Search results for " mathematical physics"
showing 10 items of 396 documents
Permutability of injectors with a central socle in a finite solvable group
2017
In response to an Open Question of Doerk and Hawkes [5, IX Section 3, page 615], we shall show that if Zπ is the Fitting class formed by the finite solvable groups whose π-socle is central (where π is a set of prime numbers), then the Zπ-injectors of a finite solvable group G permute with the members of a Sylow basis in G. The proof depends on the properties of certain extraspecial groups [4].
Overlapping self-affine sets of Kakeya type
2009
We compute the Minkowski dimension for a family of self-affine sets on the plane. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.
Separation conditions on controlled Moran constructions
2017
It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.
Correspondence between some metabelian varieties and left nilpotent varieties
2021
Abstract In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈ n α with 1 α 2 and 2 α 3 instead it was established the existence of a variety of fractional polynomial growth with α = 7 2 . In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of…
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.
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.
Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
2021
Abstract We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.
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.
Some contributions to the theory of transformation monoids
2019
The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg [A theory of transformation monoids: combinatorics and representation theory. Electron. J…
Area minimizing projective planes on the projective space of dimension 3 with the Berger metric
2016
Abstract We show that, among the projective planes embedded into the real projective space R P 3 endowed with the Berger metric, those of least area are exactly the ones obtained by projection of the equatorial spheres of S 3 . This result generalizes a classical result for the projective spaces with the standard metric.