相关论文: Vanishing Flats: A Combinatorial Viewpoint on the …

We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…

This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

In this paper we give an alternative proof for a vanishing result about flat functions proved in G.Stoica, "When must a flat function be identically zero", The American Mathematical Monthly 125(7)648-649,2018. With a dynamical approach we…

It is classically known that complete flat surfaces in Euclidean 3-space are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface $f$…

This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…

We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…

The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the…

Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…

Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…

We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…

We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial…

Let's consider a control system described by the implicit equation $F(x,\dot x) = 0$. If this system is differentially flat, then the following criterion is satisfied : For some integer $r$, there exists a function $\varphi(y_0, y_1,…

A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…

In this paper, we study the dimension of planar self-affine sets, of which generating iterated function system (IFS) contains non-invertible affine mappings. We show that under a certain separation condition, the dimension equals to the…

We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension.…

For any pair of bounded observables $A$ and $B$ with pure point spectra, we construct an associated "joint observable" which gives rise to a notion of a joint (projective) measurement of $A$ and $B$, and which conforms to the intuition that…

Zhou 2013 introduced modified planar functions to describe $(2^n,2^n,2^n,1)$ relative difference sets $R$ as a graph of a function on the finite field $\F_{2^n}$, and pointed out that projections of $R$ are difference sets that can be…

We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or,…

The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any…