A new South is emerging after the post-bellum years of hesitation, uncertainty, and lack of action from the Negro in defining his new role in the amorphously defined socio-political organizations of the white man.

A small business is defined as one which is independently owned and operated and which is not dominant in its field.

Field shifts were derived from the mean value of the resonance line, defined as the field about which the first moment is zero.

Dirt, which is here defined as particulate material which is usually inorganic and is very often extremely finely divided so as to exhibit colloidal properties.

The international unit is equipotent with the USP unit adopted in 1952, which was defined as the amount of activity present in 20 mg of the USP reference substance.

The function f{t} defined in this way is multi-valued.

In some neighborhood of an isolated tangent point in the f-plane, say Af, the function Af is either double-valued or has no values defined, except at the tangent point itself, where it is single-valued.

Suppose Af is defined in the sub-interval Af.

Where boundary maintenance describes the boundaries or limits of the group, systemic linkage is defined `` as the process whereby one or more of the elements of at least two social systems is articulated in such a manner that the two systems in some ways and on some occasions may be viewed as a single unit.

The positive Kohnstamm reactivity in Condition 1 ( ( the naive state ) is not adequately explained by such a concept as suggestibility ( if suggestibility is defined as the influence on behavior by verbal cues ).

For example, property `` used in the trade or business '' of a transferor corporation, as defined in section 1231, presumably would not retain its special status following a non-taxable reorganization if it is not so used in the business of the acquiring corporation.

Planes defined as parallel to the surface also cut through it into real space, and a depth is suggested optically which is greater than that established pictorially.

**yc is defined by the geometry of the knife ; ;

The gyro angular momentum is defined by H.

But since this is a world in which people disagree about ends and goals and concerning justice and injustice, and since, in a situation where direct action and economic pressure are called for, the justice of the matter has either not been clearly defined by law or the law is not effectively present, there has to be a morality of means applied in every case in which people take it upon themselves to use economic pressures or other forms of force.

Anarchism is generally defined as the political philosophy which holds the state to be undesirable, unnecessary, and harmful ,< ref name =" definition ">

Next I refer to our program in space exploration, which is often mistakenly supposed to be an integral part of defense research and development.

the Athletic program at Carleton is considered an integral part of the activities of the College and operates under the same budgetary procedure and controls as the academic work.

Indeed, a study of the individual child is an integral part of the work of the elementary-school teacher, rather than merely an additional chore.

What Parker and his contemporaries -- Gillespie, Davis, Monk, Roach ( Tristano is an anomaly ), etc. -- did was to absorb the musical ornamentation of the older jazz into the basic structure, of which it then became an integral part, and with which it then developed.

Within only a few years, foamed plastics materials have managed to grow into an integral, and important, phase of the plastics industry -- and the end is still not yet in sight.

As in the theory of perception, established in psycho-physiology, the eye is recognized as an integral part of the brain.

As retinal images are conceded to be an integral function of the brain it seems logical to suppose that the nerves, between the inner brain and the eyes, carry the direct drive for cooperation from the various brain centers -- rather than to theorize on the transmission of an image which is already in required location.

The truth, however, is that the ecumenical church is just the local church in its own true character as an integral unit of the whole People of God throughout the world.

In Continental philosophy ( particularly phenomenology and existentialism ), there is much greater tolerance of ambiguity, as it is generally seen as an integral part of the human condition.

He is the so-called " Mad Arab " credited with authoring the imaginary book Kitab al-Azif ( the Necronomicon ), and as such is an integral part of Cthulhu Mythos lore.

With over 120 million visitors a year tourism is integral to the Alpine economy with much it coming from winter sports although summer visitors are an important component of the tourism industry.

* The Aluk religion in the Toraja society and the people of Tana Toraja, embrace religious rituals such as the funeral ceremony where a sacred cockfight, known as bulangan londong or saung, is an integral part of the ceremony and considered sacred because of the spilling of blood on the earth in spiritual appeasement.

Of particular interest to 20th-century music theorists is the attention he paid to silence as an integral part of music.

is the phase integral ( integration of reflected light ; a number in the 0 to 1 range ).

As this tension is an integral part of AA, Rudy and Greil argue that AA is best described as a quasi-religious organization.

Lobster is an integral ingredient to the cuisine, indigenous to the coastal waters of the region.

A metal case holds an integral primer to initiate the propellant and provides the gas seal to prevent the gases leaking out of the breech, this is called obturation.

However, because each schema object is integral to the definition of Active Directory objects, deactivating or changing these objects can fundamentally change or disrupt a deployment.

Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

Because of this, each of the infinitely many antiderivatives of a given function f is sometimes called the " general integral " or " indefinite integral " of f and is written using the integral symbol with no bounds:

One description for motion is made in terms of the material or referential coordinates, called material description or Lagrangian description.

In the Lagrangian description, the motion of a continuum body is expressed by the mapping function ( Figure 2 ),

In the Lagrangian description, the material derivative of is simply the partial derivative with respect to time, and the position vector is held constant as it does not change with time.

Continuity in the Lagrangian description is expressed by the spatial and temporal continuity of the mapping from the reference configuration to the current configuration of the material points.

where the functional form of in the Lagrangian description is not the same as the form of in the Eulerian description.

The vector joining the positions of a particle in the undeformed configuration and deformed configuration is called the displacement vector, in the Lagrangian description, or, in the Eulerian description.

In the canonical quantum field theory the S-matrix is represented within the interaction picture by the perturbation series in the powers of the interaction Lagrangian,

where is the interaction Lagrangian and signifies the time-ordered product of operators.

Most of this dust is orbiting the Sun in about the ecliptic plane, with a possible concentration of particles at the Earth – Sun Lagrangian point.

It also turns out that, at least in the case of Sun – Earth-missions, it is actually preferable to place the spacecraft in a large-amplitude () Lissajous orbit, instead of having it sit at the Lagrangian point, because this keeps the spacecraft off the direct Sun – Earth line, thereby reducing the impact of solar interference on Earth – spacecraft communications.

Another interesting and useful property of the collinear Lagrangian points and their associated Lissajous orbits is that they serve as " gateways " to control the chaotic trajectories of the Interplanetary Transport Network.

This same effect is present at the Lagrangian points in the Earth – Moon system, where the analogue of the string is the summed ( or net ) gravitational attraction of the two masses, and the stone is an asteroid or a spacecraft.

At Lagrangian points,,, and, a spacecraft's inertia to move away from the barycenter is balanced by the attraction of gravity toward the barycenter.

In Lagrangian mechanics, a Lagrangian is defined as the difference between the kinetic energy and the potential energy:

In Hamiltonian mechanics, the Lagrangian ( a function of generalized coordinates and their derivatives ) is replaced by a Hamiltonian that is a function of generalized coordinates and momentum.

where the momentum is obtained by differentiating the Lagrangian as above.

As in Lagrangian mechanics, if a generalized coordinate does not appear in the Hamiltonian, its conjugate momentum component is conserved.

Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies.

The gauge invariant QCD Lagrangian is

An important theoretical notion concerning the final term of the above Lagrangian is the Wilson loop variable.