Elements of ∞-Category Theory

The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

Structural and System Reliability

Based on material taught at the University of California, Berkeley, this textbook offers a modern, rigorous and comprehensive treatment of the methods of structural and system reliability analysis. It covers the first- and second-order reliability methods for components and systems, simulation methods, time- and space-variant reliability, and Bayesian parameter estimation and reliability updating. It also presents more advanced, state-of-the-art topics such as finite-element reliability methods, stochastic structural dynamics, reliability-based optimal design, and Bayesian networks. A wealth of well-designed examples connect theory with practice, with simple examples demonstrating mathematical concepts and larger examples demonstrating their applications. End-of-chapter homework problems are included throughout. Including all necessary background material from probability theory, and accompanied online by a solutions manual and PowerPoint slides for instructors, this is the ideal text for senior undergraduate and graduate students taking courses on structural and system reliability in departments of civil, environmental and mechanical engineering.

Classical and Discrete Functional Analysis with Measure Theory

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

A Study on the Conservation and Management of the Painting of Shamanistic Spirits in Chiseonggwang Buddha

This study presents a method for conserving shamanistic spirits in Chiseonggwang Buddha. Scientific investigation has revealed that these spirits have been subject to degeneration as a result of severe exfoliation and pollution. The materials and preservation treatment techniques used in create these shamanistic spirits were identified through visual inspection and using appropriate scientific equipment. The different types of background paper, background material, and color pigments used in create the shamanistic spirits were analyzed using a colorimeter, stereoscopic microscope, and SEM-EDS techniques. The analysis revealed that the pulp paper was used as the background and synthetic fiber polyester as the background material. In addition, the study of the pigment revealed that the color components were all synthetic, except for red lead [Pb3O4] and oyster shell white [CaCO3]. Moreover, it was confirmed that the green pigment, identified as emerald green [Cu(C2H3O2)2.3Cu(AsO2)2], was a major component of shamanistic spirits in the late 19th century. The shamanistic spirits in Chiseonggwang Buddha were conserved by identifying raw materials and pigments through this detailed analysis.

Neuroplasticity

As editor Bruce Tidor sets it in the preface of the book, published in the volume of the MIT Essential Knowledge series: ‘Synthesizing specialized subject matter for non-specialists and engaging critical topics through fundamentals, each of these compact volumes offers readers a point of access to complex ideas.’ (Costandi, 2016). In this book of the series Moheb Costandi provides the reader with a celar and coherent picture about neuroplasticity and neurogenesis . Not just at the level of theories and research results, but also regarding various stages of practical application. It is equally applicable for average people in areas of everyday life- adult education, lifelong learning, and mental training, too. Costandi’s book is decidedly good background material for Anders Hansen’s practical book ‘The Real Happy Pill: Power Up Your Brain by Moving Your Body’ (Németh, 2020).

Are Massive Dense Clumps Truly Subvirial? A New Analysis Using Gould Belt Ammonia Data

Dynamical studies of dense structures within molecular clouds often conclude that the most massive clumps contain too little kinetic energy for virial equilibrium, unless they are magnetized to an unexpected degree. This raises questions about how such a state might arise, and how it might persist long enough to represent the population of massive clumps. In an effort to reexamine the origins of this conclusion, we use ammonia line data from the Green Bank Ammonia Survey and Planck-calibrated dust emission data from Herschel to estimate the masses and kinetic and gravitational energies for dense clumps in the Gould Belt clouds. We show that several types of systematic error can enhance the appearance of low kinetic-to-gravitational energy ratios: insufficient removal of foreground and background material; ignoring the kinetic energy associated with velocity differences across a resolved cloud; and overcorrecting for stratification when evaluating the gravitational energy. Using an analysis designed to avoid these errors, we find that the most massive Gould Belt clumps harbor virial motions, rather than subvirial ones. As a by-product, we present a catalog of masses, energies, and virial energy ratios for 85 Gould Belt clumps.

The pursuit of a dream, Francisco Javier Sayas and the HDG methods

Franciso Javier Sayas, man of grit and determination, left his hometown of Zaragoza in 2007 in pursuit of a dream, to become a scholar in the USA. I hosted him in Minneapolis, where he spent three long years of an arduous transition before obtaining a permanent position at the University of Delaware. There, he enthusiastically worked on the unfolding of his dream until his life was tragically cut short by cancer, at only 50. In this paper, I try to bring to light the part of his academic life he shared with me. As we both worked on hybridizable discontinuous Galerkin methods, and he wrote a book on the subject, I will tell Javier’s life as it developed around this topic. First, I will show how the ideas of static condensation and hybridization, proposed back in the mid 60s, lead to the introduction of those methods. This background material will allow me to tell the story of the evolution of the hybridizable discontinuous Galerkin methods and describe Javier’s participation in it. Javier faced death with open eyes and poised dignity. I will end with a poem he liked.

Spaces of Measures and their Applications to Structured Population Models

Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.

Conformal Design of a High-Performance Antenna for Energy-Autonomous UWB Communication

In view of the need for communication with distributed sensors/items, this paper presents the design of a single-port antenna with dual-mode operation, representing the front-end of a future generation tag acting as a position sensor, with identification and energy harvesting capabilities. An Archimedean spiral covers the lower European Ultra-Wideband (UWB) frequency range for communication/localization purposes, whereas a non-standard dipole operates in the Ultra High Frequency (UHF) band to wirelessly receive the energy. The versatility of the antenna is guaranteed by the inclusion of a High Impedance Surface (HIS) back layer, which is responsible for the low-profile stack-up and the insensitivity to the background material. A conformal design, supported by 3D-printing technology, is pursued to check the versatility of the proposed architecture in view of any application involving its deformation and tracking/powering operations.