Differential Equation Models in Applied Mathematics

The present book contains the articles published in the Special Issue “Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges” of the MDPI journal Mathematics. The Special Issue aimed to highlight old and new challenges in the formulation, solution, understanding, and interpretation of models of differential equations (DEs) in different real world applications. The technical topics covered in the seven articles published in this book include: asymptotic properties of high order nonlinear DEs, analysis of backward bifurcation, and stability analysis of fractional-order differential systems. Models oriented to real applications consider the chemotactic between cell species, the mechanism of on-off intermittency in food chain models, and the occurrence of hysteresis in marketing. Numerical aspects deal with the preservation of mass and positivity and the efficient solution of Boundary Value Problems (BVPs) for optimal control problems. I hope that this collection will be useful for those working in the area of modelling real-word applications through differential equations and those who care about an accurate numerical approximation of their solutions. The reading is also addressed to those willing to become familiar with differential equations which, due to their predictive abilities, represent the main mathematical tool for applying scenario analysis to our changing world

Modelling, Monitoring, Control and Optimization for Complex Industrial Processes

This reprint includes 22 research papers and an editorial, collected from the Special Issue "Modelling, Monitoring, Control and Optimization for Complex Industrial Processes", highlighting recent research advances and emerging research directions in complex industrial processes. This reprint aims to promote the research field and benefit the readers from both academic communities and industrial sectors

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

The Piratical Ethos: Textual Activity and Intellectual Property in Digital Environments

The Piratical Ethos: Textual Activity and Intellectual Property in Digital Environments examines the definition, function, and application of intellectual property in contexts of electronically mediated social production. With a focus on immaterial production - or the forms of coordinated social activity employed to produce knowledge and information in the networked information economy - this project ultimately aims to demonstrate how current intellectual property paradigms must be rearticulated for an age of digital (re)production. By considering the themes of Piracy , Intellectual Property , and Distributed Social Production this dissertation provides an overview of the current state of peer production and intellectual property in the Humanities and Writing Studies. Next, this project develops and implements a communicational-mediational research methodology to theorize how both discursive and material data lend themselves to a more nuanced understanding of the ways that technologies of communication and coordination effect attitudes toward intellectual property. After establishing both a methodology and an interdisciplinary grounding for the themes of the work, this dissertation presents a grounded theoretic analysis of piratical discourse to reveal what I call the piratical ethos , or the guiding attitudes of individuals actively contesting intellectual property in piratical acts of distributed social production. Congruently, this work also investigates the material dynamics of piratical activity by analyzing the cultural-historical activity systems wherein piratical subjectivity emerges, emphasizing the agenic capacity of interfacial technologies at the scales of user and system. Exploring the attitudes of piratical subjects and the technological genres that mediate piratical activity, I contend that the conclusions drawn from The Piratical Ethos can assist Writing Studies researchers with developing novel methodologies to study the intersections of intellectual property and distributed social production in digital worlds

Many Body Quantum Chaos

This editorial remembers Shmuel Fishman, one of the founding fathers of the research field "quantum chaos", and puts into context his contributions to the scientific community with respect to the twelve papers that form the special issue

Metrology and Many-Body Physics with Ultracold Metastable Helium

Ultracold dilute gases provide ideal settings for measurements of atomic structure. Helium has an internal structure sufficiently simple to permit highly accurate predictions of its resonances and transition rates. Precise laser spectroscopy of helium thus yields empirical constraints on such calculations. These are desirable in the ongoing investigations seeking to reconcile the disagreement between independent determinations of nuclear charge radius data in both hydrogenic and helium atoms. Either the size of these particles are truly constant and quantum electrodynamics (QED) is flawed, or the theory is correct and some new physics is at play at the atomic scale. Ultracold bose gases also serve as ideal testing ground to better understand the physics of Bose-Einstein condensation, superfluidity, and the effects of weak interactions in condensed-matter systems. The large internal energy of helium's metastable excited state enables the measurement of the momentum of single atoms, providing a new lens through which to examine both weakly-interacting and strongly-correlated systems. This feature is employed to investigate the quantum depletion of a BEC after expansion into the far-field. Finally, the appendix reports on early progress towards the realization of an optical lattice trap for helium.Comment: PhD thesis. Abstract truncated per arxiv requirement