Fixed point - Fixed point In mathematics, a fixed point of a function is a point that is mapped to itself by the function. For example, if f is defined on the real numbers by f(x) = x2 − 3x + 4, then 2 is a fixed point of f, because f(2) = 2. See also Fixed point Brouwer fixed point theorem Banach fixed point theorem Knaster-Tarski theorem Y combinator / fixed point combinator Fixed point theorems about recursive functions In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the decimal (or binary or hexadecimal) point. For example, a fixed-point number with 4 digits after the decimal point could be used to store numbers such as.
Fixed point combinator - Fixed point combinator A fixed point combinator is a function which computes fixed points of other functions. A 'fixed point' of a function is a value left 'fixed' by that function; for example, 0 and 1 are fixed points of the squaring function. In certain formalizations of mathematics, such as the lambda calculus and combinatorial calculus, every function has a fixed point. In these formalizations, it is possible to produce a function, often denoted Y, which computes a fixed point of any function it is given. Since a fixed point x of a function f is a value that has the property f(x) = x, a fixed point combinator Y is a function with the property that f(Y(f)) = Y(f) for all functions f. One well-known.
Fixed-point lemma for normal functions - Fixed-point lemma for normal functions The fixed-point lemma for normal functions is a basic result in axiomatic set theory; it states that any normal function has arbitrarily large fixed points. A formal version and proof (using the Zermelo-Fraenkel axioms) follow. Table of contents showTocToggle("show","hide") 1 Formal version 2 Proof 3 Notes Formal version Let f : Ord → Ord be a normal function. Then for every α ∈ Ord, there exists a β ∈ Ord such that β ≥ α and f(β) = β. Proof First of all, it is clear that for any α ∈ Ord, f(α) ≥ α. If this was not the case, we could choose a minimal α with f(α) < α; then, since f is normal and thus monotone, f(f(α)) <.
Floating point - Floating point A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. In particular, it represents an integer or fixed-point number (the significand or, informally, the mantissa) multiplied by a base (usually 2 in computers) to some integer power (the exponent). When the base is 2, it is the binary analog of scientific notation (in base 10). A floating-point calculation is an arithmetic calculation done with floating-point numbers, and often involves some approximation or rounding because the result of an operation may not be exactly representable, In a floating-point number, the number of significant digits (the relative precision) has a maximum, rather than the number of.
Karl Guthe Jansky - one could find what the direction was to any radio signal. After recording signals from all directions for several months, Jansky identified three types of static: nearby thunderstorms, distant thunderstorms, and a faint steady hiss of unknown origin. Jansky spent over a year investigating the third type of static. It rose and fell once a day, leading Jansky to think at first that he was seeing radiation from the Sun. But after a few months of following the signal, the brightest point moved away from the position of the Sun. The signal repeated not every 24 hours, but every 23 hours and 56 minutes. This is characteristic of the fixed stars, and other objects far from our solar system (sidereal day). He eventually figured out that the radiation was coming from.
Knaster-Tarski theorem - be a complete lattice and let f : L -> L be an order-preserving function. Then the set of fixed points of f in L is also a complete lattice. Since complete lattices cannot be empty, the theorem in particular guarantees the existence of at least one fixed point of f, and even the existence of a least (or greatest) fixed point. In many practical cases, this is the most important implication of the theorem. For example, in mathematical logic least fixed points of functions on sets of formulas are used to compute the semantics of a logic program. Sometimes a more specialized version of the theorem is used, where L is assumed to be the lattice of all subsets of a certain set ordered by subset inclusion. This reflects the.
Kolmogorov space - now simple; X is T0 if and only if every pair of distinct points is topologically distinguishable. This definition may also be formulated as follows: X is a T0 space if and only if for any two distinct points in X there exists an open subset of X which contains one of the points but not the other. This characterisation should be contrasted with an analogous characterisation of T1 spacess, where one can specify beforehand which points will belong to the open set. T0 is nice Almost every topological space studied in ordinary mathematics is T0. Indeed, when mathematicians in many fields, notably analysis, naturally run across non-T0 spaces, they usually replace them with T0 spaces, in a manner described below. In general, when dealing with a fixed topology T on.
