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71.
72.
Marco Grandis 《Applied Categorical Structures》1997,5(1):75-97
We study here a notion of simplicial satellites, as a first step towards a characterisation of simplicial derived functors, a problem unsolved since the latter were introduced.The problem comes from the fact that, in contrast with the abelian case, simplicial derived functors do not produce by themselves an exact sequence. Our solution consists in extending them to commutative k-cubes, for all k, forming thus an exact system of functors universal within the connected ones; or, in other words, a system of simplicial satellites. The tool we develop here for this extension is the homotopy kernel of a commutative k-dimensional cubic diagram, generalising the homotopy kernel of a map; its 2-dimensional version has already been proved essential in other homotopical topics. 相似文献
73.
Learning function relations or understanding structures of data lying in manifolds embedded in huge dimensional Euclidean
spaces is an important topic in learning theory. In this paper we study the approximation and learning by Gaussians of functions
defined on a d-dimensional connected compact C
∞ Riemannian submanifold of which is isometrically embedded. We show that the convolution with the Gaussian kernel with variance σ provides the uniform approximation order of O(σ
s
) when the approximated function is Lipschitz s ∈(0, 1]. The uniform normal neighborhoods of a compact Riemannian manifold play a central role in deriving the approximation
order. This approximation result is used to investigate the regression learning algorithm generated by the multi-kernel least
square regularization scheme associated with Gaussian kernels with flexible variances. When the regression function is Lipschitz
s, our learning rate is (log2
m)/m)
s/(8 s + 4 d) where m is the sample size. When the manifold dimension d is smaller than the dimension n of the underlying Euclidean space, this rate is much faster compared with those in the literature. By comparing approximation
orders, we also show the essential difference between approximation schemes with flexible variances and those with a single
variance.
Supported partially by the Research Grants Council of Hong Kong [Project No. CityU 103405], City University of Hong Kong [Project
No. 7001983], National Science Fund for Distinguished Young Scholars of China [Project No. 10529101], and National Basic Research
Program of China [Project No. 973-2006CB303102]. 相似文献
74.
Xiaomei Wu 《分析论及其应用》2008,24(2):139-148
Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi>0,m∑I=1βi=β,0<β<1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn). 相似文献
75.
For any , a truncated symmetric α-stable process is a symmetric Lévy process in with a Lévy density given by for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality
for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions
which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for
which the boundary Harnack principle fails.
The research of Panki Kim is supported by Research Settlement Fund for the new faculty of Seoul National University. The research
of Renming Song is supported in part by a joint US-Croatia grant INT 0302167. 相似文献
76.
Nicolas Th. Varopoulos 《Milan Journal of Mathematics》2007,75(1):1-60
In this paper I consider a class of non-standard singular integrals motivated by potential theoretic and probabilistic considerations.
The probabilistic applications, which are by far the most interesting part of this circle of ideas, are only outlined in Section
1.5: They give the best approximation of the solution of the classical Dirichlet problem in a Lipschitz domain by the corresponding solution by finite differences.
The potential theoretic estimate needed for this gives rise to a natural duality between the L
p
functions on the boundary ∂Ω and a class of functions A on Ω that was first considered by Dahlberg. The actual duality is given by ∫Ω
S f(x)A(x)dx = (f, A) where S f(x) = ∫∂Ω |x − y|1−n
f(y)dy is the Newtonian potential.
We can identify the upper half Lipschitz space with in the obvious way and express for an appropriate kernel K. It is the boundedness properties of the above (for , ) that is the essential part of this work. This relates with more classical (but still “rough”) singular integrals that have
been considered by Christ and Journé.
Lecture held in the Seminario Matematico e Fisico on March 14, 2005
Received: April 2007 相似文献
77.
Zhixiang Chen 《分析论及其应用》2007,23(4):325-333
The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given. 相似文献
78.
The purpose of this paper is to study certain variational principles and Sobolev-type estimates for the approximation order
resulting from using strictly positive definite kernels to do generalized Hermite interpolation on a closed (i.e., no boundary),
compact, connected, orientable, m -dimensional C
∞
Riemannian manifold , with C
∞
metric g
ij
. The rate of approximation can be more fully analyzed with rates of approximation given in terms of Sobolev norms. Estimates
on the rate of convergence for generalized Hermite and other distributional interpolants can be obtained in certain circumstances
and, finally, the constants appearing in the approximation order inequalities are explicit. Our focus in this paper will be
on approximation rates in the cases of the circle, other tori, and the 2 -sphere.
April 10, 1996. Dates revised: March 26, 1997; August 26, 1997. Date accepted: September 12, 1997. Communicated by Ronald
A. DeVore. 相似文献
79.
A study of the spatial and temporal evolution of auto-ignition kernels using time-resolved tomographic OH-LIF 总被引:1,自引:0,他引:1
Jhon Pareja Ayane Johchi Tao Li Andreas Dreizler Benjamin Böhm 《Proceedings of the Combustion Institute》2019,37(2):1321-1328
In this paper, the spatial and temporal evolution of auto-ignition kernels from methane jets propagating into a NOx-vitiated, high-turbulence, hot air co-flow was studied by means of time-resolved tomographic laser-induced fluorescence of OH (Tomo OH-LIF). Measurements were performed using a burst dye laser system at 10 kHz for volumetric laser illumination and a multi-camera arrangement (8-views) for detection of the fluorescence signal. Auto-ignition kernels were detected three-dimensionally and tracked using a robust algorithm based on the intensity gradient of the volumetrically reconstructed signals. The size and location of the detected kernels were evaluated for operating conditions with different Reynolds numbers of the fuel jet. Results showed that auto-ignition randomly occurred with high probability in a well defined fairly axisymmetric radial region with strong fluctuations in the main direction of the flow. The increase of the Reynolds number of the fuel jet resulted in a radial spread of the location of auto-ignition events. The statistical evaluation of the orientation and growth of auto-ignition kernels with respect to the mean flow field showed that the kernels were oriented tangentially to the flow and temporally evolve towards this preferential direction as the ignition events progressed. 相似文献
80.
Donggao Deng Zhongshan University China Yanchang Han South China Normal University China 《分析论及其应用》2005,21(3):280-293
Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co > 0 such that for all x ∈ supp(μ) and r > 0,μ(B(x,r)) ≤ Corn, where 0 < n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7]. 相似文献