Search results for "REPRESENTATION"
showing 10 items of 1710 documents
Coherent states: a contemporary panorama
2012
Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schr?dinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably…
Cauchy flights in confining potentials
2009
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target pdf (eventually asymptotic) equals the preselected one. To this end, dynamically distinct jump-type processes can be employed. We demonstrate that one "targeted stochasticity" scenario involves Langevin systems with a symmetric stable noise. Another derives from the L\'evy-Schr\"odinger semigroup dynamics (closely linked with topologically induced super-diffusions), which has no standard Langevin representation. For computational and visualiz…
An algebraic representation of Steiner triple systems of order 13
2021
Abstract In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF ( 5 ) 13 , with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V , which can also be characterized as the intersections of B with thirteen linear hyperplanes of V .
From Zeno to Chrysippus
2015
This chapter is about the origin and development of early Stoic epistemology. I discuss how Zeno of Citium, the founder of the Stoa, was influenced by his predecessors and interpreted by his successors. I argue that Stoicism rely on two basic assumptions for which Socrates is the main predecessor, namely that human beings are at home in the world and that it is only by using our rational abilities to detect salient truths and organize them into skills that we can successfully orient ourselves in this world. This Socratic-Stoic position relies on a naturalistic theory of concept acquisition, for which Aristotle is the main predecessor, or so I argue. I then look at how Zeno’s original episte…
Vox Naturae: The Myth of Animal Nature in the Latin Roman Republic
2016
The paper examines the representation of animals as embodiment of nature in the culture of the late Roman republic. By discussing a selection of passages from Sallust, Cicero and Lucretius in conjunction with other Greek and Latin sources, the paper shows that the typically Western myth of 'animal nature' - the cultural belief that animal mirror a perennial state of nature, as opposed to human society - played a very important role in the ethical debate of the first century BC and took in this period a form which was bound to influence the centuries to come.
Finitary formal topologies and Stone’s representation theorem
2008
AbstractWe study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theorem for distributive lattices. We work within the framework of a minimalist foundation (as proposed by Maria Emilia Maietti and the second author). Both inductive and co-inductive methods are used in most proofs.
Locally convex quasi $C^*$-normed algebras
2012
Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -normed algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-algebra over A 0 , but it is not necessarily a locally convex quasi ∗-algebra over the C ∗ -algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -normed algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
Maximal Operators with Respect to the Numerical Range
2018
Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $\mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
Apperception, content-based psychology and design
2003
A core area of scientific thinking is explaining. This means answering to the “why-questions and how questions” (Hempel 1965). Why does Sam have a fewer? Why did an organization fail abroad? Why a structure is able to support the weight of snow? How more effective valves for an engine can be designed? How to make computer games more attractive for female users? These are typical examples of design problems, all of which should be based on scientific explanation, i.e., what should be answered based on the laws of nature or as is becoming increasingly more evident, based on the laws of the human mind.
Sudoku – A Language Description Case Study
2009
A complete language description includes the structure as well as constraints, textual representation, graphical representation, and behaviour (transformation and execution). As a case study in language description, we consider Sudoku as a language, where a Sudoku puzzle is an instance of the language. Thus we are able to apply meta-model-based technologies for the creation of a language description for Sudoku, including correctness checking of a puzzle, and solving strategies. We identify what has to be expressed and how this can be done with the technology available today.