Lincoln stated Douglas's popular sovereignty theory was a threat to the nation's morality and that Douglas represented a conspiracy to extend slavery to free states.

Electron states are best represented by time-depending " mixtures " ( linear combinations ) of multiple orbitals.

The amendment was submitted to the states for ratification by Congressional joint resolution, and therefore was not subject to Presidential veto, though Johnson vigorously opposed it, again because so many southern states were not represented in the Congress.

The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.

* Wave functions and other quantum states can be represented as vectors in a complex Hilbert space.

More elaborate reactions are represented by reaction schemes, which in addition to starting materials and products show important intermediates or transition states.

This equation states that, representing the square of the length of the side that is the hypotenuse ( the side opposite the right angle ), is equal to the sum ( addition ) of the square of the other two sides whose lengths are represented by and.

The title of Emperor of Austria and the associated Empire were both abolished at the end of the First World War in 1918, when German Austria became a republic and the other kingdoms and lands represented in the Imperial Council established their independence or adhesion to other states.

This is known as the mirror image rule and is related to the Franck – Condon principle which states that electronic transitions are vertical, that is energy changes without distance changing as can be represented with a vertical line in Jablonski diagram.

Conquered states were integrated into the system and represented in the court, with their titles.

This explains also why the choice of z-axis for the directional quantization of the angular momentum vector is immaterial: an orbital of given ℓ and m ′ obtained for another preferred axis z ′ can always be represented as a suitable superposition of the various states of different m ( but same l ) that have been obtained for z.

A number of smaller radical Arab groups from Lebanon, Tunisia, Sudan, Iraq, the Persian Gulf states, and Jordan were represented at the inaugural meeting.

Marxism – Leninism asserts that society is united upon common interests represented through the communist party and other institutions of the Marxist-Leninist state and in Marxist-Leninist states where opposition political parties have been permitted they have not been permitted to advocate political platforms significantly different from the communist party.

A fundamental theorem states that every spline function of a given degree, smoothness, and domain partition, can be uniquely represented as a linear combination of B-splines of that same degree and smoothness, and over that same partition.

Originally, it was proposed that the Diet of the German Confederation ( in which all the states of Germany were represented ) should determine the fate of the duchies ; but before this scheme could be effected, Bismarck induced Austria to agree to the Gastein Convention.

In isolation, quantum objects are represented by a wavefunction which often exists in a superposition or mixture of different states.

The medieval Parliament was complete when it represented all the states in the realm: nobles, clergy, peasants and craftsmen but it was not a popular institution mainly because it meant taxation.

For example, Episcopalians are extraordinarily well represented among the presidents, compared to a current membership of about 2 % of the population ; this is partly because the Episcopal Church had been the Church of England before the American Revolution and was the state religion in some states ( such as New York and Virginia ).

An antisymmetric two-particle state is represented as a sum of states in which one particle is in state and the other in state:

In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac David Hilbert, and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors ( called " state vectors ").

Since the probability amplitudes of the states are represented with complex numbers, the phase between any two states is a meaningful parameter, which is a key difference between quantum computing and probabilistic classical computing.

( A qubit may be represented as a superposition of states, labeled and.

Mixed states can be represented by points inside the Bloch sphere.

In 1961 the first important legislative victory of the Kennedy Administration came when the principle of national responsibility for local economic distress won out over a `` state's-responsibility '' proposal -- provision was made for payment for unemployment relief by nation-wide taxation rather than by a levy only on those states afflicted with manpower surplus.

To their leaders the Constitution was a compact made by the people of sovereign states, who therefore retained the right to secede from it.

But though the Southern States, when drafting a constitution to unite themselves, narrowed the difference to this fine point by omitting to assert the right to secede, the fact remained that by seceding from the Union they had already acted on the concept that it was composed primarily of sovereign states.

If the Union conceded this to them, the same right must be conceded to each remaining state whenever it saw fit to secede: This would destroy the federal balance between it and the states, and in the end sacrifice to the sovereignty of the states all the liberty the citizens had gained by their Union.

Though his election was interpreted by many Southerners as the forerunner of a dangerous shift in the federal balance in favor of the Union, Lincoln himself proposed no such change in the rights the Constitution gave the states.

The lives so many of them gave, to forestall what they believed would be a fatal encroachment by the Union on the powers reserved to their states have continued ever since to safeguard all Americans against freedom's other foe.

Augustus Baldwin Longstreet, a preacher and a college and university president in four Southern states, published the earliest of these backwoods sketches and in the character Ransy Sniffle, in the accounts of sharp horse-trading and eye-gouging physical combat, and in the shockingly unliterary speech of his characters, he set an example followed by many after him.

progress, or lack of it, toward civil rights in the 50 states is reported in an impressive 689-page compilation issued last week by the United States Commission on Civil Rights.

But they refuse, as do the Arab states, to support the United Nations' expenses of maintaining the United Nations Emergency Force in the Middle East as a buffer between Egypt and Israel, and the U.N. troops in the Congo, which expenses are not covered by the regular budget of the United Nations, but by a special budget.

I have done all this for the freedom of the individuals concerned and also for the states which have been threatened by Communist domination.

There is a well-known relationship between probability and entropy which states that Af, where **zq is the probability that state ( i.e., volume for an ideal gas ) could be reached by chance alone.

The emotional states produced by drugs influence the cortical potentials in a characteristic manner ; ;

These are few and seemingly disjointed data, but they illustrate the important fact that fundamental alterations in conditioned reactions occur in a variety of states in which the hypothalamic balance has been altered by physiological experimentation, pharmacological action, or clinical processes.

The European customs on which international law was based were to become, by force and fiat, the customs that others were to accept as law if they were to join this community as sovereign states.

There was no law, domestic or international, except that willed by, acknowledged by, or consented to by states.

furthermore, Congress could not be presumed to have intended to obstruct mergers approved by the states.

The questionnaires were mailed in Seattle, Washington, and sent by regular mail to addresses in the states of Idaho, Montana, Oregon, and Washington.

The Middle-South Region, as defined by the National Association of Intergroup Relations Officials ( NAIRO ), consists of the states of Kentucky, Maryland, Tennessee, West Virginia, Delaware, Virginia and the District of Columbia.

The Providence Daily Journal answered the Daily Post by stating that the raid of John Brown was characteristic of Democratic acts of violence and that `` He was acting in direct opposition to the Republican Party, who proclaim as one of their cardinal principles that they do not interfere with slavery in the states ''.