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Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on…
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more…
A new class of representations of the Brauer algebra that centralizes the action of orthogonal and symplectic groups in tensor spaces is found. These representations make it possible to apply the technique of building primitive orthogonal…
We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper ``asymptotic function'', similar to but…
We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is $\CP^1$ and the function is a polynomial, we give an…
We establish an area formula for the spherical measure of intrinsic graphs of any codimension in homogeneous groups. Our approach relies on the assumption that the map defining the intrinsic graph is continuously intrinsically…
We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point…
We establish an area formula for the spherical measure of intrinsically regular submanifolds of low codimension in Heisenberg groups. The spherical measure is computed with respect to an arbitrary homogeneous distance. Among the arguments…
Let k be a field, G a smooth connected linear algebraic group and X a homogeneous space of G over k, such that the geometric stabilizers are extensions of a smooth group of multiplicative type by a smooth connected characterfree group. If k…
The paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the conditions that the asymptotic density of the number of primes in…
We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of information on the asymptotic geometry of these spaces: in…
We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…
Let $k$ be a number field and $S$ a finite set of places of $k$ containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of $S$-integers of $k$. Moreover, we give an…
We provide a rather general and very simple to compute lower bound for the asymptotic convergence factor of compact subsets of the set of complex numbers with connected complement and finitely many connected components .
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
The intrinsic volumes induced by a stationary Poisson k-flat process inside a compact and convex sampling window are considered. Using techniques from stochastic analysis, more precisely calculus with multiple stochastic integrals and a…
This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in $\mathbb{R}^d$. We obtain the rate of convergence for these functionals. The…
Let $F(x)= \sum_{\nu\in\NN^d} F_\nu x^\nu$ be a multivariate power series with complex coefficients that converges in a neighborhood of the origin. Assume $F=G/H$ for some functions $G$ and $H$ holomorphic in a neighborhood of the origin.…
In this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of fixed degree, or within a fixed number field, and bounded height.