共查询到20条相似文献,搜索用时 31 毫秒
1.
Matija Cencelj Dušan Repovš Mikhail B. Skopenkov 《Proceedings Mathematical Sciences》2007,117(3):301-306
We present a short and complete proof of the following Pontryagin theorem, whose original proof was complicated and has never
been published in detail. Let M be a connected oriented closed smooth 3-manifold, L
1(M) be the set of framed links in M up to a framed cobordism, and deg: L
1(M) → H
1(M; ℤ) be the map taking a framed link to its homology class. Then for each α ∈ H
1(M; ℤ) there is a one-to-one correspondence between the set deg−1
α and the group ℤ2d(α), where d(α) is the divisibility of the projection of α to the free part of
H
1(M; ℤ). 相似文献
2.
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
3.
David A. Grable 《Combinatorica》1999,19(2):221-239
o (n) of the n vertices. Here we show, in particular, that regular uniform hypergraphs for which the ratio of degree to maximum codegree
is , for some ɛ>0, have packings which cover all but vertices, where α=α(ɛ)>0.
The proof is based on the analysis of a generalized version of R?dl's nibble technique.
We apply the result to the problem of finding partial Steiner systems with almost enough blocks to be Steiner systems, where
we prove that, for fixed positive integers t<k, there exist partial S(t,k,n)'s with at most uncovered t-sets, improving the earlier result.
Received: September 23, 1994/Revised: November 14, 1996 相似文献
4.
We study a class of weighted shifts W
α defined by a recursively generated sequence α ≡ α0, … , α
m−2, (α
m−1, α
m
, α
m+1)∧ and characterize the difference between quadratic hyponormality and positive quadratic hyponormality. We show that a shift
in this class is positively quadratically hyponormal if and only if it is quadratically hyponormal and satisfies a finite
number of conditions. Using this characterization, we give a new proof of [12, Theorem 4.6], that is, for m = 2, W
α is quadratically hyponormal if and only if it is positively quadratically hyponormal. Also, we give some new conditions for
quadratic hyponormality of recursively generated weighted shift W
α (m ≥ 2). Finally, we give an example to show that for m ≥ 3, a quadratically hyponormal recursively generated weighted shift W
α need not be positively quadratically hyponormal. 相似文献
5.
We present a short and direct proof (based on the Pontryagin-Thom construction) of the following Pontryagin-Steenrod-Wu theorem:
(a) LetM be a connected orientable closed smooth (n + 1)-manifold,n≥3. Define the degree map deg: π
n
(M) →H
n
(M; ℤ) by the formula degf =f*[S
n
], where [S
n
] εH
n
(M; ℤ) is the fundamental class. The degree map is bijective, if there existsβ εH
2(M, ℤ/2ℤ) such thatβ ·w
2(M) ε 0. If suchβ does not exist, then deg is a 2-1 map; and (b) LetM be an orientable closed smooth (n+2)-manifold,n≥3. An elementα lies in the image of the degree map if and only ifρ
2
α ·w
2(M)=0, whereρ
2: ℤ → ℤ/2ℤ is reduction modulo 2. 相似文献
6.
Raphael Yuster 《Graphs and Combinatorics》2001,17(3):579-587
We prove that for every ε>0 and positive integer r, there exists Δ0=Δ0(ε) such that if Δ>Δ0 and n>n(Δ,ε,r) then there exists a packing of K
n
with ⌊(n−1)/Δ⌋ graphs, each having maximum degree at most Δ and girth at least r, where at most εn
2 edges are unpacked. This result is used to prove the following: Let f be an assignment of real numbers to the edges of a graph G. Let α(G,f) denote the maximum length of a monotone simple path of G with respect to f. Let α(G) be the minimum of α(G,f), ranging over all possible assignments. Now let αΔ be the maximum of α(G) ranging over all graphs with maximum degree at most Δ. We prove that Δ+1≥αΔ≥Δ(1−o(1)). This extends some results of Graham and Kleitman [6] and of Calderbank et al. [4] who considered α(K
n
).
Received: March 15, 1999?Final version received: October 22, 1999 相似文献
7.
S. V. Kerov 《Functional Analysis and Its Applications》2000,34(1):41-51
We study the Young lattice with the edge multiplicitiesϰ
α
(λ, ⋏) arising in the simplest Pieri formula for Jack symmetric polynomialsP
λ (x; α) with parameter α. A new proof of Stanley’s α-version of the hook formula is given. We also prove the formula
whereϕ(λ) = ∏
b∈λ
(a(b)α +l(b) + 1)−1 andc
α(b) is the α-contents of the new boxb=⋏/λ.
Partially supported by the Federal Grant Program “Integration,” No. 326.53, and by MSRI at Berkeley.
St. Petersburg Division of the V. A. Steklov Mathematical Institute. Translated from Funksional’nyi Analiz i Ego Prilozheniya,
Vol. 34, No. 1, pp. 51–64, January–March, 200.
