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"It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works."

Mathematics --- Elementary Problems --- make sense of the world --- mathematics beyond the classroom --- Mental Skills --- Arithmetic --- Word Problems --- Algebra --- Geometry --- Infinity

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This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Mathematics --- Topological groups --- Lie groups --- Potential theory (Mathematics) --- Partial differential equations --- Harmonic analysis --- Functional analysis --- Differential geometry

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Currently, the use of computational fluid dynamics (CFD) solutions is considered as the state-of-the-art in the modeling of unsteady nonlinear flow physics and offers an early and improved understanding of air vehicle aerodynamics and stability and control characteristics. This Special Issue covers recent computational efforts on simulation of aerospace vehicles including fighter aircraft, rotorcraft, propeller driven vehicles, unmanned vehicle, projectiles, and air drop configurations. The complex flow physics of these configurations pose significant challenges in CFD modeling. Some of these challenges include prediction of vortical flows and shock waves, rapid maneuvering aircraft with fast moving control surfaces, and interactions between propellers and wing, fluid and structure, boundary layer and shock waves. Additional topic of interest in this Special Issue is the use of CFD tools in aircraft design and flight mechanics. The problem with these applications is the computational cost involved, particularly if this is viewed as a brute-force calculation of vehicle’s aerodynamics through its flight envelope. To make progress in routinely using of CFD in aircraft design, methods based on sampling, model updating and system identification should be considered.

wake --- bluff body --- square cylinder --- DDES --- URANS --- turbulence model --- large eddy simulation --- Taylor–Green vortex --- numerical dissipation --- modified equation analysis --- truncation error --- MUSCL --- dynamic Smagorinsky subgrid-scale model --- kinetic energy dissipation --- computational fluid dynamics (CFD) --- microfluidics --- numerical methods --- gasdynamics --- shock-channel --- microelectromechanical systems (MEMS) --- discontinuous Galerkin finite element method (DG–FEM) --- fluid mechanics --- characteristics-based scheme --- multi-directional --- Riemann solver --- Godunov method --- bifurcation --- wind tunnel --- neural networks --- modeling --- unsteady aerodynamic characteristics --- high angles of attack --- hypersonic --- wake --- chemistry --- slender-body --- angle of attack --- detection --- after-body --- S-duct diffuser --- flow distortion --- flow control --- vortex generators --- aeroelasticity --- reduced-order model --- flutter --- wind gust responses --- computational fluid dynamics --- convolution integral --- sharp-edge gust --- reduced order aerodynamic model --- geometry --- meshing --- aerodynamics --- CPACS --- MDO --- VLM --- Euler --- CFD --- variable fidelity --- multi-fidelity --- aerodynamic performance --- formation --- VLM --- RANS --- hybrid reduced-order model --- quasi-analytical --- aeroelasticity --- flexible wings --- subsonic --- wing–propeller aerodynamic interaction --- p-factor --- installed propeller --- overset grid approach

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The Special Issue (SI) “Recent Advances in GPR Imaging” offers an up-to-date overview of state-of-the-art research activities dealing with the development of Ground Penetrating Radar (GPR) technology and its recent advances in imaging in the different fields of application. In fact, the advances experimented with over the last few decades with regard to the appearance of new GPR systems and the need to manage large amounts of data suggest an increasing interest in the development of new signal processing algorithms and modeling, as well as in the use of three-dimensional (3D) imaging techniques.

doline --- karst --- land cultivation --- morphometrical analysis --- distributive analysis --- conglomerate --- LiDAR --- digital elevation model (DEM) --- ground penetrating radar (GPR) --- Kranjsko polje --- ground penetrating radar --- electrical resistivity imaging --- quarry --- marble --- ground penetrating radar --- electromagnetic propagation in nonhomogeneous media --- time-domain analysis --- GPR --- clutter --- backscattering --- scattering modelling --- ground-penetrating radar --- terrestrial laser scanning --- infrared thermography --- archaeology --- 3D visualization --- toGPRi --- variational mode decomposition --- empirical mode decomposition --- IMF-slices --- GPR data processing --- GPR imaging --- time-frequency analysis --- ground penetrating radar --- non-destructive testing --- near-surface geophysics --- test site --- Ground Penetrating Radar --- railways --- signal frequency analysis --- track geometry --- railway events --- spectral domain --- network level evaluation --- ground penetrating radar (GPR) --- X-ray diffraction (XRD) --- X-ray fluorescence (XRF) --- karst --- cave sediments --- unroofed caves --- n/a

