共查询到20条相似文献,搜索用时 15 毫秒
1.
Let Θ be a smooth compact oriented manifold without boundary, imbedded in a Euclidean space E
s, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + εξ, where ε > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the
underlying spaces Θ and Λ, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator
of γ is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.
相似文献
2.
Robert Liptser 《Probability Theory and Related Fields》1996,106(1):71-104
Summary. We formulate large deviations principle (LDP) for diffusion pair (X
ɛ
,ξ
ɛ
)=(X
t
ɛ
,ξ
t
ɛ
), where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time. More
exactly, the LDP is established for (X
ɛ
,ν
ɛ
) with ν
ɛ
(dt, dz) being an occupation type measure corresponding to ξ
t
ɛ
. In some sense we obtain a combination of Freidlin–Wentzell’s and Donsker–Varadhan’s results. Our approach relies on the
concept of the exponential tightness and Puhalskii’s theorem.
Received: 29 June 1995/In revised form: 14 February 1996 相似文献
3.
We study the natural almost CR structure on the total space of a subbundle of hyperquadrics of the tangent bundle T(M) over a semi-Riemannian manifold (M, g) and show that if the Reeb vector ξ of an almost contact Riemannian manifold is a CR map then the natural almost CR structure on M is strictly pseudoconvex and a posteriori ξ is pseudohermitian. If in addition ξ is geodesic then it is a harmonic vector field. As an other application, we study pseudoharmonic vector fields on a compact strictly pseudoconvex CR manifold M, i.e. unit (with respect to the Webster metric associated with a fixed contact form on M) vector fields X ε H(M) whose horizontal lift X↑ to the canonical circle bundle S1 → C(M) → M is a critical point of the Dirichlet energy functional associated to the Fefferman metric (a Lorentz metric on C(M)). We show that the Euler–Lagrange equations satisfied by X↑ project on a nonlinear system of subelliptic PDEs on M.
Mathematics Subject Classifications (2000): 53C50, 53C25, 32V20 相似文献
4.
Ricardo Uribe-Vargas 《Bulletin of the Brazilian Mathematical Society》2005,36(3):285-307
The focal curve of an immersed smooth curve γ : θ ↦ γ (θ), in Euclidean space ℝm+1, consists of the centres of its osculating hyperspheres. This curve may be parametrised in terms of the Frenet frame of γ (t, n1, . . . , nm), as Cγ (θ) = (γ +c1n1+ c2n2 + • • • + cmnm)(θ), where the coefficients c1, . . . , cm-1 are smooth functions that we call the focal curvatures of γ . We discovered a remarkable formula relating the Euclidean curvatures κi , i = 1, . . . ,m, of γ with its focal curvatures. We show that the focal curvatures satisfy a system of Frenet equations (not vectorial, but scalar!).
We use the properties of the focal curvatures in order to give, for ℓ = 1, . . . ,m, necessary and sufficient conditions for the radius of the osculating ℓ-dimensional sphere to be critical. We also give necessary
and sufficient conditions for a point of γ to be a vertex. Finally, we show explicitly the relations of the Frenet frame and the Euclidean curvatures of γ with the Frenet frame and the Euclidean curvatures of its focal curve Cγ. 相似文献
5.
Priska Jahnke Thomas Peternell Ivo Radloff 《Central European Journal of Mathematics》2011,9(3):449-488
In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify
smooth complex projective threefolds Xwith −K
X
big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X
+ are not both birational. 相似文献
6.
M.M. Cavalcanti V.N. Domingos Cavalcanti 《NoDEA : Nonlinear Differential Equations and Applications》2000,7(3):285-307
This paper is concerned to the existence, uniqueness and uniform decay for the solutions of the coupled Klein-Gordon-Schr?dinger
damped equations
where ω is a bounded domain of R
n
, n≤ 3, F : R
2→R is a C
1-function; γ, β; θ are constants such that γ, β > 0 and 1 ≤ 2θ≤ 2.
Received January 1999 – Accepted October 1999 相似文献
7.
A. V. Osipov 《Journal of Mathematical Sciences》2008,155(4):624-631
For a subset M of a topological space X, the θ-closure {ie626-01} M is defined as the set of all x ∈ X such that any closed neighborhood of x intersects M. A Urysohn space X is said to be U-closed if, whenever X ∪ {ξ} is a Urysohn space obtained from X by adding one point ξ, the point ξ is isolated in X ∪ {ξ}. The θ-closure operator is applied to study compactness-type properties of (weakly) U-and H-closed and closed-hereditarily U-and H-closed spaces.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 48, General
Topology, 2007. 相似文献
8.
