Related papers: The M\"obius function and distal flows
We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to…
In this work, it is shown that a simply-connected, rationally-elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an almost-free, linear torus action, where this torus has rank…
The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…
We study two models of overdamped self-propelled disks in two dimensions, with and without aligning interactions. Active mesoscale flows leading to chaotic advection emerge in both models in the homogeneous dense fluid away from dynamical…
When the concentration of electrolyte solution varies along the channel the forces arise that drag the fluid toward the higher or lower concentration region inducing a flow termed diffusio-osmotic. This article investigates a flow that…
The paper presents some results for reducing the computation of the M\"obius functon of a M\"obius category that arises from a combinatorial inverse semigroup to that of locally finite partially ordered sets. We illustrate the computation…
The aim of this work is an analysis of distal and non-distal behavior in dense pairs of o-minimal structures. A characterization of distal types is given through orthogonality to a generic type in $M^{\operatorname{eq}}$, non-distality is…
There is a convolution product on 3-variable partial flag functions of a locally finite poset that produces a generalized M\"obius function. Under the product this generalized M\"obius function is a one sided inverse of the zeta function…
We reveal that realistic fluids generate microscopic-level discontinuity constantly and the discontinuity spreads out with motion of particles rather rapidly and widely. These things cannot be treated by the standard kinetic equations, and…
The auto-correlations of arithmetic functions, such as the von Mangoldt function, the M\"obius function and the divisor function, are the subject of classical problems in analytic number theory. The function field analogues of these…
For an ergodic flow, a range of rates of convergence of Birkhoff averages from the maximum rate to an arbitrarily slow rate is realized by choosing the averaging function. For torus windings, the continuity of the averaging functions is…
We study the class $\mathcal{M}$ of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in $\mathcal{M}$, with at least one essential singularity, permutes with a non-constant rational…
We construct a hydrodynamic theory of active smectics A in two-dimensional space, including the creation/annihilation and motility of dislocations with Burgers' number $\pm1$. We derive analytical criteria on the set of parameters that lead…
Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher rank abelian Anosov actions on the n-torus and the classification of equilibrium-free flows on the n-torus that possess nontrivial…
In this note we give a fairly direct proof of a recent theorem of Gorska, Lemanczyk and de la Rue which characterises the class of measure preserving transformations that are disjoint from every ergodic measure preserving transformation.…
A one-to-one continuous function from a triangle to itself is defined that has both interesting number theoretic and analytic properties. This function is shown to be a natural generalization of the classical Minkowski ?(x) function. It is…
In this note, we provide a proof of a technical result of Erd\H{o}s and Hajnal about the existence of disjoint type graphs with no odd cycles. We also prove that this result is sharp in a certain sense.
We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory…
We study the behavior of diffeomorphisms, contained in the closure $\bar {\A_\a}$ (in the inductive limit topology) of the set $\A_\a$ of real-analytic diffeomorphisms of the torus $\Bbb T^2$, conjugated to the rotation $R_\a:(x,y)\mapsto…
An unsplittable multiflow routes the demand of each commodity along a single path from its source to its sink node. As our main result, we prove that in series-parallel digraphs, any given multiflow can be expressed as a convex combination…