A year later, noted similarities between algebraic and linear dependence in his classic textbook on Modern Algebra.

Modern usages ( especially in the context of computer science with mathematical software such as model checkers, automated theorem provers, interactive theorem provers ) tend to retain of the notion of formula only the algebraic concept and to leave the question of well-formedness, i. e. of the concrete string representation of formulas ( using this or that symbol for connectives and quantifiers, using this or that parenthesizing convention, using Polish or infix notation, etc.

Modern turbochargers can use wastegates, blow-off valves and variable geometry, as discussed in later sections.

Already René Descartes in his Discourse on the Method had attested to the impact Renaissance planned new towns had upon his own thought, and much evidence exists that the Renaissance streetscape was also the perceptual stimulus that had led to the development of coordinate geometry ( see, e. g., Claudia Lacour Brodsky, Lines of Thought: Discourse, Architectonics, and the Origins of Modern Philosophy, Duke 1996 ).

He also published Raum und Zeit in der gegenwärtigen Physik (" Space and Time in Modern Physics "), which extended his earlier results by applying Poincaré's geometric conventionalism to explain Einstein's adoption of a non-Euclidean geometry in the General Theory of Relativity.

The beginning of the twentieth century saw the heightened use of Euclidean or Cartesian rectilinear geometry in Modern Architecture.

As a mathematics educator, Dodgson defended the use of Euclid's Elements as a geometry textbook ; Euclid and his Modern Rivals is a criticism of a reform movement in geometry education lead by the Association for the Improvement of Geometrical Teaching.

Modern use of the cross ratio in projective geometry began with Lazare Carnot in 1803 with his book Géométrie de Position.

Modern downhill bikes weigh between 14 and 19 kg ( 30 and 42 pounds ), and usually feature full-suspension and frame geometries that lean back farther ( slacker geometry ) than other mountain bikes.

Modern applications are also found in a wide gamut of areas including ; Finite geometry, tournament scheduling, lotteries, mathematical biology, algorithm design and analysis, networking, group testing and cryptography.

Modern steal rules were fully implemented in 1898, and steals are now only credited when a runner successfully takes an extra base while the ball is being pitched, but not already hit.

For example, as a result of heavy borrowing from Arabic into Persian, Modern Persian in fact takes more of its vocabulary from Arabic than from its direct ancestor, Proto-Indo-Iranian.

Call of Duty: Modern Warfare 3 has a level named Mind the Gap where most of the level takes place between the dockyards and Westminster while the player and a team of SAS attempt to take down cargo being shipped using London Underground.

Late Middle English and the transition to Early Modern English takes place from the early 15th century and is taken to have been complete by the beginning of the Tudor period in 1485.

* Call of Duty: Modern Warfare 3 ( 2011 ): The ending of the game takes place in 2017.

The specific expression of Modern Orthodoxy, however, takes many forms, and in fact, particularly over the past 30 – 40 years, describes a political spectrum.

* Modern Assyrian music takes off when Albert Rouel Tamras releases his first records in Baghdad in 1966 on the Bashirphone label.

Modern Carnival on Dominica takes place on the Monday and Tuesday before Ash Wednesday, and is a festive occasion during which laws against libel and slander are suspended.

Modern Llandudno takes its name from the ancient parish of Saint Tudno but also encompasses several neighbouring townships and districts including Craig-y-Don, Llanrhos and Penrhyn Bay.

Hagustald is related to the Old High German hagustalt, denoting a younger son who takes land outside the settlement ; the element ea means " stream " or " river " and ham is the Old English form of the Modern English " home " ( and the Scots and Northern English " hame ").

Modern fantasy literature has used the Matter of France far less than the Matter of Britain, although L. Sprague de Camp and Fletcher Pratt set one of their Harold Shea stories ( The Castle of Iron ) in the world of the Matter of France, and Poul Anderson's Three Hearts and Three Lions takes place in a fantasy world where it was historical fact.

The post-Infinite Crisis Kandor differs from its Silver Age version as it takes clothing and other aspects from both the Silver and Modern Age of Krypton.

Modern social structural analysis takes this into account through multivariate analysis and other techniques, but the analytic problem of how to combine various aspects of social life into a whole remains.

