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1
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On weak-strong uniqueness property for full compressible magnetohydrodynamics flows

100%
Yan W.
Open Mathematics
|
2013
|
tom 11
|
nr 11
2005-2019
EN
This paper is devoted to the study of the weak-strong uniqueness property for full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and an additional equation which describes the evolution of the magnetic field. Using the relative entropy inequality, we prove that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists.
2
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Enumeration of spanning trees in the sequence of Dürer graphs

100%
Li S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1591-1598
EN
In this paper, we calculate the number of spanning trees in the sequence of Dürer graphs with a special feature that it has two alternate states. Using the electrically equivalent transformations, we obtain the weights of corresponding equivalent graphs and further derive relationships for spanning trees between the Dürer graphs and transformed graphs. By algebraic calculations, we obtain a closed-form formula for the number of spanning trees with regard to iteration step. Finally we compare the entropy of our graph with other studied graphs and see that its value of entropy lies in the interval of those of graphs with average degree being 3 and 4.
3
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A rough curvature-dimension condition for metric measure spaces

88%
Bonciocat A.-I.
Open Mathematics
|
2014
|
tom 12
|
nr 2
362-380
EN
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.
4
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A quantitative approach to weighted Carleson condition

75%
Rivera-Ríos I. P.
Concrete Operators
|
2017
|
tom 4
|
nr 1
58-75
EN
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea [30, 31] for the operator [...] are obtained. As a consequence, some sufficient conditions for the boundedness of Min the two weight setting in the spirit of the results obtained by C. Pérez and E. Rela [26] and very recently by M. Lacey and S. Spencer [17] for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained.
5
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Weighted entropies

75%
Ebanks B.
Open Mathematics
|
2010
|
tom 8
|
nr 3
602-615
EN
We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.
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