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61.
Reflection rigidity of 2-spherical Coxeter groups 总被引:1,自引:0,他引:1
Caprace Pierre-Emmanuel; Muhlherr Bernhard 《Proceedings London Mathematical Society》2007,94(2):520-542
We prove that each finitely generated, irreducible and 2-sphericalCoxeter system (W, S) is strongly reflection rigid wheneverthe group W is of infinite order. This means in particular thatall reflection-preserving automorphisms of such a group areinner-by-graph. Our result can be seen as a first major steptowards a proof of the conjecture that all infinite, irreducibleCoxeter systems are strongly reflection rigid if they do notadmit diagram twists. 相似文献
62.
An associative ring R with unit element is called semilocal if R modulo its Jacobson radical is an artinian ring. It is proved that the multiplicative group R* of a semilocal ring R generated by R* satisfies an n-Engel condition for some positive integer n if and only if R is m-Engel as a Lie ring for some positive integer m depending only on n.Received: 21 January 2003 相似文献
63.
Bernhard Haeupler Gopal Pandurangan David Peleg Rajmohan Rajaraman Zhifeng Sun 《Random Structures and Algorithms》2016,48(3):565-587
We study randomized gossip‐based processes in dynamic networks that are motivated by information discovery in large‐scale distributed networks such as peer‐to‐peer and social networks. A well‐studied problem in peer‐to‐peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self‐stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network — new edges are added to the network — and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. This paper studies and analyzes two natural gossip‐based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., “pushes” their mutual information to each other). In the pull discovery process or the two‐hop walk, each node repeatedly requests or “pulls” a random contact from a random neighbor and connects itself to this two‐hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip. Our main result is an almost‐tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n‐node graph both processes take rounds to connect every node to all other nodes with high probability, whereas is a lower bound. We also study the two‐hop walk in directed graphs, and show that it takes time with high probability, and that the worst‐case bound is tight for arbitrary directed graphs, whereas Ω(n2) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 565–587, 2016 相似文献
64.
Let 𝒯n denote the set of unrooted unlabeled trees of size n and let k ≥ 1 be given. By assuming that every tree of 𝒯n is equally likely, it is shown that the limiting distribution of the number of nodes of degree k is normal with mean value ∼ μkn and variance ∼ σn with positive constants μk and σk. Besides, the asymptotic behavior of μk and σk for k → ∞ as well as the corresponding multivariate distributions are derived. Furthermore, similar results can be proved for plane trees, for labeled trees, and for forests. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 227–253, 1999 相似文献
65.
Bernhard Lani-Wayda 《Transactions of the American Mathematical Society》1999,351(3):901-945
We give an example of a smooth function with only one extremum, with for , and the following properties: The delay equation has an unstable periodic solution and a solution with phase curve transversally homoclinic to the orbit of the periodic solution. The complicated motion arising from this structure, and its robustness under perturbation of , are described in terms of a Poincaré map. The example is minimal in the sense that the condition (under which there would be no extremum) excludes complex solution behavior. Based on numerical observations, we discuss the role of the erratic solutions in the set of all solutions.
66.
Peter?EbenfeltEmail author Bernhard?Lamel Dmitry?Zaitsev 《Geometric And Functional Analysis》2003,13(3):546-573
We show that germs of local real-analytic CR automorphisms of a
real-analytic hypersurface M in
$\mathbb{C}$2 at a point
p M
are uniquelydetermined by their jets of some finite order at
p if and only if M is
not Levi-flat near p. This seems to be the first necessary and sufficient
result on finite jet determination and the first result of this kind in
the infinite type case.If M is of finite type at p,
we prove a stronger assertion: the local real-analytic
CR automorphisms of M fixing p
are analytically parametrized (and hence uniquely determined)
by their 2-jets at p.
This result is optimal since the automorphisms of the unit sphere are
not determined by their 1-jets at a point of the sphere. The finite
type condition is necessary since otherwise the needed jet order can
be arbitrarily high [Kow1,2], [Z2]. Moreover, we show, by an example,
that determination by 2-jets fails for finite type hypersurfaces already
in $\mathbb{C)$3.We also give an application to the dynamics of germs of local
biholomorphisms of $\mathbb{C)$2. 相似文献
67.
Towards a microchannel‐based X‐ray detector with two‐dimensional spatial and time resolution and high dynamic range 下载免费PDF全文
Bernhard W. Adams Anil U. Mane Jeffrey W. Elam Razib Obaid Matthew Wetstein Matthieu Chollet 《Journal of synchrotron radiation》2015,22(5):1202-1206
X‐ray detectors that combine two‐dimensional spatial resolution with a high time resolution are needed in numerous applications of synchrotron radiation. Most detectors with this combination of capabilities are based on semiconductor technology and are therefore limited in size. Furthermore, the time resolution is often realised through rapid time‐gating of the acquisition, followed by a slower readout. Here, a detector technology is realised based on relatively inexpensive microchannel plates that uses GHz waveform sampling for a millimeter‐scale spatial resolution and better than 100 ps time resolution. The technology is capable of continuous streaming of time‐ and location‐tagged events at rates greater than 107 events per cm2. Time‐gating can be used for improved dynamic range. 相似文献
68.
Bernhard Köck 《Compositio Mathematica》2000,124(2):195-217
We prove a certain Riemann–Roch-type formula for symmetric powers of Galois modules on Dedekind schemes which, in the number field or function field case, specializes to a formula of Burns and Chinburg for Cassou–Noguès–Taylor operations. 相似文献
69.
Lénaïc Chizat Gabriel Peyré Bernhard Schmitzer François-Xavier Vialard 《Journal of Functional Analysis》2018,274(11):3090-3123
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by [7], [15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation. 相似文献
70.
Bernhard Krötz 《Functional Analysis and Its Applications》2009,43(1):30-43
In this paper, we define a horospherical transform for a semisimple symmetric space Y. A natural double fibration is used to assign a more geometrical space Ξ of horospheres to Y. The horospherical transform relates certain integrable analytic functions on Y to analytic functions on Ξ by fiber integration. We determine the kernel of the horospherical transform and establish that the transform is injective on functions belonging to the most continuous spectrum of Y. 相似文献