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Proven Programs in Education: Science, Technology, and Mathematics (STEM)
by Robert E. SlavinLet the best evidence based practices guide you to STEM success. This series turns research into practice with practical, evidence-based advice from the world’s premier education researchers and authors. In this volume, top articles on science, technology, and math provide multiple perspectives on current STEM issues as well as strategies for effective teaching of STEM subjects at all grade levels. Each chapter offers: Research and case studies showcasing innovative approaches to teaching Best practices, validated by research, that have stood the test of time Practical advice you can put to work right away Sources for additional exploration of the research
Proving Darwin: Making Biology Mathematical
by Gregory ChaitinGroundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin's theory of evolution works on a mathematical level. For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth's life-forms evolved by blind chance. But does Darwin's theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It's a question no one has yet answered--in fact, no one has even attempted to answer it until now. In this illuminating and provocative book, Gregory Chaitin argues that we can't be sure evolution makes sense without a mathematical theory. He elucidates the mathematical scheme he's developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Chaitin presents an accessible introduction to metabiology, a new way of thinking about biological science that highlights the mathematical structures underpinning the biological world. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.
Proving Einstein Right: The Daring Expeditions that Changed How We Look at the Universe
by Cathie Pelletier S. James Gates,A thrilling adventure story chronicling the perilous journey of the scientists who set out to prove the theory of relativity--the results of which catapulted Albert Einstein to fame and forever changed our understanding of the universe.In 1911, a relatively unknown physicist named Albert Einstein published his preliminary theory of gravity. But it hadn't been tested. To do that, he needed a photograph of starlight as it passed the sun during a total solar eclipse. So began a nearly decade-long quest by seven determined astronomers from observatories in four countries, who traveled the world during five eclipses to capture the elusive sight. Over the years, they faced thunderstorms, the ravages of a world war, lost equipment, and local superstitions. Finally, in May of 1919, British expeditions to northern Brazil and the island of Príncipe managed to photograph the stars, confirming Einstein's theory.At its heart, this is a story of frustration, faith, and ultimate victory--and of the scientists whose efforts helped build the framework for the big bang theory, catapulted Einstein to international fame, and shook the foundation of physics.
Proving Ground: The Untold Story of the Six Women Who Programmed the World’s First Modern Computer
by Kathy KleimanDiscover a fascinating look into the lives of six historic trailblazers in this World War II-era story of the American women who programmed the world's first modern computer. After the end of World War II, the race for technological supremacy sped on. Top-secret research into ballistics and computing, begun during the war to aid those on the front lines, continued across the United States as engineers and programmers rushed to complete their confidential assignments. Among them were six pioneering women, tasked with figuring out how to program the world's first general-purpose, programmable, all-electronic computer—better known as the ENIAC—even though there were no instruction codes or programming languages in existence. While most students of computer history are aware of this innovative machine, the great contributions of the women who programmed it were never told—until now. Over the course of a decade, Kathy Kleiman met with four of the original six ENIAC Programmers and recorded extensive interviews with the women about their work. Proving Ground restores these women to their rightful place as technological revolutionaries. As the tech world continues to struggle with gender imbalance and its far-reaching consequences, the story of the ENIAC Programmers' groundbreaking work is more urgently necessary than ever before, and Proving Ground is the celebration they deserve.
Provisional Bibliography of Atlases, Floras and Faunas of European Cities: 1600-2014
by John G. KelceyThe bibliography provides information about the presence and distribution of plants and animals in cities throughout Europe. It will be of considerable interest to and should be used by a wide range of people including academics, researchers, librarians, school teachers, and people with a general interest in the natural history of cities. The bibliography is an important tool for the professions involved in the planning, design and management of high quality urban developments, including biologists, architects, urban designers, planners, consultants, medics. , sociologists, engineers, politicians, landscape architects, building surveyors, agronomists and landscape managers.
