His veto message objected to the measure because it conferred citizenship on the freedmen at a time when eleven out of thirty-six states were unrepresented in the Congress, and the bill also attempted to fix, by federal law, " a perfect equality of the white and black races in every State of the Union.

It extended citizenship to every person born in the United States ( except Indians on reservations ), penalized states that did not give the vote to freedmen, and most importantly, created new federal civil rights that could be protected by federal courts.

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

The Presidency of the Council rotates every six months among the governments of EU member states, with the relevant ministers of the respective country holding the Presidency at any given time ensuring the smooth running of the meetings and setting the daily agenda.

From 2007, every three-member states cooperate for their combined eighteen months on a common agenda, although only one formally holds the presidency for the normal six-month period.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

For delocalized states, for example in one dimension – that is in a nanowire, for every energy there is a state with electrons flowing in one direction and another state with the electrons flowing in the other.

Moreover, the Banach fixed point theorem states that every contraction mapping on a nonempty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

The United States Constitution mandates that a census be taken every ten years in order to apportion the number of members of the United States House of Representatives among the several states.

From a geometrical point of view, looking at the states of each variable of the system to be controlled, every " bad " state of these variables must be controllable and observable to ensure a good behaviour in the closed-loop system.

This is accomplished by the B-theorem, which states that every component of C / O ( C ) is the image of a component of C.

An underlying principle in Taoism states that within every independent entity lies a part of its opposite.

< td > The Erdős – Straus conjecture states that, for every positive integer n ≥ 2, there exists a solution in x, y, and z, all as positive integers.

In the United States, elections are held between every three and six years in most states, with exceptions such as the U. S. House of Representatives, which stands for election every two years.

# Magnetic poles ( or states of polarization at individual points ) attract or repel one another in a similar way and always come in pairs: every north pole is yoked to a south pole.

* Completion: For every state in S ( k ) of the form ( X → γ •, j ), find states in S ( j ) of the form ( Y → α • X β, i ) and add ( Y → α X • β, i ) to S ( k ).

In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, " every planar graph is four-colorable " (; ).

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not.

Wedderburn's little theorem states that the Brauer group of a finite field is trivial, so that every finite division ring is a finite field.

In most states, every attorney must be a member of that state's bar association in order to practice law.

φ states that for every x there is a y such that ... ( something ).

This formula is indeed equivalent to φ because it states that for every x, if there is a y which satisfies Q '( x, y ), then ( something ) holds, and furthermore, we know that there is such a y, because for every x ', there is a y ' which satisfies Q '( x ', y ').

The Hausdorff maximal principle states that, in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

It states that a topological space is metrizable if and only if it is regular, Hausdorff and has a σ-locally finite base.

* Open mapping theorem ( topological groups ) states that a surjective continuous homomorphism of a locally compact Hausdorff group G onto a locally compact Hausdorff group H is an open mapping if G is σ-compact.

The equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of C ( X ), the space of continuous functions on a compact Hausdorff space X, is compact if and only if it is closed, pointwise bounded and equicontinuous.

* The strong Whitney embedding theorem states that any smooth m-dimensional manifold ( required also to be Hausdorff and second-countable ) can be smoothly embedded in Euclidean 2m-space, if m > 0.

In mathematics, the Hausdorff paradox, named after Felix Hausdorff, states that if you remove a certain countable subset of the sphere S < sup > 2 </ sup >, the remainder can be divided into three disjoint subsets A, B and C such that A, B, C and B ∪ C are all congruent.

The theorem states that a topological space is metrizable if and only if it is regular and Hausdorff and has a countably locally finite ( i. e., σ-locally finite ) basis.

Urysohn's metrization theorem states that every second-countable, regular space is metrizable.

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.

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

Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular Lorentzian manifold.

When used in anesthesia to produce and maintain unconsciousness, " sleep " is metaphorical as there are no regular sleep stages or cyclical natural states ; patients rarely recover from anesthesia feeling refreshed and with renewed energy.

The Mint states that multi-ply plated steel technology, already used in Canada's smaller coinage, produces an electromagnetic signature that is harder to counterfeit than that for regular alloy coins ; also, using steel provides cost savings and avoids fluctuations in price or supply of nickel.

Public Law 93-380, enacted 21 Aug 1974, states that it is the policy of the U. S. to encourage educational agencies and institutions to prepare students to use the metric system of measurement with ease and facility as a part of the regular education program.

He thereby assumed control of all of the German states ' regular police forces and, nationalizing them, formed the Ordnungspolizei and the Kriminalpolizei.

The Mint states that multi-ply plated steel technology, already used in Canada's smaller coinage, produces an electromagnetic signature that is harder to counterfeit than that for regular alloy coins ; also, using steel provides cost savings and avoids fluctuations in price or supply of nickel.

D replies to that statement assuming that children would be getting this in addition to their regular meals, and states that this would be unhealthy.

Western nations view Russian bellicosity and belligerence as having markedly increased as of late, with tests of new nuclear-capable missiles occurring on a regular basis, military conflicts with neighboring states, claims of a Russian " sphere of influence " on the perimeter of the old Soviet Union, the rise of ultra-nationalist " Putin Youth " groups, aggressive politicization of and threats of withdrawal of natural gas supplies to Europe should the Europeans not make certain policy concessions, and even threats of a nuclear first strike against Poland have been heard to be made by certain Russian generals.

Because of the way their regular crystalline atomic structure causes their spins to interact, some metals are ferromagnetic when found in their natural states, as ores.

Strikovski states that " The knowledge one requires to become a court advocate is more than a regular ordination, and now to pass certification is much more difficult than to get ordination.

Strikovski states that " The knowledge one requires to become a court advocate is more than a regular ordination, and now to pass certification is much more difficult than to get ordination.

According to the CPT theorem of particle physics, antihydrogen atoms should have many of the characteristics regular hydrogen atoms have ; i. e., they should have the same mass, magnetic moment, and transition frequencies ( see atomic spectroscopy ) between their atomic quantum states.

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off ( in contrast to a coupled map lattice ).

Cassidy states the need for a clear delineation of behavioral expectations, the reinforcement of behavioural limits and the establishment of regular routines.

PASSIA hosts regular work ­ shops that address different but inter-connected issues pertaining to Je ­ rusalem, such as freedom of access, Israeli settlements, and the various religious, politi ­ cal, cultural, historical, and civil as ­ pects of life in the city, in addition to municipal ar ­ rangements for Jeru ­ salem as the capital of two independent states.

Later, in the Warring States Period ( 475 – 221 BC ), the script became still more regular, and settled on a form, called 六國文字 / 六国文字 liùguó wénzì " script of the six states ", that Xu Shen used as source material in the Shuowen Jiezi.

In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states.

Herrera states that local caciques paid regular visits to the fountain.

Bremen, which in 1935 had become a regular city at the de facto abolition of statehood of all component German states within the Third Reich, was reestablished as state in 1947.

Geographical and economic constraints suggest that rather than a regular centralised authority, the outer states were most likely to have been connected mainly by trade connections, which was probably a royal monopoly.

Sunoco also once sold Economy unleaded, an 86 octane slightly cheaper than regular, in all of its markets until the mid-1990s when it was withdrawn from Pennsylvania and a handful of other states, and was phased out altogether in 2003.