L²-data Dirichlet problem for weighted form Laplacians
We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.
Hodge type decomposition
In the space of polynomial p-forms in ℝⁿ we introduce some special inner product. Let be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that splits as the direct sum , where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.
A remark on semi-∇-flat functions
We give a pointwise characterization of semi-∇-flat functions on an affine manifold (M,∇).
∇-flat functions on manifolds
We investigate ∇-flat and pointwise-∇-flat functions on affine and Riemannian manifolds. We show that the set of all ∇-flat functions on (M,∇) is a ring which has interesting properties similar to the ring of polynomial functions.
Natural boundary value problems for weighted form laplacians
The four natural boundary problems for the weighted form Laplacians acting on polynomial differential forms in the -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.
On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces
Let be a -bounded, -closed, convex subset of a modular function space . We investigate the existence of common fixed points for semigroups of nonlinear mappings , i.e. a family such that , , where each is either -contraction or -nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
Recognition of atherosclerotic plaques and their extended dimensioning with computerized tomography angiography imaging
In this paper the authors raise the issue of automatic discrimination of atherosclerotic plaques within an artery lumen based on numerical and statistical thresholding of Computerized Tomography Angiographic (CTA) images and their advanced dimensioning as a support for preoperative vessel assessment. For the study, a set of tomograms of the aorta, as well as the ilio-femoral and femoral arteries were examined. In each case a sequence of about 130-480 images of the artery cutoff planes were analyzed...
Sigma order continuity and best approximation in -spaces
In this paper we give a characterization of -order continuity of modular function spaces in terms of the existence of best approximants by elements of order closed sublattices of . We consider separately the case of Musielak–Orlicz spaces generated by non--finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.
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