More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,

More rigorously, if a surface S is a union of finitely many pieces S < sub > 1 </ sub >, …, S < sub > r </ sub > which do not overlap except at their boundaries then

More rigorously, an interpretation of quantum mechanics satisfies CFD if it includes in the statistical population of measurement results, those measurements which are counterfactual by virtue of their being excluded by the quantum mechanical prohibition on simultaneous measurement of certain pairs of properties.

More rigorously, it is the localization of the polynomial ring in the multiplicative set consisting of the non-negative powers of X.

More rigorously, metonymy and synecdoche may be considered as sub-species of metaphor, intending metaphor as a type of conceptual substitution ( as Quintilian does in Institutio oratoria Book VIII ).

More rigorously, since the phases are in thermodynamic equilibrium with each other, the chemical potentials of the phases must be equal.

More rigorously, the mathematical operation involved in classical limits is a group contraction, approximating physical systems where the relevant action is much larger than Planck's constant ħ, so the " deformation parameter " ħ / S can be effectively taken to be zero.

More rigorously, any summation method that possesses these properties and which assigns a finite value to the geometric series must assign this value.

More rigorously, they are said to be isomorphic or “ structure preserving ”.

More serious consultation with a range of internationally adopted people from various professional and community-work based backgrounds needs to be included before the field of adoption study is more truly representative and rigorously informed.

More rigorously the effective temperature corresponds to the temperature at the radius that is defined by the Rosseland optical depth.

The minimal separators also form an algebraic structure: For two fixed vertices a and b of a given graph G, an ( a, b )- separator S can be regarded as a predecessor of another ( a, b )- separator T, if every path from a to b meets S before it meets T. More rigorously, the predecessor relation is defined as follows: Let S and T be two ( a, b )- separators in ' G '.

More rigorously

More broadly, eschatology may encompass related concepts such as the Messiah or Messianic Age, the end time, and the end of days.

More recently, thinkers have struggled to find a definition that could encompass formal differences as great as those between Chaucer's Canterbury Tales and Matsuo Bashō's Oku no Hosomichi, as well as differences in context spanning Tanakh religious poetry, love poetry, and rap.

More broadly, eschatology may encompass related concepts such as the Messiah or Messianic Age, the end time, and the end of days.

More specifically, equitation may refer to a rider's position while mounted, and encompass a rider's ability to ride correctly and with effective aids.

More recently the use of the term has expanded to encompass any group of advisers to a decision maker, whether or not in politics.

More recently, its ambit has grown to encompass any communication activity whose goal is to help individuals and communities select and practice behavior that will positively impact their health, such as immunization, cervical cancer check up, employing single-use syringes, etc.

More than 1, 800 alphabetical entries encompass a vast range of topics including religion, folklore, politics, art, music, theater, language and literature, places, organizations, intellectual movements, and important figures.

UCSB, Isla Vista, the City of Goleta and other unincorporated areas of the county, including the landward bluffs of More Mesa, surround and encompass the rest of the slough.

More than once I was confronted by professional gamblers, `` bookies '', loan `` sharks '', gangsters, `` thugs '' and `` finger men '' -- people of a class I did not even know existed -- to repay my husband's staggering losses, `` or else '' I shuddered to think that someone so dear to me could even associate with such a sinister milieu.

More word class ratios determined in more languages will no doubt ultimately answer the question.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

More than one century after Euler's paper on the bridges of Königsberg and while Listing introduced topology, Cayley was led by the study of particular analytical forms arising from differential calculus to study a particular class of graphs, the trees.

: More generally, a state can be represented by a so-called density operator, which is a trace class, nonnegative self-adjoint operator normalized to be of trace 1.

More generally, if one has a large number of copies of the same system, then the state of this ensemble is described by a density matrix, which is a positive matrix, or a trace class when the state space is infinite dimensional, and has trace 1.

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More formally, # P is the class of function problems of the form " compute ƒ ( x )," where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time.

More than 3, 000 students — three out of every four — take part in at least one for-credit “ service learning ” class by the time that they graduate ; nearly 45 percent participate in a service-learning class in any given year.

More generally, one can define objects by transfinite recursion on any well-founded relation R. ( R need not even be a set ; it can be a proper class, provided it is a set-like relation ; that is, for any x, the collection of all y such that y R x must be a set.

More is known about the tertiary structural features of soluble globular proteins than about membrane proteins because the latter class is extremely difficult to study using these methods.

More than 10, 000 species are described in this class.

More precisely, then, a likelihood function is any representative from an equivalence class of functions,

More than a hundred Australian thalidomide survivors are involved in the class action, according to Rowe's lawyer.

More specifically, some in Britain — especially supporters of the punk movement — regarded Genesis in particular, but also the genre more generally, as overtly middle class ( paying particular attention to Gabriel, Banks and Rutherford's private education ), and claimed that rock music was being taken away from the working class, whom they regarded as its core audience.

More precisely, an Enterprise Object is an instance of a class that implements the com. webobjects. eocontrol. EOEnterpriseObject interface.

More recent evidence, however, seems to indicate that the burning was limited to the structures and dwellings associated primarily with the elite class.

More recent historians, however, claim the importance of middle class audiences throughout the nickelodeon era and into the later 1910s.

More students were likely to be in class, and there would be less competition with other mid-week events — so he chose Wednesday, April 22.

Although he failed to achieve a first class degree in Greats, he won the Lothian and Arnold Prizes, the latter for an essay on Sir Thomas More ( about whom he confessed to having known almost nothing before commencing study, literally delivered as the clocks were chiming midnight on the day of the deadline ).

More recent textbooks stress the importance of students working with other students in pairs and groups, sometimes the entire class.

More recently the class was known as Pelecypoda, meaning " axe-foot " ( based on the shape of the soft parts of the animal ).

More generally, it often happens in combinatorics that certain values are considered to be a member of a given class by virtue of an empty sum, for instance 0 is a triangular number because of