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More and rigorously
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, 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 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 and if
More recently, the chairman of the Atomic Energy Commission, Dr. Glenn T. Seaborg, `` admitted '' to a news conference in Las Vegas, Nevada, that the US might fall behind Russia ( he apparently meant in weapons development ) if the Soviets continue to test in the atmosphere while we abstain.
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 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 generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.
More controversially, officials of the Federal Reserve assisted in the negotiations that led to this bail-out, on the grounds that so many companies and deals were intertwined with LTCM that if LTCM actually failed, they would as well, causing a collapse in confidence in the economic system.
More precisely, if S
More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.
More generally, if ƒ has a branch-point near the origin of such a nature that then
More direct government involvement can lead to specific areas of crony capitalism, even if the economy as a whole may be healthy.
More often than not, a second light will be mounted to the helmet for quick transition if the primary fails.
More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.
More often than not a cross-examiner will also attempt to undermine the credibility of a witness if he will not be perceived to be a bully ( such as discrediting a very elderly person or young child ).
More than anything else, the caddy is there to make the player's round enjoyable by taking care of menial tasks, speeding up play, and providing mental support if asked.
More total output and utility thereby results from specializing in production and trading than if each country produced its own high-tech and low-tech products.
More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b.
More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b.
More generally, if the numbers are, the geometric mean satisfies
More severe withdrawal symptoms which occur can include seizures ( some of which can be fatal ), visual and auditory hallucinations, suicidal ideation, extremely severe panic attacks, depersonalization, tremors, delirium, delirium tremens and if not treated as an emergency by a proper medical staff death from a seizure can occur.
More formally, if a, b, c, and d are all integers, then the fraction < sup > a </ sup >⁄< sub > b </ sub > is irreducible if and only if there is no other equal fraction < sup > c </ sup >⁄< sub > d </ sub > such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a.
More generally, the direct product of two cyclic groups Z < sub > m </ sub > and Z < sub > n </ sub > is isomorphic to Z < sub > mn </ sub > if and only if m and n are coprime.
More generally, if C is an arbitrary abelian category that has enough injectives, then so does C < sup > I </ sup >, and the right derived functors of the inverse limit functor can thus be defined.

More and surface
More generally, electric current can be represented as the rate at which charge flows through a given surface as:
More realistic models are tailored to a specific problem and include the transition state theory, the calculation of the potential energy surface, the Marcus theory and the Rice – Ramsperger – Kassel – Marcus ( RRKM ) theory.
More than half of the cosmic radiation observed from the Earth's surface consists of muons.
More compacted soils will have a larger amount of surface runoff than less compacted soils.
More generally, the net change in charge density within a volume of integration is equal to the area integral over the current density through the closed surface, which is in turn equal to the net current:
More broadly, some consider the effect to include the tendency of any fluid boundary layer to adhere to a curved surface, not just the boundary layer accompanying a fluid jet.
More technically, it relates the electric flux through any hypothetical closed " Gaussian surface " to the enclosed electric charge.
More generally, a meteorite on the surface of any celestial body is a natural object that has come from elsewhere in space.
More correctly, radiosity B is the energy per unit area leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy:
More than 90 % of Sri Lanka's surface lies on Precambrian strata, some of it dating back 2 billion years.
More complex Curie-point irons circulate a high-frequency AC current through the tip, using magnetic physics to direct heating only where the surface of the tip drops below the Curie point.
More generally, a ( topological ) surface with boundary is a Hausdorff topological space in which every point has an open neighbourhood homeomorphic to some open subset of the upper half-plane H < sup > 2 </ sup >.
More than 80 % of the land surface is rough, broken, and mountainous, and therefore is of limited agricultural value ( see Agriculture, ch.
More often than not, overall cloud-to-ground ( CG ) lightning activity decreases as a tornado reaches the surface and returns to the baseline level when the tornado lifts.
More experienced swimmers often find their own method of staying above the surface.
More than half of Chile's land surface is volcanic in origin.
More than 70 islands dot the surface, although during periods of low and high water, these numbers can change.
More complicated interactions which slow grain boundary motion include interactions of the surface energies of the two grains and the inclusion and are discussed in detail by C. S.
More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the region inside the surface.
More recently work has been undertaken to graft antibodies or other molecular markers onto the liposome surface in the hope of actively binding them to a specific cell or tissue type.
More generally, the gloss ( or lustre or sheen ) of the surface is determined by scattering.
More generally, orientability of an abstract surface, or manifold, measures whether one can consistently choose a " clockwise " orientation for all loops in the manifold.
More generally, an orientable surface admits exactly two orientations, and the distinction between an oriented surface and an orientable surface is subtle and frequently blurred.

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