From the commutativity of kets with ( complex ) scalars now follows that

From a more advanced perspective, each of these definitions may be interpreted as giving the unique analytic continuation of e < sup > x </ sup > to the complex plane.

From an algebraic point of view, the set of holomorphic functions on an open set is a commutative ring and a complex vector space.

From these two basic types, a few modern designs have been created, such as the Hohner CBH-2016 chromatic and the Suzuki Overdrive diatonic, which have complex covers that allow for specific functions not usually available in the traditional design.

From this scarce notice, it has been concluded that a small church which encompassed a cave complex might have been located in Nazareth in the early 4th century ," although the town was Jewish until the 7th century AD.

From a systems perspective, a complex network structure can be decomposed into individual component firms ( Zhang and Dilts, 2004 ).

From 200, 000 BP onwards, Middle Paleolithic humans began to make complex stone blades with flaked edges which were used as spear heads.

From this building, which is still in use, the present hospital complex has grown.

From 2001 through 2008, the East Front of the Capitol ( site of most presidential inaugurations until Ronald Reagan began a new tradition in 1981 ) was the site of construction for this massive underground complex, designed to facilitate a more orderly entrance for visitors to the Capitol.

From this foundation arises a complex political and ideological superstructure, where economic development impacts upon societal progress.

From such a perspective, in different research contexts complex systems are defined on the basis of their different attributes.

) use an mboxrd variation with more complex From line quoting rules.

From the late 1960s until the mid-1990s, cadets also completed SERE training in the Jacks Valley complex between their fourth-and third-class years.

From south to north, the principal temple-cities, their principal temple complex, and the gods they served, were

From about 1854 to 1900, an industrial complex existed in and around Columbia, Marietta and Wrightsville that included 11 anthracite iron furnaces and related structures, as well as canal and railroad facilities servicing them.

From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective geometry, and differential geometry ; and later topology, when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis.

From here, Route 120 heads northwest along the northern edge of the sports complex as a four-lane divided at-grade Paterson Plank Road, passing through industrial and commercial areas.

From the polemical contemporary works which describe his career have emerged the outlines of a complex figure, charting a dangerous course through the chaos of the late 5th century Athenian political scene ; although historians from ancient times to the present have offered far more specific portraits, of one form or another, it may be that nothing more than that outline will ever be known with certainty.

From that time, the pipe organ was the most complex man-made device, a distinction it retained until it was displaced by the telephone exchange in the late 19th century.

From its beginnings as the Wright brothers ' testing field, it has evolved into the headquarters for the Air Force's worldwide logistics system and all Air Force systems development and procurement, the aeronautical engineering center, a major research laboratory complex, the heart of Air Force graduate education, location of the second largest Air Force medical center, and home of the National Museum of the U. S. Air Force.

From these building blocks one can build more complex shapes like squares, triangles, circles and other composite figures.

From the ancient Greeks until the work of Carolus Linnaeus ( also known as Carl Linnaeus, or Carl von Linné ) and other 18th century naturalists, the main concept of natural history was the scala naturae or Great Chain of Being, a conceptual arrangement of minerals, vegetables, more primitive forms of animals, and more complex life forms on a linear scale of increasing " perfection ", culminating in our species.

From 1949 to 1991 the complex was used by the BBC.

From 1970 to 1984, Pratt lived mainly in France where Corto Maltese, a psychologically very complex character resulting from the travel experiences and the endless inventive capacity of his author, became the main character of a comics series.

From the primitive to the complex, those identifications indicate that the most primitive form of the music was associated with Marshall, Texas – and that the left-hand bass lines grew more complex as the distance from Marshall increased.

From the point of view of syntactic analysis the head word in the statement is the predicator has broken, and from the point of view of meaning it would seem that the trouble centers in the breaking ; ;

From an analysis of relationships and diversities within the Asterales and with their superorders, estimates of the age of the beginning of the Asterales have been made, which range from 116 Mya to 82Mya.

From a sociological and demographic perspective, the Big Brother franchise allows the opportunity for analysis of how people react when forced into close confinement with people who lie outside their comfort zone, since they may hold different opinions or ideals from other contestants, or simply belong to a different group of people than a contestant normally interacts with.

From basic functional analysis we know that any ket can be written as

From politics past to politics future: an integrated analysis of current and emergent paradigms.

From a psychoanalytical perspective, after the Lacanian notion of " the Real ", Slavoj Žižek offered new aspects of " the gaze " extensively used in contemporary film analysis.

From this analysis, the financial planner can determine to what degree and in what time the personal goals can be accomplished.

From pictures on the wall to movies to television to video games to computers, each successive generation has been exposed to richer optical displays than the one before and may have become more adept at visual analysis.

From the point of view of functional analysis, calculus is the study of two linear operators: the differential operator, and the indefinite integral operator.

From these few references, which are the only surviving evidence apart from place name analysis, it would seem that the Balts Pytheas would have encountered were past the Common Balto-Slavic stage, but still spoke one language, which would have been Proto-Baltic.

From this analysis, it is clear that the transmission speed is a characteristic of the teleprinter while the shift ( the difference between the tones representing mark and space ) is a characteristic of the modem.

There is an extensive critical analysis of Le Fanu's supernatural stories ( particularly " Green Tea ", " Schalken the Painter " and " Carmilla ") in Jack Sullivan's book Elegant Nightmares: The English Ghost Story From Le Fanu to Blackwood ( 1978 ).

From the Gramsci analysis derived the political science denotation of hegemony as leadership ; thus, the historical example of Prussia as the militarily and culturally predominant province of the German Empire ( Second Reich 1871 – 1918 ); and the personal and intellectual predominance of Napoleon Bonaparte upon the French Consulate ( 1799 – 1804 ).

From this perspective, heuristics are part of a larger experiential processing system that is often adaptive, but vulnerable to error in situations that require logical analysis.

From 1988 to 1989, Poindexter was senior scientist at Presearch, Inc., which had primarily been involved with defense studies and analysis.

From the 1950s onward, Hans Keller developed a ' two-dimensional ' method of analysis that explicitly considered form and structure from the point of view of listener expectations.

From 1911 he collaborated with J. E. Littlewood, in extensive work in mathematical analysis and analytic number theory.

From 1970 to 1989, the show used the Wall Street Week Index ( later known as the WSW Technical Market Index ), a technical analysis developed by Robert Nurock.

From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is now often an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.

From a geological point of view, analysis of Uluru-Kata Tjuta and Watarrka National Parks reveals an awe-inspiring history.

From analysis of fossil pollen in peat samples, it is apparent that elms, an abundant tree in prehistoric times, all but disappeared from northwestern Europe during the mid-Holocene period about 6000 years ago, and to a lesser extent 3000 years ago.

From this it is supposed that there is a theoretical fourth passive element since there are only five elements in total ( not including the various dependent sources ) found in linear network analysis.

From the perspective of dimensional analysis, the unit Hertz ( Hz ) is also correct, but in practice it is only used for ordinary frequency f, and almost never for ω.

From 1925 until 1934, she was the Secretary of the International Psychoanalytical Association while she continued child analysis and seminars and conferences on the subject.