X-ray emissions from magnetic polar regions of neutron stars

Structures of X-ray emitting magnetic polar regions on neutron stars in X-ray pulsars are studied in the accretion rate range 1017 g s−1–1018 g s−1. It is shown that a thin but tall, radiation-energy-dominated, X-ray emitting polar cone appears at each of the polar regions. The height of the polar cone is several times as large as the neutron star radius. The energy gain due to the gravity of the neutron star in the polar cone exceeds the energy loss due to photon diffusion in the azimuthal direction of the cone, and a significant amount of energy is advected to the neutron star surface. Then, the radiation energy carried with the flow should become large enough for the radiation pressure to overcome the magnetic pressure at the bottom of the cone. As a result, the matter should expand in the tangential direction along the neutron star surface, dragging the magnetic lines of force, and form a mound-like structure. The advected energy to the bottom of the cone should finally be radiated away from the surface of the polar mound and the matter should be settled on the neutron star surface there. From such configurations, we can expect an X-ray spectrum composed of a multi-color blackbody spectrum from the polar cone region and a quasi-single blackbody spectrum from the polar mound region. These spectral properties agree with observations. A combination of a fairly sharp pencil beam and a broad fan beam is expected from the polar cone region, while a broad pencil beam is expected from the polar mound region. With these X-ray beam properties, basic patterns of pulse profiles of X-ray pulsars can be explained too.

PROJECTIONS ONTO THE CONE OF OPTIMAL TRANSPORT MAPS AND COMPRESSIBLE FLUID FLOWS

The system of isentropic Euler equations in the potential flow regime can be considered formally as a second order ordinary differential equation on the Wasserstein space of probability measures. This interpretation can be used to derive a variational time discretization. We prove that the approximate solutions generated by this discretization converge to a measure-valued solution of the isentropic Euler equations. The key ingredient is a characterization of the polar cone to the cone of optimal transport maps.

Characterizations of nonsmooth generalized polarly cone-monotone maps

In this paper we consider different types of generalized cone-mono-tone maps: polarly C-monotone, strictly polarly C-monotone, strongly polarly C-monotone, polarly C-pseudomonotone, strictly polarly C-pseudomonotone and polarly C-quasimonotone maps, where C is a cone in a finite-dimensional space Rm. We characterize these maps in the case when they are radially continuous with respect to the positive polar cone C+ of the cone C, generalizing some well known results. In the obtained theorems we use first and higher-order lower Dini directional derivatives.

Geometric modelling of boundless grasps

SUMMARYThis paper describes the development of the topological and geometric approach to the analysis and synthesis of form-closed grasps of arbitrary objects. Concepts of wrench spaces and the relevant subsets of the positive cone, the affine hull, the convex huli, and the related polar cone are used, and applied to a representative example.

Iterative methods for nonlinear quasi complementarity problems

In this paper, we consider and study an iterative algorithm for finding the approximate solution of the nonlinear quasi complementarity problem of findingu ϵ k(u)such thatTu ϵ k*(u) and (u−m(u),Tu)=0wheremis a point-to-point mapping,Tis a (nonlinear) continuous mapping from a real Hilbert spaceHinto itself andk*(u)is the polar cone of the convex conek(u)inH. We also discuss the convergence criteria and several special cases, which can be obtained from our main results.

A nonlinear complementarity problem in mathematical programming in Hilbert space

In this paper we prove the following existence and uniqueness theorem for the nonlinear complementarity problem by using the Banach contraction principle. If T: K → H is strongly monotone and lipschitzian with k2 < 2c < k2+1, then there is a unique y ∈ K, such that Ty ∈ K* and (Ty, y) = 0 where H is a Hilbert space, K is a closed convex cone in H, and K* the polar cone.