Translated by S. V. Kerov 相似文献
8.
Ferenc Móricz 《Acta Mathematica Hungarica》2012,134(3):356-368
We consider complex-valued functions f∈L
1(ℝ+), where ℝ+:=[0,∞), and prove sufficient conditions under which the sine Fourier transform [^(f)]s\hat{f}_{s} and the cosine Fourier transform [^(f)]c\hat{f}_{c} belong to one of the Lipschitz classes Lip (α) and lip (α) for some 0<α≦1, or to one of the Zygmund classes Zyg (α) and zyg (α) for some 0<α≦2. These sufficient conditions are best possible in the sense that they are also necessary if f(x)≧0 almost everywhere. 相似文献
9.
Eugen Popa 《Positivity》2006,10(3):555-571
It is proved that the Laplace transform establishes a bijection between a class of resolvents (Vα)α>0 and a class of semi-groups Φ of kernels, acting on an abstract ordered convex cone. The compactness (in some weak topology)
of the closed convex envelopes of the trajectories: Φ(t, x), t > 0, resp. of (nVn)kx, n, k ∈ ȑ, plays a central role in these results. 相似文献
10.
E. I. Pancheva 《Journal of Mathematical Sciences》1998,92(3):3911-3920
Given an extremal process X: [0,∞)→[0,∞)d with lower curve C and associated point process N={(tk, Xk):k≥0}, tk distinct and Xk independent, given a sequence ζ
n
=(τ
n
, ξ
n
), n≥1, of time-space changes (max-automorphisms of [0,∞)d+1), we study the limit behavior of the sequence of extremal processes Yn(t)=ξ
n
-1
○ X ○ τn(t)=Cn(t) V max {ξ
n
-1
○ Xk: tk ≤ τn(t){ ⇒ Y under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn. The limit class consists of self-similar (with respect to a group ηα=(σα, Lα), α>0, of time-space changes) extremal processes. By self-similarity here we mean the property Lα ○ Y(t)
=
d
Y ○ αα(t) for all α>0. The univariate marginals of Y are max-self-decomposable. If additionally the initial extremal process X is
assumed to have homogeneous max-increments, then the limit process is max-stable with homogeneous max-increments.
Supported by the Bulgarian Ministry of Education and Sciences (grant No. MM 234/1996).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. 相似文献
11.
Radu Zaharopol 《Israel Journal of Mathematics》1979,33(1):52-58
Cet article a deux parties. Dans la première nous allons étudier les normes des opérateurs d'uneL
2-résolvante. Dans la deuxième partie on va associer à chaqueL
2-résolvante (G
α)α>0 un processus (f
α)α>0 (l'idée de considérer ce processus appartient à I. Cuculescu). En ce qui concerne ce processus (f
α)α>0 on va montrer que si (G
α)α>0 est uneL
2-résolvante qui correspond à un espace de Dirichlet fortement régulier sur (E, ℬ, μ) oùE est un espace métrique compact, ℬ est le corp borélien engendré par les ouverts deE et μ est une probabilité (ou une mesure finie), alors l'ensemble des zeros de chaquef
α est un ensemble fermé avec l'intérieur vide. 相似文献
12.
V. A. Ustimenko 《Journal of Mathematical Sciences》2007,140(3):461-471
The paper is devoted to the study of a linguistic dynamical system of dimension n ≥ 2 over an arbitrary commutative ring K,
i.e., a family F of nonlinear polynomial maps f
α : K
n
→ K
n
depending on “time” α ∈ {K − 0} such that f
α
−1 = f
−αM, the relation f
α1 (x) = f
α2 (x) for some x ∈ Kn implies α1 = α2, and each map f
α has no invariant points. The neighborhood {f
α (υ)∣α ∈ K − {0}} of an element v determines the graph Γ(F) of the dynamical system on the vertex set Kn. We refer to F as a linguistic dynamical system of rank d ≥ 1 if for each string a = (α1, υ, α2), s ≤ d, where αi + αi+1 is a nonzero divisor for i = 1, υ, d − 1, the vertices υ
a = f
α1 × ⋯ × f
αs
(υ) in the graph are connected by a unique path. For each commutative ring K and each even integer n ≠= 0 mod 3, there is a family of linguistic dynamical systems Ln(K) of rank d ≥ 1/3n. Let L(n, K) be the graph of the dynamical system Ln(q). If K = Fq, the graphs L(n, Fq) form a new family of graphs of large girth. The projective limit L(K) of L(n, K), n → ∞, is well defined for each commutative
ring K; in the case of an integral domain K, the graph L(K) is a forest. If K has zero divisors, then the girth of K drops
to 4. We introduce some other families of graphs of large girth related to the dynamical systems Ln(q) in the case of even q. The dynamical systems and related graphs can be used for the development of symmetric or asymmetric
cryptographic algorithms. These graphs allow us to establish the best known upper bounds on the minimal order of regular graphs
without cycles of length 4n, with odd n ≥ 3. Bibliography: 42 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 214–234. 相似文献
13.
