Related papers: Distal and non-Distal Behavior in Pairs
This paper investigates expansions of distal structures by a unary subset that arises as the image of a projection map. We first provide a sufficient condition for such an expansion to remain distal. Based on this criterion, we establish…
A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural `dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets…
In two nearby atoms, the dipole-dipole interaction can couple transitions with orthogonal dipole moments. This orthogonal coupling accounts for a number of interesting effects, but strongly depends on the geometry of the setup. Here, we…
We give definitions for different types of moving spatially localized objects in discrete nonlinear lattices. We derive general analytical relations connecting frequency, velocity and localization length of moving discrete breathers and…
We show that the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP (= the non-independence property), this provides a new proof that $T_{\log}$ is NIP. Finally, we show…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…
In this paper the dynamic behavior of an oscillating tip-microlever system at the proximity of a surface is discussed. We show that the nonlinear behavior of the oscillator is able to explain the high sensitivity of the oscillating tip…
The theory of descriptive nearness is usually adopted when dealing with sets that share some common properties even when the sets are not spatially close, i.e., the sets have no members in common. Set description results from the use of…
We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout…
This is the second in a series of papers devoted to open string field theory in two dimensions. In this paper we aim to clarify the origin and the role of discrete physical states in the theory. To this end, we study interactions of…
Let L^1(G) and M(G) be group algebra and measure algebra of a locally compact group G, respectively and D:L^1(G)-->M(G) be a continuous linear map. We consider D behaving like derivation or anti-derivation at orthogonal elements for several…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for…
Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
Multivariate correlation analysis plays a key role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric association measure between more than two variables based on the concept of…
Some algebraic, geometric and geometroalgebraic characteristics of pairs of operators are discussed.