Provisioning, Recovery, and In-Operation Planning in Elastic Optical Networks
by Luis Velasco Marc RuizExplains the importance of Elastic Optical Networks (EONs) and how they can be implemented by the world’s carriers This book discusses Elastic Optical Networks (EONs) from an operational perspective. It presents algorithms that are suitable for real-time operation and includes experimental results to further demonstrate the feasibility of the approaches discussed. It covers practical issues such as provisioning, protection, and defragmentation. It also presents provisioning and recovery in single layer elastic optical networks (EON). The authors review algorithms for provisioning point-to-point, anycast, and multicast connections, as well as transfer-based connections for datacenter interconnection. They also include algorithms for recovery connections from failures in the optical layer and in-operation planning algorithms for EONs. Provisioning, Recovery and In-operation Planning in Elastic Optical Network also examines multi-layer scenarios. It covers virtual network topology reconfiguration and multi-layer recovery, and includes provisioning customer virtual networks and the use of data analytics in order to bring cognition to the network. In addition, the book: Presents managing connections dynamically—and the flexibility to adapt the connection bitrate to the traffic needs fit well for new types of services, such as datacenter interconnection and Network Function Virtualization (NFV) Examines the topic in a holistic and comprehensive way, addressing control and management plane issues for provisioning, recovery, and in-operation planning Covers provisioning, recovery, and in-operation planning for EONs at the proposed exhaustive level The rapid expanse of new services has made the use of EONs (a relatively new concept) a necessity. That’s why this book is perfect for students and researchers in the field of technologies for optical networks (specifically EONs), including network architectures and planning, dynamic connection provisioning, on-line network re-optimization, and control and management planes. It is also an important text for engineers and practitioners working for telecom network operators, service providers, and vendors that require knowledge on a rapidly evolving topic.
Provocative Plastics: Their Value in Design and Material Culture
by Susan LambertPlastics have now been our most used materials for over fifty years. This book adopts a new approach, exploring plastics’ contribution from two perspectives: as a medium for making and their value in societal use. The first approach examines the multivalent nature of plastics materiality and their impact on creativity through the work of artists, designers and manufacturers. The second perspective explores attitudes to plastics and the different value systems applied to them through current research undertaken by design, materials and socio-cultural historians. The book addresses the environmental impact of plastics and elucidates the ways in which they can and must be part of the solution. The individual viewpoints are provocative and controversial but together they present a balanced and scholarly un-picking of the debate that surrounds this ubiquitous group of materials. The book is essential reading for a wide academic readership interested in the Arts and Humanities, especially Design and Design History; Anthropology; and Cultural, Material and Social Histories.
Proximity Labeling: Methods and Protocols (Methods in Molecular Biology #2008)
by Murat Sunbul Andres JäschkeThis book provides detailed protocols and untold tips and tricks regarding the most well-known examples of proximity labeling methods, in which the protein of interest is genetically fused to or labeled with an enzyme that can generate short-lived reactive species to non-specifically label molecules within a certain radius of up to twenty nanometers. Beginning with peroxidase-based proximity labeling methods, the volume continues with BioID, proximity labeling methods that describe the proximity ligation assay to detect RNA-DNA interactions, UV cross-linking to demonstrate RNA-protein interactions, and how chemical and enzymatic reactivities can be improved upon DNA-DNA and protein-protein interactions, as well as “proximity-induced self-labeling,” where the radius of labeling is zero. Written for the highly successful Methods in Molecular Biology series, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and practical, Proximity Labeling: Methods and Protocols serves as an ideal guide for researchers exploring the crucial roles that proximity-driven reactions play in biological systems.
Proxy: An Avalon Novella
by Mindee ArnettProxy is an action-packed introduction to a world like nothing readers have seen before, and it sets a spark to the powder keg that will explode in Mindee Arnett's sci-fi thriller Avalon.If you need something stolen from any star system in the Confederation, you need look no further than the Shades. Jeth Seagrave and his band of teenage mercenaries have been making a name for themselves for being able to steal anything--and for disappearing before anyone is the wiser. Their latest job, a jewel heist on Grakkus, should be no different. But when Jeth's boss replaces a key member of his crew just before takeoff, and Jeth discovers a betrayal within his own ranks, he begins to suspect that not everyone is going to be coming back from his job alive.HarperTeen Impulse is a digital imprint focused on young adult short stories and novellas, with new releases the first Tuesday of each month.
