The existence of a local curve corotating and counter-rotating vortex pairs was proven by Hmidi Mateu in via desingularization pair point vortices. In this paper, we construct global continuation these curves. That is, consider solutions which are more than mere perturbation trivial solution. Indeed, while the analysis relies on study linear equation at solution, requires deeper understanding t...

(Morphometric analysis of the Brasiliorchis picta complex (Orchidaceae)). One of the largest genera of Orchidaceae in the Neotropics with about 450 species, Maxillaria presents several taxonomic uncertainties about its generic circumscription and the delimitation of species groups, mainly due to the large variability of some species. The present study aims at verifying the morphological variati...

An equality between the spectral flow of a family $A$ self-adjoint Fredholm operators and index associated differential operator $\frac{d}{dt}-iA$ with Atiyah-Patodi-Singer-style boundary conditions is shown. This generalizes result by C.B\"ar A. Strohmaier used to show their Lorentzian version Atiyah-Patodi-Singer Index Theorem.

In this work we find the isomonodromic (Jimbo-Miwa) tau-function corresponding to Frobenius manifold structures on Hurwitz spaces. We discuss several applications of this result. First, we get an explicit expression for the G-function (solution of Getzler’s equation) of the Hurwitz Frobenius manifolds. Second, in terms of this tau-function we compute the genus one correction to the free energy ...

and this index is constant on continuous families of such L. Suppose that D is an elliptic operator of order m on sections of a vector bundle E± over a smooth, compact manifold M . Let H (Γ (M,E±)) denote the Sobolev s-norm completion of the space of sections Γ (M,E), with respect to a chosen metric. Then D can be extended to be a bounded linear operator Ds : H s (Γ (M,E)) → Hs−m (Γ (M,E−)) tha...

We study a wide class of free-fermion systems on a hypercubic lattice in spatial dimensions d ≥ 1. When the system is insulating, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analogue ...

A new singer identification system is presented in this thesis. The system is based on the idea of using only the vocal segments of a song to build the model of a particular singer. The most important contribution of the technique is the way these vocal segments are located. The borders between vocal and instrumental parts are first detected with the Bayesian Information Criterion(BIC), which i...

Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifoldM , with compact quotient GnM . There is an assembly map W K .M/ ! K .B/ which associates to any Gequivariant K-homology class onM , an element of the topological K-theory of a suitable Banach completion B of the convolution algebra of continuous compactly supported functions on G. The a...

Under two boundary conditions: the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary.