Related papers: A new formula for rotation number
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…
We propose a simple numerical method which computes an approximate value of the winding number of a mapping from 3D torus~$T^3$ to the unitary group~$U(N)$, when $T^3$ is approximated by discrete lattice points. Our method consists of a…
An iterative method is presented for solving the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to…
We consider the class of Beltrami fields (eigenfields of the curl operator) on three-dimensional Riemannian solid tori: such vector fields arise as steady incompressible inviscid fluids and plasmas. Using techniques from contact geometry,…
Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number…
We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast to nonrotating waves, for high rotation…
Let B denote a three-dimensional body of rotation, with respect to one coordinate axis, whose boundary is sufficiently smooth and of bounded nonzero Gaussian curvature throughout, except for the two boundary points on the axis of rotation,…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
We study evolution of a closed embedded plane curve with the normal velocity depending on the curvature, the orientation and the position of the curve. We propose a new method of tangential redistribution of points by curvature adjusted…
In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
First, we give a formula for the foci of an ellipse, $E_0$, as a function of the coefficients of an equation of $E_0$(see Theorem <ref>T2</ref>). To prove Theorem <ref>T2</ref>, we use two interesting formulas proven in <cite>B</cite> and…
A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…
The balanced superelliptic rotation is a periodic map on an oriented closed surface of order $k\geq 3$. We give a positive factorization for the balanced superelliptic rotation.
The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…
We give a formula to compute all the top degree graded Betti numbers of the path ideal of a cycle. Also we will find a criterion to determine when Betti numbers of this ideal are non zero and give a formula to compute its projective…
We study the properties of rotation numbers for some groups of piecewise linear homeomorphisms of the circle. We use these properties to obtain results on PL rigidity, non isomorphicity, non exoticity of automorphisms, non smoothability for…
Using representation theoretic work on the Whitehouse module, a formula is obtained for the cycle structure of a riffle shuffle followed by a cut. This result will be merged with the paper [F6].
Two new invariants that are closely related to Milnor's curvature-torsion invariant are introduced. The first, the spiral index of a knot, captures the minimum number of maxima among all knot projections that are free of inflection points.…