Prozac: Questions and Answers
by Ronald R. FieveFeatured on the cover of "Newsweek" and "New York Magazine. ". . debated on television and radio, written about in daily newspapers, "Prozac has raised hopes and sparked controversies across the country. But how much do you really know about "Prozac, the alleged "miracle drug" that doctors worldwide have employed to help alleviate crippling clinical depression in their patients?The bestselling author of "Moodswing," Dr. Ronald R. Fieve is one of the nation's foremost experts on "Prozac and its uses. In a clear, concise and easy-to-use format, he provides detailed and authoritative answers to the most commonly asked questions about "Prozac. . . giving essential information to help make "informed" decisions on this complex, often confusing, prescription, and offering interpretation of the effects of "Prozac on personality as well as the dangers of prescribing "Prozac to "misdiagnosed" patients.
Prozess- und Anlagensicherheit
by Ulrich HauptmannsStörfälle in technischen Anlagen sind Zufallsereignisse. Deshalb kann man sie nicht gänzlich vermeiden. Wohl aber lassen sich die Wahrscheinlichkeit ihres Auftretens und das Schadensausmaß verringern. In diesem Buch werden, ausgehend von Gefährdungen durch Stoffe und Betriebsbedingungen, mögliche technische und organisatorische Maßnahmen aufgezeigt, Gefährdungen zu mindern. Qualitative Analysemethoden zum Auffinden von Schwachstellen und zur Erhöhung der Sicherheit sowie Modelle zur Abschätzung von Störfallfolgen werden dargestellt. Die quantitative Bewertung der Wirksamkeit von Maßnahmen zur Verbesserung von Anlagentechnik und Sicherheit wird erläutert. Dabei spielen Unsicherheiten, die aus dem Zufallscharakter des Störfalls und aus Kenntnislücken bei einigen der zu behandelnden Phänomene folgen, eine Rolle. Der Leser wird mit Methoden der Störfallsimulation sowie Sicherheits- und Risikoanalysen vertraut gemacht und lernt, Möglichkeiten und Grenzen mathematischer Modellierung einzuschätzen. Als Grundlage sicherheitsrelevanter Entscheidungen wird die Risikoermittlung u.a. auf die Beurteilung der „funktionalen Sicherheit“ und die Bestimmung „angemessener Sicherheitsabstände“ zwischen Industrie und Bebauung angewandt. Zahlreiche ausgearbeitete Beispiele und Fallstudien realer Anlagen und Situationen vertiefen die Inhalte und erleichtern das Selbststudium.Die zweite Auflage des vorliegenden Buches eröffnete die Möglichkeit, den Text gründlich durchzusehen und eine Reihe von Korrekturen vorzunehmen. Zusätzliche Beispiele, die sich aus Anfragen aus der Praxis ergaben, wurden aufgenommen. Das Kapitel über „angemessene Sicherheitsabstände“ wurde um aktuelle Erfahrungen aus der Beratertätigkeit des Verfassers erweitert.
