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.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Proof by exhaustionProof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: A proof that the set of cases is exhaustive; i.e.
OLEDAn organic light-emitting diode (OLED), also known as organic electroluminescent (organic EL) diode, is a light-emitting diode (LED) in which the emissive electroluminescent layer is a film of organic compound that emits light in response to an electric current. This organic layer is situated between two electrodes; typically, at least one of these electrodes is transparent. OLEDs are used to create digital displays in devices such as television screens, computer monitors, and portable systems such as smartphones and handheld game consoles.
Mathematical inductionMathematical induction is a method for proving that a statement is true for every natural number , that is, that the infinitely many cases all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step). A proof by induction consists of two cases.
Electronic paperElectronic paper, also known as electronic ink (e-ink) or intelligent paper, is a display device that mimics the appearance of ordinary ink on paper. Unlike conventional flat panel displays that emit light, an electronic paper display reflects ambient light, like paper. This may make them more comfortable to read, and provide a wider viewing angle than most light-emitting displays. The contrast ratio in electronic displays available as of 2008 approaches newspaper, and newly developed displays are slightly better.
Organic matterOrganic matter, organic material, or natural organic matter refers to the large source of carbon-based compounds found within natural and engineered, terrestrial, and aquatic environments. It is matter composed of organic compounds that have come from the feces and remains of organisms such as plants and animals. Organic molecules can also be made by chemical reactions that do not involve life. Basic structures are created from cellulose, tannin, cutin, and lignin, along with other various proteins, lipids, and carbohydrates.
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.
Organic semiconductorOrganic semiconductors are solids whose building blocks are pi-bonded molecules or polymers made up by carbon and hydrogen atoms and – at times – heteroatoms such as nitrogen, sulfur and oxygen. They exist in the form of molecular crystals or amorphous thin films. In general, they are electrical insulators, but become semiconducting when charges are either injected from appropriate electrodes, upon doping or by photoexcitation. In molecular crystals the energetic separation between the top of the valence band and the bottom conduction band, i.
Organic solar cellAn organic solar cell (OSC) or plastic solar cell is a type of photovoltaic that uses organic electronics, a branch of electronics that deals with conductive organic polymers or small organic molecules, for light absorption and charge transport to produce electricity from sunlight by the photovoltaic effect. Most organic photovoltaic cells are polymer solar cells. The molecules used in organic solar cells are solution-processable at high throughput and are cheap, resulting in low production costs to fabricate a large volume.
Indium tin oxideIndium tin oxide (ITO) is a ternary composition of indium, tin and oxygen in varying proportions. Depending on the oxygen content, it can be described as either a ceramic or an alloy. Indium tin oxide is typically encountered as an oxygen-saturated composition with a formulation of 74% In, 18% Sn, and 8% O by weight. Oxygen-saturated compositions are so typical that unsaturated compositions are termed oxygen-deficient ITO. It is transparent and colorless in thin layers, while in bulk form it is yellowish to gray.
Self-determinationThe right of a people to self-determination is a cardinal principle in modern international law (commonly regarded as a jus cogens rule), binding, as such, on the United Nations as authoritative interpretation of the Charter's norms. It states that peoples, based on respect for the principle of equal rights and fair equality of opportunity, have the right to freely choose their sovereignty and international political status with no interference. The concept was first expressed in the 1860s, and spread rapidly thereafter.
Solid-state physicsSolid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. Along with solid-state chemistry, it also has direct applications in the technology of transistors and semiconductors.
Solid-state electronicsSolid-state electronics are semiconductor electronics; electronic equipment that use semiconductor devices such as transistors, diodes and integrated circuits (ICs). The term is also used as an adjective for devices in which semiconductor electronics that have no moving parts replace devices with moving parts, such as the solid-state relay in which transistor switches are used in place of a moving-arm electromechanical relay, or the solid-state drive (SSD) a type of semiconductor memory used in computers to replace hard disk drives, which store data on a rotating disk.
Public transportPublic transport (also known as public transportation, public transit, mass transit, or simply transit) is a system of transport for passengers by group travel systems available for use by the general public unlike private transport, typically managed on a schedule, operated on established routes, and that charge a posted fee for each trip. There is no rigid definition of which kinds of transport are included, and air travel is often not thought of when discussing public transport—dictionaries use wording like "buses, trains, etc.
Quantum dotQuantum dots (QDs) – also called semiconductor nanocrystals, are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology and materials science. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band.
High-level synthesisHigh-level synthesis (HLS), sometimes referred to as C synthesis, electronic system-level (ESL) synthesis, algorithmic synthesis, or behavioral synthesis, is an automated design process that takes an abstract behavioral specification of a digital system and finds a register-transfer level structure that realizes the given behavior. Synthesis begins with a high-level specification of the problem, where behavior is generally decoupled from low-level circuit mechanics such as clock-level timing.
Logic synthesisIn computer engineering, logic synthesis is a process by which an abstract specification of desired circuit behavior, typically at register transfer level (RTL), is turned into a design implementation in terms of logic gates, typically by a computer program called a synthesis tool. Common examples of this process include synthesis of designs specified in hardware description languages, including VHDL and Verilog. Some synthesis tools generate bitstreams for programmable logic devices such as PALs or FPGAs, while others target the creation of ASICs.
Rail transportRail transport (also known as train transport) is a means of transport that transfers passengers and goods on wheeled vehicles running on rails, which are incorporated in tracks. In contrast to road transport, where the vehicles run on a prepared flat surface, rail vehicles (rolling stock) are directionally guided by the tracks on which they run. Tracks usually consist of steel rails.Rolling stock in a rail transport system generally encounters lower frictional resistance than rubber-tyred road vehicles, so passenger and freight cars (carriages and wagons) can be coupled into longer trains.
Thin-film solar cellThin-film solar cells are made by depositing one or more thin layers (thin films or TFs) of photovoltaic material onto a substrate, such as glass, plastic or metal. Thin-film solar cells are typically a few nanometers (nm) to a few microns (μm) thick–much thinner than the wafers used in conventional crystalline silicon (c-Si) based solar cells, which can be up to 200 μm thick. Thin-film solar cells are commercially used in several technologies, including cadmium telluride (CdTe), copper indium gallium diselenide (CIGS), and amorphous thin-film silicon (a-Si, TF-Si).