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Geomorphometry is the science of quantitative terrain characterization and analysis, and has traditionally focused on the investigation of terrestrial and planetary landscapes. However, applications of marine geomorphometry have now moved beyond the simple adoption of techniques developed for terrestrial studies, driven by the rise in the acquisition of high-resolution seafloor data and by the availability of user-friendly spatial analytical tools. Considering that the seafloor represents 71% of the surface of our planet, this is an important step towards understanding the Earth in its entirety.This volume is the first one dedicated to marine applications of geomorphometry. It showcases studies addressing the five steps of geomorphometry: sampling a surface (e.g., the seafloor), generating a Digital Terrain Model (DTM) from samples, preprocessing the DTM for subsequent analyses (e.g., correcting for errors and artifacts), deriving terrain attributes and/or extracting terrain features from the DTM, and using and explaining those terrain attributes and features in a given context. Throughout these studies, authors address a range of challenges and issues associated with applying geomorphometric techniques to the complex marine environment, including issues related to spatial scale, data quality, and linking seafloor topography with physical, geological, biological, and ecological processes. As marine geomorphometry becomes increasingly recognized as a sub-discipline of geomorphometry, this volume brings together a collection of research articles that reflect the types of studies that are helping to chart the course for the future of marine geomorphometry.

bedforms --- forage fish --- Pacific sand lance --- sediment habitats --- bathymetry --- currents --- seabed mapping --- marine geology --- submarine topography --- marine geomorphology --- terrain analysis --- multibeam echosounder --- bathymetry --- DEM --- satellite imagery --- multi beam echosounder --- filter --- geomorphology --- coral reefs --- Acoustic applications --- object segmentation --- seafloor --- underwater acoustics --- Cretaceous --- Cenomanian–Turonian --- paleobathymetry --- paleoclimate --- paleoceanography --- reconstruction --- simulation --- shelf-slope-rise --- geomorphometry --- GIS --- spatial scale --- spatial analysis --- terrain analysis --- seafloor geomorphometry --- domes --- volcanoes --- digital elevation models (DEMs) --- Canary Basin --- Atlantic Ocean --- cold-water coral --- carbonate mound --- habitat mapping --- spatial prediction --- image segmentation --- geographic object-based image analysis --- random forest --- accuracy --- confidence --- global bathymetry --- Seabed 2030 --- Nippon Foundation/GEBCO --- seafloor mapping technologies --- seafloor mapping standards and protocols --- benthic habitats --- shelf morphology --- eastern Brazilian shelf --- geomorphometry --- terrain analysis --- bathymetry --- surface roughness --- benthic habitat mapping --- python --- geomorphology --- submerged glacial bedforms --- deglaciation --- sedimentation --- multibeam --- acoustic-seismic profiling --- swath geometry --- multibeam spatial resolution --- integration artefacts --- Multibeam bathymetry --- benthic habitat mapping --- multiscale --- Random Forests --- pockmarks --- automated-mapping --- ArcGIS --- Glaciated Margin --- North Sea --- Malin Basin --- Barents Sea --- bathymetry --- thalwegs --- canyons --- Alaska --- Bering Sea --- multibeam sonar --- carbonate banks --- semi-automated mapping --- polychaete --- Northwestern Australia --- Oceanic Shoals Australian Marine Park --- Bonaparte Basin --- Timor Sea --- bathymetry --- digital terrain analysis --- geomorphometry --- geomorphology --- habitat mapping --- marine remote sensing