The Chow ring of hyperkähler varieties of $$K3^{[2]}$$-type via Lefschetz actions

We propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of $$K3^{[2]}$$ K 3 [ 2 ] -type to the Chow ring of correspondences $$\mathrm{CH}^*(X \times X)$$ CH ∗ ( X × X ) in terms of a canonical lift of the Beauville–Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a K3 surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of X of Shen and Vial agrees with the eigenspace decomposition of a canonical lift of the cohomological grading operator.

Some existence theorems for semilinear Neumann problems with Landesman-Lazer condition revisited

In this paper, existence theorems are established for Neumann problems for semilinear elliptic equations at resonance together with Landesman-Lazer condition revisited. Our existence results follow as an application of the Saddle point Theorem together with a standard eigenspace decomposition.

Lawson homology for abelian varieties

In this paper we study the action of the Fourier–Mukai transform on the Lawson homology of abelian varieties and a Beauville-type eigenspace decomposition of Lawson homology with rational coefficients.

Background Modeling Approach Based on Eigenspace Decomposition

In this work principal component analysis (PCA) was adopted to construct a background model and moving objects were detected by background subtraction method. Firstly, constructed the matrix of training samples by means of converting the video sequence to vectors. Then calculated the covariance matrix C of the training set, and acquired the eigenvalues and eigenvectors of C through SVD decomposition. Next, sorted the eigenvalues and reconstructed the background model by using several image vectors which had higher cumulative contribution. Finally, comparison experiments are performed with the detection results by GMM approach. Experimental results show that the proposed method in this paper could establish background models more accurate and have better effective of object detection.