相关论文: On the Structure of Space-Time at the Planck Scale

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…

The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion, form a lattice constructible from top to bottom in terms of intersections of maximal ground spaces. In this paper we characterize the lattice…

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…

It is suggested in the paper by A.J. Chambers {\it et al.} (Phys. Rev. Lett. 118, 242001 (2017), arXiv:1703.01153) that the time-ordered current-curent correlator in the nucleon calculated on the lattice is to be identified as the forward…

The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…

Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…

In multipath systems, available degrees of freedom can be considered as a key performance indicator, since the channel capacity grows linearly with the available degrees of freedom. However, a fundamental question arises: given a size…

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of…

We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they…

Assuming fractality of hadronic constituents, we introduce elements of special realization of the relativity principle applied to physical quantities expressed with respect to various fractal structures. The construction is inspired by the…

We study the appearance of notable interval structures -- lattices, modular lattices, distributive lattices, and boolean lattices -- in both the Bruhat and weak orders of Coxeter groups. We collect and expand upon known results for…

Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in…

There are four variants of passive, linear time-invariant systems, described by rational functions: Continuous or Discrete time, Positive or Bounded real. By introducing a quadratic matrix inequality formulation, we present a unifying…

In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…

A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…

In this note we discuss the possibility to define a space-time with a DSR based approach. We show that the strategy of defining a non linear realization of the Lorentz symmetry with a consistent vector composition law cannot be reconciled…

This article focuses on the relationship between pseudo-t-norms and the structure of lattices. First, we establish a necessary and sufficient condition for the existence of a left-continuous t-norm on the ordinal sum of two disjoint…

The classical dynamics and pulse propagation are presented for a series of lattice-like structures whose spatial dimensionality ranges from one to four: four representing a hyper lattice. The lattices are connected one-dimensional wave…

The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept…

Since the spatially extended periodic parity-time (PT) symmetric potential can possess certain unique properties compared to a single PT cell (with only a pair of coupled gain-loss components), various schemes have been proposed to realize…