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Deep neural networks, as a powerful system to represent high dimensional complex functions, play a key role in deep learning. Convergence of deep neural networks is a fundamental issue in building the...
近日,地球物理著名期刊《Geophysical Research Letters》正式刊发了中国地质大学胡祥云教授团队研究成果 -“Downward continuation and transformation of total-field magnetic anomalies into magnetic gradient tensors between arbitrary surfaces u...
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe's constructive proof of the Riemann ma...
In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random e ects data sets. We apply bootstrap reweighting independently to the lev...
We present a smooth surface construction based on the manifold approach of Grimm and Hughes. We demonstrate how this approach can relatively easily produce a number of desirable properties which are h...
We establish existence of travelling fronts in thermo-diffusive systems of the KPP type in a shear flow with an arbitrary Lewis number and a positive heat-loss at the boundary. We then prove that the ...
We consider KPP-type systems in a cylinder with an arbitrary Lewis number (the ratio of thermal and material diffusivities) in the presence of a shear flow. We show that traveling fronts solutions exi...
We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction g 2κ +1 (ΨΨ)ˉ κ +1 and with mass m. Using the exact analytic form for rest frame solitary waves of the for...
Almost all the existing wireless data aggregation approaches;need a topology construction step before scheduling. These solutions assume the availability of flexible topology controls. However, in rea...
For a given odd prime p, we define a certain p-stabilization of the Siegel Eisenstein series of arbitrary genus so that the resulting eigenvalue of a generalized Atkin operator at p is a p-adic unit (...
In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere Sn+d under integral curvature conditions. As a consequence, we obtain several di...
We study general (not necessarily Hamiltonian) first-order symmetric systems $J y'(t)-B(t)y(t)=\D(t) f(t)$ on an interval $[a,b> $ with the regular endpoint $a$. The deficiency indices $n_\pm$ of the ...
Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized first Betti numbers o...
We consider a natural extension of the Petersson scalar product to the entire space of modular forms of integral weight $k\ge 2$ for a finite index subgroup of the modular group. We show that Hecke op...

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