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Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.

Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Elliptic. --- Green's Function. --- Parabolic. --- Partial Differential Equation.

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This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT–invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power–law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed.

Research & information: general --- Technology: general issues --- non-Hermitian quantum dynamics --- unitary vicinity of exceptional points --- degenerate perturbation theory --- Hilbert-space geometry near EPs --- relativistic wave equation --- Klein–Gordon equation --- Dirac equation --- Proca equation --- supersymmetry --- quantum mechanics --- shape invariance --- curved space --- position-dependent mass --- supersymmetric quantum mechanics --- self-adjoint extensions --- infinite square well --- contact potentials --- power-law duality --- classical and quantum mechanics --- semiclassical quantization --- quark confinement --- spreading wave function --- scattering --- localization --- Klein–Gordon oscillator --- Green’s function --- semiclassical theories and applications --- classical general relativity --- n/a --- Klein-Gordon equation --- Klein-Gordon oscillator --- Green's function

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As CMOS scaling is approaching the fundamental physical limits, a wide range of new nanoelectronic materials and devices have been proposed and explored to extend and/or replace the current electronic devices and circuits so as to maintain progress with respect to speed and integration density. The major limitations, including low carrier mobility, degraded subthreshold slope, and heat dissipation, have become more challenging to address as the size of silicon-based metal oxide semiconductor field effect transistors (MOSFETs) has decreased to nanometers, while device integration density has increased. This book aims to present technical approaches that address the need for new nanoelectronic materials and devices. The focus is on new concepts and knowledge in nanoscience and nanotechnology for applications in logic, memory, sensors, photonics, and renewable energy. This research on nanoelectronic materials and devices will be instructive in finding solutions to address the challenges of current electronics in switching speed, power consumption, and heat dissipation and will be of great interest to academic society and the industry.

quantum mechanical --- n/a --- neuromorphic computation --- off-current (Ioff) --- double-gate tunnel field-effect-transistor --- topological insulator --- back current blocking layer (BCBL) --- CMOS power amplifier IC --- information integration --- distributed Bragg --- spike-timing-dependent plasticity --- electron affinity --- enhancement-mode --- current collapse --- gallium nitride (GaN) --- band-to-band tunneling --- vertical field-effect transistor (VFET) --- ionic liquid --- luminescent centres --- thermal coupling --- vision localization --- PC1D --- UAV --- ZnO/Si --- dual-switching transistor --- memristor --- field-effect transistor --- higher order synchronization --- shallow trench isolation (STI) --- memristive device --- on-current (Ion) --- low voltage --- reflection transmision method --- dielectric layer --- source/drain (S/D) --- high efficiency --- nanostructure synthesis --- InAlN/GaN heterostructure --- supercapacitor --- high-electron mobility transistor (HEMTs) --- heterojunction --- p-GaN --- recessed channel array transistor (RCAT) --- gate field effect --- charge injection --- saddle FinFET (S-FinFET) --- L-shaped tunnel field-effect-transistor --- conductivity --- energy storage --- hierarchical --- PECVD --- sample grating --- MISHEMT --- bistability --- threshold voltage (VTH) --- bandgap tuning --- oscillatory neural networks --- UV irradiation --- Mott transition --- third harmonic tuning --- topological magnetoelectric effect --- cross-gain modulation --- 2D material --- solar cells --- silicon on insulator (SOI) --- Green’s function --- optoelectronic devices --- semiconductor optical amplifier --- ZnO films --- graphene --- AlGaN/GaN --- polarization effect --- two-photon process --- conductive atomic force microscopy (cAFM) --- 2DEG density --- vanadium dioxide --- interface traps --- potential drop width (PDW) --- pattern recognition --- drain-induced barrier lowering (DIBL) --- atomic layer deposition (ALD) --- normally off power devices --- gate-induced drain leakage (GIDL) --- insulator–metal transition (IMT) --- zinc oxide --- synaptic device --- subthreshold slope (SS) --- landing --- silicon --- corner-effect --- conditioned reflex --- quantum dot --- gallium nitride --- bismuth ions --- conduction band offset --- variational form --- Green's function --- insulator-metal transition (IMT)

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This book of Molecules is dedicated to Professor John B. Goodenough (born July 25, 1922, Jena, Germany), an American physicist, who won the 2019 Nobel Prize for Chemistry for his work on developing lithium-ion batteries.

