then there exists a linear extension of to the whole space V, i. e., there exists a linear functional ψ such that

then there exists a linear extension of φ to the whole space V, i. e., there exists a K-linear functional ψ such that

The American-Negro Suite is in a sense an extension of the Cotton Club songs in that it is a collection of Negro songs, not for a night club, but for the concert stage.

You should make any request for an extension early so that if it is refused, your return may still be on time.

An extension of 2 months beyond the regular due date for filing is also available to taxpayers making returns for a fiscal year.

Such interest must be paid even though an extension of time for filing is granted.

( To avoid any possible excuse for a dripping parade through your house, it is a good idea to have a telephone extension near the pool as well as a direct outdoor route between the pool, and the parking area.

The observational data determining the concentration distribution have a range of error which is magnified in the extension into the micrometeorite region.

The other misconception is that our ecumenical problems will be solved if only the knowledge of the church in its world-wide extension and its interdenominational connections, now comprehended by many national leaders, can be communicated to all congregations.

In general, friendly contact with a member followed by contact with a clergyman will account for a major share of recruitment by the churches, making it quite evident that the extension of economic integration through co-optation is the principal form of mission in the contemporary church ; ;

`` The important thing from now on '', he said, `` is not to mourn the past but to seize the future opportunity to prevent the loss in northern Viet Nam from leading to the extension of Communism throughout Southeast Asia ''.

The " tail " is only possessed by the male and is an extension of the cloaca and used to inseminate the female.

Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo – Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann – Bernays – Gödel set theory, a conservative extension of ZFC.

In the case of a Galois extension L / K the subgroup of all automorphisms of L fixing K pointwise is called the Galois group of the extension.

An extension of this is the sacred cockfight, ” a popular form of fertility worship among almost all Southeast Asians ” considered by some in the Judeo-Christian ethic as a form of ’ fertility worship ’ or Baalim.

The more humid regions have a richer vegetation ; dense forest where the rainfall is greatest and variations of temperature least, conditions found chiefly on the tropical coasts, and in the west African equatorial basin with its extension towards the upper Nile ; and savanna interspersed with trees on the greater part of the plateaus, passing as the desert regions are approached into a scrub vegetation consisting of thorny acacias, etc.

Also from there is the word bung, from the Sydney pidgin English ( and ultimately from the Sydney Aboriginal language ), meaning " dead ", with some extension to " broken " or " useless ".

In abstract algebra, a field extension L / K is called algebraic if every element of L is algebraic over K, i. e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions that are not algebraic, i. e. which contain transcendental elements, are called transcendental.

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

In other words, the promulgators of the murder plan made clear that physically exterminating the Jews was but an extension of the anti-Semitic measures already operating in every phase of German life, and that the new conspiracy counted on the general anti-Semitism that had made those measures effective, as a readiness for murder.

Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.

The 64-bit extension of x86, x86-64, has been further generalized to 14 instead of 6 general registers.

An extension of this expansion is the parametrized post-Newtonian ( PPN ) formalism, which allows quantitative comparisons between the predictions of general relativity and alternative theories.

It is named for Hans Hahn and Stefan Banach who proved this theorem independently in the late 1920s, although a special case was proved earlier ( in 1912 ) by Eduard Helly, and a general extension theorem from which the Hahn – Banach theorem can be derived was proved in 1923 by Marcel Riesz.

More broadly the term is used in a wide number of contexts for an image, picture, or representation ; it is a sign or likeness that stands for an object by signifying or representing it either concretely or by analogy, as in semiotics ; by extension, icon is also used, particularly in modern culture, in the general sense of symbol — i. e. a name, face, picture, edifice or even a person readily recognized as having some well-known significance or embodying certain qualities: one thing, an image or depiction, that represents something else of greater significance through literal or figurative meaning, usually associated with religious, cultural, political, or economic standing.

It is unclear whether these flames are an extension of her telekinesis and telepathy or a more general property of the Phoenix Force.

Out of this came the implementation of the concept of library service – the democratic extension of library services to the general public regardless of wealth or education.

Stories earlier in the timeline feature technology such as Bussard ramjets, Drouds ( wires capable of directly stimulating the pleasure centers of the brain ) and explore how organ transplantation technology enables the new crime of organlegging ( as well as the general sociological effects of widespread transplant technology ), while later stories feature hyperdrive, invulnerable starship hulls, stasis fields, molecular monofilaments, transfer booths ( teleporters used only on planetary surfaces ), the lifespan-extending drug boosterspice, and the tasp which is an extension of the wirehead development which works without direct contact.

A marathon is a distance race of 42. 195 km ( 26 miles 385 yards ) and, by extension, in general speech a lengthy, arduous or time-consuming undertaking.

Press accounts framed Nancy as her husband's " chief protector ", an extension of their general initial framing of her as a helpmate and a Cold War domestic ideal.

An extension mechanism was proposed in RFC 2449 to accommodate general extensions as well as announce in an organized manner support for optional commands, such as TOP and UIDL.

The distinction between the embedded description and the bearer itself is similar to that between the extension and the intension of a general term, or between connotation and denotation.

The extension of a general term like " dog " is just all the dogs that are out there ; the extension is what the word can be used to refer to.

They are studied and copied by violin makers, contributing to the extension of the general knowledge we have on the viola da gamba, its forms, and the different techniques used for its manufacture.

Some fundamental formulations in the field of general semantics rely heavily on a valuation of extension over intension.

The extension of this idea to substances in general necessarily led him to the law of multiple proportions, and the comparison with experiment brilliantly confirmed his deduction.

In his seminal Die Grundgesetze der Arithmetik ( Basic Laws of Arithmetic ) he built up arithmetic from a system of logic with a general principle of comprehension, which he called " Basic Law V " ( for concepts F and G, the extension of F equals the extension of G if and only if for all objects a, Fa if and only if Ga ), a principle that he took to be acceptable as part of logic.

An extension of such a theory to the general case of the L-subsets is possible ( see Gerla 2006 ).

The beauty of the scenery, and the facilities offered to travellers by the general extension of mountain railways, make the northern side of the range, the Bernese Oberland, one of the portions of the Alps most visited by tourists.

By extension, assuming that the labels assigned to subjects are truly representative of their trustworthiness, then the no-read-up and no-write-down rules rigidly enforced by the reference monitor are provably sufficient to constrain Trojan horses, one of the most general classes of attack ( sciz., the popularly reported worms and viruses are specializations of the Trojan horse concept ).

The element x is not uniquely determined ; the field can also be regarded, for instance, as an extension of C ( y ).

Specifically, it implies that as a Galois extension of K, L is uniquely determined by the set of primes of K that split completely in it.

Together with A. Chervyakov, Kleinert developed an extension of the theory of distributions from linear spaces to semigroups by defining their products uniquely ( in the mathematical theory, only linear combinations are defined ).