Search results for "Mathematical proof"
showing 10 items of 61 documents
Conformal equivalence of visual metrics in pseudoconvex domains
2017
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between pseudoconvex domains. The proofs are inspired by Mostow's proof of his rigidity theorem and are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the Bonk-Schramm hyperbolic fillings.
Multiplicity results for Sturm-Liouville boundary value problems
2009
Multiplicity results for Sturm-Liouville boundary value problems are obtained. Proofs are based on variational methods.
Waveguides. Radiation Principle. Scattering Matrices
2021
Chapter 2 exposes a mathematical model of a waveguide with several cylindrical ends going to infinity, basic notions and mathematical results (with complete proofs) needed in successive chapters: waves, continuous spectrum eigenfunctions, intrinsic radiation principle, and scattering matrices.
On Using the Theory of Regular Functions to Prove the ε-Optimality of the Continuous Pursuit Learning Automaton
2013
Published version of a chapter in the book: Recent Trends in Applied Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-38577-3_27 There are various families of Learning Automata (LA) such as Fixed Structure, Variable Structure, Discretized etc. Informally, if the environment is stationary, their ε-optimality is defined as their ability to converge to the optimal action with an arbitrarily large probability, if the learning parameter is sufficiently small/large. Of these LA families, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. The…
Quantum Security Proofs Using Semi-classical Oracles
2019
We present an improved version of the one-way to hiding (O2H) Theorem by Unruh, J ACM 2015. Our new O2H Theorem gives higher flexibility (arbitrary joint distributions of oracles and inputs, multiple reprogrammed points) as well as tighter bounds (removing square-root factors, taking parallelism into account). The improved O2H Theorem makes use of a new variant of quantum oracles, semi-classical oracles, where queries are partially measured. The new O2H Theorem allows us to get better security bounds in several public-key encryption schemes.
On a question of C. Bonnafé on characters and multiplicity free constituents
2019
Abstract In 2006, C. Bonnafe posed a general question on characters of finite groups. A positive answer would have reduced drastically some proofs by G. Lusztig.
Strong Converse Results for Linking Operators and Convex Functions
2020
We consider a family B n , ρ c of operators which is a link between classical Baskakov operators (for ρ = ∞ ) and their genuine Durrmeyer type modification (for ρ = 1 ). First, we prove that for fixed n , c and a fixed convex function f , B n , ρ c f is decreasing with respect to ρ . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators B n , ρ c applied to convex functions.
Global fixed point proof of time-dependent density-functional theory
2011
We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point question for potentials on a given time-interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as wel…
Dorronsoro's theorem in Heisenberg groups
2020
A theorem of Dorronsoro from the 1980s quantifies the fact that real-valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions which are independent of the last variable. As an application, we deduce new proofs for certain vertical vs. horizontal Poincare inequalities for real-valued functions on the Heisenberg group, originally due to Austin-Naor-Tessera and Lafforgue-Naor.
Representation Theorems for Indefinite Quadratic Forms Revisited
2010
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring the second representation theorem to hold is proved. A new simple and explicit example of a self-adjoint operator for which the second representation theorem does not hold is also provided.