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Advanced Problems in Mathematics: Preparing for University

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Book Series: OBP Series in Mathematics ISSN: 2397-1126 / 2397-1134 ISBN: 9781783747764 9781783747771 Pages: 186 DOI: 10.11647/OBP.0181 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2019-10-29 12:26:38
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This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Quantum Probability and Randomness

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ISBN: 9783038977148 9783038977155 Year: Pages: 276 DOI: 10.3390/books978-3-03897-715-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-04-25 16:37:17
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The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics&mdash;in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.

Keywords

quantum logic --- groups --- partially defined algebras --- quasigroups --- viable cultures --- quantum information theory --- bit commitment --- protocol --- entropy --- entanglement --- orthogonality --- quantum computation --- Gram–Schmidt process --- quantum probability --- potentiality --- complementarity --- uncertainty relations --- Copenhagen interpretation --- indefiniteness --- indeterminism --- causation --- randomness --- quantum information --- quantum dynamics --- entanglement --- algebra --- causality --- geometry --- probability --- quantum information theory --- realism --- reality --- entropy --- correlations --- qubits --- probability representation --- Bayes’ formula --- quantum entanglement --- three-qubit random states --- entanglement classes --- entanglement polytope --- anisotropic invariants --- quantum random number --- vacuum state --- maximization of quantum conditional min-entropy --- quantum logics --- quantum probability --- holistic semantics --- epistemic operations --- Bell inequalities --- algorithmic complexity --- Borel normality --- Bayesian inference --- model selection --- random numbers --- quantum-like models --- operational approach --- information interpretation of quantum theory --- social laser --- social energy --- quantum information field --- social atom --- Bose–Einstein statistics --- bandwagon effect --- social thermodynamics --- resonator of social laser --- master equation for socio-information excitations --- quantum contextuality --- Kochen–Specker sets --- MMP hypergraphs --- Greechie diagrams --- quantum foundations --- probability --- irreducible randomness --- random number generators --- quantum technology --- entanglement --- quantum-like models for social stochasticity --- contextuality

Risk Analysis and Portfolio Modelling

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ISBN: 9783039216246 9783039216253 Year: Pages: 224 DOI: 10.3390/books978-3-03921-625-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Business and Management
Added to DOAB on : 2019-12-09 11:49:15
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Financial Risk Measurement is a challenging task, because both the types of risk and the techniques evolve very quickly. This book collects a number of novel contributions to the measurement of financial risk, which address either non-fully explored risks or risk takers, and does so in a wide variety of empirical contexts.

Financial Econometrics

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ISBN: 9783039216260 9783039216277 Year: Pages: 136 DOI: 10.3390/books978-3-03921-627-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Economics
Added to DOAB on : 2019-12-09 11:49:15
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Financial econometrics has developed into a very fruitful and vibrant research area in the last two decades. The availability of good data promotes research in this area, specially aided by online data and high-frequency data. These two characteristics of financial data also create challenges for researchers that are different from classical macro-econometric and micro-econometric problems. This Special Issue is dedicated to research topics that are relevant for analyzing financial data. We have gathered six articles under this theme.

Quantum Foundations. 90 Years of Uncertainty

Authors: --- --- ---
ISBN: 9783038977544 Year: Pages: 188 DOI: 10.3390/books978-3-03897-755-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2019-04-05 10:34:31
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The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.

Stochastic Processes: Theory and Applications

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ISBN: 9783039219629 9783039219636 Year: Pages: 216 DOI: 10.3390/books978-3-03921-963-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics --- Statistics
Added to DOAB on : 2020-01-07 09:08:26
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The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited to: Markov chains and processes; large deviations and limit theorems; random motions; stochastic biological model; reliability, availability, maintenance, inspection; queueing models; queueing network models; computational methods for stochastic models; applications to risk theory, insurance and mathematical finance.

Keywords

measure of information --- cumulative inaccuracy --- mutual information --- lower record values --- parabolic equation --- Cauchy problem --- Monte Carlo method --- unbiased estimator --- von-Neumann–Ulam scheme --- compound poisson insurance risk model --- expected discounted penalty function --- estimation --- Fourier transform --- Fourier-cosine series --- multidimensional birth-death process --- inhomogeneous continuous-time Markov chain --- rate of convergence --- one dimensional projection --- Wiener–Poisson risk model --- survival probability --- Nonparametric threshold estimation --- wet periods --- total precipitation volume --- asymptotic approximation --- extreme order statistics --- random sample size --- testing statistical hypotheses --- queueing systems --- rate of convergence --- non-stationary --- Markovian queueing models --- limiting characteristics --- queuing network --- retrials --- state-dependent marked Markovian arrival process --- wireless telecommunication networks --- time-dependent queue-length probability --- discrete-time Geo/D/1 queue --- closed-form solution --- Monte Carlo method --- quasi-Monte Carlo method --- Koksma-Hlawka inequality --- quasi-random sequences --- stochastic processes --- processor heating and cooling --- markovian arrival process --- phase-type service time distribution --- impatience --- Quasi-Birth-and-Death process --- matrix-geometric solution --- truncated distribution --- Markovian arrival process --- multi-class arrival processes --- product form --- equity-linked death benefits --- Fourier cosine series expansion --- guaranteed minimum death benefit --- option --- valuation --- Lévy process --- compound Poisson risk model --- generalized Gerber–Shiu discounted penalty function --- Laplace transform --- Dickson–Hipp operator --- recursive formula

