Search results for " Mathematica"
showing 10 items of 689 documents
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
2019
AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz
2003
Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove that there exists a simple arc gamma joining one of the boundary component of the annulus to the other one, such that gamma is disjoint from its n first iterates under h. As a corollary, we obtain that the rigid rotation of angle alpha can be approximated by homeomorphisms conjugate to h. The first result stated above is an analog of a theorem of J. Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimension…
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
The perturbation classes problem for closed operators
2017
We compare the perturbation classes for closed semi-Fredholm and Fredholm operators with dense domain acting between Banach spaces with the corresponding perturbation classes for bounded semi-Fredholm and Fredholm operators. We show that they coincide in some cases, but they are different in general. We describe several relevant examples and point out some open problems.
Biorthogonal vectors, sesquilinear forms, and some physical operators
2018
Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized Riesz systems, enjoying certain properties. In particular we discuss what happens when they forms two $\D$-quasi bases.
Bounded compositions on scaling invariant Besov spaces
2012
For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $��: \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ ��$ is bounded on the homogeneous, scaling invariant Besov space $\dot{B}^s_{n/s,q}(\real^n)$, where the emphasis is on the case $q\not=n/s$, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces $\dot{F}^s_{n/s,q}(\real^n)$ with $0 < s < 1$ and $0 < q \leq \infty$.
SPECTRAL INVARIANCE FOR CERTAIN ALGEBRAS OF PSEUDODIFFERENTIAL OPERATORS
2001
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of non-compact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using two-sided semi-ideals, one using commutators, and one based on Schwartz spaces on the groupoid.
Stochastic model for electrical loads in Mediterranean residential building: validation and applications
2014
A major issue in modelling the electrical load of residential building is reproducing the variability between dwellings due to the stochastic use of different electrical equipment. In that sense and with the objective to reproduce this variability, a stochastic model to obtain load profiles of household electricity is developed. The model is based on a probabilistic approach and is developed using data from the Mediterranean region of Spain. A detailed validation of the model has been done, analysing and comparing the results with Spanish and European data. The results of the validation show that the model is able to reproduce the most important features of the residential electrical consum…
Is the Ghosh model interesting?
2009
International audience; The overall value of the Ghosh model is appraised. Its treatment of quantities and prices is scrutinized by examining the variant with data in quantities and prices, and the variant with data in value and price indexes. The methodology involves returning to the accounting equations and shows that: (i) the Ghosh model offers solutions of limited interest, being incapable of providing prices or price indexes separately from quantities; (ii) what is taken to be the equation of Ghosh's value model is actually that of Ghosh's physical model; (iii) the Ghosh model may serve for cost-push exercises, but the dual of the Leontief model performs the same task in a much simpler…
Character correspondences in blocks with normal defect groups
2014
Abstract In this paper we give an extension of the Glauberman correspondence to certain characters of blocks with normal defect groups.