Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

Given a specific task to solve, and a class of functions, learning means using a set of observations to find which solves the task in some optimal sense.

Given the fluid flow conditions and the desired shaft output speed, the specific speed can be calculated and an appropriate turbine design selected.

Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement.

Given a context pertaining to a specific OSI layer, PDU is sometimes used as a synonym for its representation at that layer.

Given that noise-equivalent power can be expressed as a function of the responsivity ( in units of or ) and the noise spectral density ( in units of or ) as, it's common to see the specific detectivity expressed as.

Given a day mandated for seasonal rejoicing ( Shemini Atzeret ) with no specific obligations as to the focus of the rejoicing ( such as sukkah, lulav or etrog ), it is not surprising that the celebration of the conclusion of the annual reading was absorbed into the celebration of Shemini Atzeret.

Given a rebbe's physical awareness of God, and the Rebbe's transcendent perception of Godliness, many hasidim take special care to observe the specific and sometimes minute practices of their Rebbe.

) Given the diffusion of different Piers / Ploughman texts, it is usually not possible to be certain about what someone means to refer to when they mention " Piers Plowman " unless they provide specific identifying details — and most writers do not.

Given the finite supply of natural resources at any specific cost and location, agriculture that is inefficient or damaging to needed resources may eventually exhaust the available resources or the ability to afford and acquire them.

The specific problems are: Given two, three or four points on a straight line, find another point on it such that its distances from the given points satisfy the condition that the square on one or the rectangle contained by two has a given ratio either ( 1 ) to the square on the remaining one or the rectangle contained by the remaining two or ( 2 ) to the rectangle contained by the remaining one and another given straight line.

Given that the tune was developed in an oral tradition, it is impossible to say for certain which of these influences may have played a specific role in the creation of this tune, but it is certain that numerous folk influences from different cultures such as these were prominent in the musical culture of the camp meeting, and that such influences were freely combined in the music-making that took place in the revival movement.

Given at the discretion of the Council of the Academy on the recommendation of a nominating committee, the prize is awarded to a person for his or her total literary achievement rather than for a specific work.

Given the specific gravity of a substance, its actual density can be calculated by rearranging the above formula:

Many of these procedures are under investigation in the U. S. Given that PRK is not reversible, a patient considering PRK is recommended to contact an eye-care practitioner for assistance in making an informed decision concerning the potential benefits and liabilities that may be specific to him or her.

Given the total mass and the scalars r and v at a single point of the orbit, one can compute the specific orbital energy, allowing an object orbiting a larger object to be classified as having not enough energy to remain in orbit, hence being " suborbital " ( a ballistic missile, for example ), having enough energy to be " orbital ", but without the possibility to complete a full orbit anyway because it eventually collides with the other body, or having enough energy to come from and / or go to infinity ( as a meteor, for example ).

Given that field experiments necessarily take place in a specific geographic and political setting, the extent to which findings can be extrapolated to formulate a general theory regarding economic behavior is a concern.

" Given the Rules ' permissive backdrop and their inclusion of a specific rule on expert testimony that does not mention ' general acceptance ,' the assertion that the Rules somehow assimilated Frye is unconvincing.

Given the cost of an item, one can compute the selling price required to achieve a specific gross margin.

Given a finite symmetric group S < sub > n </ sub > and specific Young tableau λ corresponding to a numbered partition of n, define two permutation subgroups and of S < sub > n </ sub > as follows:

Given a specific set of characters in each scenario, based on a scene from each of the movies, up to two players can control them, using their different abilities.

Given the large number of rDNA genes ( several hundreds ) available for transcription, the first mechanism involves adjustments in the number of genes being transcribed at a specific time.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given that in such a case pits the freedom of an innocent child against the freedom of the evil-doer, it is not clear why God would not intervene for the sake of the child.

Given a parameterized family of probability density functions ( or probability mass functions in the case of discrete distributions )

Given the structure of the experiment, it may or may not be possible to actually perform it, and, in the case that it is possible for it to be performed, there need be no intention of any kind to actually perform the experiment in question.

Given that propensity to noble rot was a factor in Hungarian vineyard demarcations some 50 years before a messenger was supposedly mugged on his way to Schloss Johannisberg in Germany, the Hungarians probably have a better case.

:: Example: Given this option to reinstate the contract on its original terms when a plan is proposed, it may be anomalous to require the payment of interest at a market rate while a case is pending.

Given a general triangle ABC, the following conditions would need to be fulfilled for the case to be ambiguous:

Given that there is no constitutional office of Deputy Prime Minister, with the position being recreated on a case by case basis, the person who holds the post has no official residence.

Given a case for which the class is unknown, guess that it belongs to the same class as the majority in its immediate neighborhood.

Given that some common statistical packages ( e. g., SAS, SPSS ) do not provide likelihood ratio test statistics, it can be more difficult to assess the contribution of individual predictors in the multiple logistic regression case.

Given its lightning-like success, one could clearly make the case that the Olds 88 with its V-8 was the first ' musclecar '..."

Given a concrete category C, it is often the case that the opposite category C < sup > op </ sup > per se is abstract.

Given that only 2, 000 of the 785, 000 copies sold worldwide were sold in the United Kingdom, this lead numerous scholars to cite the case as an example of libel tourism.

Given these improvements dating back to 1728, a case could be made that Boston Common is in fact the world's first public urban park, since these developments precede the establishment of the earliest public urban parks in England — Derby Arboretum ( 1840 ), Peel Park, Salford ( 1846 ), and Birkenhead Park ( 1847 )— which are often considered the first.

Given the small overall amount of power produced per cubic meter, there is a substantial case for increasing water flow to the natural channel, now that Arnacrusha is producing so small a proportion of ESB's power.

Given that he resorted to cannibalism so near to food supplies, and that he killed and consumed the remains of all those present, it was revealed that Swift Runner's was not a case of pure cannibalism as a last resort to avoid starvation, but rather of a man suffering from Wendigo psychosis.

Given the interpretation via linear mappings and direct sums, there is a special type of block matrix that occurs for square matrices ( the case m = n ).

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Given time, these deposits form much like how a stalactite takes shape in a cave, except in this case on a flat surface.

Given that Suzanne's uncle Antonio works for the Count, it seems likely she was hired on his recommendation when the Countess moved into the palace and a maid was needed for her, in which case she and Figaro would have met after the events of The Barber of Seville.

is also true in the case of compact manifolds, due to Yau's proof of the Calabi conjecture: Given a compact, Kähler, holomorphically symplectic manifold ( M, I ), it is always equipped with a compatible hyperkähler metric.

Given this method of scoring, it is possible for the defendant to be found guilty or lose the case but for the defense team to still win the round.

Given source material, Rabin – Karp can rapidly search through a paper for instances of sentences from the source material, ignoring details such as case and punctuation.

Given the apparent impracticality of massive retaliation strategy, Army Chiefs of Staff Matthew Ridgeway and his successor Maxwell Taylor argued within JCS that deterrence, instead of the " worst case " scenario of a full-scale nuclear war, should be the focus.