We establish a new fundamental relationship between total curvature of knots and crossing number. If K is a smooth knot in R3, R the cross-section radius of a uniform tube neighborhood K, L the arclength of K, and κ the total curvature of K, then (up to some coefficient), crossing number of K ≤ L R κ . The proof generalizes to show that for smooth knots in R3, the crossing number, writhe, Möbiu...

We obtain nearly sharp estimates for the L p (R 2) norms of certain convolution operators. For n 1 let n be the measure on R 2 obtained by multiplying normalized arclength measure on fjxj = 1g by the oscillating factor e inarg(x). For 1 p 1, let C(p; n) denoted the norm of the operator T n f : = n f on L p (R 2). The purpose of this note is to estimate the rate of decay of C(p; n) as n ! 1. By ...

We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler–Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting conjugate points, with local minima corresp...

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients principal curvature as function arclength through natural change variables. The trapezoidal rule applied those Fourier-type integrals and resulting formula fits in framework non-uniform ...

We study traveling waves for the vortex sheet with surface tension. We use the anglearclength description of the interface rather than Cartesian coordinates, and we utilize an arclength parameterization as well. In this setting, we make a new formulation of the traveling wave ansatz. For this problem, it should be possible for traveling waves to overturn, and notably, our formulation does allow...