Formal proofIn logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system.
WaterWater is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and nearly colorless chemical substance, and it is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a solvent). It is vital for all known forms of life, despite not providing food energy, or organic micronutrients. Its chemical formula, , indicates that each of its molecules contains one oxygen and two hydrogen atoms, connected by covalent bonds.
Proof of spaceProof of space (PoS) is a type of consensus algorithm achieved by demonstrating one's legitimate interest in a service (such as sending an email) by allocating a non-trivial amount of memory or disk space to solve a challenge presented by the service provider. The concept was formulated in 2013 by Dziembowski et al. and (with a different formulation) by Ateniese et al.. Proofs of space are very similar to proofs of work (PoW), except that instead of computation, storage is used to earn cryptocurrency.
Hydrothermal ventA hydrothermal vent is a fissure on the seabed from which geothermally heated water discharges. They are commonly found near volcanically active places, areas where tectonic plates are moving apart at mid-ocean ridges, ocean basins, and hotspots. Hydrothermal deposits are rocks and mineral ore deposits formed by the action of hydrothermal vents. Hydrothermal vents exist because the earth is both geologically active and has large amounts of water on its surface and within its crust.
Field extensionIn mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
Jet fuelJet fuel or aviation turbine fuel (ATF, also abbreviated avtur) is a type of aviation fuel designed for use in aircraft powered by gas-turbine engines. It is colorless to straw-colored in appearance. The most commonly used fuels for commercial aviation are Jet A and Jet A-1, which are produced to a standardized international specification. The only other jet fuel commonly used in civilian turbine-engine powered aviation is Jet B, which is used for its enhanced cold-weather performance.
Water coolingWater cooling is a method of heat removal from components and industrial equipment. Evaporative cooling using water is often more efficient than air cooling. Water is inexpensive and non-toxic; however, it can contain impurities and cause corrosion. Water cooling is commonly used for cooling automobile internal combustion engines and power stations. Water coolers utilising convective heat transfer are used inside high-end personal computers to lower the temperature of CPUs and other components.
Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
Proof of workProof of work (PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their part. The concept was invented by Moni Naor and Cynthia Dwork in 1993 as a way to deter denial-of-service attacks and other service abuses such as spam on a network by requiring some work from a service requester, usually meaning processing time by a computer.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
CompilerIn computing, a compiler is a computer program that translates computer code written in one programming language (the source language) into another language (the target language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program. There are many different types of compilers which produce output in different useful forms.
Furnace (central heating)A furnace (American English), referred to as a heater or boiler in British English, is an appliance used to generate heat for all or part of a building. Furnaces are mostly used as a major component of a central heating system. Furnaces are permanently installed to provide heat to an interior space through intermediary fluid movement, which may be air, steam, or hot water. Heating appliances that use steam or hot water as the fluid are normally referred to as a residential steam boilers or residential hot water boilers.
