Search results for "Mathematic"

Errors Generated by Uncertain Data

2014

In this chapter, we study effects caused by incompletely known data. In practice, the data are never known exactly, therefore the results generated by a mathematical model also have a limited accuracy. Then, the whole subject of error analysis should be treated in a different manner, and accuracy of numerical solutions should be considered within a framework of a more complicated scheme, which includes such notions as maximal and minimal distances to the solution set and its radius.

Applications in Mathematical Physics

2009

It turns out that pip-space methods have many applications in physics, although they are seldom mentioned as such. To draw on a literary analogy, like Moliere’s Monsieur Jourdain speaking in prose without knowing so, many authors have been using pip-space language without realizing it. In particular, chains or lattices of Hilbert spaces are quite common in many fields of mathematical physics. Some of these applications will be discussed at length in this chapter. To mention a few examples: quantum mechanics, in particular singular interactions (Section 7.1.3), scattering theory (Section 7.2), quantum field theory (Section 7.3), representations of Lie groups (Section 7.4), etc.

General Theory: Topological Aspects

2009

In Chapter 1, we have analyzed the structure of pip-spaces from the algebraic point of view only, (i.e., the compatibility relation). Here we will discuss primarily the topological structure given by the partial inner product itself. The aim is to tighten the definitions so as to eliminate as many pathologies as possible. The picture that emerges is reassuringly simple: Only two types of pip-spaces seem sufficiently regular to have any practical use, namely lattices of Hilbert spaces (LHS) or Banach spaces (LBS), that we have introduced briefly in the Introduction. Our standard reference on locally convex topological vector spaces (LCS) will be the textbook of Kothe [Kot69]. In addition, fo…

Optimal control of the Schrödinger equation with two or three levels

2007

In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.

Appendix: Feynman rules

2010

Multiparametric Rational Solutions of Order N to the KPI Equation and the Explicit Case of Order 3

2021

We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N(N +1)−2 in x, y and t by a polynomial of degree 2N(N +1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.

The Impact of Financial Development and Macroeconomic Fundamentals on Nonperforming Loans among Emerging Countries: An Assessment Using the NARDL App…

2022

The relationship between financial development indicators and non-performing loans (NPLs) has garnered significant attention, especially in emerging countries. The puzzle of whether financial sector development increases or decreases Non-performing Loans (NPL)s has not been resolved to the satisfaction of the curious mind. This research attempts to answer the above question by studying the asymmetric and symmetric association between financial sector development and NPLs, by utilizing the novel non-linear autoregressive distribution lag (NARDL) and the linear autoregressive distribution lag (ARDL) approach. Moreover, to make the study inclusive, we have added a series of proxies to measure …

Comparison results for a linear elliptic equation with mixed boundary conditions

2003

In this paper we study a linear elliptic equation having mixed boundary conditions, defined in a connected open set $\Omega $ of $\mathbb{R}^{n}$. We prove a comparison result with a suitable ``symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of $ \partial \Omega $. Regularity results for non-uniformly elliptic equations are also given.

Modelling and assessing public health policies to counteract Italian measles outbreaks

2021

This study aims to understand, through explanatory research, the key factors that led to the 2017 measles outbreak in Italy, the causes of the low level of immunisation and the causes of possible cyclical phenomena of measles epidemics. This topic's comprehension has required a holistic approach, merging epidemiological aspects, socioeconomic aspects (including the evolution of mistrust in vaccinations, infodemy and fake news) and health law constraints. A specific SIR System Dynamics (SD) model was built to reproduce the relevant cause-and-effect relationships between social interactions, the public institutions behaviour and the measles outbreaks. SD results permit the assessment of the h…

A dynamic performance management approach to support local strategic planning

2015

In spite of efforts devoted in the last decades to local strategic planning, such field of research and practice has been frequently characterized by a lack of implementation. We argue here that this phenomenon is due to the limitations of the static and linear approach to local strategic planning in fostering the development of common shared view among policy makers on the relevant system's structure and behavior. By means of a case-study, we illustrate how an approach based on system dynamics modeling applied to Performance Management can be useful to overcome such weaknesses. The proposed approach enhances a better understanding of the causes and effects related to adopted policies, unde…