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1.
We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labelled by an arbitrary finite-dimensional representation. As a special case, we obtain a categorification of the coloured Jones polynomial of links.  相似文献   
2.
The Gelfand-Levitan-Marchenko representation is used to analyze the initialboundary value problem of two-component nonlinear Schr¨odinger equation on the half-line.It has shown that the global relation can be effectively analyzed by the Gelfand-LevitanMarchenko representation. we also derive expressions for the Dirichlet-to-Neumann map to characterize the unknown boundary values.  相似文献   
3.
In this paper we introduce a modal theory iHσ which is sound and complete for arithmetical Σ1-interpretations in HA, in other words, we will show that iHσ is the Σ1-provability logic of HA. Moreover we will show that iHσ is decidable. As a by-product of these results, we show that HA+ has de Jongh property.  相似文献   
4.
We derive trace formulas for a pair of self-adjoint operators H+V and H under the assumption that (H?i)?1V is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10].  相似文献   
5.
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in Rd and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.  相似文献   
6.
系统研究了Cu分别替代Fe和Ni对Ni_(55)Fe_(18)Ga_(27)结构和磁性的影响.结果表明:熔炼Ni_(55)Fe_(18-x)Cu_xGa_(27 )(x=1, 2, 3, 4)虽仍为奥氏体相结构,但伴有γ相出现;居里温度随Cu含量增加而降低,这是由于Cu掺杂引起过渡金属近邻原子间相互交换作用减弱所致;交流磁化率随Cu含量增加而降低,原因在于Fe是磁性的主要贡献者,Cu替代Fe会削弱Fe的磁矩,从而导致合金磁性降低.熔炼、退火和甩带Ni_(51)Cu_4Fe_(18)Ga_(27)均存在马氏体相变.熔炼样品马氏体相变温度最高,退火和甩带样品基本相同.这一特点表明热处理方式能够改变原子排列的有序度,因此可以通过改变热处理方式来调控马氏体相变温度.  相似文献   
7.
For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an oscillatory behaviour when they are close to the trivial (constant) one. The existence of such branches is derived using local and global bifurcation methods, that rely on the analysis of eigenfunction expansions of solutions to the associated linearized problem. Numerical analysis is performed on two different models to observe the oscillatory behaviour of solutions predicted by bifurcation theory, and to study further properties of branches far away from bifurcation points.  相似文献   
8.
Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, 2κ=κ+3=λ+, and the tree property holds at κ++=λ. Next we generalize this result to an arbitrary cardinal μ such that κ<cf(μ) and λ+μ. This result provides more information about possible relationships between the tree property and the continuum function.  相似文献   
9.
Let G=(V,E) be a locally finite connected weighted graph, and Δ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut=Δu + f(u) on G. The blow-up phenomenons for ut=Δu + f(u) are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.  相似文献   
10.
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