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1.
Persistent homology captures the topology of a filtration—a one-parameter family of increasing spaces—in terms of a complete
discrete invariant. This invariant is a multiset of intervals that denote the lifetimes of the topological entities within
the filtration. In many applications of topology, we need to study a multifiltration: a family of spaces parameterized along
multiple geometric dimensions. In this paper, we show that no similar complete discrete invariant exists for multidimensional
persistence. Instead, we propose the rank invariant, a discrete invariant for the robust estimation of Betti numbers in a multifiltration, and prove its completeness in one
dimension.
The first author was partially supported by NSF under grant DMS-0354543. The second author was partially supported by DARPA
under grant HR 0011-06-1-0038 and by ONR under grant N 00014-08-1-0908. Both authors were partially supported by DARPA under
grant HR 0011-05-1-0007. 相似文献
2.
We study the connection between stringy Betti numbers of Gorenstein toric varieties and the generating functions of the Ehrhart
polynomials of certain polyhedral regions. We use this point of view to give counterexamples to Hibi's conjecture on the unimodality
of δ-vectors of reflexive polytopes.
The first author was partially supported by NSF grant DMS 0500127 and the second author was supported by a Graduate Research
Fellowship from the NSF 相似文献
3.
We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition
are finitely q-based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra
that is not finitely q-based.
The first author was partially supported by the grant # 201/02/0594 of the Grant Agency of the Czech Republic, and by the
Institutional grant MSM0021620839; the second author was partially supported by the grant No. Tn37877 of the Hungarian National
Foundation for Scientific Research (OTHA); the third author was supported by the NSF grant # DMS-9971352. 相似文献
4.
We investigate the recently introduced notion of rotation numbers for periodic orbits of interval maps. We identify twist
orbits, that is those orbits that are the simplest ones with given rotation number. We estimate from below the topological
entropy of a map having an orbit with given rotation number. Our estimates are sharp: there are unimodal maps where the equality
holds. We also discuss what happens for maps with larger modality. In the Appendix we present a new approach to the problem
of monotonicity of entropy in one-parameter families of unimodal maps.
This work was partially done during the first author’s visit to IUPUI (funded by a Faculty Research Grant from UAB Graduate
School) and his visit to MSRI (the research at MSRI funded in part by NSF grant DMS-9022140) whose support the first author
acknowledges with gratitude. The second author was partially supported by NSF grant DMS-9305899, and his gratitude is as great
as that of the first author. 相似文献
5.
On the multiplicity of periodic solutions of mountain pass type for a class of semilinear PDE’s 总被引:1,自引:0,他引:1
We prove the existence of many mountain pass periodic solutions for a semilinear elliptic PDE on a torus.
The first author was supported by the National Science Foundation grant #0300319 and by the RFBR grant #050101119. The second
author was supported by the NSF grant #MCS-8110556. 相似文献
6.
In this paper, we address the finite element method and discontinuous Galerkin method for the stochastic scattering problem
of Helmholtz type in ℝ
d
(d = 2, 3). Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on
the accuracy of the approximations are illustrated. Results of the numerical experiments are provided to examine our theoretical
results.
The first author is supported by NSF under grand number 0609918 and AFOSR under grant numbers FA9550-06-1-0234 and FA9550-07-1-0154,
the second author is supported by NSFC(10671082, 10626026, 10471054), and the third author is supported by NNSF (No. 10701039
of China) and 985 program of Jilin University. 相似文献
7.
Under the Generalized Riemann Hypothesis, it is proved that for any integer k⩾770 there is Nk>0 depending onk only such that every even integer ⩾Nk is a sum of two odd prime numbers andk powers of 2.
The research is partially supported by RGC research grant (HKU 518/96P). The first author is supported by Post-Doctoral Fellowship
of The University of Hong Kong. 相似文献
8.
The Hausdorff dimension of the set of numbers which can be written using digits 0, 1,t in base 3 is estimated. For everyt irrational a lower bound 0.767 … is found.
Support from NSF grant DMS-0072312 and Penn State in the form of a sabbatical leave is acknowledged. This work was partly
done when the author was visiting the Mathematical Institute of the Polish Academy of Sciences in Warsaw. 相似文献
9.
We study the possibility of splitting any bounded analytic function ƒ with singularities in a closed set E ⋃ F as a sum of two bounded analytic functions with singularities in E and F respectively. We obtain some results under geometric restrictions on the sets E and F and we provide some examples showing the sharpness of the positive results.
The first author is partially supported by RFBR grant #06-01-00313 and by the grant for Leading Scientific Schools #NSH-2266-2003.1.
The last author is supported by DGICYT grant MTM2005-08984-C02-02 and the CIRIT grant 2005SGR00611. 相似文献
10.