We give a short and direct proof for the computation of the Szlenk index of the C(K) spaces, when K is a countable compact space and determine their Lavrientiev indices. We also compute the Szlenk index of certain C(α) spaces, where α is an uncountable ordinal. Finally, we show that if the Szlenk index of a Banach space is ω (first infinite
ordinal), then its weak*-dentability index is at most ω2 and that this estimate is optimal.
The first author was supported by the grants: Institutional Research Plan AV0Z10190503, A100190502, GA ČR 201/04/0090. 相似文献
14.
We study Karhunen-Loève expansions of the process(X
t
(α))
t∈[0,T) given by the stochastic differential equation $
dX_t^{(\alpha )} = - \frac{\alpha }
{{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)
$
dX_t^{(\alpha )} = - \frac{\alpha }
{{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)
, with the initial condition X
0(α) = 0, where α > 0, T ∈ (0, ∞), and (B
t
)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X
(α). As applications, we calculate the Laplace transform and the distribution function of the L
2[0, T]-norm square of X
(α) studying also its asymptotic behavior (large and small deviation). 相似文献
15.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
16.
Sándor Csörgő 《Acta Appl Math》2007,96(1-3):159-174
We consider the generalized convolution powers G
α
*u
(x) of an arbitrary semistable distribution function G
α
(x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G
α
(k,j)(x;u)=∂
k+j
G
α
*u
(x)/∂
x
k
∂
u
j
, x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in
merge theorems from the domain of geometric partial attraction of semistable laws.
An erratum to this article can be found at 相似文献
17.
18.
Leopold Flatto 《Israel Journal of Mathematics》1973,15(2):167-184
LetN
α, m equal the number of randomly placed arcs of length α (0<α<1) required to cover a circleC of unit circumferencem times. We prove that limα→0
P(Nα,m≦(1/α) (log (1/α)+mlog log(1/α)+x)=exp ((−1/(m−1)!) exp (−x)). Using this result for m=1, we obtain another derivation of Steutel's resultE(Nα,1)=(1/α) (log(1/α)+log log(1/α)+γ+o(1)) as α→0, γ denoting Euler's constant. 相似文献
19.
V. A. Belonogov 《Algebra and Logic》2005,44(6):357-369
Let P(n) be the set of all partitions of a natural number n. In the representation theory of symmetric groups, for every partition
α ∈ P(n), the partition h(α) ∈ P(n) is defined so as to produce a certain set of zeros in the character table for Sn. Previously, the analog f(α) of h(α) was obtained pointing out an extra set of zeros in the table mentioned. Namely, h(α)
is greatest (under the lexicographic ordering ≤) of the partitions β of n such that χα(gβ) ≠ 0, and f(α) is greatest of the partitions γ of n that are opposite in sign to h(α) and are such that χα(gγ) ≠ 0, where χα is an irreducible character of Sn, indexed by α, and gβ is an element in the conjugacy class of Sn, indexed by β. For α ∈ P(n), under some natural restrictions, here, we construct new partitions h′(α) and f′(α) of n possessing
the following properties. (A) Let α ∈ P(n) and n ⩾ 3. Then h′(α) is identical is sign to h(α), χα(gh′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of h(α), and h′(α) < γ < h(α). (B) Let α ∈ P(n), α ≠ α′,
and n ⩾ 4. Then f′(α) is identical in sign to f(α), χα(gf′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of f(α), and f′(α) < γ < f(α). The results obtained are
then applied to study pairs of semiproportional irreducible characters in An.
Supported by RFBR grant No. 04-01-00463.
__________
Translated from Algebra i Logika, Vol. 44, No. 6, pp. 643–663, November–December, 2005. 相似文献
20.
We say that n independent trajectories ξ1(t),…,ξ
n
(t) of a stochastic process ξ(t)on a metric space are asymptotically separated if, for some ɛ > 0, the distance between ξ
i
(t
i
) and ξ
j
(t
j
) is at least ɛ, for some indices i, j and for all large enough t
1,…,t
n
, with probability 1. We prove sufficient conitions for asymptotic separationin terms of the Green function and the transition
function, for a wide class of Markov processes. In particular,if ξ is the diffusion on a Riemannian manifold generated by
the Laplace operator Δ, and the heat kernel p(t, x, y) satisfies the inequality p(t, x, x) ≤ Ct
−ν/2 then n trajectories of ξ are asymptotically separated provided . Moreover, if for some α∈(0, 2)then n trajectories of ξ(α) are asymptotically separated, where ξ(α) is the α-process generated by −(−Δ)α/2.
Received: 10 June 1999 / Revised version: 20 April 2000 / Published online: 14 December 2000
RID="*"
ID="*" Supported by the EPSRC Research Fellowship B/94/AF/1782
RID="**"
ID="**" Partially supported by the EPSRC Visiting Fellowship GR/M61573 相似文献