共查询到20条相似文献,搜索用时 15 毫秒
1.
We propose an algorithm to sample and mesh a k-submanifold M{\mathcal{M}} of positive reach embedded in
\mathbbRd{\mathbb{R}^{d}} . The algorithm first constructs a crude sample of M{\mathcal{M}} . It then refines the sample according to a prescribed parameter e{\varepsilon} , and builds a mesh that approximates M{\mathcal{M}} . Differently from most algorithms that have been developed for meshing surfaces of
\mathbbR 3{\mathbb{R} ^3} , the refinement phase does not rely on a subdivision of
\mathbbR d{\mathbb{R} ^d} (such as a grid or a triangulation of the sample points) since the size of such scaffoldings depends exponentially on the
ambient dimension d. Instead, we only compute local stars consisting of k-dimensional simplices around each sample point. By refining the sample, we can ensure that all stars become coherent leading
to a k-dimensional triangulated manifold [^(M)]{\hat{\mathcal{M}}} . The algorithm uses only simple numerical operations. We show that the size of the sample is O(e-k){O(\varepsilon ^{-k})} and that [^(M)]{\hat{\mathcal{M}}} is a good triangulation of M{\mathcal{M}} . More specifically, we show that M{\mathcal{M}} and [^(M)]{\hat{\mathcal{M}}} are isotopic, that their Hausdorff distance is O(e2){O(\varepsilon ^{2})} and that the maximum angle between their tangent bundles is O(e){O(\varepsilon )} . The asymptotic complexity of the algorithm is T(e) = O(e-k2-k){T(\varepsilon) = O(\varepsilon ^{-k^2-k})} (for fixed M, d{\mathcal{M}, d} and k). 相似文献
2.
Sinan Ünver 《Mathematische Annalen》2010,348(4):833-858
Let ${k[\varepsilon]_{2}:=k[\varepsilon]/(\varepsilon^{2})}Let k[e]2:=k[e]/(e2){k[\varepsilon]_{2}:=k[\varepsilon]/(\varepsilon^{2})} . The single valued real analytic n-polylogarithm
Ln: \mathbbC ? \mathbbR{\mathcal{L}_{n}: \mathbb{C} \to \mathbb{R}} is fundamental in the study of weight n motivic cohomology over a field k, of characteristic 0. In this paper, we extend the construction in ünver (Algebra Number Theory 3:1–34, 2009) to define additive
n-polylogarithms lin:k[e]2? k{li_{n}:k[\varepsilon]_{2}\to k} and prove that they satisfy functional equations analogous to those of Ln{\mathcal{L}_{n}}. Under a mild hypothesis, we show that these functions descend to an analog of the nth Bloch group Bn¢(k[e]2){B_{n}' (k[\varepsilon]_{2})} defined by Goncharov (Adv Math 114:197–318, 1995). We hope that these functions will be useful in the study of weight n motivic cohomology over k[ε]2. 相似文献
3.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}Let
G < SL(2, \mathbb Z){\Gamma < {\rm SL}(2, {\mathbb Z})} be a free, finitely generated Fuchsian group of the second kind with no parabolics, and fix two primitive vectors
v0, w0 ? \mathbb Z2 \ {0}{v_{0}, w_{0} \in \mathbb {Z}^{2} \, {\backslash} \, \{0\}}. We consider the set S{\mathcal {S}} of all integers occurring in áv0g, w0?{\langle v_{0}\gamma, w_{0}\rangle}, for g ? G{\gamma \in \Gamma} and the usual inner product on
\mathbb R2{\mathbb {R}^2}. Assume that the critical exponent δ of Γ exceeds 0.99995, so that Γ is thin but not too thin. Using a variant of the circle method, new bilinear forms estimates
and Gamburd’s 5/6-th spectral gap in infinite-volume, we show that S{\mathcal {S}} contains almost all of its admissible primes, that is, those not excluded by local (congruence) obstructions. Moreover, we
show that the exceptional set
\mathfrak E(N){\mathfrak {E}(N)} of integers |n| < N which are locally admissible (n ? S (mod q) for all q 3 1){(n \in \mathcal {S} \, \, ({\rm mod} \, q) \, \, {\rm for\,all} \,\, q \geq 1)} but fail to be globally represented, n ? S{n \notin \mathcal {S}}, has a power savings,
|\mathfrak E(N)| << N1-e0{|\mathfrak {E}(N)| \ll N^{1-\varepsilon_{0}}} for some ${\varepsilon_{0} > 0}${\varepsilon_{0} > 0}, as N → ∞. 相似文献
4.
