a graded ideal by describing its generators in terms of a subset of vertices of the graph. We characterize when KP(Λ) is semisimple, and obtain a complete structure theorem for a semisimple Kumjian–Pask algebra. As a consequence of this structure theorem, every semisimple Kumjian–Pask algebra can be obtained as a Leavitt path algebra of a directed graph. 相似文献
849.
In ([11]), we have studied quadratic Leibniz algebras that are Leibniz algebras endowed with symmetric, nondegenerate, and associative (or invariant) bilinear forms. The nonanticommutativity of the Leibniz product gives rise to other types of invariance for a bilinear form defined on a Leibniz algebra: the left invariance, the right invariance. In this article, we study the structure of Leibniz algebras endowed with nondegenerate, symmetric, and left (resp. right) invariant bilinear forms. In particular, the existence of such a bilinear form on a Leibniz algebra 𝔏 gives rise to a new algebra structure ☆ on the underlying vector space 𝔏. In this article, we study this new algebra, and we give information on the structure of this type of algebras by using some extensions introduced in [11]. In particular, we improve the results obtained in [22]. 相似文献
850.
Huanyin Chen 《代数通讯》2013,41(3):911-921
ABSTRACT We prove that an ideal I of a regular ring R is separative if and only if each a ? R satisfying Rr(a)aR = Ra?(a)R = RaR(1 ? a)R ? I is unit-regular. If I is a separative ideal of a regular ring R, then each a ? R satisfying Rar(a2) = ?(a2)aR = R(a ? a2) R ? I is clean. Some applications are also obtained. 相似文献