This paper concerns the moduli spaces of rank two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D) pairs and stable Higgs bundles is determined. Using Morse theory, the moduli space of parabolic Higgs bundles is shown to be a noncompact, connected, simply connected manifold, and a computation of its Poincaré polynomial ...

We address the dynamics of fundamental and higher-order dark solitons on the intense parabolic background in a planar graded-index waveguide with self-defocusing nonlinearity. It is shown that dark solitons on the parabolic background can propagate stably, and feature the properties similar to dark solitons for standard nonlinear Schrödinger equation. We present an approximate solution for dark...

The mapping class group of a d-pointed Riemann surface has a natural C∞ action on any moduli space of parabolic bundles with the marked points as the parabolic points. We prove that under some numerical conditions on the parabolic data, the induced action of the mapping class group on the cohomology algebra of the moduli space of parabolic bundles factors through the natural epimorphism of the ...

A surface in hyperbolic space H 3 invariant by a group of parabolic isometries is called a parabolic surface. In this paper we investigate parabolic surfaces of H 3 that satisfy a linear Weingarten relation of the form aκ1 + bκ2 = c or aH + bK = c, where a, b, c ∈ R and, as usual, κi are the principal curvatures, H is the mean curvature and K is de Gaussian curvature. We classify all parabolic ...

Parabolic dish solar concentrators are very expensive devices with a cost of up to a half of the total cost of a solar power station. The specific technology of parabolic mirror manufacturing makes the decrease of the cost very problematic. Even in mass production the cost of a parabolic mirror is estimated as $500 per square meter. There is another way to make a parabolic concentrator by appro...

This paper is concerned with the numerical solution of parabolic equations coupled to gradient equations. The gradient equations are ordinary diierential equations whose solutions deene positions of particles in the spatial domain of the parabolic equations. The vector eld of the gradient equations is determined by gradients of solutions to the parabolic equations. Such mixed parabolic-gradient...

‎in this paper‎, ‎we study the $l^p$ ($1

Let X be a smooth projective surface and D be a smooth divisor over an algebraically closed field k. In this paper, we discuss the moduli schemes of the ideals of points of X with parabolic structures at D. They are called parabolic Hilbert schemes. The first result is that the parabolic Hilbert schemes are smooth. And then some of the studies of Ellingsrud-Strømme, Göttsche, Cheah, Nakajima an...

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper we calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submani...