共查询到20条相似文献,搜索用时 327 毫秒
1.
Shuichi Iida 《Mathematische Annalen》2010,346(3):669-717
We construct a function on the orbifold fundamental group of the moduli space of smooth theta divisors, which we call the
Meyer function for smooth theta divisors. In the construction, we use the adiabatic limits of the η-invariants of the mapping torus of theta divisors. We shall prove that the Meyer function for smooth theta divisors cobounds
the signature cocycle, and we determine the values of the Meyer function for the Dehn twists. In particular, we give an analytic
construction of the Meyer function of genus two. 相似文献
2.
Let F be a non-Archimedean local field of residual characteristic two and let d be an odd positive integer. Let D be a central F-division algebra of dimension d
2. Let π be one of: an irreducible smooth representation of D
× , an irreducible cuspidal representation of GL
d
(F), an irreducible smooth representation of the Weil group of F of dimension d. We show that, in all these cases, if π is self-contragredient then it is defined over
\mathbb Q{\mathbb Q} and is orthogonal. We also show that such representations exist. 相似文献
3.
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-ρ approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence S of length d log2
n, where n = #G and d ≥ 2 is a constant, we find that its expected running time is O(?n log n){O(\sqrt{n}\,{\rm log}\,n)} group operations (we give a rigorous proof for d > 4), and it only needs to store O(1) group elements. We consider applications to class groups of imaginary quadratic fields, and to finding isogenies between
elliptic curves over a finite field. 相似文献
4.
Yuji Kobayashi 《Archiv der Mathematik》2005,85(3):227-232
Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family
of finitely presented groups Gn over a fixed finite alphabet with solvable word problem such that
Received: 22 July 2004 相似文献
(1) | the center of Gn is trivial for every |
(2) | the dimension d(n) of the center of the group algebra K · Gn over K is either 1 or k, and |
(3) | it is undecidable given n whether d(n) = 1 or d(n) = k. |
5.
In any finite group G, the commutativity degree of G (denoted by d(G)) is the probability that two randomly chosen elements of G commute. More generally, for every n ≥ 2 the nth commutativity degree (denoted by d
n
(G)) is the probability that a randomly chosen ordered (n + 1)-tuple of the group elements is mutually commuting. The aim of this paper is to generalize the definition of d(G) and d
n
(G) to every compact group G (infinite and even uncountable). We shall state some results concerning compact groups and we will extend some results in
Erfanian et al. (Comm. Algebra 35 (2007), 4183–4197) and Lescot (J. Algebra 177 (1995), 847–869). 相似文献
6.
In this paper we develop a criterion for existence or non-existence of self-intersection local time (SILT) for a wide class of Gaussian
′(
d)-valued processes, we show that quite generally the SILT process has continuous paths, and we give several examples which illustrate existence of SILT for different ranges of dimensions (e.g., d ≤ 3, d ≤ 7 and 5 ≤ d ≤ 11 in the Brownian case). Some of the examples involve branching and exhibit “dimension gaps”. Our results generalize the work of Adler and coauthors, who studied the special case of “density processes” and proved that SILT paths are cadlag in the Brownian case making use of a “particle picture” approximation (this technique is not available for our general formulation). 相似文献
7.
Ilir Snopce 《Archiv der Mathematik》2009,92(1):19-25
For a prime p > 3 we determine all pro-p groups that satisfy d(G) = d(H) = 3 for all open subgroups H of G.
Received: 29 July 2008 相似文献
8.
Toshiyuki Abe 《Mathematische Zeitschrift》2007,255(4):755-792
We give an example of an irrational C
2-cofinite vertex operator algebra whose central charge is −2d for any positive integer d. This vertex operator algebra is given as the even part of the vertex operator superalgebra generated by d pairs of symplectic fermions, and it is just the realization of the c = −2-triplet algebra given by Kausch in the case d = 1. We also classify irreducible modules for this vertex operator algebra and determine its automorphism group.
This research is supported in part by a grant from Japan Society for the Promotion of Science. 相似文献
9.
James Allen Fill 《Journal of Theoretical Probability》2009,22(3):587-600
An (upward) skip-free Markov chain with the set of nonnegative integers as state space is a chain for which upward jumps may
be only of unit size; there is no restriction on downward jumps. In a 1987 paper, Brown and Shao determined, for an irreducible
continuous-time skip-free chain and any d, the passage time distribution from state 0 to state d. When the nonzero eigenvalues ν
j
of the generator on {0,…,d}, with d made absorbing, are all real, their result states that the passage time is distributed as the sum of d independent exponential random variables with rates ν
j
. We give another proof of their theorem. In the case of birth-and-death chains, our proof leads to an explicit representation
of the passage time as a sum of independent exponential random variables. Diaconis and Miclo recently obtained the first such
representation, but our construction is much simpler.
We obtain similar (and new) results for a fastest strong stationary time T of an ergodic continuous-time skip-free chain with stochastically monotone time-reversal started in state 0, and we also
obtain discrete-time analogs of all our results.
In the paper’s final section we present extensions of our results to more general chains.
Research supported by NSF grant DMS–0406104, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement
of Research in Statistics. 相似文献
10.
A nice group structure on the orbit space of unimodular rows 总被引:1,自引:0,他引:1
If A is an affine algebra of dimension d ≥ 2, over a perfect field k, where char k ≠ 2 and c.d.2
k ≤ 1, or if A = R[X], where R is a local, noetherian ring of dimension d ≥ 2, in which 2R = R, then the group structure of W. van der Kallen on the orbit space Um
d+1(A)/E
d+1(A) is given by coordinatewise multiplication via the product formula
相似文献
11.
