Search results for "Mathematical structure"
showing 7 items of 17 documents
Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations
2016
We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. Thes…
Deducing the USLE mathematical structure by dimensional analysis and self-similarity theory
2010
The Universal Soil Loss Equation (USLE) was originally deduced by a statistical analysis of a large data set of soil loss measurements. The multiplicative structure of the model has been criticised due to the considerable interdependence between the variables. Using the soil erosion representative variables and the reference condition adopted in the USLE, the aim of this paper was to apply dimensional analysis and self-similarity theory to deduce the functional relationship among the selected variables. The analysis yielded a multiplicative equation, similar to the USLE. Therefore, this study suggested that the USLE has a logical structure with respect to the variables used to simulate the …
Algorithmic Analysis of Programs with Well Quasi-ordered Domains
2000
AbstractOver the past few years increasing research effort has been directed towards the automatic verification of infinite-state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems) which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a preorder which is a well quasi-ordering, such that the transition relation is “monotonic” (a simulation) with respect to the preorder. We show that the following properties are decidable for wel…
Quantum Field Theory
2018
Quantum field theory (QFT) shares many of its philosophical problems with quantum mechanics. This applies in particular to the quantum measurement process and the connected interpretive problems, to which QFT contributes hardly any new aspects, let alone solutions. The question as to how the objects described by the theory are spatially embedded was already also discussed for quantum mechanics. However, the new mathematical structure of QFT promises new answers, which renders the spatiotemporal interpretation of QFT the pivotal question. In this chapter, we sketch the mathematical characteristics of QFT and show that a particle as well as a field interpretation breaks down.
Age-Structured Human Population Dynamics
2006
ABSTRACT A von Foerster-McKendrick model to study age-structured human population dynamics is presented in this paper. Forecasts of population density (population per age unit) depending on ages are possible using this model. The model consists of a quasi-linear first order partial differential equation for the dynamics of population density per age-unit (except for the zero-age), a boundary condition for the births flow at zero-age, and an initial condition for the population density at the initial instant. A general solution independent of the particular human-system under study is obtained based on some hypotheses about the mathematical structure of its input variables. The model has bee…
A Side-by-Side Single Sex Age-Structured Human Population Dynamic Model: Exact Solution and Model Validation
2008
A side-by-side single sex age-structured population dynamic model is presented in this paper. The model consists of two coupled von Foerster-McKendrick-type quasi-linear partial differential equations, two initial conditions, and two boundary conditions. The state variables of the model are male and female population densities. The solutions of these partial differential equations provide explicit time and age dependence of the variables. The initial conditions define the male and female population densities at the initial time, while the boundary conditions compute the male and female births at zero-age by using fertility rates. The assumptions of the nontime-dependence of the death and fe…
Objects, Structures, and Logics
2022
This book offers Novel In-Depth Discussions of the Relationship Between Logic and Metaphysics Attempts to Develop a New Framework for the Concept of Mathematical Structure Emphasizes the Importance of Mathematical Practice to the Philosophy of Mathematics