Related papers: The Andreadakis Problem for the McCool groups
We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…
This paper concerns arithmetic families of $\varphi$-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons is lower semicontinuous around any rigid point. If the slope polygons are locally constant…
We prove two results. First, we establish that the normal bundle of any smooth curve of genus 7 having maximal Clifford index is stable. Note that 7 is the smallest genus for which such a result could possibly hold. We then show that rank…
The classical Benjamin and Lighthill conjecture about steady water waves states that the non-dimensional flow force constant of a solution is bounded by the corresponding constants of the supercritical and subcritical uniform streams…
We first improve an old result of McMahon and show that a metric minimal flow whose enveloping semigroup contains less than $2^{\mathfrak{c}}$ (where ${\mathfrak{c}} ={2^{\aleph_0}}$) minimal left ideals is PI. Then we show the existence of…
Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…
In this paper, we consider the 2D second grade fluid past an obstacle satisfying the standard non-slip boundary condition at the surface of the obstacle. Second grade fluid model is a well-known non-Newtonian model, with two parameters:…
We prove the analogue of Helly's theorem for systolic complexes. Namely, we show that 7-systolic complexes have Helly dimension less or equal to 1, whereas 6-systolic complexes have Helly dimension bounded from the above by 2.
Rigid particles suspended on a micropolar fluid provide microstructure that coexists and interacts with the local rotation of the fluid given by the vorticity. In this work we prove that the particles' angular velocity and the vorticity…
We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered…
We build a multifractal object and use it as a support to study percolation. We identify some differences between percolation in a multifractal and in a regular lattice. We use many samples of finite size lattices and draw the histogram of…
We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to…
The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1-bipolar knots which are not…
We study the stability of the Couette-Taylor flow between porous cylinders with radial throughflow. It had been shown earlier that this flow can be unstable with respect to non-axisymmetric (azimuthal or helical) waves provided that the…
We give a partly new proof of the fluctuation bounds for the second class particle and current in the stationary asymmetric simple exclusion process. One novelty is a coupling that preserves the ordering of second class particles in two…
Following the proposals of Donaldson-Thomas, Haydys and Gaiotto-Moore-Witten, we give a construction of Fukaya-Seidel categories for a suitable class of Morse Landau-Ginzburg models using the complex gradient flow equation, which has the…
We consider the symmetric simple exclusion with open boundaries that are in contact with particle reservoirs at different densities. The reservoir densities changes at a slower time scale with respect to the natural time scale the system…
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…
We compare the colimit and 2-colimit of strict 2-functors in the 2-category of groupoids, over a certain type of posets. These posets are of special importance, as they correspond to coverings of a topological space. The main result of this…
It is known that no length or time measurements are possible in sub-Planckian regions of spacetime. The Volovich hypothesis postulates that the micro-geometry of spacetime may therefore be assumed to be non-archimedean. In this letter, the…