Specifically, he demonstrated an upper limit, known as Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.

Specifically, the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that

Specifically, Hadamard's inequality states that if N is the matrix having columns v < sub > i </ sub >, then

Specifically it states that for any integers n ≥ 0 and m ≥ 1, the functions J < sub > n </ sub >( x ) and J < sub > n + m </ sub >( x ) have no common zeros other than the one at x = 0.

Specifically, after acknowledging the various popular theories in vogue at the time, of how atoms were reasoned to attach to each other, i. e. " hooked atoms ", " glued together by rest ", or " stuck together by conspiring motions ", Newton states that he would rather infer from their cohesion, that " particles attract one another by some force, which in immediate contact is exceedingly strong, at small distances performs the chemical operations, and reaches not far from the particles with any sensible effect.

The first isomorphism theorem states that the image of any group G under a homomorphism is always isomorphic to a quotient of G. Specifically, the image of G under a homomorphism is isomorphic to where ker ( φ ) denotes the kernel of φ.

" Specifically in response to the " majesty and power " reading, Harrington states " My opinion is that ’ s just pure bullshit.

Specifically the final point stated: " A general association of nations must be formed under specific covenants for the purpose of affording mutual guarantees of political independence and territorial integrity to great and small states alike.

According to Stephen Suleyman Schwartz, in his book " The Two Faces of Islam ", “ some say that during this vagabondage Ibn Abdul Wahhab came into contact with certain Englishmen who encouraged him to personal ambition as well as to a critical attitude about Islam .” Specifically, Mir ’ at al Harramin, a Turkish work by Ayyub Sabri Pasha, written in 1888, states that in Basra, Abdul Wahhab had come into contact with a British spy by the name of Hempher, who “ inspired in him the tricks and lies that he had learned from the British Ministry of the Commonwealth .”

" Specifically, Congress intended the Act to outlaw the practice of requiring otherwise qualified voters to pass literacy tests in order to register to vote, a principal means by which Southern states had prevented African Americans from exercising the franchise.

Specifically, its shorelines lie in the German federal states of Bavaria and Baden-Württemberg, the Austrian federal-state of Vorarlberg, and the Swiss cantons of Thurgau and St. Gallen.

Specifically, the College Board states that use of the SAT in combination with high school grade point average ( GPA ) provides a better indicator of success in college than high school grades alone, as measured by college freshman GPA.

Specifically, the CPT theorem states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.

Specifically, it states that for every ε > 0 there exist only finitely many triples ( a, b, c ) of positive coprime integers with a + b = c such that

Specifically, Pantaleo states research has shown, " NAFTA, as a capitalist approach, has directly created a devaluation of women and an increase ingendered violence.

Specifically, Oden states ( pg.

Specifically, Article 6 of the treaty states that if any captured Americans, be it done by Moroccans or by other Barbary Coast states dock at a Moroccan city, said Americans would be set free and be under the protection of the Moroccan state.

Specifically, Randolph promoted the Principles of ' 98, which said that individual states could judge the constitutionality of central government laws and decrees, and could refuse to enforce laws deemed unconstitutional.

Specifically, DoD policy stated that " the medal will be issued only to those taken prisoner by an enemy during armed conflict ," and further states that " hostages of terrorists and persons detained by governments with which the US is not actively engaged in armed conflict are not eligible for the medal .” However, the 1989 amendment to the POW Medal Statute that created an exception to the armed conflict requirement was overlooked in the July 1990 version of the DoD Manual of Military Decorations and Awards, presumably because the 1989 amendment occurred in November, during the staffing window for the 1990 revision to the manual.

Specifically, the resolution stated that the war was being waged for the reunion of the states, and not to abolish the south's " peculiar institution " of slavery.

Specifically, many realist critics claim that the effect ascribed to democratic, or liberal, peace, is in fact due to alliance ties between democratic states which in turn are caused, one way or another, by realist factors.

Specifically, the Knowledge Argument is an attack on the physicalist claim about the completeness of physical explanations of mental states.

