Search results for "Set theory"
showing 10 items of 751 documents
Wellfounded Trees and Dependent Polynomial Functors
2004
We set out to study the consequences of the assumption of types of wellfounded trees in dependent type theories. We do so by in- vestigating the categorical notion of wellfounded tree introduced in [16]. Our main result shows that wellfounded trees allow us to define initial algebras for a wide class of endofunctors on locally cartesian closed cat- egories.
On a conjecture about class numbers of totally positive quadratic forms in totally real algebraic number fields
1979
Zusammenfassung Mittels einer fruheren Klassenzahlabschatzung fur quadratische Formen wird als Verallgemeinerung einer Vermutung von Siegel bewiesen, das Geschlechter totalpositiver Formen mit mindestens drei Variablen und vorgegebener Klassenzahl nur in endlich vielen totalreellen algebraischen Zahlkorpern vorkommen. Bei binaren Formen folgt mit einer neuen Klassenzahlformel aus der verallgemeinerten Riemannschen Vermutung dieselbe Aussage. Ohne Annahme einer Hypothese gilt, das die Anzahl der totalreellen Korper eines festen Grades mit totalpositiven binaren Formen vorgegebener Klassenzahl endlich ist.
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.
Positivity, complex FIOs, and Toeplitz operators
2018
International audience; We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz operators on the Bargmann space is implied by the boundedness of their Weyl symbols.
The identity type weak factorisation system
2008
We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the right class of the weak factorisation system. This characterisation is applied to relate identity types and the homotopy theory of groupoids.
Some approximation properties by a class of bivariate operators
2019
WOS: 000503431300041
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 Bryce and cossey type theorem in a class of locally finite groups
2001
In this paper the subgroup-closed saturated Fitting formations of radical locally finite groups with min-p for all p are fully characterised. Moreover the study of a class of generalised nilpotent groups introduced by Ballester-Bolinches and Pedraza is continued.
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