Research & information: general --- Chemistry --- Physical chemistry --- structure --- bonding --- physical properties --- collective or localized electrons --- exchange integral --- p-magnetism --- boron sub-oxide --- interstitial atoms --- DFT --- DOS --- ELF --- charge density plots --- bifunctional catalyst --- hybrid catalyst --- oxygen reduction reaction --- oxygen evolution reaction --- four-electron pathway --- lithium ionic conductor --- perovskite structure --- solid electrolyte --- oxide --- lithium-sulfur batteries --- tungsten oxide nanowire --- interlayer --- thiosulfate mediator --- Keywords: spin exchange --- magnetic orbitals --- ligand p-orbital tails --- M–L–M exchange --- M–L…L–M exchange --- α-CuV2O6 --- LiCuVO4 --- (CuCl)LaNb2O7 --- Cu3(CO3)2(OH)2 --- spin Hamiltonian --- magnetism --- energy-mapping analysis --- four-state method --- Green’s function method --- magnetic ground state --- spin exchange --- magnetic anisotropy --- molecular anion --- MPS3 --- qualitative rules --- batteries --- positive electrode --- vanadium phosphates --- covalent vanadyl bond --- mixed anion --- density functional theory --- quantum Monte Carlo --- fast Li+ ion conductor --- Li-ion battery --- spinel --- solid-state battery --- cathode-electrolyte interface --- indigo carmine --- solid polymer electrolyte --- solid state battery --- LMP® technology --- organic battery --- layered oxide cathodes --- alkali–alkali interactions --- electronic structure --- Li diffusion --- defect engineering --- perovskite electrolyte --- lithium-ion battery --- migration pathway --- anisotropic response --- cathode --- polyanion --- high-voltage --- n/a --- M-L-M exchange --- M-L...L-M exchange --- Green's function method --- alkali-alkali interactions

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This book of Molecules is dedicated to Professor John B. Goodenough (born July 25, 1922, Jena, Germany), an American physicist, who won the 2019 Nobel Prize for Chemistry for his work on developing lithium-ion batteries.

structure --- bonding --- physical properties --- collective or localized electrons --- exchange integral --- p-magnetism --- boron sub-oxide --- interstitial atoms --- DFT --- DOS --- ELF --- charge density plots --- bifunctional catalyst --- hybrid catalyst --- oxygen reduction reaction --- oxygen evolution reaction --- four-electron pathway --- lithium ionic conductor --- perovskite structure --- solid electrolyte --- oxide --- lithium-sulfur batteries --- tungsten oxide nanowire --- interlayer --- thiosulfate mediator --- Keywords: spin exchange --- magnetic orbitals --- ligand p-orbital tails --- M–L–M exchange --- M–L…L–M exchange --- α-CuV2O6 --- LiCuVO4 --- (CuCl)LaNb2O7 --- Cu3(CO3)2(OH)2 --- spin Hamiltonian --- magnetism --- energy-mapping analysis --- four-state method --- Green’s function method --- magnetic ground state --- spin exchange --- magnetic anisotropy --- molecular anion --- MPS3 --- qualitative rules --- batteries --- positive electrode --- vanadium phosphates --- covalent vanadyl bond --- mixed anion --- density functional theory --- quantum Monte Carlo --- fast Li+ ion conductor --- Li-ion battery --- spinel --- solid-state battery --- cathode-electrolyte interface --- indigo carmine --- solid polymer electrolyte --- solid state battery --- LMP® technology --- organic battery --- layered oxide cathodes --- alkali–alkali interactions --- electronic structure --- Li diffusion --- defect engineering --- perovskite electrolyte --- lithium-ion battery --- migration pathway --- anisotropic response --- cathode --- polyanion --- high-voltage --- n/a --- M-L-M exchange --- M-L...L-M exchange --- Green's function method --- alkali-alkali interactions