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A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil's conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil's conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting ℓ-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors.Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil's conjecture. The proof of the product formula will appear in a sequel volume.
Weil conjectures. --- Conjecture, Weil's --- Conjectures, Weil --- Tate conjectures, Weil --- -Weil-Tate conjectures --- Weil's conjecture --- Geometry, Algebraic --- Frobenius automorphism. --- G-bundles. --- Grothendieck–Lefschetz. --- Weil's conjecture. --- Weill's conjecture. --- affine group. --- algebraic geometry. --- algebraic topology. --- analogue. --- cohomology. --- continuous Künneth decomposition. --- factorization homology. --- function fields. --- global "ient stacks. --- infinity. --- local-to-global principle. --- moduli stack. --- number theory. --- rational functions. --- sheaves. --- trace formula. --- triangulated category.
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Carbon fiber is an oft-referenced material that serves as a means to remove mass from large transport infrastructure. Carbon fiber composites, typically plastics reinforced with the carbon fibers, are key materials in the 21st century and have already had a significant impact on reducing CO2 emissions. Though, as with any composite material, the interface where each component meets, in this case the fiber and plastic, is critical to the overall performance.
cellulose derivative --- stack --- lignin --- contact problem --- single fibre pull out --- fatigue --- composite --- sandwich composite --- toughness --- aluminum UNS A97050 --- surface quality --- Carbon fiber --- epoxy curing --- kerf taper --- block copolymers --- conductive yarn --- X-ray transmission --- electron beam --- CT cradle --- thin-wall --- microwave heating --- Seebeck coefficient --- tendon --- air blowing --- epoxy resins --- monocoque structure --- prepreg --- carbon fiber --- surface treatment --- strengthening --- carbon fibre --- surface modification --- epoxy composite --- prestressed near-surface mounted reinforcement (NSMR) --- recycled carbon fiber --- composites --- thermocouple --- structural analysis --- interfacial adhesion --- three-wheeler vehicle --- SOM/SEM --- polycarbonate --- low consumption vehicle --- computed tomography --- thermoforming --- AWJM --- isotropic pitch --- nickel-coated carbon fiber --- finite element model --- dual curing --- fast-cure epoxy resin --- lightweight design --- macrogeometric deviations --- ethylene tar --- CFRP
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What is the future of CMOS? Sustaining increased transistor densities along the path of Moore's Law has become increasingly challenging with limited power budgets, interconnect bandwidths, and fabrication capabilities. In the last decade alone, transistors have undergone significant design makeovers; from planar transistors of ten years ago, technological advancements have accelerated to today's FinFETs, which hardly resemble their bulky ancestors. FinFETs could potentially take us to the 5-nm node, but what comes after it? From gate-all-around devices to single electron transistors and two-dimensional semiconductors, a torrent of research is being carried out in order to design the next transistor generation, engineer the optimal materials, improve the fabrication technology, and properly model future devices. We invite insight from investigators and scientists in the field to showcase their work in this Special Issue with research papers, short communications, and review articles that focus on trends in micro- and nanotechnology from fundamental research to applications.
