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

Given the rigorous admission process it is not surprising that CUNY BA boasts a 70 % graduation rate within an average of 2. 2 years and that 60 % graduate with academic honors.

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.

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 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 the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

Given two groups G and H and a group homomorphism f: G → H, let K be a normal subgroup in G and φ the natural surjective homomorphism G → G / K ( where G / K is a quotient group ).

Given that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

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 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 a natural transformation Φ from h < sup > A </ sup > to F, the corresponding element of F ( A ) is.

Given a morphism f: B → A the associated natural transformation is denoted Hom ( f ,–).

Given a diagram F: J → C ( thought of as an object in C < sup > J </ sup >), a natural transformation ψ: Δ ( N ) → F ( which is just a morphism in the category C < sup > J </ sup >) is the same thing as a cone from N to F. The components of ψ are the morphisms ψ < sub > X </ sub >: N → F ( X ).

Given his socialist agenda in Egypt, the Ba ' ath should have been his natural ally, but Nasser was hesitant to share power.

Given the reputed humorous character of Valencians, it was natural that they began to burn figurines depicting people and events of the past year.

Given this natural tendency to glide forward, terza rima is especially well-suited to narration and description ".

Given this, it is quite natural and convenient to designate a general sequence a < sub > n </ sub > by by the formal expression, even though the latter is not an expression formed by the operations of addition and multiplication defined above ( from which only finite sums can be constructed ).

Given a series with values in a normed abelian group G and a permutation σ of the natural numbers, one builds a new series, said to be a rearrangement of the original series.

Given a natural number x, h outputs the index of the partial computable function that performs the following computation:

Given its central location, Athlone is a natural hub for transport, with frequent bus and rail schedules.

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.

Given this difference, it is necessary that logistic regression take the natural logarithm of the odds ( referred to as the logit or log-odds ) to create a continuous criterion.

Given that the logit is not generally interpreted and that the inverse of the natural logarithm, the exponential function of the logit is generally interpreted instead, it is also helpful to examine this function ( denoted: ).

Given a presheaf, a natural question to ask is to what extent its sections over an open set U are specified by their restrictions to smaller open sets V < sub > i </ sub > of an open cover of U. A presheaf is separated if its sections are " locally determined ": whenever two sections over U coincide when restricted to each of V < sub > i </ sub >, the two sections are identical.

Given that some countries now ban docking, breeders are again attempting to select dogs with the genes for natural bob tails.

Given such a G-module M, it is natural to consider the subgroup of G-invariant elements:

Given its native distribution the species is also a potential natural vagrant to Western Europe and there have been records in areas such as Cornwall and the Isles of Scilly which some observers consider may relate to wild birds ; however, given the Wood Duck's popularity in captivity it would be extremely difficult to prove their provenance one way or another.

* Given a partial function f from the natural numbers into the natural numbers, f is a partial recursive function if and only if the graph of f, that is, the set of all pairs such that f ( x ) is defined, is recursively enumerable.