Specifically, addiction is hypothesized to function as a compensatory means to modulate effects and treat distressful psychological states, whereby individuals choose the drug that will most appropriately manage their specific type of psychiatric distress and help them achieve emotional stability.

Specifically, neurotypical people have neurological development and states that are consistent with what most people would perceive as normal, particularly with respect to their ability to process linguistic information and social cues.

Specifically, the theorem is equivalent to the Boolean prime ideal theorem, a weakened choice principle which states that every Boolean algebra has a prime ideal.

Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error.

Specifically, it is not typically important whether the error term follows a normal distribution.

Specifically, the amplifier measures voltage in the first few milliseconds of the cycle, generates the error signal, and spends the rest of the cycle passing current to reduce that error.

Specifically, it counts the number of marked entries in an-element list, with error making only queries, where is the number of marked elements in the list.

Specifically, it is possible to furnish estimators that improve considerably upon the maximum likelihood estimate in terms of mean squared error.

Specifically published software and systems topics are specification, design, implementation, methods of development, methods of maintenance, software modeling, testing, validation, reliability, diagnostic procedures, test procedures, error control ( including redundancy ), evaluation ( including measurement ), productivity factors, cost models, schedule issues, standards, organizational issues, tools, databases, parallel or distributed computing issues, comprehensive historical reviews, and hardware-software interrelationships.

The inequality states that

" Also known as the kinship theory of genomic imprinting, this hypothesis states that the inequality between parental genomes due to imprinting is a result of the differing interests of each parent in terms of the evolutionary fitness of their genes.

Samuelson's inequality is a result that states, given that the sample mean and variance have been calculated from a particular sample, bounds on the values that individual values in the sample can take.

The Cauchy – Schwarz inequality states that for all vectors x and y of an inner product space it is true that

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side ( and, if the setting is a Euclidean space, then the inequality is strict if the triangle is non-degenerate ).< ref name = Khamsi >

For instance, Daisy Myers has been hailed as " The Rosa Parks of the North ", who helped expose the northern states ' problems with racial inequality of that time.

The Chebyshev inequality states that if is a random variable with standard deviation σ, then the probability that the outcome of is no less than away from its mean is no more than:

Markov's inequality states that for any real-valued random variable Y and any positive number a, we have Pr (| Y | > a ) ≤ E (| Y |)/ a.

In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden variable theories.

It would appear from both these later derivations that the only assumptions really needed for the inequality itself ( as opposed to the method of estimation of the test statistic ) are that the distribution of the possible states of the source remains constant and the detectors on the two sides act independently.

An equivalent formulation states that for any ε > 0, there exists a constant K such that, for all triples of coprime positive integers ( a, b, c ) satisfying a + b = c, the inequality

In the language of measure theory, Markov's inequality states that if ( X, Σ, μ ) is a measure space, ƒ is a measurable extended real-valued function, and, then

This provides an interesting twist on Wallerstein's neo-Marxist interpretation of the international order which faults differences in power relations between ' core ' and ' periphery ' states as the chief cause for economic and political inequality ( However, the Singer-Prebisch thesis also works with different bargaining positions of labour in developed and developing countries ).

# The Bishop – Gromov inequality states that if a complete m-dimensional Riemannian manifold has non-negative Ricci curvature, then the volume of a ball is smaller or equal to the volume of a ball of the same radius in Euclidean m-space.

In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean after convex transformation ; it is a simple corollary that the opposite is true of concave transformations.

The isoperimetric inequality states that

Denote by L the length of C and by A the area enclosed by C. The spherical isoperimetric inequality states that

In full generality, the isoperimetric inequality states that for any set S ⊂ R < sup > n </ sup > whose closure has finite Lebesgue measure

Each inequality states that your opponent's net gain is more than zero.

On the issue of markets in a socialist society, Webb states, " Admittedly, market mechanisms in a socialist society can generate inequality, disproportions and imbalances, destructive competition, downward pressure on wages, and monopoly cornering of commodity markets – even the danger of capitalist restoration.

The geodesic minimizes the entropy, due to the Cauchy – Schwarz inequality, which states that the action is bounded below by the length of the curve, squared.

Then Bernstein's inequality states that for M non-zero,