Given this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.

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 Pinckney's lack of political experience, he would have been expected to be open to Hamilton's influence.

Given the lack of evidence of many Freudian hypotheses, some scientific researchers proposed the existence of unconscious mechanisms that are very different from the Freudian ones.

Given the CIA's purposeful destruction of most records, its failure to follow informed consent protocols with thousands of participants, the uncontrolled nature of the experiments, and the lack of follow-up data, the full impact of MKUltra experiments, including deaths, will never be known.

Given the lack of a significant outer convection zone, theory predicts the absence of a magnetic dynamo in earlier A stars.

Given that many open source projects fail due to lack of developer support, exposure to such a large community of developers can continually breathe new life into a project.

Given Orff's previous lack of commercial success, the monetary factor of Carmina Buranas acclaim was significant to him.

Given inconsistencies and the lack of reliable data and completely contradicting and unpredictable behavior, the true nature of ball lightning is still unknown and was often regarded as a fantasy or a hoax.

Given the many available models, it appears that the material removal mechanism in EDM is not yet well understood and that further investigation is necessary to clarify it, especially considering the lack of experimental scientific evidence to build and validate the current EDM models.

Given its lack of a D ' Oyly Carte or Savoy connection, Thespis has a tenuous claim to be a " Savoy Opera.

Given the lack of concrete historical knowledge about one of the most potent figures in British mythology, it is unlikely that any definitive conclusions about the claims for these places will ever be established ; nevertheless it is both interesting and important to try to evaluate the body of evidence which does exist and examine it critically.

Given the lack of paved highways in America, this turned out to be a shrewd business move that enlarged Barnum's geographical reach.

Given the influence of the temperature of water, as well as the lack of complete adjustment for age, alcohol consumption and smoking, the study concludes that there is limited evidence, but hot mate drinking is " probably carcinogenic to humans ".

Given glam metal's lack of a major format presence on radio, bands were left without a clear way to reach their audience.

Given inconsistencies and the lack of reliable data, the true nature of ball lightning is still unknown.

Given the focus on intramodal competition and the lack of intermodal competition, there was little concern about statutory or regulatory language that set different regulatory burdens for different technology modes.

Given this lack of semantic transparency, researchers, outreach workers, critical theorists and LGBT activists have proposed and use terms such as institutionalized homophobia, state (- sponsored ) homophobia, sexual prejudice, anti-gay bigotry, straight privilege, The Straight Mind ( a collection of essays by French writer Monique Wittig ), heterosexual bias, compulsory heterosexuality or the much lesser known terms heterocentrism, homonegativity, and from gender theory and queer theory, heteronormativity.

Given the baseball's lack of popularity in the United Kingdom, the issues were unsuccessful.

Given the then lack of antibiotics, this " could not be considered an unusual pattern for pneumonia in a man in his seventh decade.

Given their general lack of interest in the area, the British decided to abandon the Sudan in December 1883, holding only several northern towns and Red Sea ports, such as Khartoum, Kassala, Sannar, and Sawakin.

Given the lack of surviving objects, we cannot know how common the techniques employed were, but the quality of the execution suggests that the binder was experienced in them.

Given the lack of budget, in many regions systematization did not constitute an effective plan, good or bad, for development.

Given the lack of standardized road signs at the time, it was decided to place distinctive bells along the route, hung on supports in the form of an high shepherd's crook, also described as " a Franciscan walking stick.

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

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given that John of Worcester wrote his chronicle after the eruption of the Canterbury – York supremacy struggle, the story of Ealdred renouncing any claims to Worcester needs to be considered suspect.

Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

* 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 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 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 any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given x ∈ A, the holomorphic functional calculus allows to define ƒ ( x ) ∈ A for any function ƒ holomorphic in a neighborhood of Furthermore, the spectral mapping theorem holds:

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 any vector space V over a field F, the dual space V * is defined as the set of all linear maps ( linear functionals ).

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

Given a left neutral element and for any given then A4 ’ says there exists an such that.

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

Given that Gable and Cukor had worked together before, in Manhattan Melodrama and Gable had no objection to working with him then, and given Selznick's desperation to get Gable for Rhett Butler, if Gable had any objections to Cukor, certainly they would have been expressed before he signed his contract for the film.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

We have seen a few cavities of the appropriate size and shape for ivory-bills, but these can be old, or exceptionally large Pileated Woodpecker cavities, or mammal-enlarged Pileated Woodpecker cavities .… Given the results, it is unlikely a population of any meaningful size of Ivory-billed Woodpeckers exists in south Florida.

Given a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given the above-mentioned problems, regulators face the challenging task of regulating a market that is changing very rapidly, without stifling any type of innovation, and without improperly disadvantaging any competitor.

Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.

: Given any positive number ε, there is a sequence