Steingrimsson’s coloring complex and Jonsson’s unipolar complex are interpreted in terms of hyperplane arrangements. This
viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions.
These convex ear decompositions impose strong new restrictions on the chromatic polynomials of all finite graphs. Similar
results are obtained for characteristic polynomials of submatroids of type ℬ
n
arrangements.
The first author was supported by NSF grant DMS-0500638. The second author was supported by NSF grant DMS-0245623. 相似文献
11.
The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
12.
13.
Catarina Carvalho Víctor Dalmau Petar Marković Miklós Maróti 《Algebra Universalis》2009,60(3):293-307
We prove that the constraint languages invariant under a short sequence of Jónsson terms (containing at most three non-trivial
ternary terms) are tractable by showing that they have bounded width. This improves a previous result by Kiss and Valeriote
and presents some evidence that the Larose–Zádori conjecture holds in the congruence-distributive case.
The first author was supported by EPSRC grant EP/C54384X/1. The second author was supported by the MEC under grant TIN 2006-15387-C03-03,
the EU PASCAL Network of Excellence IST-2002-506778, and the MODNET Marie Curie Research Training Network MRTN-CT-2004-512234.
The third author was supported by grant no. 144011G of the Ministry of Science and Environment of Serbia. The fourth author
was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 48809 and K 60148. 相似文献
14.
We characterize complex measures μ on the unit disk for which the Toeplitz operator T
μ
is bounded or compact on the analytic Besov spaces B
p
with 1 ≤ p < ∞.
Research supported in part by NSF grant, DMS 0200587 (first author); and by a NSERC grant (third author). 相似文献
15.
Dedicated to the memory of Paul Erdős
We extend a result of J. Alexander and D. Zagier on the Garsia entropy of the Erdős measure. Our investigation heavily relies
on methods from combinatorics on words. Furthermore, we introduce a new singular measure related to the Farey tree.
Received October 7, 1999
RID="†"
ID="†" This author is supported by the START-project Y96-MAT of the Austrian Science Fund
RID="‡"
ID="‡" This author is supported by the Austrian Science Fund (FWF) grant P14200-MAT
RID="*"
ID="*" This author is supported by the Austrian Science Fund (FWF) grant S8307-MAT 相似文献
16.
AssumeCH. There exists a strongly meager setX⊆2ω and a continuous functionF: 2ω → 2ω such thatF″ (X)=2ω. The analogous statement for the strong measure zero, the notion dual to strongly meager, is false.
The first author was partially supported by NSF grant DMS 9971282 and the Alexander von Humboldt Foundation.
The second author was partially supported by grant BW 5100-5-0231-2. 相似文献
17.
We prove a generalization to the totally real field case of the Waldspurger’s formula relating the Fourier coefficient of
a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger’s formula as a combination
of two ingredients – an equality between global distributions, and a dichotomy result for theta correspondence. As applications
we generalize the Kohnen–Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half
integral weight forms and a case of the Lindel?f hypothesis for integral weight forms. We also study the Kohnen space in the
adelic setting.
The first author was partially supported by NSF grant DMS-0070762. The second author was partially supported by NSF grant
DMS-0355285.
Received: July 2005 Accepted: August 2005 相似文献
18.
Abstract. – We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely
presented counterexample to von Neumann’s problem. Our group is an extension of a group of finite exponent n ≫ 1 by a cyclic group, so it satisfies the identity [x,y]
n
= 1.
Manuscrit reĉu le 8 février 2001.
RID="*"
ID="*"Both authors were supported in part by the NSF grant DMS 0072307. In addition, the research of the first author was
supported in part by the Russian Fund for Basic Research 99-01-00894 and by the INTAS grant, the research of the second author
was supported in part by the NSF grant DMS 9978802. 相似文献
19.
In this paper, we prove that the K?hler–Ricci flow converges to a K?hler–Einstein metric when E
1 energy is small. We also prove that E
1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.
The first named author is partially supported by a NSF grant, while the third author was partially supported by a NSF supplement
grant. 相似文献
20.
Qiuhui Chen Charles A. Micchelli Yuesheng Xu 《Advances in Computational Mathematics》2007,26(1-3):173-204
We survey the main techniques for the construction of multivariate filter banks and present new results about special matrices
of order four and eight suitable for their construction.
Qiuhui Chen: Supported in part by NSFC under grant 10201034 and project-sponsored by SRF for ROCS, SEM.
Charles A. Micchelli: Supported in part by the US National Science Foundation under grant CCR-0407476.
Yuesheng Xu: All correspondence to this author. Supported in part by the US National Science Foundation under grant CCR-0407476,
by the Natural Science Foundation of China under grant 10371122 and by the Chinese Academy of Sciences under the program “One
Hundred Distinguished Chinese Young Scientists”. 相似文献