Isabelle Chalendar Antoine Flattot Nadine Guillotin-Plantard 《Archiv der Mathematik》2008,90(4):353-359
In this paper we study the point spectrum of the operator
where d ≥ 1, 1 ≤ p ≤ ∞([0, 1]
d
) and τ is an irrational rotation on [0, 1]
d
. For a particular class of weights w, the point spectrum of T
w,τ is shown to be empty, generalizing Davie’s result [3], who considered the case p = 2, d = 1.
Received: 1 June 2007, Revised: 16 October 2007 相似文献
12.
Maks A. Akivis Vladislav V. Goldberg Valentin V. Lychagin 《Selecta Mathematica, New Series》2005,10(4):431-451
We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g
4(x, y),..., g
d
(x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g
4, and d − 4 PDEs of the second order with respect to f and g
4,..., g
d
. For d = 4, this result confirms Blaschke’s conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give
the Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage. 相似文献
13.
Hiroaki Taniguchi 《Graphs and Combinatorics》2008,24(3):229-236
In [3], a new d-dimensional dual hyperoval S in PG(d(d + 3)/2, 2) for d ≥ 3 was constructed based on Veronesean dual hyperoval. In this note, we determine the automorphism group of the dual hyperoval
S.
Received: January 26, 2007. Final Version received: January 7, 2008. 相似文献
14.
We give characterizations of radial Fourier multipliers as acting on radial L
p
functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of
corresponding results for general Hankel multipliers. Besides L
p
− L
q
bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces. Applications include
results on interpolation of multiplier spaces.
G. Garrigós partially supported by grant “MTM2007-60952” and Programa Ramón y Cajal, MCyT (Spain). A. Seeger partially supported by NSF grant DMS 0652890. 相似文献
15.
For a simplicial complex or more generally Boolean cell complex Δ we study the behavior of the f- and h-vector under barycentric subdivision. We show that if Δ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version
of the Charney–Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary
complex of a simple polytope. For a general (d − 1)-dimensional simplicial complex Δ the h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d − 1 converge to a set of d − 1 real numbers which only depends on d.
F. Brenti and V. Welker are partially supported by EU Research Training Network “Algebraic Combinatorics in Europe”, grant
HPRN-CT-2001-00272 and the program on “Algebraic Combinatorics” at the Mittag-Leffler Institut in Spring 2005. 相似文献
16.
d 《European Journal of Combinatorics》2002,23(8):1079
Assume that d ≥ 4. Then there exists a d -dimensional dual hyperoval in PG(d + n, 2) for d + 1 ≤ n ≤ 3 d − 7. 相似文献
17.
Let n, k, τ, d be positive integers with 1 ≤ k, τ, d ≤ n. As natural extensions of the bases, the kth local bases, the kth upper bases and the kth lower bases of primitive non-powerful signed digraphs, we introduce a number of new, though, intimately related parameters
called the generalized τ-bases of primitive non-powerful signed digraphs. Moreover, some sharp bounds for the generalized τ-bases of primitive non-powerful signed digraphs with n vertices and d loops are obtained, respectively. 相似文献
18.
Consider an arbitrary transient random walk on ℤ
d
with d∈ℕ. Pick α∈[0,∞), and let L
n
(α) be the spatial sum of the αth power of the n-step local times of the walk. Hence, L
n
(0) is the range, L
n
(1)=n+1, and for integers α, L
n
(α) is the number of the α-fold self-intersections of the walk. We prove a strong law of large numbers for L
n
(α) as n→∞. Furthermore, we identify the asymptotic law of the local time in a random site uniformly distributed over the range. These
results complement and contrast analogous results for recurrent walks in two dimensions recently derived by Černy (Stoch.
Proc. Appl. 117:262–270, 2007). Although these assertions are certainly known to experts, we could find no proof in the literature in this generality.
相似文献
19.
We study multivariate linear problems in the average case setting with respect to a zero-mean Gaussian measure whose covariance
kernel has a finite-order weights structure. This means that the measure is concentrated on a Banach space of d-variate functions that are sums of functions of at most q
* variables and the influence of each such term depends on a given weight. Here q
* is fixed whereas d varies and can be arbitrarily large. For arbitrary finite-order weights, based on Smolyak’s algorithm, we construct polynomial-time algorithms that use standard information. That is, algorithms that solve the d-variate problem to within ε using of order
function values modulo a power of ln ε
−1. Here p is the exponent which measures the difficulty of the univariate (d=1) problem, and the power of ln ε
−1 is independent of d. We also present a necessary and sufficient condition on finite-order weights for which we obtain strongly polynomial-time algorithms, i.e., when the number of function values is independent of d and polynomial in ε
−1. The exponent of ε
−1 may be, however, larger than p. We illustrate the results by two multivariate problems: integration and function approximation. For the univariate case
we assume the r-folded Wiener measure. Then p=1/(r+1) for integration and
for approximation.
相似文献
20.
Kinkar Ch. Das 《Graphs and Combinatorics》2007,23(6):625-632
Let G = (V,E) be a simple graph with n vertices, e edges and d1 be the highest degree. Further let λi, i = 1,2,...,n be the non-increasing eigenvalues of the Laplacian matrix of the graph G. In this paper, we obtain the following result: For connected graph G, λ2 = λ3 = ... = λn-1 if and only if G is a complete graph or a star graph or a (d1,d1) complete bipartite graph.
Also we establish the following upper bound for the number of spanning trees of G on n, e and d1 only:
The equality holds if and only if G is a star graph or a complete graph. Earlier bounds by Grimmett [5], Grone and Merris [6], Nosal [11], and Kelmans [2] were
sharp for complete graphs only. Also our bound depends on n, e and d1 only.
This work was done while the author was doing postdoctoral research in LRI, Université Paris-XI, Orsay, France. 相似文献