L. A. Petrov 《Functional Analysis and Its Applications》2009,43(4):279-296
We construct a two-parameter family of diffusion processes X
α,θ
on the Kingman simplex, which consists of all nonincreasing infinite sequences of nonnegative numbers with sum less than
or equal to one. The processes on this simplex arise as limits of finite Markov chains on partitions of positive integers.
For α = 0, our process coincides with the infinitely-many-neutral-alleles diffusion model constructed by Ethier and Kurtz (1981)
in population genetics. The general two-parameter case apparently lacks population-genetic interpretation. In the present
paper, we extend Ethier and Kurtz’s main results to the two-parameter case. Namely, we show that the (two-parameter) Poisson-Dirichlet
distribution PD(α,θ) is the unique stationary distribution for the process X
α,θ
and that the process is ergodic and reversible with respect to PD(α, θ). We also compute the spectrum of the generator of X
α,θ
. The Wright-Fisher diffusions on finite-dimensional simplices turn out to be special cases of X
α,θ
for certain degenerate parameter values. 相似文献
9.
Marc Coppens 《Geometriae Dedicata》2007,125(1):25-38
Let X be a smooth irreducible quasi-projective variety of dimension n in P
N
with N ≥ 2n + 2. Let γ be its Gauss map, let be the embedding obtained from the general projection in P
N
and let γ′ be its Gauss map. We say that the general projection preserves the injectivity of the Gauss map if γ(Q) ≠ γ(Q′) implies γ′(Q) ≠ γ′ (Q′). We prove that this property holds in the following cases: N≥ 3n + 1; N ≥ 3n with n ≥ 2; N ≥ 3n−1 with n ≥ 4 and X does not contain a linear (n−1)-space. In case N = 3n−1 and X does contain a linear (n−1)-space (such smooth varieties exist) then the general projection does not preserver the injectivity of the Gauss map. This
shows that there does not exist a straightforward kind of Bertini theorem for properties related to the Gauss map.
The author is affiliated with the University at Leuven as a research fellow. This paper belongs to the FWO-project G.0318.06. 相似文献
10.
We will consider global problems in the ringK[X
1, …,X
n] on the polynomials with coefficients in a subfieldK ofC.
LetP=(P
1, …,P
n):K
n
→K
n be a polynomial map such that (P
1,…,P
n) is a quasi-regular sequence generating a proper ideal, the main thing we do is to use the algebraic residues theory (as
described in [5]) as a computational tool to give some result to test when a map (P
1, …,P
n) is a proper map by computing a finite number of residue symbols. 相似文献
11.
Dirk Schütz 《Mathematische Zeitschrift》2006,252(3):623-654
Let X be a finite connected CW-complex and ρ: a regular covering space with free abelian covering transformation group. For ξ ∈ H1 (Xℝ) we define the notion of ξ-contractibility of X. This notion is closely related to the vanishing of the Novikov homology of the pair (X,ξ). We show that finite domination of is equivalent to X being ξ-contractible for every nonzero ξ with ρ*ξ =0 ∈ H1(; ℝ). If M is a closed connected smooth manifold the condition that M is ξ-contractible is necessary for the existence of a nonsingular closed 1-form representing ξ. Also ξ-contractibility guarantees the definition of the Latour obstruction τL(M,ξ) whose vanishing is then sufficient for the existence of a nonsingular closed 1-form provided dim M≥6. Now if ρ: is a finitely dominated regular ℤk-covering space we get that τL(M,ξ) is defined for every nonzero ξ with ρ*ξ=0 and the vanishing of one such obstruction implies the vanishing of all such τL(M,ξ). 相似文献
12.
Let k be a p-adic field of odd residue characteristic and let C be a hyperelliptic (or elliptic) curve defined by the affine equation Y
2=h(X). We discuss the index of C if h(X)=ɛf(X), where ɛ is either a non-square unit or a uniformising element in O
k
and f(X) a monic, irreducible polynomial with integral coefficients. If a root θ of f generates an extension k(θ) with ramification index a power of 2, we completely determine the index of C in terms of data associated to θ. Theorem 3.11 summarizes our results and provides an algorithm to calculate the index for
such curves C.
Received: 14 July 1997 / Revised version: 16 February 1998 相似文献
13.
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
14.
