Given its different forms, there are various ways of representing uncertainty and modelling economic agents ' responses to it.

Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide.

Given the diversity of functions performed by neurons in different parts of the nervous system, there is, as expected, a wide variety in the shape, size, and electrochemical properties of neurons.

Given a sinewave generator of very low inherent distortion, it can be used as input to amplification equipment, whose distortion at different frequencies and signal levels can be measured by examining the output waveform.

Given that different languages have different grammatical features, the actual test for which nouns are mass nouns may vary between languages.

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 a fixed physical relationship in space between the different individual microphone transducer array elements, simultaneous DSP ( digital signal processor ) processing of the signals from each of the individual microphone array elements can create one or more " virtual " microphones.

Given an initial allocation of goods among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement.

Given X and Y, several different embeddings of X in Y may be possible.

Given the potential for sampling biases of individual survey reports, researchers and investors try sometimes to average the values of different index reports into a single aggregated measure of consumer confidence.

About the new markets, Ergen said, " Given the assets we've been accumulating, I don't think it's hard to see we're moving in a different direction from simply pay-TV, which is a market that's becoming increasingly saturated.

Given that Melampus had two sons, Abas and Mantius, different sources made Coeranus, father of Polyeidos, son or grandson of either of the two.

Given all the different Indian dialects, it would not be all that wrong to pronounce a more familiar sounding hi lu la hi with the suffix on the end to tag it as a settlement.

Given below are various Curie temperatures for different substances.

) 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 variety of approaches, Economic Geography has taken to many different subject matters, including: the location of industries, economies of agglomeration ( also known as " linkages "), transportation, international trade, economic development, real estate, gentrification, ethnic economies, gendered economies, core-periphery theory, the economics of urban form, the relationship between the environment and the economy ( tying into a long history of geographers studying culture-environment interaction ), and globalization.

: Given an integer n, choose some integer a coprime to n and calculate a < sup > n − 1 </ sup > modulo n. If the result is different from 1, then n is composite.

Given a function, the goal of the attack is to find two different inputs such that.

Given the absurdity of the conclusion, Chalmers ’ rejects the initial premise that agents with identical causal organization can have different experiences.

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 that abstract thought is thus limited, he went on to consider how historical formations give rise to different philosophies and ways of thinking.

Given the opportunity, adults eat hatchlings, which may be protected by separating the two groups with a net, breeding box or separate tank.

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 two groups (< var > G </ var >, *) and (< var > H </ var >, ), a group isomorphism from (< var > G </ var >, *) to (< var > H </ var >, ) is a bijective group homomorphism from < var > G </ var > to < var > H </ var >.

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 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 the role that many social groups have in the development of public policy and the extensive connections between state bureaucracies and other institutions, it has become increasingly difficult to identify the boundaries of the state.

Given Switzerland's particularly strong opinions on who is " Swiss " and who is " other ", it is easy to see that groups such as Stoffunita make use of the fact that hip hop " is still considered a voice for the oppressed " as hip hop scholar and author Jeff Chang notes.

Given the type of warfare that had been carried out in the conflict — wherein highly mobile groups of soldiers and rebels continued to move to and from on the desert terrain, retreating at a time and then suddenly attacking to regain control of small towns and villages in the Eastern rebel held parts of Libya — had led to the technical becoming a vehicle of choice for both sides.

Given two groups A and H there exist two variations of the wreath product: the unrestricted wreath product A Wr H ( also written A ≀ H ) and the restricted wreath product A wr H. Given a set Ω with an H-action there exists a generalisation of the wreath product which is denoted by A Wr < sub > Ω </ sub > H or A wr < sub > Ω </ sub > H respectively.

Given two reductive groups and a ( well behaved ) morphism between their corresponding L-groups, this conjecture relates their automorphic representations in a way that is compatible with their L-functions.

Given a positive integer n, it is not at all a routine matter to determine how many isomorphism types of groups of order n there are.

