Search results for "Theorem"

On Boundary Conditions for Wedge Operators on Radial Sets

2008

We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.

The onset of convection in a two-layered porous medium with anisotropic permeability

2019

We consider convection in a horizontal porous layer of uniform thickness which is heated from below and which is composed of two anisotropic sublayers with principal axes lying in the three coordinate directions. The aim is to determine criteria for the onset of convection by finding the critical Rayleigh number, wavenumber and roll orientation relative to the coordinate axes. The full set of nondimensional parameters has at least six members even when the sublayers are considered to be thermally isotropic, and therefore, we select some special cases in order to illuminate the type of qualitative behaviour which may be expected. One such case is where the anisotropic sublayers are identical…

Magnetic field amplification and magnetically supported explosions of collapsing, non-rotating stellar cores

2014

We study the amplification of magnetic fields in the collapse and the post-bounce evolution of the core of a non-rotating star of 15 solar masses in axisymmetry. To this end, we solve the coupled equations of magnetohydrodynamics and neutrino transport in the two-moment approximation. The pre-collapse magnetic field is strongly amplified by compression in the infall. Initial fields of the order of 1010 G translate into proto-neutron star fields similar to the ones observed in pulsars, while stronger initial fields yield magnetar-like final field strengths. After core bounce, the field is advected through the hydrodynamically unstable neutrino-heating layer, where non-radial flows due to con…

When a convergence of filters is measure-theoretic

2022

Abstract Convergence almost everywhere cannot be induced by a topology, and if measure is finite, it coincides with almost uniform convergence and is finer than convergence in measure, which is induced by a metrizable topology. Measures are assumed to be finite. It is proved that convergence in measure is the Urysohn modification of convergence almost everywhere, which is pseudotopological. Extensions of these convergences from sequences to arbitrary filters are discussed, and a concept of measure-theoretic convergence is introduced. A natural extension of convergence almost everywhere is neither measure-theoretic, nor finer than a natural extension of convergence in measure. A straightforw…

On the number of singularities, zero curvature points and vertices of a simple convex space curve

1995

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

A four vertex theorem for strictly convex space curves

1993

Fixed point theory for almost convex functions

1998

Traditionally, metric fixed point theory has sought classes of spaces in which a given type of mapping (nonexpansive, assymptotically or generalized nonexpansive, uniformly Lipschitz, etc.) from a nonempty weakly compact convex set into itself always has a fixed point. In some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used. With this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings.

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

2001

Integrated Simulation and Formal Verification of a Simple Autonomous Vehicle

2018

This paper presents a proof-of-concept application of an approach to system development based on the integration of formal verification and co-simulation. A simple autonomous vehicle has the task of reaching an assigned straight path and then follow it, and it can be controlled by varying its turning speed. The correctness of the proposed control law has been formalized and verified by interactive theorem proving with the Prototype Verification System. Concurrently, the system has been co-simulated using the Prototype Verification System and the MathWorks Simulink tool: The vehicle kinematics have been simulated in Simulink, whereas the controller has been modeled in the logic language of t…

ON the NATURE of HYDROSTATIC EQUILIBRIUM in GALAXY CLUSTERS

2016

In this paper we investigate the level of hydrostatic equilibrium (HE) in the intra-cluster medium of simulated galaxy clusters, extracted from state-of-the-art cosmological hydrodynamical simulations performed with the Smoothed-Particle-Hydrodynamic code GADGET-3. These simulations include several physical processes, among which stellar and AGN feedback, and have been performed with an improved version of the code that allows for a better description of hydrodynamical instabilities and gas mixing processes. Evaluating the radial balance between the gravitational and hydrodynamical forces, via the gas accelerations generated, we effectively examine the level of HE in every object of the sam…