Conservative Judaism takes a more lenient approach in application of the halakhic rules than Modern Orthodox Judaism.

Despite its scholarly subject and content, the work takes the form of a whimsical dialogue, principally between a mathematician named Minos ( taken from Minos, judge of the underworld in Greek mythology ) and a " devil's advocate " named Professor Niemand ( German for ' nobody ') who represents the " Modern Rivals " of the title.

His performance included his own takes on Bowie's " Unwashed and Somewhat Slightly Dazed ", " Let Me Sleep Beside You ", " Rock and Roll Suicide " and " Modern Love ".

Part V takes place at the Modern Language Association conference in New York at the end of 1979.

The story takes place in the future, a post-apocalyptic time following the release of Anthrasax at the height of Modern Civilization.

Modern locomotives often make use of a pushbutton switch, which takes away the fine control over the way the whistle is sounded.

The Tate Modern, also in London is another example of adaptive reuse in the European continent, unlike other adaptive reuse galleries in Europe, the Tate Modern takes full advantage of the site of the former Bankside Power Station, which involved the refurbishment of the old, abandoned power station.

Certain complementisers and other adverbial features present in the standard Modern Greek dialect are absent from Tsakonian, with the exception of the Modern που () relativiser, which takes the form πη () in Tsakonian ( note: the traditional Tsakonian orthography uses the digraph πφ + η, giving πφη ).

** Rick is also host of the Sonic Modern Rock Countdown, a countdown show airing on weekends that takes a look back at events that happened over the past week, while counting down the top songs.

* Modern Orthodoxy comprises a fairly broad spectrum of movements, each drawing on several distinct, though related, philosophies, which in some combination provide the basis for all variations of the movement today.

Modern Orthodoxy comprises a fairly broad spectrum of movements each drawing on several distinct, though related, philosophies, which in some combination provide the basis for all variations of the movement today ; these are discussed below.

" Modern orthodoxy ", then, as opposed to constituting an ideological spectrum centred on a common core of values, is, in fact, ( tending towards ) several entirely separate movements.

Within Orthodox Judaism there is a spectrum of communities and practices, including Modern Orthodox Judaism, Haredi Judaism, and a variety of movements that have their origins in Hasidic Judaism.

Modern scholarship on the Talmud has a spectrum of views from Joseph Klausner, R. Travers Herford and Peter Schäfer who see some traces of a historical Jesus in the Talmud, to the views of Johann Maier, and Jacob Neusner who consider that there are little or no historical traces and texts have been applied to Jesus in later editing, and others such as Boyarin ( 1999 ) who argue that Jesus in the Talmud is a literary device used by Rabbis to comment on their relationship to and with early Christians.

At the opposite end of the spectrum to this, the argument has been put forward to suggest that ringforts were in use, if not being built in the Later Medieval and possibly Early Modern period in Gaelic Ireland.

Modern digital cameras filter out most of the infrared spectrum that their sensors detect.

Modern CDMA and TDMA systems are more complex: A channel in TDMA is a frequency pair, and a time slot, and a channel in CDMA is a spread spectrum key but the principle of channel reuse still applies.

Modern joint service aerospace forces offer the most responsive, flexible, lethal, and devastating form of power projection across the spectrum of conflict, employing a range of aerospace weaponry such as maritime patrol aircraft, attack and troop-lift helicopters, land-based long-range aircraft, and battlefield rocket artillery systems.

Modern violinist Félix Lajkó based his jazz-like opus on a broad spectrum of influences from the music of Pannonian plain, including Hungarian, Vojvodinian and Roma music.

A. Wheeler and J. Tiomno, " Energy spectrum of electrons from meson decay ," Reviews of Modern Physics 21, 144-152 ( 1949 ).

Modern, automated sorting applies optical sensors ( visible spectrum, near infrared, X-ray, ultraviolet ), that can be coupled with electrical conductivity and magnetic susceptibility sensors, to control the mechanical separation of ore into two or more categories on an individual rock by rock basis.

Modern secure communication techniques use such methods as spread spectrum modulation to resist the deleterious effects of jamming.