Kohen - Publishing The below text has been taken from the public domain 1906 "Jewish Encyclopaedia". It should be used to help construct an entirely new entry. It is not yet in a form useful for laypeople, nor does it represent any modern scholarship. In ancient Israel one was not required to be specially consecrated in order to perform the sacrificial functions; any one might approach the altar and offer sacrifices. Thus Gideon, of the tribe of Manasseh (Judges vi. 26), and the Danite Manoah (ib. xiii. 16, 19) sacrificed in person at the express command of God and the angel of God respectively; similarly, David sacrificed on the altar he had built at God's command on the thrashing-floor of Araunah (II Sam. xxiv. 25); and Solomon, before the ark in Jerusalem (I.
Korteweg-de Vries equation - variables, x and t. Its solutions clump up into solitons. To see how this works, consider solutions in which a fixed wave form (given by f(x)) maintains its shape as it travels to the right at speed c. Such a solution is given by φ(x,t) = f(x-ct). This gives the differential equation or, integrating with respect to x, is a constant of integration. Interpreting the independent variable x above as a time variable, this means f satisfies Newton's equation of motion in a cubic potential. If parameters are adjusted so that f(x) has local maximum at x=0, there is a solution in which f(x) starts at this point at 'time' -∞, eventually slides down to the local minimum, then back up the other side, reaching an equal height, then reverses direction,.
Vector bundle - mathematics, a vector bundle is a geometrical construct where to every point of a topological space (or manifold, or algebraic variety) we attach a vector space in a compatible way, so that all those vectorspaces, "glued together", form another topological space (or manifold or variety). A typical example is the tangent bundle of a differentiable manifold: to every point of the manifold we attach the tangent space of the manifold at that point. Or consider a smooth curve in R2, and attach to every point of the curve the line normal to the curve at that point; this yields the "normal bundle" of the curve. This article deals mostly with real vector bundles, with finite-dimensional fibers. Complex vector bundles are important in many cases, too; they are a special case, meaning.
Jacobin Club - almost entirely of professional men, such as Robespierre, or well-to-do bourgeois, like Santerre. From the first, however, other elements were present. Besides Louis Philippe, duc de Chartres (afterwards king of the French), liberal aristocrats of the type of the due d'Aiguillon, the prince de Broglie, or the vicomte de Noailles, and the bourgeois who formed the mass of the members, the club contained such figures as "Père" Michel Gerard, a peasant proprietor from Tuel-en-Montgermont, in Brittany, whose rough common sense was admired as the oracle of popular wisdom, and whose countryman’s waistcoat and plaited hair were later on to become the model for the Jacobin fashion. The provincial branches were from the first far more democratic, though in these too the leadership was usually in the hands of members of the.
Vehicle for hire - from other modes of public transportation in that vehicle for hire passengers are more or less free to choose their starting and ending locations (point of origin and destination), whereas in other modes, the passenger must choose from a limited selection of locations designated by the service provider. This mode should also be distinguished from hiring a vehicle for driving oneself (see car rental). The most common vehicle for hire around the world is the taxicab; other vehicles for hire include limousines, rickshaws, velotaxis (pedicabs), horse-drawn carriages (including hackney carriages and caleches), and water taxis. Jitneys, paratransit, and shuttle buses are hybrids--halfway between taxicabs and buses--and operate along somewhat fixed routes, with some flexibility in where passengers may be picked up or dropped off. Some of these routes may be very.
Jewish music - the ban on singing and music, although not formally lifted by any council, soon became understood as only a ban outside of religious services. Within the synagogue the custom of singing soon re-emerged. In later years, the practice became to allow singing for feasts celebrating religious life-cycle events such as weddings, and over time the formal ban against singing and performing music lost its force altogether. It was with the piyyutim (liturgical poems) that Jewish music began to crystallize into definite form. The cantor sang the piyyutim to melodies selected by their writer or by himself, thus introducing fixed melodies into synagogal music. The prayers he continued to recite as he had heard his predecessors recite them; but in moments of inspiration he would give utterance to a phrase of unusual.
Video game light gun - in a way that allows the computer to judge where the gun is pointing based on when the diode detects light. The first detection method, used by the Zapper, involves drawing each target sequentially in white light after the screen blacks out. The computer knows that if the diode detects light as it is drawing a square (or after the screen refreshes), that is the target the gun is pointed at. Essentially the diode tells the computer whether or not you hit something, and for n objects, the sequence of the drawing of the targets tell the computer which target you hit after 1 + ceil(log2(n)) refreshes (one to determine if any target at all was hit and ceil(log2(n)) to do a binary search for the object that was hit). An.
