Related papers: A local Jordan-Brouwer separation theorem

We prove a version of the Stokes formula for differential forms on locally convex spaces. The main tool used for proving this formula is the surface layer theorem proved in another paper by the author. Moreover, for differential forms of a…

We define the notion of Mumford divisors, argue that they are the natural divisors to study on reduced but non-normal varieties and prove a structure theorem for the Mumford class group. v.2: references added

We prove a local limit theorem for nearest neighbours random walks in stationary random environment of conductances on Z without using any of both classic assumptions of uniform ellipticity and independence on the conductances. Besides the…

In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of…

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem,…

In this paper, we prove the local converse theorem for split even special orthogonal groups over a non-Archimedean local field of characteristic zero. This is the only case left on local converse theorems of split classical groups and the…

We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.

We will present a novel elementary, self-contained, and explicit proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on…

We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.

The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid graphs, under different input settings, in theories of bounded…

We publicise a proof of the Jordan Curve Theorem which relates it to the Phragmen-Brouwer Property, and whose proof uses the van Kampen theorem for the fundamental groupoid on a set of base points.

The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld and the author.

We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…

The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.

In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with…

This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…

We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded…

In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…

Let G be a p-adic Lie group. This paper is about the Jordan-Hoelder series of locally analytic G-representations which are induced from locally algebraic representations of a parabolic subgroup.

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…