Search results for "Regular"
showing 10 items of 855 documents
Mappings of Lp-integrable distortion: regularity of the inverse
2016
Let be an open set in ℝn and suppose that is a Sobolev homeomorphism. We study the regularity of f–1 under the Lp-integrability assumption on the distortion function Kf. First, if is the unit ball and p > n – 1, then the optimal local modulus of continuity of f–1 is attained by a radially symmetric mapping. We show that this is not the case when p ⩽ n – 1 and n ⩾ 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for ∣Df–1∣ in terms of the Lp-integrability assumptions of Kf.
Acoustic wave guides as infinite-dimensional dynamical systems
2015
We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster's model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Webster's model at the limit of vanishing waveguide intersection.
Regularity and modulus of continuity of space-filling curves
2019
We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed
Envelopes for sets and functions II: generalized polarity and conjugacy
2018
International audience; Let X,Y be two nonempty sets, Φ an extended real-valued bivariate coupling function on X × Y and Γ a subset of X × Y. The present paper provides extensions to the well-known generalized Φ-conjugacy and Γ-polarity of diverse results of our previous work [2] related to φ-conjucacy and Λ-polarity, where Λ is a subset of a vector space E and φ is a function on E defining the particular coupling function (x,y)→φ(x−y) on E × E. A particular attention is devoted to the conjugacy functions (resp. polarity sets) which are mutually generating. Finally, for a superadditive conjugacy function Φ, we obtain a full description of the class of Φ-envelopes.
The Relocation of the Canons Regular Monastery in Żagań as an Element in the Reform of Interior Life
2019
The location in which a church was based played an important role in the life of religious communities in the Middle Ages. Interactions with society and the mutual influence of a monastery on the surrounding societies could support or inhibit the development of an abbey. There were situations when monks were moved to serve in different locations. In Silesia, we have two examples of canons regular monasteries. Both the monastery of the Blessed Virgin Mary in Wrocław and the convent of Żagań were originally located in other places. As described in the monastery chronicle, the transfer of the monastery from Nowogród Bobrzański to Żagań in 1284 was an event that opened new opportunities and per…
Towarzyszenie duchowe małżonkom i osobom w sytuacjach nieregularnych w świetle adhortacji "Amoris laetitia"
2017
W artykule podjęto źródłową analizę posługi towarzyszenia duchowego małżonkom sakramentalnym i osobom w sytuacjach nieregularnych na podstawie posynodalnej adhortacji apostolskiej Amoris laetitia papieża Franciszka. Pojęcie towarzyszenia jest wiodącym terminem w kolejnych rozdziałach dokumentu. Przybliżony został zakres znaczeniowy pojęcia towarzyszenia oraz charakterystyka posługi przedstawiona przez papieża. Następnie scharakteryzowano kolejne konteksty towarzyszenia podejmowane w adhortacji. Kwestia towarzyszenia jest omówiona w odniesieniu do małżeństw i obejmuje kolejne etapy rozwoju miłości oraz sytuacje wymagające szczególnej uwagi. W kluczu troski o dzieci i integracji ze wspólnotą…
Lebesgue-type decomposition for sesquilinear forms via differences
2022
Definitions of regularity and singularity are proposed for sesquilinear forms with respect to a non-negative one and a correspondent Lebesgue-type decomposition is proved. In contrast to other Lebesgue-type decompositions established in the literature for sesquilinear forms with generic sign, the underlying idea in this paper is to write symmetric forms as the difference of non-negative sesquilinear forms.
Singular (p, q)-equations with superlinear reaction and concave boundary condition
2020
We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a (Formula presented.) -equation) with a singular and (Formula presented.) -superlinear reaction and a Robin boundary condition with (Formula presented.) -sublinear boundary term (Formula presented.). So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.
One-loop corrections to light cone wave functions: the dipole picture DIS cross section
2018
We develop methods needed to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark-antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using …
Splines in convex sets under constraints of two‐sided inequality type in a hyperplane
2008
The problem of minimization of a smoothing functional under inequality constraints is considered in a hyperplane. The conditions of the existence of a solution are obtained and some properties of this solution are investigated. It is proved that the solution is a spline. The method for its construction is suggested. First Published Online: 14 Oct 2010