Search results for "Distortion"
showing 10 items of 309 documents
An example concerning the zero set of the Jacobian
2006
AbstractLet f∈W1,1(Ω,Rn) be a homeomorphism of finite distortion K. It is known that if K1/(n−1)∈L1(Ω), then the Jacobian Jf of f is positive almost everywhere in Ω. We will show that this integrability assumption on K is sharp in any Orlicz-scale: if α is increasing function (satisfying minor technical assumptions) such that limt→∞α(t)=∞, then there exists f such that K1/(n−1)/α(K)∈L1(Ω) and Jf vanishes in a set of positive measure.
Proper 1-ball contractive retractions in Banach spaces of measurable functions
2005
In this paper we consider the Wosko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k > 1 for which there exists a k-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct. 1. Introduction Let X be an infinite-dimensional Banach space with unit closed ball B(X) and unit sphere S(X). It is well known that, in this setting, there is a retraction of B(X) onto S(X), that is, a continuous mapping R : B(X) ! S(X) with Rx = x for all x 2 S(X). In (4) Benyamini and Sternf…
Tilted phases of fatty acid monolayers
1995
X‐ray diffraction data from water‐supported monolayers of fatty acids with chain lengths from 19 to 22 is presented. The structures of the tilted mesophases L2’, L2, and Ov are characterized in detail. The contributions to the unit cell distortion from the tilt and the ordering of the backbone planes of the molecules are separated. It is shown that at the swiveling transition L2’–L2, not only the tilt azimuth but also the packing of the backbone planes change discontinuously. We demonstrate that the tilting transition LS–L2 is accompanied by the ordering of the backbone planes and may be discontinuous. Evidence is presented for a herringbone ordering transition within the L2 region. The dis…
Mappings of finite distortion: Removable singularities for locally homeomorphic mappings
2004
Let f be a locally homeomorphic mapping of finite distortion in dimension larger than two. We show that when the distortion of f satisfies a certain subexponential integrability condition, small sets are removable. The smallness is measured by a weighted modulus.
Sharpness of Rickman’s Picard theorem in all dimensions
2015
We show that given \({n \geqslant 3}\), \({q \geqslant 1}\), and a finite set \({\{y_1, \ldots, y_q \}}\) in \({\mathbb{R}^n}\) there exists a quasiregular mapping \({\mathbb{R}^n\to \mathbb{R}^n}\) omitting exactly points \({y_1, \ldots, y_q}\).
Mappings of finite distortion: Removable singularities
2003
We show that certain small sets are removable for bounded mappings of finite distortion for which the distortion function satisfies a suitable subexponential integrability condition. We also give an example demonstrating the sharpness of this condition.
Mappings of finite distortion: The Rickman-Picard theorem for mappings of finite lower order
2004
We show that an entire mappingf of finite distortion with finite lower order can omit at most finitely many points when the distortion function off is suitably controlled. The proof uses the recently established modulus inequalities for mappings of finite distortion [15] and comparison inequalities for the averages of the counting function. A similar technique also gives growth estimates for mappings having asymptotic values.
Mappings of finite distortion and asymmetry of domains
2013
We establish an anisotropic Bonnesen inequality for images of balls under homeomorphisms with exponentially integrable distortion. Mathematics Subject Classification (2000): 30C65, 46E35.
Deeply bound pionic states with the (? ?,?) reaction
1992
We study the reactionΣ− +A→Λ + (Aπ−) with the π− bound in the nucleus, as a means of producing deeply bound pionic states in nuclei, so far unobserved. The reaction is similar to the (n, p) reaction but, because of theΣ−, Λ mass difference, it allows the reaction to occur with smaller momentum transfer, thus increasing the transition probability and reducing the effects of distortion. The ratios of signal to background are one to two orders of magnitude better than in the (n, p) reaction.
MAPPINGS OF FINITE DISTORTION: $L^n \log^{\alpha} L$ -INTEGRABILITY
2003
Recently, systematic studies of mappings of finite distortion have emerged as a key area in geometric function theory. The connection with deformations of elastic bodies and regularity of energy minimizers in the theory of nonlinear elasticity is perhaps a primary motivation for such studies, but there are many other applications as well, particularly in holomorphic dynamics and also in the study of first order degenerate elliptic systems, for instance the Beltrami systems we consider here.