Search results for "PDE"
showing 10 items of 558 documents
A third order partial differential equation for isotropic boundary based triangular Bézier surface generation
2011
Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.
Explicit Bézier control net of a PDE surface
2017
The PDE under study here is a general fourth-order linear elliptic Partial Differential Equation. Having prescribed the boundary control points, we provide the explicit expression of the whole control net of the associated PDE Bézier surface. In other words, we obtain the explicit expressions of the interior control points as linear combinations of free boundary control points. The set of scalar coefficients of these combinations works like a mould for PDE surfaces. Thus, once this mould has been computed for a given degree, real-time manipulation of the resulting surfaces becomes possible by modifying the prescribed information. The work was partially supported by Spanish Ministry of Econo…
Laboratorisko iekaisuma marķieru prognostiskā nozīme nozokomiālās infekcijas diagnostikā smagas termiskas apdeguma traumas pacientam
2017
Darba pamatojums. Zelta standarts intrahospitālās infekcijas un sepses diagnostikā, pacientiem ar apdeguma traumu, vēl joprojām balstās uz mikrobioloģisko izmeklēšanu, kura var aizkavēt antibakteriālas terapijas uzsākšanas laiku. Līdz ar to ir mērķtiecīgi atrast prognostisko faktoru, kurš var agrīni norādīt uz intrahospitālas infekcijas attīstību, pacientiem ar smagu apdeguma traumu. Izvirzītā hipotēze: laboratoriskie radītāji var agrīni norādīt uz draudošo intrahospitālas infekcijas attīstību, pacientiem ar smagu termisku apdeguma traumu. Materiāli un metodes. Pētījums norisinājās RAKUS stacionārā “Biķernieki”, Valsts apdeguma centrā. Pētījumā tika iekļauti pacienti, kuri guvuši smagu term…
Exponential instability in the fractional Calder\'on problem
2017
In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…
Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement
2020
We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.
Existence results and asymptotic behavior for nonlocal abstract Cauchy problems
2008
AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.
Nonlocal (Pair Site) Reactivity from Second-Order Static Density Response Function: Gas- and Solution-Phase Reactivity of the Acetaldehyde Enolate a…
1999
A nonlocal (pair site) reactivity scheme is developed and tested. The theory is cast in terms of the first-order Fukui response function f(r,r‘), previously proposed by Fuentealba and Parr [J. Chem. Phys. 1991, 94, 5559]. A change of variables is introduced by using the softness s(r) and t(r) = [∂s(r)/∂N]υ(r) (the variation of softness with respect to the changes in the total number of electrons N at constant external potential υ(r)) that leads to a simple expression for the variation of the Fukui function at site k, namely = − for an electrophilic attack. The first term describes a local contribution, proportional to the variation of the electrostatic potential that can be induced, for exa…
Infinite lie groups of point transformations leaving invariant the linear equation which describes in the hodograph plane the isentropic one-dimensio…
1991
Abstract The group analysis of the hodograph equation which is equivalent to the non-linear system of one-dimensional isentropic gas dynamics reveals the existence of infinite groups of symmetry in correspondence with particular pressure laws. These turn out to be polytropes with selected indices, as is expected, as well as a new type of pressure. In all these cases the hodograph equation can be transformed, by a suitable change of variables, into the wave equationψ ζ = 0.
Complex powers and non-compact manifolds
2002
We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras, ``extended Weyl algebras,'' whose definition was inspired by Guillemin's paper on the subject. An extended Weyl algebra can be thought of as an algebra of ``abstract pseudodifferential operators.'' Many algebras of pseudodifferential operators are extended Weyl algebras. Several results typical for algebras of pseudodifferential operators (asymptotic completeness, construction of Sobolev spaces, boundedness between apropriate Sobolev spaces, >...) generalize to…
Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces
2018
In this paper we extend the duality theory of the multi-marginal optimal transport problem for cost functions depending on a decreasing function of the distance (not necessarily bounded). This class of cost functions appears in the context of SCE Density Functional Theory introduced in "Strong-interaction limit of density-functional theory" by M. Seidl.