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51.
Elisa Gorla 《Transactions of the American Mathematical Society》2006,358(2):819-869
In this paper, we discuss some necessary and sufficient conditions for a curve to be arithmetically Cohen-Macaulay, in terms of its general hyperplane section. We obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non-arithmetically Cohen-Macaulay curve of . We prove that almost all the degree matrices with positive subdiagonal that occur for the general plane section of a non-arithmetically Cohen-Macaulay curve of , arise also as degree matrices of some smooth, integral, non-arithmetically Cohen-Macaulay curve, and we characterize the exceptions. We give a necessary condition on the graded Betti numbers of the general plane section of an arithmetically Buchsbaum (non-arithmetically Cohen-Macaulay) curve in . For curves in , we show that any set of Betti numbers that satisfies that condition can be realized as the Betti numbers of the general plane section of an arithmetically Buchsbaum, non-arithmetically Cohen-Macaulay curve. We also show that the matrices that arise as a degree matrix of the general plane section of an arithmetically Buchsbaum, integral, (smooth) non-arithmetically Cohen-Macaulay space curve are exactly those that arise as a degree matrix of the general plane section of an arithmetically Buchsbaum, non-arithmetically Cohen-Macaulay space curve and have positive subdiagonal. We also prove some bounds on the dimension of the deficiency module of an arithmetically Buchsbaum space curve in terms of the degree matrix of the general plane section of the curve, and we prove that they are sharp.
52.
David A. Jorgensen 《Proceedings of the American Mathematical Society》1999,127(6):1575-1582
Let be a commutative Noetherian local ring, and let where is a non-zerodivisor of contained in . Then a finitely generated -module is said to lift to if there exists a finitely generated -module such that is -regular and . In this paper we give a general construction of finitely generated -modules of finite projective dimension over which fail to lift to provided and the depth of is at least 2.
53.
Mohd.?Salmi?Md. NooraniEmail author 《Bulletin of the Brazilian Mathematical Society》2003,34(2):275-285
We consider distribution results for closed orbits of the
partially hyperbolic system: an ergodic toral automorphism Ã
with respect to a (G,
)–extension A. In particular we obtain an analogue of the
Chebotarev theorem in this situation which is an asymptotic
formula for the number of closed orbits of the base
transformation according to how they lift onto the extension
space. To arrive at this result we introduce a cyclic extension
 of A and deduce that  and A is essentially a group extension
and homogeneous extension of à respectively. This observation of
a group extension is similar to the setting previously studied
by Parry & Pollicott and using the prime orbit theorem of
Waddington we then derive at an auxiliary result for the group
extension analogoues to Parry & Pollicott. Finally we relate
this auxiliary result to the homogeneous extension by resorting
to the work of Noorani & Parry. 相似文献
54.
提升和投射具有伪轨跟踪性质或可扩性的连续流 总被引:3,自引:0,他引:3
本文证明了紧度量空间上的连续流经提升或投射后,其伪轨跟踪性质及可扩性是不变的;做为应用给出了不定向闭曲面上具有伪轨跟踪性质的Cr流的特征。 相似文献
55.
本文研究了M-纤维式纤维化的问题,利用M-纤维式升腾函数获得了M-纤维式纤维化的特征,以及证明了M-纤维式上纤维化诱导的映射空间之间的M-纤维式映射在一定条件下也是M-纤维式纤维化. 相似文献
56.
We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices. Additionally, we present a comparison between our approximation scheme and earlier techniques, including the use of common quadratic Lyapunov functions and a method based on matrix liftings. Theoretical results and numerical investigations show that our approach yields tighter approximations. 相似文献
57.
This article is devoted to the construction of a Hermite-type regularization operator transforming functions that are not necessarily into globally finite-element functions that are piecewise polynomials. This regularization operator is a projection, it preserves appropriate first and second order polynomial traces, and it has approximation properties of optimal order. As an illustration, it is used to discretize a nonhomogeneous Navier-Stokes problem, with tangential boundary condition.
58.
Motivated by Sasaki’s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is efficient, especially for sparse bivariate polynomials. 相似文献
59.
60.
Tolulope Fadina Frederik Herzberg 《Stochastics An International Journal of Probability and Stochastic Processes》2019,91(1):52-66
The hyperfinite G-expectation is a nonstandard discrete analogue of G-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time G-expectation operator is defined as a hyperfinite G-expectation which is infinitely close, in the sense of nonstandard topology, to the continuous-time G-expectation. We develop the basic theory for hyperfinite G-expectations and prove an existence theorem for liftings of (continuous-time) G-expectation. For the proof of the lifting theorem, we use a new discretization theorem for the G-expectation (also established in this paper, based on the work of Dolinsky et al. [Weak approximation of G-expectations, Stoch. Process. Appl. 122(2) (2012), pp. 664–675]). 相似文献