; Algebraically closed field: A field F is algebraically closed if every polynomial in F has a root in F ; equivalently: every polynomial in F is a product of linear factors.

Algebraically, a map is anticonformal if at every point the Jacobian is a scalar times an orthogonal matrix with negative determinant: in two dimensions the Jacobian must be a scalar times a reflection at every point.

Algebraically, a lattice is a set with two associative, commutative idempotent binary operations linked by corresponding absorption laws.

Algebraically, the projectivization of this vector space is Proj of its symmetric algebra, that is,

Algebraically, this dilution factor will give us the physiologic dead space as calculated by the Bohr equation:

; Algebraically independent elements: Elements of an extension field of F are algebraically independent over F if they don't satisfy any non-zero polynomial equation with coefficients in F.

Algebraically compact modules share many other properties with injective objects because of the following: there exists an embedding of R-Mod into a Grothendieck category G under which the algebraically compact R-modules precisely correspond to the injective objects in G.

Algebraically, these units can be thought of as the squares of the corresponding length units.

Algebraically, this means that the standard MV-algebra generates the variety of all MV-algebras.

The angle generated by the platform servo **yf multiplied by G is the effective acceleration acting on the accelerometer.

If the Z gyro is drifting, a current generated by the autocollimator is delivered to the gyro torquer to cancel the drift.

Clearly there is always at least one such string for any n, as otherwise all possible strings ( infinitely many ) could be generated by the ( finitely many ) programs with lower complexity, so GenerateComplexString must always return.

Power generated by muscles, however, is limited by force – velocity relationship, and even at the optimal contraction speed for power production, total work done by the muscle will be less than half of what could be done if the muscle were contracting over the same distance at very slow speeds, resulting in less than 1 / 4 the projectile launch velocity possible without the limitations of the force – velocity relationship.

The Shawn Carlson's double-blind chart matching tests, in which 28 astrologers agreed to match over 100 natal charts to psychological profiles generated by the California Psychological Inventory ( CPI ) test, is one of the most renowned tests of astrology.

The large and diverse population of antibodies is generated by random combinations of a set of gene segments that encode different antigen binding sites ( or paratopes ), followed by random mutations in this area of the antibody gene, which create further diversity.

Sacrificial anodes are particularly needed for systems where a static charge is generated by the action of flowing liquids, such as pipelines and watercraft.

When analog television was developed, no affordable technology for storing any video signals existed ; the luminance signal has to be generated and transmitted at the same time at which it is displayed on the CRT.

In a healthy individual, the number of CD4 + lymphocytes is in balance with the cells generated by the bone marrow ; however, in HIV-positive patients, this balance is lost due to an inability of the bone marrow to regenerate CD4 + cells.

In flame AAS a steady-state signal is generated during the time period when the sample is aspirated.

In ET AAS a transient signal is generated, the area of which is directly proportional to the mass of analyte ( not its concentration ) introduced into the graphite tube.

The volatile hydride generated by the reaction that occurs is swept into the atomization chamber by an inert gas, where it undergoes decomposition.

Another source of background absorption, particularly in ET AAS, is scattering of the primary radiation at particles that are generated in the atomization stage, when the matrix could not be removed sufficiently in the pyrolysis stage.

The graphics are generated by a custom graphics chip called MARIA which is very different from other second and third generation consoles, and made it more difficult for game programmers to make the transition.

When in “ 7800 ” mode ( signified by the appearance of the full screen Atari logo ), the graphics are generated entirely by the MARIA graphics processing unit, all system RAM is available and game data is accessed in larger 48K blocks.

At the speed of sound the way that lift is generated changes dramatically, from being dominated by Bernoulli's principle to forces generated by shock waves.

Artin's theorem states that in an alternative algebra the subalgebra generated by any two elements is associative.

A generalization of Artin's theorem states that whenever three elements in an alternative algebra associate ( i. e. ) the subalgebra generated by those elements is associative.

A corollary of Artin's theorem is that alternative algebras are power-associative, that is, the subalgebra generated by a single element is associative.

It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.

The place is inhabited by several hundred warlike women who are anachronisms of the Twentieth Century -- stone age amazons who live in an all-female, matriarchal society which is self-sufficient ''.

since Bourbon whiskey, though of Kentucky origin, is at least as much favored by liberals in the North as by conservatives in the South.

In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.

But apart from racial problems, the old unreconstructed South -- to use the moderate words favored by Mr. Thomas Griffith -- finds itself unsympathetic to most of what is different about the civilization of the North.

The two main charges levelled against the Bourbons by liberals is that they are racists and social reactionaries.

It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.

Ratified in the Republican Party victory in 1952, the Positive State is now evidenced by political campaigns being waged not on whether but on how much social legislation there should be.

He was, and is, with the RAND Corporation, a nonprofit pool of thinkers financed by the U.S. Air Force.

They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.

It is softened by the saltbush and the bluebush, has a peaceful quality, the hills roll softly.

On Fridays, the day when many Persians relax with poetry, talk, and a samovar, people do not, it is true, stream into Chehel Sotun -- a pavilion and garden built by Shah Abbas 2, in the seventeenth century -- but they do retire into hundreds of pavilions throughout the city and up the river valley, which are smaller, more humble copies of the former.

Poetry in Persian life is far more than a common ground on which -- in a society deeply fissured by antagonisms -- all may stand.

Nostalgic Yankee readers of Erskine Caldwell are today informed by proud Georgians that Tobacco Road is buried beneath a four-lane super highway, over which travel each day suburbanite businessmen more concerned with the Dow-Jones average than with the cotton crop.

All but the most rabid of Confederate flag wavers admit that the Old Southern tradition is defunct in actuality and sigh that its passing was accompanied by the disappearance of many genteel and aristocratic traditions of the reputedly languid ante-bellum way of life.

Westbrook further bemoans the Southern writers' creation of an unreal image of their homeland, which is too readily assimilated by both foreign readers and visiting Yankees: `` Our northerner is suspicious of all this crass evidence ( of urbanization ) presented to his senses.

As his disciples boast, even though his emphasis is elsewhere, Faulkner does show his awareness of the changing order of the South quite keenly, as can be proven by a quick recalling of his Sartoris and Snopes families.

The unit of form is determined subjectively: `` the Heart, by the way of the Breath, to the Line ''.