MOSFET --- n/a --- total ionizing dose (TID) --- low power consumption --- process simulation --- two-dimensional material --- negative-capacitance --- power consumption --- technology computer aided design (TCAD) --- thin-film transistors (TFTs) --- band-to-band tunneling (BTBT) --- nanowires --- inversion channel --- metal oxide semiconductor field effect transistor (MOSFET) --- spike-timing-dependent plasticity (STDP) --- field effect transistor --- segregation --- systematic variations --- Sentaurus TCAD --- indium selenide --- nanosheets --- technology computer-aided design (TCAD) --- high-? dielectric --- subthreshold bias range --- statistical variations --- fin field effect transistor (FinFET) --- compact models --- non-equilibrium Green’s function --- etching simulation --- highly miniaturized transistor structure --- compact model --- silicon nanowire --- surface potential --- Silicon-Germanium source/drain (SiGe S/D) --- nanowire --- plasma-aided molecular beam epitaxy (MBE) --- phonon scattering --- mobility --- silicon-on-insulator --- drain engineered --- device simulation --- variability --- semi-floating gate --- synaptic transistor --- neuromorphic system --- theoretical model --- CMOS --- ferroelectrics --- tunnel field-effect transistor (TFET) --- SiGe --- metal gate granularity --- buried channel --- ON-state --- bulk NMOS devices --- ambipolar --- piezoelectrics --- tunnel field effect transistor (TFET) --- FinFETs --- polarization --- field-effect transistor --- line edge roughness --- random discrete dopants --- radiation hardened by design (RHBD) --- low energy --- flux calculation --- doping incorporation --- low voltage --- topography simulation --- MOS devices --- low-frequency noise --- high-k --- layout --- level set --- process variations --- subthreshold --- metal gate stack --- electrostatic discharge (ESD) --- non-equilibrium Green's function
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Satellite altimetry is a radar technique for measuring the topography of the Earth’s surface. It was initially designed for measuring the ocean’s topography, with reference to an ellipsoid, and for the determination of the marine geoid. Satellite altimetry has provided extremely valuable information on ocean science (e.g., circulation surface geostrophic currents, eddy structures, wave heights, and the propagation of oceanic Kelvin and Rossby waves). With more than 25 years of observations, it is also becoming vital to climate research, providing accurate measurements of sea level variations from regional to global scales. Altimetry has also demonstrated a strong potential for geophysical, cryospheric, and hydrological research and is now commonly used for the monitoring of Arctic and Antarctic ice sheet topography and of terrestrial surface water levels. This book aims to present reviews and recent advances of general interest in the use of radar altimetry in Earth sciences. Manuscripts are related to any aspect of radar altimetry technique or geophysical applications. We also encourage manuscripts resulting from the application of new altimetric technology (SAR, SARin, and Ka band) and improvements expected from missions to be launched in the near future (i.e., SWOT).
water level --- ALES --- wet path delay --- CryoSat-2 --- water volume transport --- water level time series --- storm surge --- filtering --- validation --- polar ocean --- ocean tides --- satellite altimetry --- lake level --- classification --- ENVISAT --- numerical modelling --- PISTACH --- water levels --- evaporation --- geodesy --- waveform --- ALES retracker --- waveform retracking --- unsupervised classification --- CryosSat-2 SAR --- peakiness --- Envisat --- Jason-2 --- calibration --- SARAL --- ACC --- microwave radiometer --- ocean geostrophy --- data processing --- fine scale --- SWOT --- orbit decay --- Aral Sea --- geodetic orbit --- radar altimetry --- oceanography --- streamflow --- K-medoids --- retracking --- ice --- SWOT simulator --- coastal altimetry --- Ka-band --- western Mediterranean Sea --- topography of the intertidal zone --- FVCOM --- HY-2A --- inland water --- tide gauge --- discharge --- ERS-2 --- marine gravity --- wet tropospheric correction --- South China Sea --- stack data --- upper layer thickness --- drifting orbit --- hydrology --- Sentinel-3 --- two-layer ocean model --- satellite geodesy --- Fram Strait --- space gravity --- leads --- satellite altimeter --- range precision --- sensor calibration --- ROMS model --- X-TRACK --- SAR --- Inner Niger Delta --- Greenland Sea --- Gravity Recovery and Climate Experiment (GRACE) --- Mekong Basin --- altimetry --- Hong Kong coast --- soil moisture --- Argo --- Southern Ocean --- Landsat --- dielectric permittivity --- sea surface height --- lake volume
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HVAC systems, load shifting, indoor climate, and energy and ventilation performance analyses are the key topics when improving energy performance in new and renovated buildings. This development has been boosted by the recently established nearly zero energy building requirements that will soon be in use in all EU Member States, as well as similar long-term zero energy building targets in Japan, the US, and other countries. The research covered in this Special Issue provides evidence of how new technical solutions have worked, in practice, in new or renovated buildings, and also discusses problems and how solutions should be further developed. Another focus is on the more detailed calculation methods needed for the correct design and sizing of dedicated systems, and for accurate quantification of energy savings. Occupant behavior and building operation is also examined, in order to avoid common performance gaps between calculated and measured performance. These topics demonstrate the challenge of high performance buildings as, in the end, comfortable buildings with good indoor climate which are easy and cheap to operate and maintain are expected by end customers. Ventilation performance, heating and cooling, sizing, energy predictions and optimization, load shifting, and field studies are some of the key topics in this Special Issue, contributing to the future of high performance buildings with reliable operation.