Joseph Justus Scaliger - years, profiting not only by the lectures but even more by the library of Cujas, which filled no fewer than seven or eight rooms and included five hundred manuscripts. The massacre of St Bartholomew--occurring as he was about to accompany the bishop of Valence on an embassy to Poland--induced him with other Huguenots to retire to Geneva, where he was received with open arms, and was appointed a professor in the academy. He lectured on the Organon of Aristotle and the De finibus of Cicero with much satisfaction to the students but with little to himself. He hated lecturing, and was bored with the importunities of the fanatical preachers; and in 1574 he returned to France, and made his home for the next twenty years with Chastaigner. Of his life during.
View camera - a ground glass plate. As the ground glass image is sometimes difficult to view, the photographer may use a cloth to cover their head and the rear of the camera to assist in composition. To take the picture the glass is replaced with a sheet of film in a film holder. The lens and film standards are not fixed relative to each other (unlike most cameras), this allows movements of the lens and film plane in respect to each other. Generally, view cameras are built for large film formats (measurements in inches): 4x5, 5x7, 4x10, 5x12, 8x10, 11x14, 8x20, 12x20, 20x24, and 30x40 are all popular formats. The advantages of view cameras are : Large film format allows a very detailed picture and allows for enlargement with less "grain" or loss.
Vivendi - a company with various activities : Canal+: television Cegetel: Fixed and mobile phone Maroc Telecom Vivendi Environnement History In 1853, a water company named "Compagnie Générale des Eaux" (CGE) was created by Imperial decree in order supply water to the public in Lyon. It served in this capacity for over a hundred years. Beginning in 1980, CGE began diversifying its operations from water into waste management, energy, transport services, and construction and property. In 1983, CGE helped to found Canal+, the first Pay-TV channel in France, and in the 1990s, they began expanding into telecommunications and mass media. In 1996, Vivendi created Cegetel to take advantage of the 1998 deregulation of the French telecommunications market; it is currently a leading provider of both fixed and mobile services. Vivendi's CanalSatellite is the.
Joint product pricing - There are complexities in the production function also. Their production could be linked in the sense that they are bi-products (referred to as compliments in production), or they could be linked in the sense that they can be produced by the same inputs (referred to as substitutes in production). Also, production of the joint product could be in fixed proportions or in variable proportions. When setting prices in a situation as complex as this, microeconomic marginal analysis is helpful. In a simple case of a single product, price is set at that quantity demanded where marginal cost exactly equals marginal revenue. This is exactly what is done when joint products are produced in variable proportions. Each product is treated separately. In fact, it might even be possible to construct separate cost.
John F. Kennedy assassination - PM. Shortly thereafter, Dallas police officer J. D. Tippit was shot less than one mile from Oswald's rooming house. The Warren Commission saw enough evidence to believe that Oswald shot Tippit at about 1:16 PM. The situation at Parkland Hospital had deteriorated. Even as the press contingent grew, a priest had been summoned for Kennedy, as a Catholic, so that Last Rites might be performed. It had become apparent to those inside the hospital that President Kennedy was already dead. Governor Connally, meanwhile, was in emergency surgery. According to the Warren Report, Lee Harvey Oswald had attempted to hide in the Texas Theatre at about 1:45 PM, doing so by ducking into the building without paying while the box office attendant was distracted. Police radio alerted nearby units to apprehend him.
Joe Charboneau - die his hair unnatural colors, open beer bottles with his eye socket, and drink beer with a straw through his nose, and other stories that emerged about how he did his own dental work and fixed a broken nose with a pair of pliers and a few shots of Jack Daniels whiskey, stood out in 1980. By mid-season, Charboneau was the subject of a song--"Go Joe Charboneau"--that reached #3 on the local charts. He finished the season with 87 runs batted in and a .289 batting average while winning the American League Rookie of the Year award--all in spite of being stabbed with a ball-point pen by a crazed fan as he waited for the team bus on March 8. The pen penetrated an inch and hit a rib, but Charboneau.