For a resistance form ${(X, \mathcal{D}(\varepsilon),\varepsilon)}For a resistance form (X, D(e),e){(X, \mathcal{D}(\varepsilon),\varepsilon)} and a point x0 ? X{x_0 \in X} as boundary, on the space X0:=X \{x0}{X_0:=X {\setminus}\{x_0\}} we consider the Dirichlet space Dx0:={f ? D(e) | f(x0)=0}{\mathcal{D}_{x_0}:=\{f\in\mathcal{D}(\varepsilon)\, |\, f(x_0)=0\}} and we develop a good potential theory. For any finely open subset D of X
0 we consider a localized resistance form (DX0 \ D,eD{\mathcal{D}_{X_0 {\setminus} D},\varepsilon_{D}}) where DX0 \ D:={f ? Dx0 | f=0{\mathcal{D}_{X_0 {\setminus} D}:=\{f\in\mathcal{D}_{x_0}\, |\, f=0} on X0 \ D}, eD(f,g):=e(f,g){X_0 {\setminus} D\},\, \varepsilon_D(f,g):=\varepsilon(f,g)} for all f,g ? DX0 \ D{f,g\in\mathcal{D}_{X_0 {\setminus} D}}. The main result is the equivalence between the local property of the resistance form and the sheaf property for the excessive
elements on finely open sets. 相似文献
5.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
6.
We study the family of divergence-type second-order parabolic equations
we(x)\frac?u?t=div(a(x)we(x) ?u), x ? \mathbbRn{\omega_\varepsilon(x)\frac{\partial u}{\partial t}={\rm div}(a(x)\omega_\varepsilon(x) \nabla u), x \in \mathbb{R}^n} , with parameter ${\varepsilon >0 }${\varepsilon >0 } , where a(x) is uniformly elliptic matrix and we=1{\omega_\varepsilon=1} for x
n
< 0 and we=e{\omega_\varepsilon=\varepsilon} for x
n
> 0. We show that the fundamental solution obeys the Gaussian upper bound uniformly with respect to e{\varepsilon} . 相似文献
7.
Let ${\mathbb {F}}Let
\mathbb F{\mathbb {F}} a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra uniformity seminorm U
k
(X) for an ergodic action
(Tg)g ? \mathbb Fw{(T_{g})_{{g} \in \mathbb {F}^{\omega}}} of the infinite abelian group
\mathbb Fw{\mathbb {F}^{\omega}} on a probability space X = (X, B, m){X = (X, \mathcal {B}, \mu)} is generated by phase polynomials f: X ? S1{\phi : X \to S^{1}} of degree less than C(k) on X, where C(k) depends only on k. In the case where
k £ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} we obtain the sharp result C(k) = k. This is a finite field counterpart of an analogous result for
\mathbb Z{\mathbb {Z}} by Host and Kra [HK]. In a companion paper [TZ] to this paper, we shall combine this result with a correspondence principle
to establish the inverse theorem for the Gowers norm in finite fields in the high characteristic case
k £ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} , with a partial result in low characteristic. 相似文献
8.
I. E. Shparlinski 《Archiv der Mathematik》2002,78(6):445-448
We prove that for any $ \varepsilon > 0 $ \varepsilon > 0 there is k (e) k (\varepsilon) such that for any prime p and any integer c there exist k \leqq k(e) k \leqq k(\varepsilon) pairwise distinct integers xi with 1 \leqq xi \leqq pe, i = 1, ?, k 1 \leqq x_{i} \leqq p^{\varepsilon}, i = 1, \ldots, k , and such that¶¶?i=1k [1/(xi)] o c (mod p). \sum\limits_{i=1}^k {{1}\over{x_i}} \equiv c\quad (\mathrm{mod}\, p). ¶¶ This gives a positive answer to a question of Erdös and Graham. 相似文献
9.
Given g { l\fracn2 g( lj x - kb ) }jezjezn ,where lj \left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L
2(R
n
) are given. For a class of functions g{ ezrib( j,x ) g( x - lk ) }jezn ,kez\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} to be a frame. 相似文献
10.
D. R. Heath-Brown 《Journal of Mathematical Sciences》2010,171(6):813-823
Subject to the abc-conjecture, we improve the standard Weyl estimate for cubic exponential sums in which the argument is a
quadratic irrational. Specifically. we show that
?n \leqslant N e( an3 ) << e, aN\tfrac57 + e \sum\limits_{n \leqslant N} {e\left( {\alpha {n^3}} \right){ \ll_{\varepsilon, \alpha }}{N^{\tfrac{5}{7} + \varepsilon }}} 相似文献
11.
In the Euclidean Space
\mathbb Rn+1{\mathbb {R}^{n+1}} with a density
ee\frac12 n m2 |x|2, (e = ±1){e^{\varepsilon \frac12 n \mu^2 |x|^2},} {(\varepsilon =\pm1}), we consider the flow of a hypersurface driven by its mean curvature associated to this density. We give a detailed account
of the evolution of a convex hypersurface under this flow. In particular, when e = -1{ \varepsilon=-1} (Gaussian density), the hypersurface can expand to infinity or contract to a convex hypersurface (not necessarily a sphere)
depending on the relation between the bound of its principal curvatures and μ. 相似文献
12.