V. V. Shurygin 《Journal of Mathematical Sciences》2011,177(5):758-771
The Lie jet L
θ
λ of a field of geometric objects λ on a smooth manifold M with respect to a field θ of Weil A-velocities is a generalization of the Lie derivative L
v
λ of a field λ with respect to a vector field v. In this paper, Lie jets L
θ
λ are applied to the study of A-smooth diffeomorphisms on a Weil bundle T
A
M of a smooth manifold M, which are symmetries of prolongations of geometric objects from M to T
A
M. It is shown that vanishing of a Lie jet L
θ
λ is a necessary and sufficient condition for the prolongation λ
A
of a field of geometric objects λ to be invariant with respect to the transformation of the Weil bundle T
A
M induced by the field θ. The case of symmetries of prolongations of fields of geometric objects to the second-order tangent bundle T
2
M are considered in more detail. 相似文献
15.
Kaisa Matomäki 《Monatshefte für Mathematik》2008,155(2):167-189
Let 1/5 < θ ≤ 1. We prove that there exists a positive constant δ such that the number of even integers in the interval [X, X + X
θ] which are not a sum of two primes is 《 X
θ−δ. The proof uses the circle method, a sieve method, exponential sum estimates and zero-density estimates for L-functions.
Current address: Department of Mathematics, 20014 University of Turku, Finland.
Author’s address: Department of Mathematics, University of London, Royal Holloway, Egham, Surrey TW20 0EX, UK 相似文献
16.
A necessary and sufficient condition for a lower bound for fourth-order pseudodifferential operators
We give necessary and sufficient conditions for the lower bound {fx55-01} to hold for any compact setK ⊂X, an open set ofR
n
, andP =P* ∃ ψ
phg
4
(X) with p(x, ξ) ~ q
2
2
+ p3 + p2 + ..., q2 beingtransversally elliptic with respect to the characteristic manifold Σ =q
2
-1 (0). 相似文献
17.
Summary In this note we use the Hopf map π: S3 → S2 to construct an interesting family of Riemannian metrics hfon the 3-sphere, which are parametrized on the space of positive smooth functions f on the 2-sphere. All these metrics make the Hopf map a Riemannian submersion. The Hopf tube over an immersed curve γ in S2 is the complete lift π-1(γ) of γ, and we prove that any geodesic of this Hopf tube satisfies a Clairaut relation. A Hopf tube plays the role in S3 of the surfaces of revolution in R3. Furthermore, we show a geometric integration method of the Frenet equations for curves in those non-standard S3. Finally, if we consider the sphere S3 equipped with a family hf of Lorentzian metrics, then a new Clairautrelation is also obtained for timelike geodesics of the Lorentzian Hopf tube, and
a geometric integration method for curves is still possible. 相似文献
18.
Elizabeth Meckes 《Journal of Theoretical Probability》2012,25(2):333-352
Let X be a d-dimensional random vector and X
θ
its projection onto the span of a set of orthonormal vectors {θ
1,…,θ
k
}. Conditions on the distribution of X are given such that if θ is chosen according to Haar measure on the Stiefel manifold, the bounded-Lipschitz distance from X
θ
to a Gaussian distribution is concentrated at its expectation; furthermore, an explicit bound is given for the expected distance,
in terms of d, k, and the distribution of X, allowing consideration not just of fixed k but of k growing with d. The results are applied in the setting of projection pursuit, showing that most k-dimensional projections of n data points in ℝ
d
are close to Gaussian, when n and d are large and k=clog (d) for a small constant c. 相似文献
19.
Paweł Strzelecki Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2006,25(4):431-467
Motivated by previous work on elastic rods with self-contact, involving the concept of the global radius of curvature for
curves (as defined by Gonzalez and Maddocks), we define the global radius of curvature Δ[X] for a wide class of continuous parametric surfaces X for which the tangent plane exists on a dense set of parameters. It turns out that in this class of surfaces a positive lower
bound Δ[X] ≥ θ > 0 provides, naively speaking, the surface with a thickness of magnitude θ; it serves as an excluded volume constraint
for X, prevents self-intersections, and implies that the image of X is an embedded C1-manifold with a Lipschitz continuous normal. We also obtain a convergence and a compactness result for such thick surfaces,
and show one possible application to variational problems for embedded objects: the existence of ideal surfaces of fixed genus
in each isotopy class.
The proofs are based on a mixture of elementary topological, geometric and analytic arguments, combined with a notion of the
reach of a set, introduced by Federer in 1959.
Mathematics Subject Classification (2000) 49Q10, 53A05, 53C45, 57R52, 74K15 相似文献
20.
The aim of this paper is to derive consequences of a result of G?tze and Zaitsev (2008). We show that the i.i.d. case of this result implies a multidimensional version of some results of Sakhanenko (1985). We establish bounds for the rate of strong Gaussian approximation of sums of i.i.d. R
d
-valued random vectors ξ
j
having finite moments E IIξ
j
IIγ, γ>2. Bibliography: 13 titles. 相似文献