Forest Hydrology and Watershed

Authors: --- --- ---
ISBN: 9783039213856 9783039213863 Year: Pages: 206 DOI: 10.3390/books978-3-03921-386-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General)
Added to DOAB on : 2019-12-09 11:49:15
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Hydrological processes in forested watersheds are influenced by environmental, physiological, and biometric factors such as precipitation, radiation, temperature, species type, leaf area, and extent and structure of forest ecosystems. Over the past two centuries, forest coverage and forest structures have been impacted globally by anthropogenic activities, for example, forest harvesting, and conversion of forested landscapes for plantations and urbanization. In addition, since the industrial revolution, climate change has resulted in profound impacts on forest ecosystems due to higher carbon dioxide (CO2) concentration or CO2 fertilization, warmer temperatures, changes in frequency and intensity of extreme weather events and natural disturbances. As a result, hydrological processes in forested watersheds have been altered by these natural and anthropogenic factors and these changes are expected to accelerate due to future changing climatic conditions.

HVDC for Grid Services in Electric Power Systems

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ISBN: 9783039217625 9783039217632 Year: Pages: 176 DOI: 10.3390/books978-3-03921-763-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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The modern electric power system has evolved into a huge nonlinear complex system due to the interconnection of thousands of generation and transmission systems. The unparalleled growth of renewable energy resources (RESs) has caused significant concern regarding grid stability and power quality, and it is essential to find ways to control such a massive system for effective operation. The controllability of HVDC and FACTS devices allows for improvement of the dynamic behavior of grids and their flexibility. Research is being carried out at both the system and component levels of modelling, control, and stability. This Special Issue aims to present novel HVDC topologies and operation strategies to prevent abnormal grid conditions.

Marine Oil Spills 2018

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ISBN: 9783038978541 9783038978558 Year: Pages: 288 DOI: 10.3390/books978-3-03897-855-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering --- Environmental Engineering
Added to DOAB on : 2019-04-25 16:37:17
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The mitigation of oil spills is an important facet of environmental protection. Understanding oil spills is a first step toward preventing and minimizing their damage to the environment. This compilation presents several of the current studies related to such an understanding of oil spills and the environment.This book is a compilation of 14 papers presenting new developments in the field of oil spills, giving insight into the rapidly changing world of oil spill studies and technology. The 14 papers included cover topics varying from risk analysis to oil spill remote sensing. Broadly categorized, included are six papers on modeling, four papers on remote sensing, three papers on risk assessment, and one paper on oil spill countermeasures. Each paper presents a unique insight into a facet of oil spill research and technology. The authors of these papers represent many different countries and affiliations around the world.

Keywords

RANS --- non-breaking ocean waves --- random walk method --- Lagrangian particle dispersion --- oil spill model --- oil spill --- impact modeling --- simulation --- contingency planning --- oil spill model --- ocean trajectory --- GNOME --- BLOSOM --- Salish Sea --- Point Wells --- Foss Barge --- hindcast --- windage --- model comparison --- oil spill model --- FVCOM --- OSCAR --- M/V Marathassa oil spill --- the English Bay --- Vancouver Harbour --- oil spill response --- sea-coastal zones --- methods of vulnerability mapping to oil --- the problems of vulnerability maps development --- ordinal values --- arithmetic operations with rank values --- marine pollution --- oil spill pollution --- oil spill accidents --- oil spill mitigation plans --- coastal protection --- statistical analysis --- PROMETHEE methodology --- Access Western Blend (condensate/bitumen-dilbit) --- Western Canadian Select (condensate mixed with synthetic crude/bitumen-dilsynbit) --- Synthetic Bitumen (synthetic crude/bitumen-Synbit) --- Heidrun --- dispersant --- wave tank --- dispersion effectiveness (DE) --- oil-slick discrimination algorithm --- petrogenic oil-slick category --- naturally-occurring oil seeps --- man-made oil spills --- exploratory data analysis --- remote sensing --- synthetic aperture radar --- RADARSAT --- Gulf of Mexico --- Campeche Bay --- oil spill --- Italian seas --- numerical forecasting tool --- emergency management --- oil spill --- remote sensing --- reflection coefficient --- electromagnetic roughness --- multi-frequency detector --- multiple observations --- probability density function --- probability of detection --- contingency planning --- marine information systems --- environmental monitoring --- proactive systems --- decision support systems --- signal integration --- oil spills --- oil slicks characterization --- oil thickness --- polarized SAR data --- polarimetric SAR data (PolSAR) --- statistical region-based classification --- uncertainty maps --- UAVSAR --- trajectory model --- oil spill model --- oil spill response --- oil spill risk analysis --- Gulf of Mexico --- Outer Continental Shelf --- environmental resources --- risk modelling --- Princeton Ocean Model --- trajectory analysis --- oil spill --- numerical simulation --- LES --- low atmosphere --- coastal flow --- contingency plan --- Kotor bay --- n/a

