Given that millions of organic compounds are known, rigorous use of systematic names can be cumbersome.

Given the Federal budget deficit, the Obama Administration moved to apply an " evidence-based approach " to government spending, including rigorous methods of program evaluation.

Given behavior adaptation and migration, the current rigorous Interstate effectiveness of 14 % and CLRS on single-lane highways effectiveness of 14 % could be over-estimations of the actual " big-picture " reduction.

Given the celebrations of 40 years of Maltese independence, the 25 years of the closure of the British Base in Malta, and the anticipated admission of Malta into the European Union, the three Lodges of the Irish Constitution met on 5 September 2003 and resolved to form themselves into a Sovereign Grand Lodge.

Given the atypical Romanian university admission system ( usually another exam making up for the rest of the process ), these percentages mean even less.

Given the tendency for real negotiations in Japan to be conducted privately ( in the nemawashi, or root binding, process of consensus building ), the shingikai often represented a fairly advanced stage in policy formulation in which relatively minor differences could be thrashed out and the resulting decisions couched in language acceptable to all.

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 low efficiency of the laser amplification process ( about 1 to 1. 5 %), and the losses in generation ( steam-driven turbine systems are typically about 35 % efficient ), fusion gains would have to be on the order of 350 just to break even.

Given its " grandfathered " status, opium tincture has never been required to undergo the strict FDA drug review and approval process.

Given a stream of symbols and their probabilities, a range coder produces a space efficient stream of bits to represent these symbols and, given the stream and the probabilities, a range decoder reverses the process.

Given a stochastic process, the natural filtration for ( or induced by ) this process is the filtration where is generated by all values of up to time s

The inscription reads: “ Belonging to Ahaz ( son of ) Yehotam, King of Judah .” Given the process that created and preserved bullae, they are virtually impossible to forge.

Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.

Given a closed system in an initial state, if work is done on the system in an adiabatic ( i. e. no heat transfer ) way, and given the final state after a process, the amount of work required to be transferred to the system is the same, irrespective of how this work is performed.

Given the advent of high-throughput protein analysis and lower limits of detection, however, there has been interest in developing one-step probing systems that would allow the process to occur faster and with less consumables.

Given a discrete-time stationary ergodic stochastic process on the probability space, AEP is an assertion that

Given the intensity of community involvement in all these process related activities, many staff members have developed their own forms of practice, and some of them have become well known teachers.

Given an adapted process with define

Given the right overall conditions of the compressed fuel — high enough density and temperature — this heating process will result in a chain reaction, burning outward from the center where the shock wave started the reaction.

Given the complicated legal process and the sheer number of exiting cul-de-sac streets, however, such efforts would be slow to produce results and may only have a marginal impact in changing the landscape of existing districts.

Given the assumptions of the model ( for example, that the profits are reinvested and that capital accumulation does not substitute for skilled labor in production ), the process becomes self-sustaining and leads to modernization and economic development.

Given the preceding jurisprudence regarding due process, Chief Justice Taney was not entirely breaking ground in his Dred Scott opinion when, without elaboration, he pronounced the Missouri Compromise unconstitutional because an " act of Congress that deprived a citizen of his liberty or property merely because he came himself or brought his property into a particular territory of the United States, and who had committed no offence against the laws, could hardly be dignified with the name of due process of law.

Given is the most capped Republic of Ireland player as he holds 125 caps and had 55 clean sheets in the process.

Given the complexity of this process, software is increasingly used to simplify the task, while better supporting reproducible and more justifiable results.

Given that many of those most actively involved in early efforts were academics ( drawn from a variety of disciplines including Anthropology, Computing Science, Development Studies, Information Science and Systems, Management, Planning, Sociology, and Social Work among others ) it is only inevitable that a process of " sense-making " with respect to these efforts would follow on quite quickly from the flurry of " tool-making " efforts.

Given that the orkz of Warhammer 40, 000 reproduce asexually, through a symbiotic relationship with a type of fungal spore, it is very likely that the two races are in fact one and the same and that the details of this process as outlined in Warhammer 40, 000 background material apply to the Orcs of Warhammer also.

Given the fact that no science can today be mastered by a single individual, Lonergan advocated sub-division of the scientific process in all fields.

: Given any family of nonempty sets, their Cartesian product is a nonempty set.

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

" Given that Thomas Aquinas died six years before Albertus Magnus ' death, this legend as stated is unlikely.

Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

Given the other ZF axioms, the axiom of regularity is equivalent to the axiom of induction.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

Given its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.

Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is

Given this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

Given the then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given such a sweeping definition, it is apparent that cognition is involved in everything a human being might possibly do ; that every psychological phenomenon is a cognitive phenomenon.