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, 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 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 detailed instructions may be obtained from your local building supply houses and craftsmen.

More rarely, a script may have separate letters for tones, as is the case for Hmong and Zhuang.

More complex alkenes may be named using the E-Z notation, used to describe molecules having three or four different substituents ( side groups ).

More specialized bicycle components may require more complex tools, including proprietary tools specific for a given manufacturer.

More complexly, an economy may be unable to export enough goods to pay for its imports, but is able to find funds elsewhere.

More recent research into the Pygmy subspecies suggests this may be an underestimate.

More direct government involvement can lead to specific areas of crony capitalism, even if the economy as a whole may be healthy.

More complex computations may involve many operations and data elements together.

( More rarely, crystals may be deposited directly from gas ; see thin-film deposition and epitaxy.

* More than one assignment may be performed in a single statement.

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 generally, unspecific coercion may be the form taken by disciplinary coercion, and this appears to be in fact the case within the most effective command systems of the modern world.

More generally among Baptists, a variety of parachurch agencies and evangelical educational institutions may be supported generously or not at all, depending entirely upon the local congregation's customs and predilections.

More broadly speaking, Chinese classic texts may refer to texts, be they written in vernacular Chinese or in classical Chinese, that existed before 1912, when the last imperial Chinese dynasty, the Qing Dynasty, fell.

" In addition to the various works of Brewster already mentioned, the following may be added: Notes and Introduction to Carlyle's translation of Legendre's Elements of Geometry ( 1824 ); Treatise on Optics ( 1831 ); Letters on Natural Magic, addressed to Sir Walter Scott ( 1832 ); The Martyrs of Science, or the Lives of Galileo, Tycho Brahe, and Kepler ( 1841 ); More Worlds than One ( 1854 ).

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

More rarely, other beaters such as cartwheel mallets ( known to kit drummers as " soft sticks ") may be used.

More generally, a function may map equivalent arguments ( under an equivalence relation ~< sub > A </ sub >) to equivalent values ( under an equivalence relation ~< sub > B </ sub >).

More generally, a function may map equivalent arguments ( under an equivalence relation on ) to equivalent values ( under an equivalence relation on ).

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

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 generally, one may use the fact that the operators do not commute,

More generally, the observed IQ improvement may be the result of the slow reduction in environmental neurotoxins, including lead, cadmium, mercury, unfiltered coal smoke, tobacco, and ethanol.

More potent a charm to bring back that time of life than this record of a few pictures and a few remembered facts would be a catalogue of the minutiae which are of the very stuff of the mind, intrinsic, because they were known in the beginning not by the eye alone but by the hand that held them.

More attendants, nurses and doctors should be hired.

More importantly, several of the more advanced of the less developed countries have found through experience that they must plan their own complex investment programs for at least 5 years forward and tentatively for considerably more than that if they are to be sure that the various interdependent activities involved are all to take place in the proper sequence.

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 believed that a man could be both serious and gay.

Secondly, to find a learned diversion and a pleasing joke in More's account of the stupid brutalities of early sixteenth century wars, of the anguish of the poor and dispossessed, of the insolence and cruelty of the rich and powerful requires a callousness toward suffering and sin that would be surprising in a moral imbecile and most surprising in More himself.

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.

If the compiler finds that there are no more electronic switches available for assignment, the warning message `` No More Electronic Switches Available '' will be placed in the object program listing, the table will be altered to show that electronic switches 1 through 30 are available, and assignment will continue as before.

More importantly, he also happens to be the brother-in-law of Sam Rayburn, Speaker of the House.

More local particular weather examples could be found in examples such as the ; Azores High, Benguela Current, Nor ' easter.

More complex mathematical modeling continues to be done today.

More indirectly, Christie ’ s famous character of Hercule Poirot can be compared to an archaeologist in his detailed scrutiny of all facts both large and small.

More alpha channels can be added for accurate spectral color filtration applications.

More recently, James Page has suggested that aesthetic ethics might be taken to form a philosophical rationale for peace education.

More technically, the law is concerned with the speedup achievable from an improvement to a computation that affects a proportion P of that computation where the improvement has a speedup of S. ( For example, if an improvement can speed up 30 % of the computation, P will be 0. 3 ; if the improvement makes the portion affected twice as fast, S will be 2.

More than one string orchestra can be utilized.

More recent IUPAC recommendations now suggest the newer term " hydronium " be used in favor of the older accepted term " oxonium " to illustrate reaction mechanisms such as those defined in the Brønsted – Lowry and solvent system definitions more clearly, with the Arrhenius definition serving as a simple general outline of acid – base character.

More general type of asymptotes can be defined in this case.

In More Poems, he buries his love for Moses Jackson in the very act of commemorating it, as his feelings of love break his friendship, and must be carried silently to the grave:.

More controversially, Disraeli also proposed to alter the workings of the income tax ( direct taxation ) by " differentiating "– i. e., different rates would be levied on different types of income.