A new technique for computing the Analytic SVD is proposed. The idea is to follow a branch of just one simple singular value and the corresponding left/right singular vector. Numerical computation may collapse at non-generic points; we will consider the case when the continuation gets stuck due to a nonzero multiple singular value. We interpret such a point as a singularity of the branch. We em...

Let MIP 3(c1, c2) be the moduli space of stable rank-2 vector bundles on IP 3 with Chern classes c1, c2. We prove the following results. 1) Let 0 ≤ β < γ be two integers, (γ ≥ 2), such that 2γ− 3β > 0; then MIP 3(0, 2γ 2 − 3β) is singular (the case β = 0 was previously proved by M. Maggesi). 2) Let 0 ≤ β < γ be two odd integers (γ ≥ 5), such that 2γ − 3β + 1 > 0; then MIP 3(−1, 2(γ/2) 2 − 3(β/2...

A class of matrix valued functions defined by singular values of nonsymmetric matrices are shown to have many properties analogous to matrix valued functions defined by eigenvalues of symmetric matrices. In particular, the (smoothed) matrix valued Fischer-Burmeister function is proved to be strongly semismooth everywhere. This result is also used to show the strong semismoothness of the (smooth...

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since no...

Introducing a higher order modulus of smoothness based on qintegers, in this paper first we obtain Jackson-type estimates in approximation by Jackson-type generalizations of the q-Picard and q-Gauss-Weierstrass singular integrals and give their global smoothness preservation property with respect to the uniform norm. Then, we study approximation and geometric properties of the complex variants ...

In this paper, we show that perturbing a simple 3-d quadratic system with a center-type singular point can yield at least 10 small-amplitude limit cycles around a singular point. This result improves the 7 limit cycles obtained recently in a simple 3-d quadratic system around a Hopf singular point. Compared with Bautin’s result for quadratic planar vector fields, which can only have 3 small-amp...

In this paper, a block-based watermarking scheme based on the Singular Value Decomposition (SVD) is proposed. Our watermark, a pseudo-random Gaussian sequence, is embedded by modifying the angles formed by the right singular vectors of each block of the original image. The orthogonality property of the right singular vector matrix is preserved during the embedding process. Several experiments h...

In this paper, we prove the existence of 12 small-amplitude limit cycles around a singular point in a planar cubic-degree polynomial system. Based on two previously developed cubic systems in the literature, which have been proved to exhibit 11 small-amplitude limit cycles, we applied a different method to show 11 limit cycles. Moreover, we show that one of the systems can actually have 12 smal...