Prozessanalytik: Strategien und Fallbeispiele aus der industriellen Praxis
by Herausgegeben Von Rudolf W. KesslerIn den letzten Jahren hat sich der Trend zu einer hoheren Komplexitat in der Fertigung industrieller Guter verstarkt. Optische und spektroskopische Methoden zur Prozessanalytik sind sehr schnell, messen beruhrungslos und damit zerstorungsfrei. Mit geringem Aufwand wird so eine hundertprozentige Kontrolle bei der Qualitatsprufung moglich. Kernpunkt einer neuen Strategie ist der Einsatz von analytischen Online-Methoden als Qualitatskontrolle sowie die Kombination dieser Techniken mit den Methoden der Datenanalyse zur Steuerung von Produktionsprozessen. Das Buch liefert sowohl einen Uberblick uber die industriell bedeutenden Analyseverfahren als auch praktische Beispiele zur Einfuhrung der Online-Analytik in den industriellen Alltag. Damit wird die gesamte Prozess- und Fertigungsindustrie angesprochen - von der chemischen, pharmazeutischen, biotechnologischen und verfahrenstechnischen Industrie bis zur Kunststoff-, Automobil- und der klassischen Fertigungsindustrie. Nach einer Lehre als Chemielaborant, einem Chemie-Ingenieurstudium an der Fachhochschule Reutlingen und einem Chemiestudium an der Universitat in Tubingen hat Rudolf W. Kessler 1980 am Institut fur Physikalische Chemie in Tubingen promoviert. Seine berufliche Laufbahn fuhrte ihn uber die Forschung bei Daimler Benz 1985 an die Fachhochschule Reutlingen. Als Grundungsdirektor des Institutes fur Angewandte Forschung 1990 und dessen Leiter bis zum Jahr 2000 war er ma?geblich am Aufbau der Prozessanalytik in Forschung und Lehre der Hochschule Reutlingen beteiligt. Zahlreiche nationale und viele internationale Projekte, sowie Forschungsaufenthalte in China, USA, England und vor kurzem auch wieder ein Jahr in der Industrie haben den Praxisbezug der Lehre und der Forschung auf dem Gebiet der optischen Online-Spektroskopie hergestellt. Seit einigen Jahren beschaftigt sich Rudolf W. Kessler auch mit der Nahfeldspektroskopie und dem "Chemical Imaging" von Werkstoffen und Oberflachen.
Prudent Practices in the Laboratory
by The National Academy of SciencesThe National Research Council published two guides during the early 1980s, updated and combined them in 1995, and in 2007 began the process of creating a new edition. Throughout its history, the reference has been intended to be useful to laboratory workers and managers, but also to help inform regulatory policy. Among the topics are the culture of laboratory safety, emergency planning, managing chemicals, working with laboratory equipment, laboratory security, and relevant safety laws and standards. The accompanying disk contains supplemental materials such as a sample incident report form, and procedures for the laboratory-scale treatment of surplus and waste chemicals. Annotation ©2011 Book News, Inc. , Portland, OR (booknews. com)
Prüfungstrainer Elektrotechnik: Erst verstehen, dann bestehen
by Martin PoppeDieses Buch bereitet gezielt auf eine Prüfung vor dem Bachelor-Abschluss vor. Es enthält Antworten auf Prüfungsfragen, Lösungsstrategien für Klausuraufgaben und Begründungen der wesentlichen Gesetze der Elektrotechnik und Elektronik. Die Fragen sind nach Schwierigkeitsgrad geordnet. So können die Studierenden Lücken im eigenen Wissen finden und durch ein vertieftes Verständnis ersetzen. Über 300 Abbildungen helfen dem Verständnis und vollständig durchgerechnete aktuelle Praxisbeispiele veranschaulichen den Stoff.Die 3. Auflage wurde aktualisiert, vollständig überarbeitet und enthält nun zusätzlich zu den mehr als 200 Klausuraufgaben 160 neue Fragen aus mündlichen Prüfungen und verständlich begründete Antworten. Das Buch wendet sich an Studierende der Elektrotechnik im Haupt- oder Nebenfach, die sich gezielt auf eine Prüfung vor dem Bachelor-Abschluss vorbereiten wollen.
Prüfungstrainer Elektrotechnik: Erst verstehen, dann bestehen
by Martin PoppeDieses Buch soll helfen, Prüfungen auf dem Gebiet der Elektrotechnik zu bestehen. Die 4. Auflage wurde aktualisiert, vollständig überarbeitet und bietet den Zugang zu mehr als 300 elektronischen Karteikarten („Flash Cards“), mit deren Hilfe die Kenntnis elementarer elektrotechnischer Begriffe und Zusammenhänge gefestigt werden kann. Das Buch enthält 160 Fragen aus mündlichen Prüfungen und verständlich begründete Antworten sowie mehr als 200 nach Schwierigkeitsgrad geordnete Klausuraufgaben. Zu diesen Aufgaben werden ausführliche Lösungen vorgerechnet und Lösungsstrategien vermittelt.Zu jedem der acht Themengebiete werden in einem Theorieteil die grundlegenden Zusammenhänge erläutert. Über 300 Abbildungen helfen dem Verständnis und vollständig durchgerechnete aktuelle Praxisbeispiele veranschaulichen den Stoff.