We construct an explicit intertwining operator L{\mathcal L} between the Schr?dinger group eit \frac\triangle2{e^{it \frac\triangle2}} and the geodesic flow on certain Hilbert spaces of symbols on the cotangent bundle T*X Γ of a compact hyperbolic surface X Γ = Γ\D. We also define Γ-invariant eigendistributions of the geodesic flow PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} (Patterson-Sullivan distributions) out of pairs of \triangle{\triangle} -eigenfunctions, generalizing the diagonal case j = k treated in Anantharaman and Zelditch (Ann. Henri Poincaré 8(2):361–426, 2007). The operator L{\mathcal L} maps PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} to the Wigner distribution WGj,k{W^{\Gamma}_{j,k}} studied in quantum chaos. We define Hilbert spaces HPS{\mathcal H_{PS}} (whose dual is spanned by {PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}}}), resp. HW{\mathcal H_W} (whose dual is spanned by {WGj,k}{\{W^{\Gamma}_{j,k}\}}), and show that L{\mathcal L} is a unitary isomorphism from HW ? HPS.{\mathcal H_{W} \to \mathcal H_{PS}.} 相似文献
13.
A class Uk1 (J){\mathcal{U}}_{\kappa 1} (J) of generalized J-inner mvf’s (matrix valued functions) W(λ) which appear as resolvent matrices for bitangential interpolation problems in the generalized Schur class of p ×q mvf¢s Skp ×qp \times q \, {\rm mvf's}\, {\mathcal{S}}_{\kappa}^{p \times q} and some associated reproducing kernel Pontryagin spaces are studied. These spaces are used to describe the range of the
linear fractional transformation TW based on W and applied to Sk2p ×q{\mathcal{S}}_{\kappa 2}^{p \times q}. Factorization formulas for mvf’s W in a subclass U°k1 (J) of Uk1(J){\mathcal{U}^{\circ}_{\kappa 1}} (J)\, {\rm of}\, {\mathcal{U}}_{\kappa 1}(J) found and then used to parametrize the set Sk1+k2p ×q ?TW [ Sk2p ×q ]{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} \cap T_{W} \left[ {\mathcal{S}}_{\kappa 2}^{p \times q} \right]. Applications to bitangential interpolation problems in the class Sk1+k2p ×q{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} will be presented elsewhere. 相似文献
14.
Wolfgang Müller 《Monatshefte für Mathematik》1989,108(4):301-323
LetK be a quadratic number field with discriminantD and denote byF(n) the number of integral ideals with norm equal ton. Forr≥1 the following formula is proved $$\sum\limits_{n \leqslant x} {F(n)F(n + r) = M_K (r)x + E_K (x,r).} $$ HereM k (r) is an explicitly determined function ofr which depends onK, and for every ε>0 the error term is bounded by \(|E_K (x,r)|<< |D|^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} + \varepsilon } x^{{5 \mathord{\left/ {\vphantom {5 6}} \right. \kern-0em} 6} + \varepsilon } \) uniformly for \(r<< |D|^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} x^{{5 \mathord{\left/ {\vphantom {5 6}} \right. \kern-0em} 6}} \) Moreover,E k (x,r) is small on average, i.e \(\int_X^{2X} {|E_K (x,r)|^2 dx}<< |D|^{4 + \varepsilon } X^{{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-0em} 2} + \varepsilon } \) uniformly for \(r<< |D|X^{{3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-0em} 4}} \) . 相似文献
15.
F. Talay Akyildiz Dennis A. Siginer 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,11(1):741-748
The effect of surface roughness on developed laminar flow in microtubes is investigated. The tube boundary is defined by r=R[1+e sin( lq)]{r=R\left[{1+\varepsilon\, {\rm sin}\left( {\lambda \theta }\right)}\right]}, with R representing the reference radius and e{\varepsilon} and λ the roughness parameters. The momentum equation is solved using Fourier–Galerkin–Tau method with slip at the boundary.
A novel semi-analytical method is developed to predict friction factor and pressure drop in corrugated rough microtubes for
continuum flow and slip flow that are not restricted to small values of el{\varepsilon \lambda } . The analytical solution collapses onto the perturbation solution ofDuan and Muzychka (J. Fluids Eng., 130:031102, 2008) for small enough values of el{\varepsilon \lambda } . 相似文献
16.
Kengo Matsumoto 《Mathematische Zeitschrift》2010,265(4):735-760
A C*-symbolic dynamical system ${(\mathcal{A}, \rho, \Sigma)}
17.
In this paper, we consider the Schrödinger type operator ${H = (-\Delta _{\mathbb {H}}^n)^2 +V ^{2}}
18.
Ahmed Bonfoh Maurizio Grasselli Alain Miranville 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(6):663-695
We consider a singular perturbation of the one-dimensional Cahn–Hilliard equation subject to periodic boundary conditions. We construct a family of exponential attractors ${\{{\mathcal M}_\epsilon\}, \epsilon\geq 0}
19.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}
20.
Wei HUANG Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2005,21(5):1057-1070
Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n|Sk|,n≥1.Suppose limn→∞ESn^2/n=:σ^2〉0 and ∑n^∞=1 ρ^2/d(2^n)〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E|X|^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2(r-p)/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1(-1)^k/(2k+1)^2(r-p)/(2-p)E|Z|^2(r-p)/2-p,where Z has a normal distribution with mean 0 and variance σ^2. 相似文献
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