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991.
A general design for the relaxed proximal point algorithm using the notion of A-maximal-relaxed accretiveness is developed, and then the convergence analysis for this algorithm in the context of solving a general class of nonlinear inclusion problems is examined along with some other results of interest involving A-maximal-relaxed accretive mappings in a real Banach space setting. 相似文献
992.
In this paper, we prove that the K?hler–Ricci flow converges to a K?hler–Einstein metric when E
1 energy is small. We also prove that E
1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.
The first named author is partially supported by a NSF grant, while the third author was partially supported by a NSF supplement
grant. 相似文献
993.
994.
Instance-optimality in probability with an -minimization decoder 总被引:1,自引:0,他引:1
Ronald DeVore Guergana Petrova Przemyslaw Wojtaszczyk 《Applied and Computational Harmonic Analysis》2009,27(3):275-288
Let Φ(ω), ωΩ, be a family of n×N random matrices whose entries i,j are independent realizations of a symmetric, real random variable η with expectation and variance . Such matrices are used in compressed sensing to encode a vector by y=Φx. The information y holds about x is extracted by using a decoder . The most prominent decoder is the ℓ1-minimization decoder Δ which gives for a given the element which has minimal ℓ1-norm among all with Φz=y. This paper is interested in properties of the random family Φ(ω) which guarantee that the vector will with high probability approximate x in to an accuracy comparable with the best k-term error of approximation in for the range kan/log2(N/n). This means that for the above range of k, for each signal , the vector satisfies with high probability on the draw of Φ. Here, Σk consists of all vectors with at most k nonzero coordinates. The first result of this type was proved by Wojtaszczyk [P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press] who showed this property when η is a normalized Gaussian random variable. We extend this property to more general random variables, including the particular case where η is the Bernoulli random variable which takes the values with equal probability. The proofs of our results use geometric mapping properties of such random matrices some of which were recently obtained in [A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491–523]. 相似文献
995.
In this paper we establish results on the existence of nontangential limits for weighted
-harmonic functions in the weighted Sobolev space
, for some q>1 and w in the Muckenhoupt A
q
class, where
is the unit ball in
. These results generalize the ones in Sect. 3 of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996, where the weight was identically equal to one. Weighted
-harmonic functions are weak solutions of the partial differential equation
where
for some fixed q∈(1,∞), where 0<α≤β<∞, and w(x) is a q-admissible weight as in Chap. 1 of Heinonen et al., Nonlinear Potential Theory, 2006.
Later, we apply these results to improve on results of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996 and Martio and Srebro, Math. Scand. 85, 49–70, 1999 on the existence of radial limits for bounded quasiregular mappings in the unit ball of
with some growth restriction on their multiplicity function.
相似文献
996.
A matricial computation of quadrature formulas for orthogonal rational functions on the unit circle, is presented in this paper. The nodes of these quadrature formulas are the zeros of the para-orthogonal rational functions with poles in the exterior of the unit circle and the weights are given by the corresponding Christoffel numbers. We show how these nodes can be obtained as the eigenvalues of the operator Möbius transformations of Hessenberg matrices and also as the eigenvalues of the operator Möbius transformations of five-diagonal matrices, recently obtained. We illustrate the preceding results with some numerical examples. 相似文献
997.
We find all the flat surfaces in the unit 3-sphere $\mathbb{S}^{3}We find all the flat surfaces in the unit 3-sphere
that pass through a given regular curve of
with a prescribed tangent plane distribution along this curve. The formula that solves this problem may be seen as a geometric
analogue of the classical D’Alembert formula that solves the Cauchy problem for the homogeneous wave equation. We also provide
several applications of this geometric D’Alembert formula, including a classification of the flat M?bius strips of
.
相似文献
998.
Daniel Guan 《Central European Journal of Mathematics》2009,7(1):84-123
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds. 相似文献
999.
The design and construction of nanostructured materials using proper self-assembling molecular building blocks is a real challenge to scientists. Here, we present the formation of a new nano-architecture, i.e., nanostaircase in the solid state by using molecular building blocks, which are amenable to self-assembly in a directed manner to form the specific nanostructure. The molecular building blocks are terephthalamides 1-4, which are bis-terephthalamides of methyl esters of various α-amino acids including l-leucine 1, d-leucine 2, l-isoleucine 3, and α-aminoisobutyric acid (Aib) 4. All terephthalamides presented here, irrespective of their different side chain residues or stereochemistry, self-assemble to form supramolecular nanostaircase structures in crystals. Each terephthalamide contains two good hydrogen-bond donors and two hydrogen-bond acceptors. Two N-H?O hydrogen bonds and C-H?π interactions are responsible for the formation and stabilization of the nanostaircase structures in crystals. The molecular building blocks are packed orthogonally to each other in crystals and this arrangement can help the formation of nanostaircase structure upon self-assembly. 相似文献
1000.