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, 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 rigorously, Pickover's " biomorphs " encompass the class of organismic morphologies created by small changes to traditional convergence tests in the field of " Julia set " theory.

More industrial acreage lies vacant in St. Clair county than in any other jurisdiction in the St. Louis area.

More time was spent in trying to marry these incompatibles than over any subject discussed at Yalta.

If, at any time during the assignment pass, the compiler finds that there are no more index words available for assignment, the warning message `` No More Index Words Available '' will be placed in the object program listing, the table will be altered to show that index words 1 through 96 are available, and the assignment will continue as before.

More than 20 million people live on farms and they own a fourth of the nation's trucks, buy more gasoline than any other industry and provide a major market for home appliances, chemicals and other products.

More efficient amplifiers run cooler, and often do not need any cooling fans even in multi-kilowatt designs.

More specifically in regards to the Mets, critics point out that with Selig's personal relationship with Wilpon has allowed him to stall any possible removal of Wilpon as that club's principal owner.

More generally, calculus ( plural calculi ) refers to any method or system of calculation guided by the symbolic manipulation of expressions.

More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other.

More conceptually, this rule expresses the fact that a change in the x < sub > i </ sub > direction may change all of g < sub > 1 </ sub > through g < sub > k </ sub >, and any of these changes may affect f.

More Cessna 172s have been built than any other aircraft.

More recently, with the advent of personal computing, and the growth of home recording, the term computer music is now sometimes used to describe any music that has been created using computing technology.

* Change of any variable quantity, in mathematics and the sciences ( More specifically, the difference operator.

More generally, values may be of any of the kinds described as a level of measurement.

More specifically, " habitats can be defined as regions in environmental space that are composed of multiple dimensions, each representing a biotic or abiotic environmental variable ; that is, any component or characteristic of the environment related directly ( e. g. forage biomass and quality ) or indirectly ( e. g. elevation ) to the use of a location by the animal.

More generally, the ELIZA effect describes any situation where, based solely on a system's output, users perceive computer systems as having " intrinsic qualities and abilities which the software controlling the ( output ) cannot possibly achieve " or " assume that reflect a greater causality than they actually do.

More modern Soviet designs, including the MiG-3, LaGG-3 and Yak-1, had not yet arrived in numbers and in any case were still inferior to the Messerschmitt Bf 109.

More generally, the fundamental group of any graph is a free group.

More than any single factor though, firearms have proliferated due to the advent of mass production-enabling arms manufacturers to produce large quantities of weaponry to a consistent standard.

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 recent examples of usage for almost any type of playful cleverness are wetware hackers (" hack your brain "), media hackers and " hack your reputation ".

More generally any quadratically closed subfield of or will suffice for this purpose, e. g., the algebraic numbers, but when it is a proper subfield ( i. e., neither nor ) even finite-dimensional inner product spaces will fail to be metrically complete.

: More generally, any Euclidean space < sup > n </ sup > with the dot product is an inner product space

More players have won the coveted Ballon d ' Or award while playing at a Serie A club than any other league in the world.

More compounds of carbon exist than any other chemical element except for hydrogen.

:" More than any other single factor or incident, Mojave Desert incident from Frémont's second expedition report is where the Kit Carson legend was born ..."

More compactly, using the Einstein summation notation, del is written as

More general abelian and Tauberian theorems give similar results for more general summation methods.

More unitized lumber is being shipped on flat cars, and NLRDA studies show that flat cars loaded with the new Type 6-B floating-load method can be unloaded for as little as $.054/mbf.

More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory.

More recent experiments have suggested that these morphological descriptions of endocytic events may be inadequate, and a more appropriate method of classification may be based upon the clathrin-dependence of particular pathways, with multiple subtypes of clathrin-dependent and clathrin-independent endocytosis.

More recently, Smith has devoted her time to what she terms ' pure photography ' ( a method of capturing still objects without using a flash ), which she began to pursue following the death of her husband in 1994.

More advanced irons for use in electronics have a mechanism with a temperature sensor and method of temperature control to keep the tip temperature steady ; more power is available if a connection is large.

Originally proposed by Alcoholics Anonymous ( AA ) as a method of recovery from alcoholism, the Twelve Steps were first published in the book Alcoholics Anonymous: The Story of How More Than One Hundred Men Have Recovered from Alcoholism in 1939.

More specifically synthetic phonics is now the accepted method of teaching reading in the education systems in the UK and Australia.

More experienced swimmers often find their own method of staying above the surface.

More systematic and more efficient ( but also more formalised and more rule-based, and more removed from an overall holistic picture of what division is achieving ), a person who knows the multiplication tables can divide two integers using pencil and paper using the method of short division, if the divisor is simple.

More modern spinning machines use a mechanical means to rotate the spindle, as well as an automatic method to draw out fibers, and devices to work many spindles together at speeds previously unattainable.

More commonly, only the name of the library ( and not the path ) is stored in the executable, with the operating system supplying a method to find the library on-disk based on some algorithm.

More than 300 videotaped network series and specials used this method over a 12-year period, including the fast-paced Rowan & Martin's Laugh-In.

More than 1, 000 years later, John Loudon McAdam invented a road construction method called macadamisation.

More modern cameras no longer use this method ; the simplification helps reduce cost.

More formally, the Law of Demeter for functions requires that a method of an object may only invoke the methods of the following kinds of objects:

More recently, a more systematic method has been used to classify zinc finger proteins instead.

More sophisticated algorithms use some method of preventing the walker from doubling back.

More consistent with the scientific method than traditional, faith-based religion, the Kalama Sutta insists on a proper assessment of evidence, rather than a reliance on faith, hearsay or speculation:

More recently, the " Trap-Neuter-Return " method has been used in many locations as an alternate means of managing the feral cat population.

More precisely, his method of infinite descent was an exploitation in particular of the possibility of halving rational points on an elliptic curve E by inversion of the doubling formulae.

** More information about the method of Cavalieri

More generally, Duhem was critical of Newton's description of the method of physics as a straightforward " deduction " from facts and observations.

More recently, it is possible to discern a second method for identifying middle power status by focusing on behavioural attributes.