indoor air quality --- stratification --- chiller plants --- alternate operation --- displacement ventilation --- draught rate --- building --- indoor temperature after renovation --- DHW heating --- daylight factor --- energy --- energy performance modeling --- hybrid displacement device --- building energy modelling --- energy performance of buildings directive --- condenser evaporative precooling --- DHW energy use --- heating mode --- ground source heat pump --- personalized ventilation --- daylight --- existing buildings --- optimal energy management --- cooling --- mixing ventilation --- daylight survey --- user behavior --- local air change effectiveness --- basketball hall --- CFD --- sizing --- electricity use --- control strategy --- HVAC systems --- ventilation --- occupant behavior --- smart readiness indicator --- energy signature --- standard use --- building energy simulation --- outdoor air --- monitoring measurements --- COP --- qualitative control --- wind pressure --- decentralized ventilation unit --- field measurement --- thermal comfort --- student dormitories --- data-driven analysis --- energy performance --- daylight simulations --- air jet --- ISO 52016-1 --- multiple sensor nodes --- downdraught --- energy efficiency --- building pressure condition --- meteorological reanalysis data --- ISO 7730 --- thermal analysis --- Monte Carlo method --- corner impinging jet --- greenhouse --- Pro-GET-onE H2020 --- in situ measurements --- smart buildings --- skin temperature --- retirement home --- demand side management --- indoor climate --- user input data --- Indoor Environmental Quality (IEQ) --- ventilation renovation --- tracer gas --- gray box --- Jaya algorithm --- single room ventilation unit --- satellite-based solar radiation data --- chiller performance --- rooftop air conditioners --- smart grid --- TRNSYS --- stack effect --- space heating --- energy flexibility --- corner mixing ventilation --- load shifting --- heating power --- air exchange effectiveness --- indoor temperature uniformity --- demand response
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Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach.The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces.The second course, taught by Umberto Zannier, addresses the famous Pell equation-not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians.The third course, taught by Shou-Wu Zhang, originates in the Chowla-Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and verify the Colmez conjecture on average.
Arithmetical algebraic geometry. --- Algebraic geometry, Arithmetical --- Arithmetic algebraic geometry --- Diophantine geometry --- Geometry, Arithmetical algebraic --- Geometry, Diophantine --- Number theory --- Abelian variety. --- Algebraic geometry. --- Algebraic independence. --- Algebraic space. --- Analytic number theory. --- Arbitrarily large. --- Automorphic form. --- Automorphism. --- Base change. --- Big O notation. --- Class number formula. --- Cohomology. --- Complex multiplication. --- Computation. --- Conjecture. --- Conjugacy class. --- Continued fraction. --- Cusp form. --- Diagram (category theory). --- Dimension. --- Diophantine equation. --- Diophantine geometry. --- Discriminant. --- Divisible group. --- Double coset. --- Eisenstein series. --- Endomorphism. --- Equation. --- Existential quantification. --- Exponential map (Riemannian geometry). --- Fiber bundle. --- Floor and ceiling functions. --- Formal group. --- Formal power series. --- Formal scheme. --- Fundamental group. --- Geometric Langlands correspondence. --- Geometry. --- Heegner point. --- Hodge structure. --- Hodge theory. --- Homomorphism. --- I0. --- Integer. --- Intersection number. --- Irreducible component. --- Isogeny. --- Isomorphism class. --- Jacobian variety. --- L-function. --- Langlands dual group. --- Laurent series. --- Linear combination. --- Local system. --- Logarithmic derivative. --- Logarithmic form. --- Mathematics. --- Modular form. --- Moduli space. --- Monotonic function. --- Natural topology. --- P-adic analysis. --- P-adic number. --- Pell's equation. --- Perverse sheaf. --- Polylogarithm. --- Polynomial. --- Power series. --- Presheaf (category theory). --- Prime number. --- Projective space. --- Quaternion algebra. --- Rational point. --- Real number. --- Reductive group. --- Rigid analytic space. --- Roth's theorem. --- Series expansion. --- Shafarevich conjecture. --- Sheaf (mathematics). --- Shimura variety. --- Siegel zero. --- Special case. --- Stack (mathematics). --- Subset. --- Summation. --- Szpiro's conjecture. --- Tate conjecture. --- Tate module. --- Taylor series. --- Theorem. --- Theta function. --- Topological ring. --- Topology. --- Torsor (algebraic geometry). --- Upper and lower bounds. --- Vector bundle. --- Weil group. --- Witt vector. --- Zariski topology.
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