IlmeniteIlmenite is a titanium-iron oxide mineral with the idealized formula FeTiO3. It is a weakly magnetic black or steel-gray solid. Ilmenite is the most important ore of titanium and the main source of titanium dioxide, which is used in paints, printing inks, fabrics, plastics, paper, sunscreen, food and cosmetics. Ilmenite is a heavy (specific gravity 4.7), moderately hard (Mohs hardness 5.6 to 6), opaque black mineral with a submetallic luster. It is almost always massive, with thick tabular crystals being quite rare.
NanowireA nanowire is a nanostructure in the form of a wire with the diameter of the order of a nanometre (10−9 metres). More generally, nanowires can be defined as structures that have a thickness or diameter constrained to tens of nanometers or less and an unconstrained length. At these scales, quantum mechanical effects are important—which coined the term "quantum wires". Many different types of nanowires exist, including superconducting (e.g. YBCO), metallic (e.g. Ni, Pt, Au, Ag), semiconducting (e.g.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Polar decompositionIn mathematics, the polar decomposition of a square real or complex matrix is a factorization of the form , where is a unitary matrix and is a positive semi-definite Hermitian matrix ( is an orthogonal matrix and is a positive semi-definite symmetric matrix in the real case), both square and of the same size. Intuitively, if a real matrix is interpreted as a linear transformation of -dimensional space , the polar decomposition separates it into a rotation or reflection of , and a scaling of the space along a set of orthogonal axes.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Printed electronicsPrinted electronics is a set of printing methods used to create electrical devices on various substrates. Printing typically uses common printing equipment suitable for defining patterns on material, such as screen printing, flexography, gravure, offset lithography, and inkjet. By electronic-industry standards, these are low-cost processes. Electrically functional electronic or optical inks are deposited on the substrate, creating active or passive devices, such as thin film transistors; capacitors; coils; resistors.
TitaniumTitanium is a chemical element with the symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resistant to corrosion in sea water, aqua regia, and chlorine. Titanium was discovered in Cornwall, Great Britain, by William Gregor in 1791 and was named by Martin Heinrich Klaproth after the Titans of Greek mythology.
Extreme ultraviolet lithographyExtreme ultraviolet lithography (also known as EUV or EUVL) is an optical lithography technology used in semiconductor device fabrication to make integrated circuits (ICs). It uses extreme ultraviolet (EUV) wavelengths near 13.5 nm, using a laser-pulsed tin (Sn) droplet plasma (Sn ions in the ionic states from Sn IX to Sn XIV give photon emission spectral peaks around 13.5 nm from 4p64dn - 4p54dn+1 + 4dn-14f ionic state transitions.), to produce a pattern by using a reflective photomask to expose a substrate covered by photoresist.
Metalorganic vapour-phase epitaxyMetalorganic vapour-phase epitaxy (MOVPE), also known as organometallic vapour-phase epitaxy (OMVPE) or metalorganic chemical vapour deposition (MOCVD), is a chemical vapour deposition method used to produce single- or polycrystalline thin films. It is a process for growing crystalline layers to create complex semiconductor multilayer structures. In contrast to molecular-beam epitaxy (MBE), the growth of crystals is by chemical reaction and not physical deposition.
