Search results for " Geometry."
showing 10 items of 2189 documents
(Dipyrido[3,2-a:2',3'-c]phenazine)(glycinato)copper(II) perchlorate: a novel DNA-intercalator with anti-proliferative activity against thyroid cancer…
2012
Abstract A novel copper(II) heteroleptic complex of dipyrido[3,2-a:2′,3′-c]phenazine (dppz) and glycinato (gly) as chelating ancillary ligand, [Cu(dppz)(gly)]ClO 4 ( 1 ), was synthesized and characterized. X-ray crystallography revealed that the coordination geometry of the cationic [Cu(dppz)(gly)] + unit is hexacoordinated and shows a distorted octahedral coordination geometry in the solid state, with the N,N and N,O chelating atoms of dppz and glycinato, respectively, in the square plane and in which the planar units are connected in a monodimensional polymeric array by the apical copper coordination of the second carboxylic oxygen atom. Biological assays showed that 1 exhibits a remarkab…
P-T path development derived from shearband boudin microstructure
2016
This work focuses on the development of a regional P-T-path from the Malpica-Lamego Ductile Shear Zone, NW Portugal, based on the microstructures of shearband boudins evolved during progressive simple shear. The combination of microstructural analysis, fluid inclusion studies, crystallographic pre- ffered orientation and fractal geometry analyses, allows to link several stages in the internal evolution of the boudin to regional P-T conditions. The boudinage process is initiated under differential stress after the original layer achieved sufficient viscosity contrast relative to the surrounding matrix. Two main transformations occur simultaneously: i) change in the external shape with contin…
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…
Second-Order Calculus on RCD Spaces
2020
In this conclusive chapter we introduce the class of those metric measure spaces that satisfy the Riemannian curvature-dimension condition, briefly called RCD spaces, and we develop a thorough second-order differential calculus over these structures.
On deformation of Poisson manifolds of hydrodynamic type
2001
We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
2020
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.
The linearized Calderón problem on complex manifolds
2019
International audience; In this note we show that on any compact subdomain of a Kähler manifold that admits sufficiently many global holomorphic functions , the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of Kähler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot by treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holo-morphic functions with approximately prescribed critical points.…
A tour of the theory of absolutely minimizing functions
2004
A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation
Rigidity of quasisymmetric mappings on self-affine carpets
2016
We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension.
Invariant deformation theory of affine schemes with reductive group action
2015
We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we device an algorithm to compute the universal deformation of $X$ in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where $G$ is a classical group acting on a classical representation, and describe their singularities.