Quantization, Classical and Quantum Field Theory and Theta - Functions

In the abelian case (the subject of several beautiful books) fixing some combinatorial structure (so called theta structure of level k) one obtains a special basis in the space of sections of canonical polarization powers over the jacobians. These sections can be presented as holomorphic functions on the "abelian Schottky space". This fact provides various applications of these concrete analytic formulas to the integrable systems, classical mechanics and PDE's. Our practical goal is to do the same in the non abelian case that is to give an answer to the Beauville's question. In future we hope to extend this digest to a mathematical mohograph with title "VBAC".Comment: To Igor Rostislavovich Shafarevich on his 80th birthday (will be published by CRS, Canada

Origami as a Tool for Mathematical Investigation and Error Modelling in Origami Construction

Origami is the ancient Japanese art of paper folding. It has inspired applications in industries ranging from Bio-Medical Engineering to Architecture. This thesis reviews ways in which Origami is used in a number of fields and investigates unexplored areas providing insight and new results which may lead to better understanding and new uses. The OSME conference series arguably covers most of the research activities in the field of Origami and its links to Science and Mathematics. The thesis provides a comprehensive review of the work that has been presented at these conferences and published in their proceedings. The mathematics of Origami has been explored before and much of the fundamental work in this field is presented in chapter 3. Here an attempt is made to push the bounds of this field by suggesting ways in which Origami can be used as a mathematical tool for in-depth exploration of non trivial problems. A particular problem we consider is the 4-colour theorem and its proof. Looking at some well known methods for producing angles and lengths mathematically the thesis also explores how accurate these might be. This leads to the surprisingly unstudied field of error modelling in Origami. Errors in folding processes have not previously been looked at from a mathematical point of view. The thesis develops a model for error estimation in crease patterns and a framework for error modelling in Origami applications. By introducing a standardised error into alignments, uniform error bounds for each of the one-fold constructions are generated. This defines a region in which a crease could lie in order to satisfy the alignments of a given fold within a specified tolerance. Analysis of this method on some examples provides insight into how this might be used in multi-fold constructions. An algorithm to that effect is introduced

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

The 1991 International Aerospace and Ground Conference on Lightning and Static Electricity, volume 2

The proceedings of the conference are reported. The conference focussed on lightning protection, detection, and forecasting. The conference was divided into 26 sessions based on research in lightning, static electricity, modeling, and mapping. These sessions spanned the spectrum from basic science to engineering, concentrating on lightning prediction and detection and on safety for ground facilities, aircraft, and aerospace vehicles

Architectures and algorithms for dynamic overlay networks

Most of today’s Internet of Things (IoT) applications assume that data will be moved offdevices into centralized cloud platforms. While existing IoT systems leverage cloud-based analytics for meaningful data reasoning, the assumption that data should always be moved off the devices is problematic. The amount of data to be moved from devices over Internet gateways to cloud platforms is huge which potentially make it cost inefficient. In other scenarios, privacy concerns of customers or organizational rules complicate the process of transferring data to third-party data centers.This dissertation proposes architectures and dynamic overlay network algorithms for in-networkand edge processing of data offered by the globally available IoT devices and provides a global platform for meaningful and responsive data analysis and decision making. The proposed techniques shift IoT analytics from a ”collect data now and analyze it later” scenario to directlyproviding meaningful information from the in-network processing of devices data at or near thedevices. The techniques serve future IoT use cases including distributed context awareness, on-demand data analysis, and in-network decision making. The dissertation comprises three main components.The first component is a device management protocol for cloning devices’ data in proximateEdge Computing platforms. Unlike existing application-layer IoT management protocols theproposed protocol uses the LTE LTE-A radio frame structure, device-to-device communication,and IoT data properties to avoid excessive network access latency in existing technologies.The second component realizes distributed IoT analytics as overlay networks of devices clones. By means of virtual network embedding, it selects and interconnects devices’ clones to efficiently realize applications’ virtual topologies to achieve goals such as minimum latency, minimum infrastructure cost, or maximum infrastructure utilization.Finally, the dissertation presents a communication middleware that allows autonomous discovery, self-deployment, and online migration of devices’ clones across heterogeneous Edge computing platforms. The middleware ensures that communication latency between clones is kept minimum despite the uncontrolled variability of the network and hosting platforms conditions.We evaluate the proposed architectures and algorithms through simulations and prototypeimplementation of various components in controlled testbed environments, which we evaluateusing real user applications. We explore the feasibility of the proposed techniques from boththeoretical and practical perspectives.Keywords: Cloud Computing, Internet of Things, Algorithmic Game Theory, Compressive Sensin

Mass Transfer in Multiphase Systems and its Applications

This book covers a number of developing topics in mass transfer processes in multiphase systems for a variety of applications. The book effectively blends theoretical, numerical, modeling and experimental aspects of mass transfer in multiphase systems that are usually encountered in many research areas such as chemical, reactor, environmental and petroleum engineering. From biological and chemical reactors to paper and wood industry and all the way to thin film, the 31 chapters of this book serve as an important reference for any researcher or engineer working in the field of mass transfer and related topics

Implementació d'algorismes eficients per resoldre problemes matemàtics

Recull de problemes d'estil similar als de l'International Collegiate Programming Contest, de caire algorísmic o matemàtic, amb les seves respectives solucions implementades en C++ o Java. En la solució de cada problema s'explica el raonament seguit per construir-la