Recently a kind of matrix-based discriminant feature extraction approach called 2DLDA have been drawn much attention by researchers. 2DLDA can avoid the singularity problem and has low computational costs and has been experimentally reported that 2DLDA outperforms traditional LDA. In this paper, we compare 2DLDA with LDA in view of the discriminant power and find that 2DLDA as a kind of special...

Abstract. The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner singularity issue for nonlinear evolution equations in 1D, and propose two remedy procedures that effectively recover much of the accuracy of the numerical...

In this paper, we study the dependence of the unique positive solution of the periodic boundary value problem u00 þ qu 1⁄4 wðtÞu; 0 < s < 1 and q – 0; uð0Þ 1⁄4 uð1Þ; u0ð0Þ 1⁄4 u0ð1Þ on the parameter q as q ? 0. We show that this solution u(t;q) is infinitely differentiable in q and has singularity in the order of q a with a = 2/(1 s) as q ? 0. Furthermore, the graph of u(t;q) has fluctuation in...

A class of integral equations Rh = f basic in estimation theory is introduced. The description of the range of the operator R is given. The operator R is a positive rational function of a selfadjoint elliptic operator L. This operator is defined in the whole space R, it has a kernel R(x, y), and Rh := R D R(x, y)h(y)dy, where D ⊂ R is a bounded domain with a sufficiently smooth boundary S. Exam...

Accurate detection of heavy metal-induced stress on the growth of crops is essential for agricultural ecological environment and food security. This study focuses on exploring singularity parameters as indicators for a crop’s Zn stress level assessment by applying wavelet analysis to the hyperspectral reflectance. The field in which the experiment was conducted is located in the Changchun City,...

This paper reviews the efforts to construct (or prove the impossibility of) singular solutions of the Euler equations for three dimensional incompressible flow. A semi-analytic approach to this problem is formulated based on numerical computation of complex traveling wave solutions, followed by perturbation construction of a real solution, for axisymmetric flow with swirl. The perturbation anal...

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this ...

In the present paper we are concerned with boundary-value problems (BVP) for the generalized Emden–Fowler equations. Asymptotic expansions of the solution are obtained near the endpoints. We use a finite-difference scheme to approximate the solution and the convergence is accelerated by means of extrapolation methods. A variable substitution is introduced to diminish the effect of the singulari...

Starting from the dipole representation of small-x evolution we implement the running of the coupling in a self-consistent way. This results in an evolution equation for the dipole density in Borel (b) space. We show that the Borel image of the dipole density is analytic in the neighbourhood of b = 0 and that it is equal to the BFKL solution at b = 0. We study the Borel singularity structure of...