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.

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

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 crucial to the operations of the German military was Krupp's development of the famed 88 mm anti-aircraft cannon which found use as a notoriously effective anti-tank gun.

More recently, MA Taylor and M Fink crystallized the present image of melancholia as a systemic disorder that is identifiable by depressive mood rating scales, verified by the present of abnormal cortisol metabolism ( abnormal dexamethasone suppression test ), and validated by rapid and effective remission with ECT or tricyclic antidepressant agents.

From 1510, More served as one of the two undersheriffs of the City of London, a position of considerable responsibility in which he earned a reputation as an honest and effective public servant.

More affluent countries are able to subsidize vaccinations for at-risk groups, resulting in more comprehensive and effective cover.

More recently, high-grade nitrogen gas has proven an effective remedy, with the added advantage of having no polluting effect to the environment.

More precise theory shows that during the action of the laser field, the time-averaged effective potential of H < sub > 2 </ sup >< sup >+</ sup > is formed which binds the electron even if very strong electromagnetic field is present in similarity to the hydrogen molecule ion and prevents ionization.

More widely, passive solar technologies include the solar furnace and solar forge, but these typically require some external energy for aligning their concentrating mirrors or receivers, and historically have not proven to be practical or cost effective for widespread use.

More research is needed to determine which strategies will be most effective and how they can be improved for patients with brain tumors.

More generally, plotting versus and taking the slope gives the effective number of ligands that are binding cooperatively at a particular ligand concentration.

More immediate feedback will be more effective than less immediate feedback.

More effective on lighter targets are the expanding bullets, the hollow point bullet and the soft point bullet.

More effective than cryosurgery and recurrence is at a much lower rate.

The results of the meta-analysis found that “ music therapy with these clients has a highly significant, medium to large effect on clinically relevant outcomes .” More specifically, music therapy was most effective on subjects with mixed diagnoses.

More importantly, Fatio noted that, by increasing both the velocity and the elasticity of the corpuscles, the difference between the speeds of the incoming and reflected corpuscles ( and hence the difference in densities ) can be made arbitrarily small while still maintaining the same effective gravitational force.

Their slogan, which is Latin, Plus esse, quam simultatur translates to Mere at være, end at synes (" More to be, than to seem ") in Danish, meaning that the soldier's capabilities do not have to be widely recognized or boasted-they are only more effective if unknown.

More so, the enzyme purifies as a consequence of crystallization, making cycles of crystallization an effective final purification step.

* More effective at low frequencies.

* More effective above 2000 Hz

More importantly, the realistic effective range of the 8mm Lebel was increased ( due to the bullet's flatter trajectory ) to approximately using open sights.

More recent research suggests that strobe lights are not effective at waking sleeping adults with hearing loss and suggest that a different alarm tone is much more effective.

More recent dental texts strongly support the use of amalgam ; " In summary, dental amalgam is a highly successful material clinically and is very cost effective, but alternatives such as cast gold and esthetic restorative materials are now very competitive in terms of frequency of use.

More recently, farm sanitation has greatly improved and effective testing has been developed for bovine tuberculosis and other diseases, making other approaches to ensuring safety of milk more feasible ; however, pasteurization continues to be widely used to prevent infected milk from entering the food supply.

More formally, it is the theoretical temperature at which entropy reaches its minimum value.

More general results from the study were that precipitation and water use lead to above-ground primary production, solar radiation and temperature lead to belowground primary production ( roots ), and temperature and water lead to cool and warm season growth habit.

More explicitly, an energy T < sub > R </ sub > S is not available to do useful work, where T < sub > R </ sub > is the temperature of the coldest accessible reservoir or heat sink external to the system.

More sophisticated models can be made using a combination of etched sheets of brass and low temperature castings.

More generally, a higher temperature and a stronger magnetic field lead to a smaller fraction of the electrons in the superconducting band and consequently a longer London penetration depth of external magnetic fields and currents.

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.

More generally, for an attenuator at a physical temperature, the noise temperature is, giving a noise factor of:

More generally, the actual rate at which the temperature drops with altitude is called the environmental lapse rate.

More specifically, the temperature difference, produces an electric potential ( voltage ) which can drive an electric current in a closed circuit.

More recently the temperature fell to-10. 8c ( 12. 6f ) on 20 December 2010.

More recently, switches have had heaters installed in the vicinity of the points so that the temperature of the rails in these areas can be kept above freezing.

More recently, researchers have proposed that they may have helped to control the body temperature of the animal, in a similar way to the sails of the large carnivorous Spinosaurus or of the pelycosaur Dimetrodon ( and the ears of modern elephants and jackrabbits ).

More sophisticated stations may also measure the ultraviolet index, solar radiation, leaf wetness, soil moisture, soil temperature, water temperature in ponds, lakes, creeks, or rivers, and occasionally other data.

More advanced temperature profiles have been developed which use an oscillating ( usually sine or square wave ) heating rate ( Modulated Temperature Thermal Analysis ) or modify the heating rate in response to changes in the system's properties ( Sample Controlled Thermal Analysis ).

More advanced dive computers also include additional information into the calculations, for example, the water temperature or the diving cylinder pressure.

More often the temperature is taken in the mouth, axilla, ear or groin.

More than 2 W continuous-wave ( CW ) operation at-10 degrees Celsius heat-sink temperature was also reported in 1998 from a VCSEL array consisting of 1, 000 elements, corresponding to a power density of 30 W / cm < sup > 2 </ sup >.

More conventional ovens have a simple thermostat which turns the oven on and off and selects the temperature at which it will operate.

More sophisticated ovens may have complex, computer-based controls allowing a wide variety of operating modes and special features including the use of a temperature probe to automatically shut the oven off when the food is completely cooked to the desired degree.

More advanced processes, such as laser cutting and jet torches, use sudden, high temperature to shatter the stone.