Prüfungstrainer Elektrotechnik: Erst verstehen, dann bestehen
by Martin PoppeDieses Buch bereitet gezielt auf eine Prüfung vor dem Bachelor-Abschluss vor. Es enthält Antworten auf Prüfungsfragen, Lösungsstrategien für Klausuraufgaben und Begründungen der wesentlichen Gesetze der Elektrotechnik und Elektronik. Das Buch enthält zur Verdeutlichung der Lösungsstrategien mehr als 300 Abbildungen.Für die 2. Auflage neu aufgenommen wurden neben Feldberechnungen mit und ohne Magnetkreise auch diverse Praxisbeispiele und Details zum Verhalten von Leitungen.
Prüfungstrainer Spezielle Zoologie
by Isabell Schumann Stefan SchafferDieser Prüfungstrainer führt als roter Faden durch das komplexe Gebiet der Speziellen Zoologie mit einem Überblick über alle systematisch relevanten Tiergruppen. Anhand vieler Beispiele bietet dieses Buch eine Reise durch das gesamte Tierreich – von Protisten zu den Säugetieren – und greift dabei prüfungsrelevante Themen und Schwerpunkte sinnvoll auf. Körperbau, wichtige ökologische Funktionen und Verwandtschaften der Tiergruppen werden nicht nur in schlüssigen Beschreibungen und Erklärungen, sondern auch mit zahlreichen Abbildungen veranschaulicht. Durch die einheitliche Beschreibung systematisch relevanter Tiergruppen werden die komplexen und vielseitigen Inhalte der zoologischen Systematik zu einem prägnanten Basiswissen zusammengefasst. Mit zahlreichen Fragen und digitalen Karteikarten zur Wissensüberprüfung sowie freien Seiten für individuelle Notizen ist dieser Prüfungstrainer die beste Ausgangsbasis für den Einstieg in die vertiefende Literatur und den erfolgreichen Abschluss Ihrer Zoologie-Prüfung.
Prüfungstraining Organische Chemie: Für Studierende der Chemie, Biochemie, Pharmazie und anderer Naturwissenschaften
by Eberhard BreitmaierDer ideale Begleiter für die Prüfungsvorbereitung im Fach Organische Chemie Für alle Studierenden der Chemie, Biochemie, Pharmazie und anderer Naturwissenschaften an Universitäten und Fachhochschulen gehören Vorlesungen der Organischen Chemie zu den Pflichtveranstaltungen und zum Prüfungsstoff. Dieser kompakte Prüfungstrainer basiert auf der umfangreichen Lehrerfahrung des Autors und präsentiert die Grundlagen der organischen Chemie in 86 kurzen, in sich geschlossenen Lerneinheiten, auf ein bis max. zwei Doppelseiten (Zweiseitenansicht). Eine Auswahl an Verständnisfragen am Ende jedes Kapitels und Antworten im Anhang ermöglichen eine effektive Selbstkontrolle und ideale Prüfungsvorbereitung. Ob für Studierende der Chemie, Biochemie, Pharmazie, Biologie – hier werden alle wesentlichen Themen kurz und verständlich erklärt: von Atomorbitalen über Hybridorbitale zu den Molekülorbitalen kovalenter Bindungen grundlegende Definitionen und Konzepte, wie Konstitution, Konformation, Konfiguration, Chiralität, Konjugation, Mesomerie, Aromatizität Verbindungsklassen und ihre Nomenklatur, einschließlich Naturstoffe, Polymere und Biopolymere Organische Reaktionen (Typen, Mechanismen, Selektivität und Spezifität) Molekülstruktur (kurze Einführung in die Strategie der Aufklärung durch Massenspektrometrie, Lichtabsorptions-, IR- und NMR-Spektroskopie) Planung organischer Synthesen Damit ist das Prüfungstraining Organische Chemie ein unverzichtbares Repetitorium für Studierende mit den Studienabschlüssen Bachelor, Master und Staatsexamen, die ihr Wissen in der Organischen Chemie festigen wollen, um die Prüfung gut zu bestehen.
