Given the above expression, evidently the result of her ( local ) measurement is that the three-particle state would collapse to one of the following four states ( with equal probability of obtaining each ):

Given the closeness shared by the countries bordering the Mediterranean basin, and very topical interest to the consolidation of the European Union's enlargement policy, he also intended to establish trade relations with the Republic of Malta aimed at encouraging mutual knowledge and awareness in a profitable way their local communities on European issues of common interest and current.

Given the harsh conditions of the retreat, the infant was left with a local family ( Two Europeans retracing the Long March route in 2003 met a woman in rural Yunnan province, said by local officials to be Mao and He Zizhen's long-lost daughter ).

Given the presence of the KULeuven, an important European institution for academic research and education, much of the local economy is concentrated on spin-offs from academic research.

Given the range of his office-holding both regionally and at court, he did not need to draw ruinously on his own resources to dispense patronage on a grand scale and he was active in the arbitration of local disputes ; even state matters were regularly referred for his personal adjudication.

Kendall West is home to a large concentration of Colombians and Colombian Americans in the U. S. Given the local name " Little Bogota ".

Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).

Given that the four trials under consideration can indeed be consistently considered and experimentally realized, the assumptions concerning hidden variables which lead to the indicated mathematical contradiction are therefore collectively unsuitable to represent all experimental results ; namely the assumption of local hidden variables which occur equally in distinct trials.

Given the similarities with readings from people living on loess soils, the general direction of the local movement according to Price et al., is from the northeast to the southwest.

An open set U in X admits a local trivialization if and only if there exists a local section on U. Given a local trivialization one can define an associated local section by

Given an equivariant local trivialization (

Given the nature of Arthur's activities, he was always in the spotlight of the local police and crossed paths with several regular and occasional characters:

Given only a short time to prepare, Wei was only able to demonstrate Viola's equivalent capabilities for local rather than remote files at the 2003 Eolas v. Microsoft trial, and thus fell short of proving prior art to the court's satisfaction.

Given a local smooth frame ( e < sub > 1 </ sub >, …, e < sub > k </ sub >) of E over U, any section σ of E can be written as ( Einstein notation assumed ).

Given the Saint Lawrence's heavy traffic and years of mis-use, the ecoregion is negatively effected by high pollution which in turn has resulted in diminished local populations of native fauna.

Given estimates of the image gradients, a search is then carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction.

Given a polynomial equation with rational coefficients, if it has rational solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics: a global solution yields local solutions at each prime.

Given all the signs that a very large eruption was imminent, PHIVOLCS – assisted by the U. S. Geological Survey – worked to convince local inhabitants of the severity of the threat.

Given its small staff of only 24 men, the Einsatzgrupppe Ägypten would have needed as much help as possible from the local Arabs and from the Afrika Korps to kill the roughly 50, 000 Jews of Egypt, to say nothing of the half million or so Jews of the Yishuv.

The Alaska Time Zone applies to the territory of the state of Alaska east of 169 ° 30 ′ W. Given that the UTC − 9 time corresponds to the solar time at 9 × 15 ° = 135 ° W ( roughly, Juneau ), the westernmost locales of the Alaska Time Zone are off by up to 169 ° 30 ′ − 135 ° = 34 ° 30 ′ from local solar time.

Given any coordinate chart about some point on the manifold, the above identities may be written in terms of the components of the Riemann tensor at this point as:

Given a subset V of P < sup > n </ sup >, let I ( V ) be the ideal generated by all homogeneous polynomials vanishing on V. For any projective algebraic set V, the coordinate ring of V is the quotient of the polynomial ring by this ideal.

Given a coordinate system and a metric tensor, scalar curvature can be expressed as follows

Given a DMS ( Degrees, Minutes, Seconds ) coordinate such as W87 ° 43 ′ 41 ″, convert it to a number of decimal degrees using the following method:

Given a MinDec ( Degrees, Minutes, Decimal Minutes ) coordinate such as 40 ° 26. 7717N, 79 ° 56. 93172W, convert it to a number of decimal degrees using the following method ( for example for 79 ° 56. 93172W ):

Given a decimal longitudinal coordinate such as-87. 728055 it will be necessary to know whether it is a latitudinal or longitudinal coordinate in order to fully convert it.

Given coordinate functions

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

: Given such a tangent vector v, let f be the curve given in the x < sup > i </ sup > coordinate system by.

Given these changes, the classical terms " system ", " expansion " and " peripheral " no longer have the same connotations.

Given the system ( corresponding to )

Given the limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

Given that the bulk of family chores fell to women, and that they were five times more likely than men to head a single-parent family, the shortcomings of Finland's child day-care system affected women more than it did men.

Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

Given a syscall that does nothing, a full round-trip under BSD would require about 40μs, whereas on a user-space Mach system it would take just under 500μs.

Given the diversity of functions performed by neurons in different parts of the nervous system, there is, as expected, a wide variety in the shape, size, and electrochemical properties of neurons.

Given the increasing number of scientists who study the nervous system, several prominent neuroscience organizations have been formed to provide a forum to all neuroscientists and educators.

Given the complexity of NLP problems, it is often difficult to predict performance only on the basis of glass-box evaluation, but this type of evaluation is more informative with respect to error analysis or future developments of a system.

Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).

Given the poorly understood nature of the endocannabinoid system, it will take many more generations of progress to even scratch the surface of the extraordinarily complex mechanisms that control neurological development / degeneration.

Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.

Given the opportunity, for example during an illness that suppresses the immune system, the virus is reactivated and travels to the end of the nerve cell, where it causes the symptoms described above.

: Given an isolated system in equilibrium, it is found with equal probability in each of its accessible microstates.

Given Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1 / Ω.

Given the space X = Spec ( R ) with the Zariski topology, the structure sheaf O < sub > X </ sub > is defined on the D < sub > f </ sub > by setting Γ ( D < sub > f </ sub >, O < sub > X </ sub >) = R < sub > f </ sub >, the localization of R at the multiplicative system

) Given that the telephone system nominal voiceband ( including guardband ) is 4, 000 Hz, the required digital sampling rate is 8, 000 Hz ( see Nyquist rate ).

Given the structural similarities between bacterial flagella and bacterial secretory systems, it is thought that bacterial flagella may have evolved from the type three secretion system ; however, it is not known for certain whether these pores are derived from the bacterial flagella or the bacterial secretory system.

Given a system of n-dimensional variables ( physical variables ), in k ( physical ) dimensions, write the dimensional matrix M, whose rows are the dimensions and whose columns are the variables: the ( i, j ) th entry is the power of the ith unit in the jth variable.

Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.

Given a testing procedure E applied to each prepared system, we obtain a sequence of values