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Abstract

A generalization of the linear least squares method to a wide class of parametric nonlinear inverse problems is presented. The approach is based on the consideration of the operator equations, with the selected function of parameters as the solution. The generalization is based on the two mandatory conditions: the operator equations are linear for the estimated parameters and the operators have discrete approximations. Not requiring use of iterations, this approach is well suited for hardware implementation and also for constructing the first approximation for the nonlinear least squares method. The examples of parametric problems, including the problem of estimation of parameters of some higher transcendental functions, are presented.

Abstract

We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over 𝐙. This gives an analogue for K3 surfaces of Deligne’s description of the category of ordinary abelian varieties over a finite field, and refines earlier work by N.O. Nygaard and J.-D. Yu. Our main result is conditional on a conjecture on potential semi-stable reduction of K3 surfaces over p-adic fields. We give unconditional versions for K3 surfaces of large Picard rank and for K3 surfaces of small degree.

Abstract

We prove the long time existence and uniqueness of solutions to the parabolic Monge–Ampère equation on compact almost Hermitian manifolds. We also show that the normalization of solution converges to a smooth function in C topology as t. Up to scaling, the limit function is a solution of the Monge–Ampère equation. This gives a parabolic proof of existence of solutions to the Monge–Ampère equation on almost Hermitian manifolds.

Abstract

In this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

Abstract

Let C be a smooth projective curve (resp. (S,L) a polarized K3 surface) of genus g11, with Clifford index at least 3, considered in its canonical embedding in g-1 (resp. in its embedding in |L|g). We prove that C (resp. S) is a linear section of an arithmetically Gorenstein normal variety Y in g+r, not a cone, with dim(Y)=r+2 and ωY=𝒪Y(-r), if the cokernel of the Gauss–Wahl map of C (resp. H1(TSL)) has dimension larger than or equal to r+1 (resp. r). This relies on previous work of Wahl and Arbarello–Bruno–Sernesi. We provide various applications.