Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Some perturbation results through localized SVEP
2016
Some classical perturbation results on Fredholm theory are proved and extended by using the stability of the localized single-valued extension property under Riesz commuting perturbations. In the last part, we give some results concerning the stability of property (gR) and property (gb.
Lipschitz-type conditions on homogeneous Banach spaces of analytic functions
2017
Abstract In this paper we deal with Banach spaces of analytic functions X defined on the unit disk satisfying that R t f ∈ X for any t > 0 and f ∈ X , where R t f ( z ) = f ( e i t z ) . We study the space of functions in X such that ‖ P r ( D f ) ‖ X = O ( ω ( 1 − r ) 1 − r ) , r → 1 − where D f ( z ) = ∑ n = 0 ∞ ( n + 1 ) a n z n and ω is a continuous and non-decreasing weight satisfying certain mild assumptions. The space under consideration is shown to coincide with the subspace of functions in X satisfying any of the following conditions: (a) ‖ R t f − f ‖ X = O ( ω ( t ) ) , (b) ‖ P r f − f ‖ X = O ( ω ( 1 − r ) ) , (c) ‖ Δ n f ‖ X = O ( ω ( 2 − n ) ) , or (d) ‖ f − s n f ‖ X = O ( ω …
Closure properties for integral problems driven by regulated functions via convergence results
2018
Abstract In this paper we give necessary and sufficient conditions for the convergence of Kurzweil–Stieltjes integrals with respect to regulated functions, using the notion of asymptotical equiintegrability. One thus generalizes several well-known convergence theorems. As applications, we provide existence and closure results for integral problems driven by regulated functions, both in single- and set-valued cases. In the particular setting of bounded variation functions driving the equations, we get features of the solution set of measure integrals problems.
Wulff shape characterizations in overdetermined anisotropic elliptic problems
2017
We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.
Binary Hamming codes and Boolean designs
2021
AbstractIn this paper we consider a finite-dimensional vector space $${\mathcal {P}}$$ P over the Galois field $${\text {GF}}(2),$$ GF ( 2 ) , and the family $${\mathcal {B}}_k$$ B k (respectively, $${\mathcal {B}}_k^*$$ B k ∗ ) of all the k-sets of elements of $$\mathcal {P}$$ P (respectively, of $${\mathcal {P}}^*= {\mathcal {P}} \setminus \{0\}$$ P ∗ = P \ { 0 } ) summing up to zero. We compute the parameters of the 3-design $$({\mathcal {P}},{\mathcal {B}}_k)$$ ( P , B k ) for any (necessarily even) k, and of the 2-design $$({\mathcal {P}}^{*},{\mathcal {B}}_k^{*})$$ ( P ∗ , B k ∗ ) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we…
Energy dissipative solutions to the Kobayashi-Warren-Carter system
2017
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\Gamma$-convergence results concerning weighted total variations and the corresponding time-dependent cases. Finally, the regularity obtained for the solutions togethe…
Linear and cyclic radio k-labelings of trees
2007
International audience; Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that |f(x)−f(y)| ≥ k+1−dG(x,y), for any two distinct vertices x and y, where dG(x,y) is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling. The linear (cyclic, respectively) radio k-labeling number of G is the minimum span of a linear (cyclic, respectively) radio k-labeling of G. In this p…
Regular 1-harmonic flow
2017
We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to Lipschitz initial data. We prove uniqueness and, in the case of a convex domain, local existence of solutions to the flow equations. If the target manifold has non-positive sectional curvature or in the case that the datum is small, solutions are shown to exist globally and to become constant in finite time. We also consider the case where the domain is a compact Riemannian manifold without boundary, solving the homotopy problem for 1-harmonic maps under some …
Almost Planar Homoclinic Loops in R3
1996
AbstractIn this paper we study homoclinic loops of vector fields in 3-dimensional space when the two principal eigenvalues are real of opposite sign, which we call almost planar. We are interested to have a theory for higher codimension bifurcations. Almost planar homoclinic loop bifurcations generically occur in two versions “non-twisted” and “twisted” loops. We consider high codimension homoclinic loop bifurcations under generic conditions. The generic condition forces the existence of a 2-dimensional topological invariant ring (non necessarily unique), which is a topological cylinder in the “non-twisted” case and a topological Möbius band in the “twisted” case. If the third eigenvalue is…
Local regularity for quasi-linear parabolic equations in non-divergence form
2018
Abstract We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p -Laplacian type and in non-divergence form. We provide local Holder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Holder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.