Prüfungstraining Technische Mechanik
by Stefan HartmannMit „Prüfungstraining Technische Mechanik“ von Stefan Hartmann braucht man vor Klausuren und Prüfungen nicht mehr zu zittern. Mehr als 250 Aufgaben mit ausführlich durchgerechneten Lösungen aus allen Themengebieten der Technischen Mechanik – Statik, Elastostatik, Kinematik und Dynamik – helfen beim Verstehen und Vertiefen der Lerninhalte. Unerlässlich für Studierende in Ingenieurstudiengängen wie Maschinenbau, Verfahrenstechnik und Bauwesen: Insbesondere zusammen mit dem Lehrbuch „Technische Mechanik“ legt das Prüfungstraining die Grundlagen fürs weiterführende Studium.
The Prunus mume Genome (Compendium of Plant Genomes)
by Zhihong GaoThis book reviews the current status of P. mume research, highlighting how the new data coming from the release of the P. mume genomes can advance science and help to solve a number of problems facing the P. mume industry. Prunus mume, which was domesticated in China more than 3,000 years ago as an ornamental plant and for its fruit, is one of the first genomes among the Prunus subfamilies of the Rosaceae family that has been sequenced. Combining the P. mume genome with available data, scientists have succeeded in reconstructing nine ancestral chromosomes of the Rosaceae family, as well as the chromosome fusion, fission and duplication history of three major subfamilies. The P. mume genome sequence adds to our understanding of Rosaceae evolution and provides an important basis for the improvement of fruit trees. This book offers an essential a guide for all those who are interested in gene discovery, comparative genomics, molecular breeding and new breeding techniques; and will be particularly useful for scientists, breeders, university students, and public sector institutes that are involved in the P. mume industry and/or Rosaceae research.
Prussian Blue Based Batteries (SpringerBriefs in Applied Sciences and Technology)
by María José Piernas Muñoz Elizabeth Castillo MartínezThis book reviews the structure and composition of Prussian Blue materials. It presents the state-of-the-art of their application to metal-ion batteries, highlighting the benefits derived from the integration of electrochemical energy storage with clean energies. It concludes with future perspectives including prototyping and large-scale production.
Psammic Peinobiomes: Nutrient-Limited Ecosystems of the Upper Orinoco and Rio Negro Basins (Ecological Studies #247)
by Joseph Alfred Zinck Otto Huber Pedro García Montero Ernesto MedinaThe book represents a multidisciplinary approach to understanding soil–landscape–vegetation relationships and, specifically, the ecophysiology of plant communities developing on sandy soils of very low fertility that are subject to seasonal flooding. It provides an overview of the white sand ecosystems within the Amazon basin, and focuses on the forest and herbaceous (meadows) vegetation growing on the dystrophic sandy soils of the upper Negro and Orinoco river basins. Several chapters describe physiographic aspects of the study area using integrated remote sensing and in situ sampling. By doing so they attain a comprehensive description of the origin and evolution of soils and landscapes, an advanced classification of soils, and a mapping of the geographic distribution of psammophilous vegetation. This volume also provides a phytosociological classification of extensive forested areas, and a detailed description of the structure and diversity of little-known herbaceous formations.It targets professionals in the fields of ecology, ecophysiology, geomorphology, soils, vegetation, and the environmental sciences. The information it offers may be of significant use to researchers, protected area planners, and environmental policy makers.
