Search results for " Programming"
showing 10 items of 1616 documents
Bismut's Way of the Malliavin Calculus for Elliptic Pseudodifferential Operators on a Lie Group
2018
We give an adaptation of the Malliavin Calculus of Bismut type for a semi-group generated by a right-invariant elliptic pseudodifferential operator on a Lie group.
Regular solutions of transmission and interaction problems for wave equations
1989
Consider n bounded domains Ω ⊆ ℝ and elliptic formally symmetric differential operators A1 of second order on Ωi Choose any closed subspace V in , and extend (Ai)i=1,…,n by Friedrich's theorem to a self-adjoint operator A with D(A1/2) = V (interaction operator). We give asymptotic estimates for the eigenvalues of A and consider wave equations with interaction. With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces.25,32 We also treat non-linear interaction, using a theorem of Minty29.
Polynomial functors and polynomial monads
2009
We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.
Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case
2019
We consider a simple model operator P in dimension 1 and show how random perturbations give rise to Weyl asymptotics in the interior of the range of P. We follow rather closely the work of Hager (Ann Henri Poincare 7(6):1035–1064, 2006) with some input also from Bordeaux Montrieux (Loi de Weyl presque sureet resolvante pour des operateurs differentiels nonautoadjoints, these, CMLS, Ecole Polytechnique, 2008) and Hager–Sjostrand (Math Ann 342(1):177–243, 2008). Some of the general ideas appear perhaps more clearly in this special situation.
Approximations of positive operators and continuity of the spectral radius III
1994
AbstractWe prove estimates on the speed of convergence of the ‘peripheral eigenvalues’ (and principal eigenvectors) of a sequence Tn of positive operators on a Banach lattice E to the peripheral eigenvalues of its limit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of Tn to T. These results sharpen results of convergence obtained by the authors in previous papers.
Some representation theorems for sesquilinear forms
2016
The possibility of getting a Radon-Nikodym type theorem and a Lebesgue-like decomposition for a non necessarily positive sesquilinear $\Omega$ form defined on a vector space $\mathcal D$, with respect to a given positive form $\Theta$ defined on $\D$, is explored. The main result consists in showing that a sesquilinear form $\Omega$ is $\Theta$-regular, in the sense that it has a Radon-Nikodym type representation, if and only if it satisfies a sort Cauchy-Schwarz inequality whose right hand side is implemented by a positive sesquilinear form which is $\Theta$-absolutely continuous. In the particular case where $\Theta$ is an inner product in $\mathcal D$, this class of sesquilinear form cov…
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.
Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations
2019
We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.
The role of the committee of the regions (CoR) to implement the Green Deal at the local level: an overview of Italy
2021
<abstract> <p>The contribution focuses on the role of cities in the implementation of the so-called Green Deal, the ambitious program proposed by the European Commission, in accordance with the objectives set by the Paris Agreements, to implement the use of clean energy resources, favour the circular economy, restore biodiversity and reduce pollution. The Plan, which for the seven-year period 2021-2027 has a budget of economic resources of 100 billion Euro, aims to involve in transcalar perspective all territorial and administrative levels of the Member States and thus contribute to the achievement, in 2050, of climate neutrality. The main objective of the work is then to concen…
Demo: Co-simulation of UAVs with INTO-CPS and PVSio-web
2018
This demo shows our ongoing work on the co-simulation of co-operative Unmanned Aerial Vehicles (UAVs). The work is based on the INTO-CPS co-simulation engine, which adopts the widely accepted Functional Mockup Interface (FMI) standard for co-simulation, and the PVSioweb prototyping tool, that extends a system simulator based on the PVS logic language with a web-based graphical interface. Simple scenarios of Quadcopters with assigned different tasks, such as rendez-vous and space coverage, are shown. We assumed a linearized dynamic model for Quadcopters formalized in OpenModelica, and a linearized set of equations for the flight control module written in C language. The co-ordination algorit…