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In this paper, the sufficient condition in terms of the RIC and ROC for the stable and robust recovery of signals in both noiseless and noisy settings was established via weighted minimization when there is partial prior information on support of signals. An improved performance guarantee has been derived. We can obtain a less restricted sufficient condition for signal reconstruction and a tighter recovery error bound under some conditions via weighted minimization. When prior support estimate is at least 50% accurate, the sufficient condition is weaker than the analogous condition by standard minimization method, meanwhile the reconstruction error upper bound is provably to be smaller under additional conditions. Furthermore, the sufficient condition is also proved sharp. 相似文献
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《Operations Research Letters》2022,50(5):541-547
We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the -norm of q. 相似文献
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《Journal of Functional Analysis》2023,284(1):109732
We prove the existence of global minimizers to the double minimization problem where denotes the perimeter of the set E, is the p-Wasserstein distance between Borel probability measures, and is arbitrary. The result holds in all space dimensions, for all , and for all positive λ. This answers a question of Buttazzo, Carlier, and Laborde. 相似文献
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General dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the dual Minkowski problem, which concerns the characterization of dual curvature measures. In this paper, we solve the existence part of the dual Minkowski problem for and , and we also discuss the regularity of the solution. 相似文献
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Bo-Qing Dong Wenjuan Wang Jiahong Wu Zhuan Ye Hui Zhang 《Journal of Differential Equations》2019,266(10):6346-6382
This paper establishes the global existence and regularity of solutions to a two-dimensional (2D) tropical climate model (TCM) with fractional dissipation. The inviscid counterpart of this model was derived by Frierson, Majda and Pauluis [8] as a model for tropical geophysical flows. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the temperature θ. The systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances. Mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization. The aim here is the global regularity with the least dissipation. We prove two main results: first, the global regularity of the system with and for and ; and second, the global regularity of the system with for . The proofs of these results are not trivial and the requirements on the fractional indices appear to be optimal. The key tools employed here include the maximal regularity for general fractional heat operators, the Littlewood–Paley decomposition and Besov space techniques, lower bounds involving fractional Laplacian and simultaneous estimates of several coupled quantities. 相似文献
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Define a -star to be the complete bipartite graph . In a 2014 article, Hoffman and Roberts prove that a partial -star decomposition of can be embedded in a -star decomposition of where is at most if is odd and if is even. In our work, we offer a straightforward construction for embedding partial -star designs and lower these bounds to and , respectively. 相似文献
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A path decomposition of a graph is a collection of edge-disjoint paths of that covers the edge set of . Gallai (1968) conjectured that every connected graph on vertices admits a path decomposition of cardinality at most . Gallai’s Conjecture has been verified for many classes of graphs. In particular, Lovász (1968) verified this conjecture for graphs with at most one vertex with even degree, and Pyber (1996) verified it for graphs in which every cycle contains a vertex with odd degree. Recently, Bonamy and Perrett (2016) verified Gallai’s Conjecture for graphs with maximum degree at most 5, and Botler et al. (2017) verified it for graphs with treewidth at most 3. In this paper, we verify Gallai’s Conjecture for triangle-free planar graphs. 相似文献
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A decomposition of a multigraph is a partition of its edges into subgraphs . It is called an -factorization if every is -regular and spanning. If is a subgraph of , a decomposition of is said to be enclosed in a decomposition of if, for every , is a subgraph of .Feghali and Johnson gave necessary and sufficient conditions for a given decomposition of to be enclosed in some 2-edge-connected -factorization of for some range of values for the parameters , , , , : , and either , or and and , or and . We generalize their result to every and . We also give some sufficient conditions for enclosing a given decomposition of in some 2-edge-connected -factorization of for every and , where is a constant that depends only on , and . 相似文献
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Assis Azevedo Davide Azevedo Mário Bessa Maria Joana Torres 《Journal of Functional Analysis》2019,276(10):3261-3274
In this paper we prove a weak version of Lusin's theorem for the space of Sobolev- volume preserving homeomorphisms on closed and connected n-dimensional manifolds, , for . We also prove that if this result is not true. More precisely, we obtain the density of Sobolev- homeomorphisms in the space of volume preserving automorphisms, for the weak topology. Furthermore, the regularization of an automorphism in a uniform ball centered at the identity can be done in a Sobolev- ball with the same radius centered at the identity. 相似文献
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A derangement of a set is a fixed-point-free permutation of . Derangement action digraphs are closely related to group action digraphs introduced by Annexstein, Baumslag and Rosenberg in 1990. For a non-empty set and a non-empty subset of derangements of , the derangement action digraph has vertex set , and an arc from to if and only if is the image of under the action of some element of , so by definition it is a simple digraph. In common with Cayley graphs and Cayley digraphs, derangement action digraphs may be useful to model networks since the same routing and communication schemes can be implemented at each vertex. We prove that the family of derangement action digraphs contains all Cayley digraphs, all finite vertex-transitive simple graphs, and all finite regular simple graphs of even valency. We determine necessary and sufficient conditions on under which may be viewed as a simple undirected graph of valency . We investigate structural and symmetry properties of these digraphs and graphs, pose several open problems, and give many examples. 相似文献
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Gallai’s path decomposition conjecture states that the edges of any connected graph on vertices can be decomposed into at most paths. We confirm that conjecture for all graphs with maximum degree at most five. 相似文献
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Stefano Scrobogna 《Journal of Differential Equations》2019,266(5):2718-2761
We study a class of 2D solutions of a Bloch–Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are globally defined if the initial data is in . 相似文献
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《Journal of Functional Analysis》2023,284(9):109877
We prove an atomic type decomposition for the noncommutative martingale Hardy space for all by an explicit constructive method using algebraic atoms as building blocks. Using this elementary construction, we obtain a weak form of the atomic decomposition of for all , and provide a constructive proof of the atomic decomposition for which resolves a main problem on the subject left open for the last twelve years. We also study -atoms, and show that every -atom can be decomposed into a sum of -atoms; consequently, for every , the -atoms lead to the same atomic space for all . As applications, we obtain a characterization of the dual space of the noncommutative martingale Hardy space () as a noncommutative Lipschitz space via the weak form of the atomic decomposition. Our constructive method can also be applied to prove some sharp martingale inequalities. 相似文献