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The aim of this paper is to investigate the quality of approximation of almost time and almost band-limited functions by its expansion in three classical orthogonal polynomials bases: the Hermite, Legendre and Chebyshev bases. As a…
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.
By introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle $\theta \in (0, \pi/7]$ in the equal-mass four-body problem. A…
We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed $\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used to…
We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…
Recently, K.-Y. Wu introduced affine subspace concentration conditions for the cone volumes of polytopes and proved that the cone volumes of centered, reflexive, smooth lattice polytopes satisfy these conditions. We extend the result to…
We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace $X(\Omega)$ of first order distribution. A particular…
Analogues of the prime number theorem and Merten's theorem are well-known for dynamical systems with hyperbolic behaviour. In this paper a 3-adic extension of the circle doubling map is studied. The map has a 3-adic eigendirection in which…
A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include…
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely…
This preprint has been withdrawn, as the evidence for persistent currents found with the "infinite-size" DMRG algorithm has not been reproduced with the (presumably more accurate) "finite-size" version of the algorithm (M. Troyer and U.…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer assisted existence proofs. Our framework is applied to the…
The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…
We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
In spite of a recent breakthrough on upper bounds of the size of cap sets (by Croot, Lev and Pach (2017) and Ellenberg and Gijswijt (2017)), the classical cap set constructions had not been affected. In this work, we introduce a very…
We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the…
We explore the properties of two-point cosmic propagators when Perturbation Theory (PT) loop corrections are consistently taken into account. We show in particular how the interpolation scheme proposed in arXiv:1112.3895 can be explicitly…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…