Counterfeit moneyCounterfeit money is currency produced without the legal sanction of a state or government, usually in a deliberate attempt to imitate that currency and so as to deceive its recipient. Producing or using counterfeit money is a form of fraud or forgery, and is illegal. The business of counterfeiting money is nearly as old as money itself: plated copies (known as Fourrées) have been found of Lydian coins, which are thought to be among the first Western coins.
Counterfeit consumer goodsCounterfeit consumer goods (or counterfeit and fraudulent, suspect items - CFSI) are goods, often of inferior quality, made or sold under another's brand name without the brand owner's authorization. Sellers of such goods may infringe on either the trademark, patent or copyright of the brand owner by passing off its goods as made by the brand owner. Counterfeit products made up 5 to 7% of world trade in 2013, and in 2014 cost an estimated 2.5 million jobs worldwide, with up to 750,000 jobs lost in the U.S.
Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Intuitionistic type theoryIntuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Radio-frequency identificationRadio-frequency identification (RFID) uses electromagnetic fields to automatically identify and track tags attached to objects. An RFID system consists of a tiny radio transponder, a radio receiver and transmitter. When triggered by an electromagnetic interrogation pulse from a nearby RFID reader device, the tag transmits digital data, usually an identifying inventory number, back to the reader. This number can be used to track inventory goods. Passive tags are powered by energy from the RFID reader's interrogating radio waves.
Counterfeit watchA counterfeit watch (or replica watch) is an unauthorised copy of an authentic watch. High-end luxury watches such as Rolex, Patek Philippe and Richard Mille are frequently counterfeited and sold on city streets and online. With technological advancements, many non-luxury and inexpensive quartz watches are also commonly counterfeited. According to estimates by the Swiss Customs Service, there are some 30 to 40 million counterfeit watches put into circulation each year.
Path tracingPath tracing is a computer graphics Monte Carlo method of rendering images of three-dimensional scenes such that the global illumination is faithful to reality. Fundamentally, the algorithm is integrating over all the illuminance arriving to a single point on the surface of an object. This illuminance is then reduced by a surface reflectance function (BRDF) to determine how much of it will go towards the viewpoint camera. This integration procedure is repeated for every pixel in the output image.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
