In this paper, we consider the learning rates of multi-kernel linear programming classifiers. Our analysis shows that the convergence behavior of multi-kernel linear programming classifiers is almost the same as that of multi-kernel quadratic programming. This is implemented by setting a stepping stone between the linear programming and the quadratic programming. An upper bound is presented for general probability distributions and distribution satisfying some Tsybakov noise condition.
In this paper, we obtain the uniqueness and existence of viscosity solutions with prescribed asymptotic behavior at infinity to Hessian equations in exterior domains.
We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When
The definition for weakly (
It is shown that the conforming
Let
We give the necessary and sufficient conditions for a general crossed product algebra equipped with the usual tensor product coalgebra structure to be a Hopf algebra. Furthermore, we obtain the necessary and sufficient conditions for the general crossed product Hopf algebra to be a braided Hopf algebra which generalizes some known results.
The purpose of this article is to derive an integral inequality of Ricci curvature with respect to Reeb field in a Finsler space and give a new geometric characterization of Finsler metrics with constant flag curvature 1.
In this paper, the collision local times for two independent fractional Brownian motions are considered as generalized white noise functionals. Moreover, the collision local times exist in
It was conjectured by A. Bouchet that every bidirected graph which admits a nowhere-zero
This paper is concerned with the quasineutral limit of the bipolar quantum hydrodynamic model for semiconductors. It is rigorously proved that the strong solutions of the bipolar quantum hydrodynamic model converge to the strong solution of the so-called quantum hydrodynamic equations as the Debye length goes to zero. Moreover, we obtain the convergence of the strong solutions of bipolar quantum hydrodynamic model to the strong solution of the compressible Euler equations with damping if both the Debye length and the Planck constant go to zero simultaneously.
The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. Some properties concerning the singular values of a real rectangular tensor were discussed by K. C. Chang et al. [J. Math. Anal. Appl., 2010, 370: 284-294]. In this paper, we give some new results on the Perron-Frobenius Theorem for nonnegative rectangular tensors. We show that the weak Perron-Frobenius keeps valid and the largest singular value is really geometrically simple under some conditions. In addition, we establish the convergence of an algorithm proposed by K. C. Chang et al. for finding the largest singular value of nonnegative primitive rectangular tensors.