The prime mechanism then appeared to be this: Given a space X carrying a vector bundle, that implied in the homotopy category a mapping from X to a classifying space BG, for the relevant linear group G. For the homotopy theory the relevant information is carried by compact subgroups such as the orthogonal groups and unitary groups of G. Once the cohomology H *( BG ) was calculated, once and for all, the contravariance property of cohomology meant that characteristic classes for the bundle would be defined in H *( X ) in the same dimensions.

Given that Neukölln was heavily penetrated by Soviet combat groups, Krukenberg prepared fallback positions for Sector C defenders around Hermannplatz.

Given this scenario, many more of the remaining advocates may well defect to more conservative groups also, leaving the UCC as perhaps the U. S .' most politically and theologically liberal Christian group.

Given a base scheme S, an algebraic torus over S is defined to be a group scheme over S that is fpqc locally isomorphic to a finite product of multiplicative groups.

Given any finite flat commutative group scheme G over S, its Cartier dual is the group of characters, defined as the functor that takes any S-scheme T to the abelian group of group scheme homomorphisms from the base change G < sub > T </ sub > to G < sub > m, T </ sub > and any map of S-schemes to the canonical map of character groups.

Given the intense interest in ethnicity, genetic genealogists and other scientists have studied population groups.

Given Japan had surrendered to the Allies at the end of World War II, the Japanese forces in Indochina stepped aside and allowed nationalist groups to take over public buildings in most of the major cities.

' Given the nature of the most famous of texts from both groups, ZAMM, is of the latter nature style of title ( and, rather than in ) one must ask if ZAMM is not a product of the archery text, but rather, an ' unintended ' or ' inadvertent ' ( and unknown to Pirsig during writing and publication

Given the difference between their roles and emphases, some scholars have speculated that the interactions between the Æsir and the Vanir reflect the types of interaction that were occurring between social classes ( or clans ) within Norse society at the time.

" Given the situation in Spain for several years regarding terrorist attacks, these ties can be considered objectively as a threat to democracy ," the court said, also adding that these parties " contradicted the concept of a ' democratic society ' and presented a major danger to Spain's democracy ".

" Given that declaration, along with seven years of bombings and the wording of their communiques throughout that time that strove to present an image of a powerful organization spread secretly throughout all sectors of society, the authorities took significant action.

Given that France and Britain had been at war since early 1793, administering or making such oaths turned the society into something more than a liberal pressure group.

Given the degree of change in Ovimbundu society and the involvement of the Ovimbundu with UNITA, it was difficult to determine their long-range role in Angolan politics.

Given enough variety of " species " they might even form a type of ecology, or — should they also have a form of artificial intelligence — a society.

:: Given the marginalized position of homosexuals in society, the metamessage that flows almost inevitably from excluding same-sex couples from such an important social institution is essentially that society considers such relationships to be less worthy of respect, concern and consideration than relationships involving members of the opposite sex.

Given the transformations influenced by globalization, there is a growing necessity to expand beyond this rather limited view of social work to better suit the needs of modern society.

Given the overall low level of water tariffs in developing countries even at higher levels of consumption, most consumption subsidies benefit the wealthier segments of society.

Given the importance in Greek society of cultivating the masculinity of the adult male and the perceived feminizing effect of being the passive partner, relations between adult men of comparable social status were considered highly problematic, and usually associated with social stigma.

Given the assumptions of biological positivism, the only reasonable rationale for punishing offenders is to incapacitate them for as long as possible so that they no longer posed a threat to the peace and security of society.

Given that Communist Romania was a police state, and unprecedented measures of strict control and surveillance were supposed to have been enforced in all areas of society ( phone calls were routinely monitored, correspondence was intercepted, and secret police informants were common ) a plan such as the one allegedly designed by the group would have been exceedingly difficult to carry out.

Given that Plex resided on the starship Marvel it is uncertain whether or not it was as central to Kree society as Supremor is.

Given this stance, it emphasises the practical teachings of subjects with a sound theoretical background, while at the same time actively adapting the lesson material and courses to the job market demands and the realities of today ’ s society.