Solving Problems in Point Geometry (1版)

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【簡介】 For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of auxiliary graphics and cumbersome calculations. Inspired by Leibniz's query, this book introduces a groundbreaking method: point geometry. By operating directly on points, it integrates the strengths of coordinate, vector, and mass point methods, simplifying operations and problem-solving. Central to this method is the identity approach, which streamlines complex problems into concise equations, unlocking multiple propositions with ease. Through meticulously crafted examples, readers are invited to explore the joy of mathematical thinking. Beyond mathematics, point geometry holds promise for artificial intelligence, offering a simple yet rich knowledge representation and reasoning method. With most solutions generated by computer programs, the potential for simplifying reasoning methods is immense, paving the way for a brighter future in both education and AI advancement. In this ambitious endeavor, the authors seek to simplify knowledge representation and reasoning, reduce the burden of learning, and accelerate the progress of artificial intelligence. This book is not just a guide to geometry; it's a catalyst for transformative thinking and discovery. Request Inspection Copy 【目錄】

Vibration Problems in Machines: Diagnosis and Resolution (1版)

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【簡介】 【目錄】 Vibration Problems in Machines: Diagnosis and Resolution explains how to infer information about the internal operations of rotating machines from external measurements. In doing so, the book examines the vibration signals arising under various fault conditions, such as rotor imbalance, misalignment, cracked rotors, gear wear, whirling instabilities, and other problems. Covering a wide range of techniques required in the monitoring, analysis, and diagnosis of operational rotating machinery, this text: Discusses topics ranging from the presentation of complex data to methods for reconciling model and plant data Describes the physical basis of fault signals as well as the necessary signal and data processing techniques Delivers fresh insight into misalignment phenomena and the future of smart machinery Vibration Problems in Machines: Diagnosis and Resolution includes case studies with real plant data, MATLAB® scripts and functions for the modelling and analysis of rotating machines, end-of-chapter questions, and a solutions manual with qualifying course adoption. The book provides an invaluable resource for those seeking to optimize the use of complex and often apparently contradictory data.

Computing and Analysing Energy Minimisation Problems in Liquid Crystals

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How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects? There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc. This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems. Sample Chapter(s) Preface Chapter 1: Introduction Chapter 2: A Mathematical Model of Nematics and Cholesterics Contents: Introduction Nematic and Cholesteric Liquid Crystals: A Mathematical Model of Nematics and Cholesterics A Robust Multigrid Algorithm for the Augmented Director Block Numerical Experiments for Nematics and Cholesterics Ferronematic Liquid Crystals: A Mathematical Model of Ferronematics Computing Multiple Solutions Using Deflation Numerical Verifications for Ferronematics Smectic Liquid Crystals: A Mathematical Model of Smectics Finite Element Discretisation Numerical Experiments for Smectics Conclusions and Perspectives: Summary and Conclusions Appendices: Stability of the Newton System Equilibrium Equations in Two Dimensions Readership: Advanced undergraduate and graduate students interested in numerical modelling of liquid crystals; researchers in the fields of mathematical theories and numerical aspects in liquid crystals.