Pseudo-Bosoni e Loro Stati Coerenti
by Fabio BagarelloL'analisi proposta in questo libro si focalizza su particolari deformazioni delle regole di commutazione canoniche suggerite dal recente, e sempre crescente, interesse per la meccanica quantistica PT-simmetrica. Se ne considerano diverse conseguenze di natura matematica, ma anche loro possibili applicazioni alla fisica. Queste includono l'analisi di diverse Hamiltoniane non autoaggiunte, il calcolo di integrali di cammino associati a tali Hamiltoniane per mezzo di stati bi-coerenti, ed una nuovo punto di vista sugli operatori posizione e momento. Il libro è prevalentemente destinato ai ricercatori ma è anche pensato per essere fruibile da studenti di magistrale e di dottorato. Fornisce inoltre una introduzione ad alcuni aspetti delicati dell'analisi funzionale e della meccanica quantistica per osservabili non autoaggiunte.
Pseudo-Complex General Relativity
by Walter Greiner Mirko Schäfer Peter O. HessThis book explores the role of singularities in general relativity (GR): The theory predicts that when a sufficient large mass collapses, no known force is able to stop it until all mass is concentrated at a point. The question arises, whether an acceptable physical theory should have a singularity, not even a coordinate singularity. The appearance of a singularity shows the limitations of the theory. In GR this limitation is the strong gravitational force acting near and at a super-massive concentration of a central mass. First, a historical overview is given, on former attempts to extend GR (which includes Einstein himself), all with distinct motivations. It will be shown that the only possible algebraic extension is to introduce pseudo-complex (pc) coordinates, otherwise for weak gravitational fields non-physical ghost solutions appear. Thus, the need to use pc-variables. We will see, that the theory contains a minimal length, with important consequences. After that, the pc-GR is formulated and compared to the former attempts. A new variational principle is introduced, which requires in the Einstein equations an additional contribution. Alternatively, the standard variational principle can be applied, but one has to introduce a constraint with the same former results. The additional contribution will be associated to vacuum fluctuation, whose dependence on the radial distance can be approximately obtained, using semi-classical Quantum Mechanics. The main point is that pc-GR predicts that mass not only curves the space but also changes the vacuum structure of the space itself. In the following chapters, the minimal length will be set to zero, due to its smallness. Nevertheless, the pc-GR will keep a remnant of the pc-description, namely that the appearance of a term, which we may call "dark energy", is inevitable. The first application will be discussed in chapter 3, namely solutions of central mass distributions. For a non-rotating massive object it is the pc-Schwarzschild solution, for a rotating massive object the pc-Kerr solution and for a charged massive object it will be the Reissner-Nordström solution. This chapter serves to become familiar on how to resolve problems in pc-GR and on how to interpret the results. One of the main consequences is, that we can eliminate the event horizon and thus there will be no black holes. The huge massive objects in the center of nearly any galaxy and the so-called galactic black holes are within pc-GR still there, but with the absence of an event horizon! Chapter 4 gives another application of the theory, namely the Robertson-Walker solution, which we use to model different outcomes of the evolution of the universe. Finally the capability of this theory to predict new phenomena is illustrated.
Pseudo-Hermitian Random Matrices
by Mauricio Porto PatoThis book is a comprehensive guide to pseudo-Hermitian random matrices, their properties, and their role in many models that are relevant to physical processes. The book starts by showing how the concept of pseudo-Hermiticity emerged from studies of PT-symmetric systems which aroused the interest of the random matrix theory community. The chapters that follow discuss the consequences of the pseudo-Hermitian condition to the eigen-decomposition of non-Hermitian matrices, and an investigation of pseudo-Hermitian random matrices in tridiagonal form, discussing the scenario with real eigenvalues, and the appearance of complex eigenvalues generated by unbound and non-positive metrics. Subsequently, the author introduces pseudo-Hermitian Gaussian matrices and their properties including characteristic polynomials, and statistical properties of their eigenvalues. Finally, in the last chapter, the time invariance of the metric is upended and a pseudo-Hermitian model with a time dependent metricis constructed to discuss the time evolution of entangled states.