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181.
On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks
We answer some questions on the asymptotics of ballot walks raised in [S. B. Ekhad and D. Zeilberger, April 2021] and prove that these models are not D-finite. This short note demonstrates how the powerful tools developed in the last decades on lattice paths in convex cones help us to answer some challenging problems that were out of reach for a long time. On the way we generalize tandem walks to the family of large tandem walks whose steps are of arbitrary length and map them bijectively to a generalization of ballot walks in three dimensions.
相似文献182.
The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating 1-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (good groups) where the 1-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.Oblatum 20-II-1995 & 26-V-1995The first author is supported by the IHES, the Guggenheim foundation and the NSF.The second author is supported by the IHES and the Humboldt foundation. 相似文献
183.
Summary We show that the set
of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic groupG is dense in the product of the sets
over all maximal parabolic subgroupsP. The set
of equivalence classes of biautomatic structures onG is isomorphic to the product of the sets
over the cusps (conjugacy classes of maximal parabolic subgroups) ofG. Each maximal parabolicP is a virtually abelian group, so
and
were computed in [NS1].We show that any geometrically finite hyperbolic group has a generating set for which the full language of geodesics forG is regular. Moreover, the growth function ofG with respect to this generating set is rational. We also determine which automatic structures on such a group are equivalent to geodesic ones. Not all are, though all biautomatic structures are.Oblatum 14-VI-1993 & 4-I-1994Both authors acknowledge support from the NSF for this research. 相似文献
184.
Michael V. Matveev 《Rendiconti del Circolo Matematico di Palermo》1995,44(2):169-172
There exists a countable spaceV ω such that:
- V ω has a single non-isolated point,
- V ω has no pseudocompactificationX witht(X)=ω.
185.
Adams MR Aïd S Anthony PL Averill DA Baker MD Baller BR Banerjee A Bhatti AA Bratzler U Braun HM Breidung H Busza W Carroll TJ Clark HL Conrad JM Davisson R Derado I Dhawan SK Dietrich FS Dougherty W Dreyer T Eckardt V Ecker U Erdmann M Faller F Fang GY Figiel J Finlay RW Gebauer HJ Geesaman DF Griffioen KA Guo RS Haas J Halliwell C Hantke D Hicks KH Hughes VW Jackson HE Jancso G Jansen DM Jin Z Kaufman S Kennedy RD Kinney ER Kirk T Kobrak HG Kotwal AV Kunori S Lancaster S Lord JJ Lubatti HJ 《Physical review letters》1995,74(9):1525-1529
186.
187.
188.
189.
Braverman Michael SH.; Stepanov Vladimir D. 《Bulletin London Mathematical Society》1994,26(3):283-287
Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given. 相似文献
190.
Michael Renardy 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(3):497-501
We study a singular Sturm-Liouville eigenvalue problem which arises in studying the stability of rotating shallow-water shear flows on an equatorial -plane. Earlier studies have shown that the problem has only stable eigenvalues if a certain parameter exceeds 3/4. On the other hand, numerical studies have found unstable eigenvalues if is sufficiently small. In this note, we give an analytical proof that the bound of 3/4 is indeed sharp, i.e. there are instabilities for any < 3/4. 相似文献