Proof theoryProof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
NanomaterialsNanomaterials describe, in principle, materials of which a single unit is sized (in at least one dimension) between 1 and 100 nm (the usual definition of nanoscale). Nanomaterials research takes a materials science-based approach to nanotechnology, leveraging advances in materials metrology and synthesis which have been developed in support of microfabrication research. Materials with structure at the nanoscale often have unique optical, electronic, thermo-physical or mechanical properties.
Conductive polymerConductive polymers or, more precisely, intrinsically conducting polymers (ICPs) are organic polymers that conduct electricity. Such compounds may have metallic conductivity or can be semiconductors. The main advantage of conductive polymers is that they are easy to process, mainly by dispersion. Conductive polymers are generally not thermoplastics, i.e., they are not thermoformable. But, like insulating polymers, they are organic materials. They can offer high electrical conductivity but do not show similar mechanical properties to other commercially available polymers.
Quantum yieldIn particle physics, the quantum yield (denoted Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system. The fluorescence quantum yield is defined as the ratio of the number of photons emitted to the number of photons absorbed. Fluorescence quantum yield is measured on a scale from 0 to 1.0, but is often represented as a percentage. A quantum yield of 1.0 (100%) describes a process where each photon absorbed results in a photon emitted.
Proof by contradictionIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.
Electron mobilityIn solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility. Electron and hole mobility are special cases of electrical mobility of charged particles in a fluid under an applied electric field. When an electric field E is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity, .
Ultrafast laser spectroscopyUltrafast laser spectroscopy is a spectroscopic technique that uses ultrashort pulse lasers for the study of dynamics on extremely short time scales (attoseconds to nanoseconds). Different methods are used to examine the dynamics of charge carriers, atoms, and molecules. Many different procedures have been developed spanning different time scales and photon energy ranges; some common methods are listed below. Dynamics on the as to fs time scale are in general too fast to be measured electronically.
