Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator

The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $A+B$ provided that $A, B$ are maximally monotone and $A$ is a linear relation, as soon as Rockafellar's constraint qualification holds: \dom A\cap\inte\dom B\neq\varnothing. Moreover, $A+B$ is of type (FPV).Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1010.4346, arXiv:1005.224

YBCO-buffered NdBCO film with higher thermal stability in seeding REBCO Growth

In this work, we report a strengthened superheating effect caused by a buffering YBa2Cu3Oy (Y123 or YBCO) layer in the Nd1+xBa2-xCu3O7-y (Nd123 or NdBCO) thin film with MgO substrate (i.e., NdBCO/YBCO/MgO thin film). In the cold-seeding melt-textured (MT) growth, the NdBCO/YBCO/MgO film presented an even higher superheating level, about 20 {\deg}C higher than that of non-buffered NdBCO film (i.e., NdBCO/MgO film). Using this NdBCO/YBCO/MgO film as seeds and undergoing a maximum processing temperature (Tmax) up to 1120 {\deg}C, we succeeded in growing various RE1+xBa2-xCu3O7-y (REBCO, RE=rare elements) bulk superconductors, including Gd1+xBa2-xCu3O7-y (GdBCO), Sm1+xBa2-xCu3O7-y (SmBCO) and NdBCO that have high peritectic temperatures (Tp). The pole figure (X-Ray \phi-scan) measurement reveals that the NdBCO/YBCO/MgO film has better in-plane alignment than the NdBCO/MgO film, indicating that the induced intermediate layer improves the crystallinity of the NdBCO film, which could be the main origin of the enhanced thermal stability. In short, possessing higher thermal stability and enduring a higher Tmax in the MT process, the NdBCO/YBCO/MgO film is beneficial to the growth of bulk superconductors in two aspects: (1) broad application for high-Tp REBCO materials; (2) effective suppression against heterogeneous nucleation, which is of great assistance in growing large and high-performance REBCO crystals.Comment: 9 pages, 4 figure

Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations

We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in numerical computation. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find agree with direct simulation of the model and seem to have some stability

Editorial to special issue on evolutionary computation in dynamic and uncertain environments

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