Related papers: Reidemeister's theorem using transversality

We recover a nonlinear magnetic Schr\"odinger potential from measurement on an arbitrarily small open subset of the boundary on a compact Riemann surface. We assume that the magnetic potential satisfies suitable analytic properties, in…

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the…

We prove an asymptotic formula for the smoothed shifted convolution of the generalised divisor function $d_k(n)$ and the divisor function $d(n)$, with a power-saving error term independent of $k$. In particular, when $k$ is large, this is…

Stokes theorem holds for Lipschitz forms on a smooth manifold.

A didatic approach of the Noether's theorem in classical mechanics is derived and used to obtain the laws of conservation.

The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister…

We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated…

We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

We prove an inversion formula for summatory arithmetic functions. As an application, we obtain an arithmetic relationship between summatory Piltz divisor functions and a sum of the M\"obius function over certain integers, denoted by…

We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…

We show that on a two-dimensional compact nontrapping Riemannian manifold with strictly convex boundary, a piecewise constant function can be recovered from its integrals over geodesics. We adapt the injectivity proof which uses variations…

We prove a new cross theorem for separately holomorphic functions.

We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.

We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.

In this paper we compute the Hilbert functions of irreducible (or smooth) and reduced arithmetically Gorenstein schemes that are twisted anti-canonical divisors on arithmetically Cohen-Macaulay schemes. We also prove some folklore results…

We obtained that any 2-form and any smooth function on 2-manifolds with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric, respectively.

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…

The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and…

We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.