: Given an isolated system in equilibrium, it is found with equal probability in each of its accessible microstates.

Given the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given enough time, natural change in isolated language can obliterate any meaningful linguistic evidence of a known common genetic source for the languages.

Given that her lord's kinsmen ( þæt monnes magas ) are described as taking measures to separate the speaker from him, a probable interpretation of the speaker's initial circumstances is that she has been entered into an exogamous relationship typical within the Anglo-Saxon heroic tradition, and her marital status has left her isolated among her husband's people, who are hostile to her, whether due to her actions or merely due to political strife beyond her control.

Given the level of surveillance, and consistent with the conspiratorial traditions of Irish political movements, the union proceeded clandestinely, forming small groups of trusted friends in order to keep informers at bay, meeting in isolated locations and in subway tunnels.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given the apparent magnitude (> 20 ) of all but the biggest trans-Neptunian objects, the physical studies are limited to the following:

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 a system of n-dimensional variables ( physical variables ), in k ( physical ) dimensions, write the dimensional matrix M, whose rows are the dimensions and whose columns are the variables: the ( i, j ) th entry is the power of the ith unit in the jth variable.

Given that controls are imperfect, strong physical security applies the principle of defense in depth using appropriate combinations of overlapping and complementary controls.

Given the rank of Lieutenant, he was posted to the Army School of Physical Training at Frankston, Victoria, to act as a divisional supervisor of physical training.

Given a rebbe's physical awareness of God, and the Rebbe's transcendent perception of Godliness, many hasidim take special care to observe the specific and sometimes minute practices of their Rebbe.

Given the explosion of medical knowledge in the 20th century, it is easily appreciated that this led to a vast expansion of the book, which threatened to collapse under its own weight in a metaphorical and physical sense.

Given these orbital elements and the physical characteristics known so far, Ananke is thought to be the largest remnant of an original break-up forming the Ananke group.

: Given that the particle begins at position x < sub > 1 </ sub > at time t < sub > 1 </ sub > and ends at position x < sub > 2 </ sub > at time t < sub > 2 </ sub >, the physical trajectory that connects these two endpoints is an extremum of the action integral.

Given Vanier's physical state, Pearson was hesitant to advise the Queen to act along those lines, but his worry was short lived, as the following day, after hearing the Holy Sacrifice of the Mass and receiving Holy Communion in the chapel, the Governor General died.

Given below are the fundamental differences between physical goods and services:

Given the physical punishment suffered by catchers, the pieces of equipment associated with the position are often referred to as " the tools of ignorance ".

Given her husband's weak physical and mental condition, she exerted a strong influence on imperial life, and was an active patron of Japanese Red Cross Society.

Given his young age ( 17 ), size, and ability to quickly adapt to the more physical style of hockey in North America, Bonk became a " can't miss " prospect.

Given the similarity of the orbital elements and the homogeneity of the physical characteristics with other members of the Gallic group, it was suggested that these satellites could have a common origin in the break-up of a larger moon.

Given a system, we say that a physical event is a stimulus for the system if and only if the probability that the system suffers a change or be perturbed ( in its elements or in its processes ) when the event occurs is strictly greater than the prior probability that suffers a change independently of:

Given that the details of characters ' physical appearances are not often given in His Dark Materials ( for example, it is a long time before it is mentioned that the protagonist, Lyra, is blonde ), this is an unusual attention to physical detail.

Given that ( A ) the Georges are among the most rational, principled and educated persons on the planet, and ( B ) their differences from normal humans are purely physical, they conclude that in any situation where the Three laws would come into play, their own orders should take priority over that of a regular human.

Given the physical resemblance between the Eternals and Olympians, both parties formed an alliance, with the Eternals acting representing the gods on Earth.

Given that stamp duty is only payable on physical share certificates, there is no stamp duty payable on shares settled via CREST.

Given the lack of ability to inspect merchandise before purchase, consumers are at higher risk of fraud on the part of the merchant than in a physical store.

Given these changes, the classical terms " system ", " expansion " and " peripheral " no longer have the same connotations.

Given the system ( corresponding to )

Given the limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

Given that the bulk of family chores fell to women, and that they were five times more likely than men to head a single-parent family, the shortcomings of Finland's child day-care system affected women more than it did men.

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 proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

Given a syscall that does nothing, a full round-trip under BSD would require about 40μs, whereas on a user-space Mach system it would take just under 500μs.

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 the increasing number of scientists who study the nervous system, several prominent neuroscience organizations have been formed to provide a forum to all neuroscientists and educators.

Given the complexity of NLP problems, it is often difficult to predict performance only on the basis of glass-box evaluation, but this type of evaluation is more informative with respect to error analysis or future developments of a system.

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 poorly understood nature of the endocannabinoid system, it will take many more generations of progress to even scratch the surface of the extraordinarily complex mechanisms that control neurological development / degeneration.

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 the opportunity, for example during an illness that suppresses the immune system, the virus is reactivated and travels to the end of the nerve cell, where it causes the symptoms described above.

Given Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1 / Ω.

Given the space X = Spec ( R ) with the Zariski topology, the structure sheaf O < sub > X </ sub > is defined on the D < sub > f </ sub > by setting Γ ( D < sub > f </ sub >, O < sub > X </ sub >) = R < sub > f </ sub >, the localization of R at the multiplicative system

) Given that the telephone system nominal voiceband ( including guardband ) is 4, 000 Hz, the required digital sampling rate is 8, 000 Hz ( see Nyquist rate ).

Given the structural similarities between bacterial flagella and bacterial secretory systems, it is thought that bacterial flagella may have evolved from the type three secretion system ; however, it is not known for certain whether these pores are derived from the bacterial flagella or the bacterial secretory system.

Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.

Given a testing procedure E applied to each prepared system, we obtain a sequence of values