Search results for "Infinity"

Radó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting)

2018

A remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically onto Q . Numerous extensions of this result for linear and nonlinear elliptic PDEs are known, but only when ⌦ is a Jordan domain or, if not, under additional assumptions on the boundary map. On the other hand, the newly developed theory of Sobolev mappings between Euclidean domains and Riemannian manifolds demands to extend this theorem to the setting on simply connected domains. This is the primary goal of our article. The class of the p -harmonic equations is wide enou…

Embedding finite linear spaces in projective planes, II

1987

Abstract It is shown that a finite linear space with maximal point degree n + 1 can be embedded in a projective plane of order n, provided that the line sizes are big enough.

On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian

2012

Abstract This paper concerns the best Lipschitz extension problem for a discrete distance that counts the number of steps. We relate this absolutely minimizing Lipschitz extension with a discrete ∞-Laplacian problem, which arises as the dynamic programming formula for the value function of some e -tug-of-war games. As in the classical case, we obtain the absolutely minimizing Lipschitz extension of a datum f by taking the limit as p → ∞ in a nonlocal p -Laplacian problem.

Graphs of stable maps from closed surfaces to the projective plane

2018

Abstract We describe how to attach a weighted graph to each stable map from closed surfaces to projective plane and prove that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane.

Embedding linear spaces with two line degrees in finite projective planes

1986

In this paper we shall classify all finite linear spaces with line degrees n and n-k having at most n2+n+1 lines. As a consequence of this classification it follows: If n is large compared with k, then any such linear space can be embedded in a projective plane of order n−1 or n.

Transformations by diagonal matrices in a normed space

1962

A RADIATION CONDITION FOR UNIQUENESS IN A WAVE PROPAGATION PROBLEM FOR 2-D OPEN WAVEGUIDES

2009

We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Final…

H∞ static output-feedback control design with constrained information for offshore wind turbine system

2013

Abstract This paper deals with H ∞ static output-feedback control design with constrained information for offshore wind turbines. Constrained information indicates that a special zero–nonzero structure is imposed on the static output-feedback gain matrix. A practical use of such an approach is to design a decentralized controller for a wind turbine. This will also benefit the controller in such a way that it is more tolerant to sensor failure. Furthermore, the model under consideration is obtained by using the wind turbine simulation software FAST. Sufficient conditions to design an H ∞ controller are given in terms of Linear Matrix Inequalities ( LMI s ). Simulation results are given to il…

Planar systems with critical points: multiple solutions of two-point nonlinear boundary value problems

2005

Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. First, we consider the planar systems equivalent to equation x ″ = f ( x ) , where f ( x ) has multiple zeros and the respective system has centers and saddle points in various combinations. Estimations of the number of solutions are given. Then results are extended to nonautonomous equations which have superlinear behavior at infinity.

Finite Model Reasoning in Expressive Fragments of First-Order Logic

2017

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard translation of modal logic to first-order logic. This applies most notably to the guarded fragment, where quantifiers are appropriately relativized by atoms, and the fragment defined by restricting the number of variables to two. The aim of this talk is to review recent work concerning these fragments and their popular extensions. When presenting the material special attention is given to decision procedures for the finite satisfiability problems, as many of t…