Entropy Applications in Environmental and Water Engineering

Authors: --- ---
ISBN: 9783038972228 Year: Pages: 512 DOI: 10.3390/books978-3-03897-223-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Environmental Engineering --- General and Civil Engineering --- Technology (General)
Added to DOAB on : 2019-03-21 15:50:41
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Entropy theory has wide applications to a range of problems in the fields of environmental and water engineering, including river hydraulic geometry, fluvial hydraulics, water monitoring network design, river flow forecasting, floods and droughts, river network analysis, infiltration, soil moisture, sediment transport, surface water and groundwater quality modeling, ecosystems modeling, water distribution networks, environmental and water resources management, and parameter estimation. Such applications have used several different entropy formulations, such as Shannon, Tsallis, Reacutenyi Burg, Kolmogorov, Kapur, configurational, and relative entropies, which can be derived in time, space, or frequency domains. More recently, entropy-based concepts have been coupled with other theories, including copula and wavelets, to study various issues associated with environmental and water resources systems. Recent studies indicate the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering, including establishing and explaining physical connections between theory and reality. The objective of this Special Issue is to provide a platform for compiling important recent and current research on the applications of entropy theory in environmental and water engineering. The contributions to this Special Issue have addressed many aspects associated with entropy theory applications and have shown the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering.

Keywords

complexity --- streamflow --- water level --- composite multiscale sample entropy --- trend --- Poyang Lake basin --- four-parameter exponential gamma distribution --- principle of maximum entropy --- precipitation frequency analysis --- methods of moments --- maximum likelihood estimation --- flood frequency analysis --- generalized gamma (GG) distribution --- principle of maximum entropy (POME) --- entropy theory --- principle of maximum entropy (POME) --- GB2 distribution --- flood frequency analysis --- non-point source pollution --- ANN --- entropy weighting method --- data-scarce --- multi-events --- spatio-temporal variability --- soil water content --- entropy --- arid region --- joint entropy --- NDVI --- temperature --- precipitation --- groundwater depth --- Hei River basin --- turbulent flow --- canopy flow --- randomness --- coherent structures --- Shannon entropy --- Kolmogorov complexity --- entropy --- information transfer --- optimization --- radar --- rainfall network --- water resource carrying capacity --- forewarning model --- entropy of information --- fuzzy analytic hierarchy process --- projection pursuit --- accelerating genetic algorithm --- entropy production --- conditional entropy production --- stochastic processes --- scaling --- climacogram --- turbulence --- water resources vulnerability --- connection entropy --- changing environment --- set pair analysis --- Anhui Province --- cross-entropy minimization --- land suitability evaluation --- spatial optimization --- monthly streamflow forecasting --- Burg entropy --- configurational entropy --- entropy spectral analysis time series analysis --- entropy --- water monitoring --- network design --- hydrometric network --- information theory --- entropy applications --- hydrological risk analysis --- maximum entropy-copula method --- uncertainty --- Loess Plateau --- entropy --- water engineering --- Tsallis entropy --- principle of maximum entropy --- Lagrangian function --- probability distribution function --- flux concentration relation --- uncertainty --- information --- informational entropy --- variation of information --- continuous probability distribution functions --- confidence intervals --- precipitation --- variability --- marginal entropy --- crop yield --- Hexi corridor --- flow duration curve --- Shannon entropy --- entropy parameter --- modeling --- spatial and dynamics characteristic --- hydrology --- tropical rainfall --- statistical scaling --- Tsallis entropy --- multiplicative cascades --- Beta-Lognormal model --- rainfall forecast --- cross entropy --- ant colony fuzzy clustering --- combined forecast --- information entropy --- mutual information --- kernel density estimation --- ENSO --- nonlinear relation --- scaling laws --- power laws --- water distribution networks --- robustness --- flow entropy --- entropy theory --- frequency analysis --- hydrometeorological extremes --- Bayesian technique --- rainfall --- entropy ensemble filter --- ensemble model simulation criterion --- EEF method --- bootstrap aggregating --- bagging --- bootstrap neural networks --- El Niño --- ENSO --- neural network forecast --- sea surface temperature --- tropical Pacific --- entropy --- cross elasticity --- mean annual runoff --- water resources --- resilience --- quaternary catchment --- complement --- substitute --- entropy theory --- complex systems --- hydraulics --- hydrology --- water engineering --- environmental engineering

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