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We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained…
We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of group schemes and are in correspondence with graded Hopf algebra. In this setting, graded group varieties…
A longstanding open question in sub-Riemannian geometry is the smoothness of (the arc-length parameterization of) length-minimizing curves. In [6], this question is negative answered, with an example of a $C^2$ but not $C^3$…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
A smooth Hermitian surface $X$ is a projective surface isomorphic to the Fermat surface of degree $q+1$ in positive characteristic. We study incidence relations of the rational curves of degree $q+1$ contained in $X$, and show that such…
Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
The rational Chow ring A?(S[n],Q) of the Hilbert scheme S[n] parametrising the length n zero-dimensional subschemes of a toric surface S can be described with the help of equivariant techniques. In this paper, we explain the general method…
We prove that tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. We also extend to real subanalytic sets the notion of reduced tangent cone and we show that subanalytic Lipschitz normally embedded sets have…
We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…
We show that certain submanifolds of generalized complex manifolds ("weak branes") admit a natural quotient which inherits a generalized complex structure. This is analog to quotienting coisotropic submanifolds of symplectic manifolds. In…
Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…
We study {\em generalized graph splines,} introduced by Gilbert, Viel, and the last author. For a large class of rings, we characterize the graphs that only admit constant splines. To do this, we prove that if a graph has a particular type…
We consider standard gradient descent, gradient flow and conjugate gradients as iterative algorithms for minimising a penalised ridge criterion in linear regression. While it is well known that conjugate gradients exhibit fast numerical…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely one where finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence.…
Pseudo-Hermitian Hamiltonians have recently become a field of wide investigation. Originally, the Generalized Riesz Systems (GRS) have been introduced as an auxiliary tool in this theory. In contrast, the current paper, GRSs are analysed in…
The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can…
We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.