Given the geographic diversity of the various sub-regions within the Maritimes, policies to centralize the population and economy were not initially successful, thus Maritime factories closed while those in Ontario and Quebec prospered.

Given Cerion's extensive geographic diversity, Gould later lamented that if Christopher Columbus had only cataloged a single Cerion it would have ended the scholarly debate about which island Columbus had first set foot on in America.

Given the diversity of solid state compounds, an equally diverse array of methods are used for their preparation.

Given the diversity of the metalloproteome, virtually all amino acid residues have been shown to bind metal centers.

Given the extensive linguistic, religious and ethnic diversity of the Indian population, nationalism in India in general does not fall within the purview of a solitary variant of nationalism.

Given the range of diversity in soil type, climate and occupations, these cuisines vary significantly from each other and use locally available spices, herbs, vegetables, and fruits.

Given the ethnic diversity of the city, Marbella's newspapers and magazines are published in several European languages, among which are La Tribuna de Marbella ( Spanish ), Sydkusten ( in Swedish ) and Costa del Sol Nachrichten ( in German ).

Given this diversity, it is difficult to generalize widely about the folklore of India as a unit.

Most methods of lipid extraction and isolation from biological samples exploit the high solubility of hydrocarbon chains in organic solvents. Given the diversity in lipid classes, it is not possible to accommodate all classes with a common extraction method.

Given the wide diversity of skull shape among enantiornithines, many different dietary specializations must have been present among the group.

Given the morphological diversity of the earlobes found among men, women, and children, some earlobes are large, some earlobes are pendulous, and some earlobes are large and pendulous, but some are prominent because of the structure and form of the dense, interlacing connective tissue fibers that shape the earlobe anatomy independent of the tail of the helix ( cauda helicis ).

Given the existing linguistic diversity of the PALOPs, Portuguese also serves the purpose of lingua franca allowing communication between fellow citizens of different ethno-linguistic backgrounds.

Given the diversity of CNN processors and the momentum that CNN research has gained, it is plausible that these unique analog CNN development efforts will be fairly common in the near future.

* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

* Given any set X, there is an equivalence relation over the set of all possible functions X → X.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given the name infinitesimal calculus, it allowed for precise analysis of functions within continuous domains.

Given the scale of most commercial operations and the lack of mechanized record-keeping and recording before the industrial revolution, it made sense for most owners of enterprises in those times to carry out management functions by and for themselves.

Given an arithmetic function, one can generate a bi-infinite sequence of other arithmetic functions by repeatedly applying the first summation.

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.

# Composition operator ( also called the substitution operator ): Given an m-ary function and m k-ary functions:

Given a guaranteed halting language, the computable function which is produced by Cantor's diagonal argument on all computable functions in that language is not computable in that language.

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

Given " mappings " of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of " rules ", each of the form:

So, a collection of functions with given signatures generate a free algebra, the term algebra T. Given a set of equational identities ( the axioms ), one may consider their symmetric, transitive closure E. The quotient algebra T / E is then the algebraic structure or variety.

Given that the sport functions by measuring and comparing athletes ' performances, performance-enhancing substances create an uneven playing field — athletes who do not use doping substances have a disadvantage over rivals who do.

* Given a family of continuous functions f < sub > n </ sub >: X → Y with pointwise limit f: X → Y.

Given any set Y with a family of functions

Given a subset V of A < sup > n </ sup >, we define I ( V ) to be the ideal of all functions vanishing on V:

Given n − 1 homogeneous polynomial functions in

Given any set of points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of your N points with some desired kernel, and sample from that Gaussian.

* Given a Gödel numbering of the computable functions, the set ( where is the Cantor pairing function and indicates is defined ) is recursively enumerable.

* Given a Gödel numbering of the computable functions, the set is recursively enumerable.

The general scenario is the following: Given a class S of computable functions, is there a learner ( that is, recursive functional ) which for any input of the form ( f ( 0 ), f ( 1 ),..., f ( n )) outputs a hypothesis ( an index e with respect to a previously agreed on acceptable numbering of all computable functions ; the indexed function should be consistent with the given values of f ).

Given the exclusivity of the criteria needed to become a magician, much magic is performed by specialists.

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 the need to exclude infection, chest radiography and urinalysis are usually performed.

Given the services performed by logisticians, the main fields of logistics can be broken down as follows:

Given City Hall's attractive location and park atmosphere, weddings are regularly performed on the lawn.

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 complexity of perioperative management, and the potential for catastrophic intra and postoperative complications, such surgery should be performed only at centers experienced in the management of this disorder.

Given the difficulties with the original plot, a revised version, with text changes by Arrigo Boito, was first performed at La Scala, Milan on 24 March 1881.

His first role on Broadway was a play called Any Given Day, which was performed at the Longacre Theatre.

Given that the directors can not ensure corporate success, the business judgment rule specifies that the court will not review the business decisions of directors who performed their duties ( 1 ) in good faith ; ( 2 ) with the care that an ordinarily prudent person in a like position would exercise under similar circumstances ; and ( 3 ) in a manner the directors reasonably believe to be in the best interests of the corporation.

Given that the management of Alumina's assets is performed entirely by other companies, their extensive governance structure and regular board meetings have attracted adverse comment.

Given the software limitations at the time, to make the sound work correctly required a full live orchestra, the first that Soule had ever worked with ; the orchestral tracks in Evermore had been performed by Soule and his brother by themselves, two instruments at a time.

Given the fact that few stars are visible at night on most of Klinzhai due to cloud cover, they have a mystical reverence for " the naked stars " and believe they remember acts of courage performed under them, as this poem suggests: