This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology.
Bachelorarbeit aus dem Jahr 2024 im Fachbereich Mathematik - Angewandte Mathematik, Note: 1,0, Friedrich-Alexander-Universität Erlangen-Nürnberg (Department Mathematik), Sprache: Deutsch, Abstract: In dieser Arbeit befassen wir uns mit der Entwicklung und Analyse eines Verfahrens zur Lösung kontinuierlicher, gleichungsrestringierter, nichtlinearer und stochastischer Optimierungsprobleme.
A new threshold for the existence of weak solutions to the incompressible Euler equationsTo gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties.
A classic introduction to non-linear mechanics from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.
The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic?
Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent.
Genomic signal processing (GSP) can be defined as the analysis, processing, and use of genomic signals to gain biological knowledge, and the translation of that knowledge into systems-based applications that can be used to diagnose and treat genetic diseases.
From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society.
This classic book is an introduction to dynamic programming, presented by the scientist who coined the term and developed the theory in its early stages.
This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems.
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure.
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology.
Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations.
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms.
Kiyosi Ito's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes.
This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology.
The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis.
This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic).
Ecological Informatics promotes interdisciplinary research between ecology and computer science on elucidation of principles of information processing in ecosystems, ecological sustainability by informed decision making, and bio-inspired computation.
New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevatorsControl applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states.
This book brings together a number of lectures given between 1993 and 1999 as part of a special series hosted by the Federal University of Pernambuco, in which internationally established researchers came to Recife, Brazil, to lecture on classical or celestial mechanics.
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education.
A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "e;looks"e; just like a random string to any efficient adversary.
Many industries, such as transportation and manufacturing, use control systems to insure that parameters such as temperature or altitude behave in a desirable way over time.
The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems.
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion.
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects.
