The complex elliptic genus was first introduced by Witten [21] and then studied by several authors such as Hirzebruch [13], Bott and Taubes [5] mainly in connection with its rigidity property. It was further generalized in two ways; one way to complex orbifolds and the other to singular projective varieties. Generalization to singular varieties was given by Borisov-Libgober [3], [4]. They calle...

This paper presents an O(n2 log n) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O(n3) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O(n2 log n) flops; second, the singular values...

The remarkable hearing capacities of mammals arise from various evolutionary innovations. These include the cochlear outer hair cells and their singular feature, somatic electromotility, i.e., the ability of their cylindrical cell body to shorten and elongate upon cell depolarization and hyperpolarization, respectively. To shed light on the processes underlying the emergence of electromotility,...

In this article, we associate a Hermitian matrix to multidigraph G. We call it the complex Laplacian of G and denote by L​C(G). It is shown that generalization graph. But, unlike graph, may not always be singular. obtain necessary sufficient condition for For G, if L​C(G) singular, say L​C-singular. generalize some properties Fiedler vectors undirected graphs eigenvectors corresponding second s...

where q = e. The values of j(z) at imaginary quadratic arguments in the upper half of the complex plane are known as singular moduli. Singular moduli are algebraic integers which play prominent roles in classical and modern number theory (see [C, BCSH]). For example, Hilbert class fields of imaginary quadratic fields are generated by singular moduli. Furthermore, isomorphism classes of elliptic...

— Multi-Input Multi-Output (MIMO) transmission has been a topic of great interest for a few years due to the huge spectral ef ciency gain it can provide over rich scattering transmission channels, such as indoor (e.g. wireless local area networks) or urban outdoor (e.g. mobile wireless communications). MIMO transmission channels are usually modelled by random matrices. In this paper, we use res...

<p style='text-indent:20px;'>This paper studies synchronization of singularity-perturbed complex networks (SPCNs) with a small singular perturbation parameter (SPP) via event-triggered impulsive control (ETIC). A novel dynamic mechanism is proposed where an auxiliary impulse introduced to regulate the triggering threshold dynamically for saving network resource. Based on SPP-dependent Lya...

In this paper, after analyzing the reasons of poor generalization and overfitting in neural networks, we consider some noise data as a singular value of a continuous function jump discontinuity point. The continuous part can be approximated with the simplest neural networks, which have good generalization performance and optimal network architecture, by traditional algorithms such as constructi...