In light of the physical interpretation, a vector field with constant zero divergence is called incompressible or solenoidal – in this case, no net flow can occur across any closed surface.

One can express the divergence as a particular case of the exterior derivative, which takes a 2-form to a 3-form in R < sup > 3 </ sup >.

Linear systems display sensitive dependence on initial conditions in the case of divergence.

Conversely, Elijah Delmedigo ( c. 1458 – c. 1493 ), in his Bechinat ha-Dat endeavored to show that the Zohar could not be attributed to Shimon bar Yochai, arguing that if it were his work, the Zohar would have been mentioned by the Talmud, as has been the case with other works of the Talmudic period, that had bar Yochai known by divine revelation the hidden meaning of the precepts, his decisions on Jewish law from the Talmudic period would have been adopted by the Talmud, that it would not contain the names of rabbis who lived at a later period than that of Simeon ; and that if the Kabbalah was a revealed doctrine, there would have been no divergence of opinion among the Kabbalists concerning the mystic interpretation of the precepts.

A beam may, for example, have an elliptical cross section, in which case the orientation of the beam divergence must be specified, for example with respect to the major or minor axis of the elliptical cross section.

Non-Gaussian beams also exhibit this effect, but a Gaussian beam is a special case where the product of width and divergence is the smallest possible.

The more general case is described by Poynting's theorem above, where it occurs as a divergence, which means that it can only describe the change of energy density in space, rather than the flow.

In case of any divergence of view at the chapter, the side taken by the Abbot of Cîteaux was always to prevail.

In case of an incompressible flow — for instance of a liquid, or a gas at low Mach numbers ; but not for sound waves — the velocity v has zero divergence:

In this case the flow can be determined completely from its kinematics: the assumptions of irrotationality and zero divergence of the flow.

In the antiferromagnetic case, a divergence is observed in the staggered susceptibility.

for all natural numbers n. The double natural logarithm indicates that the divergence might be very slow, which is indeed the case, see Meissel – Mertens constant.

More precisely, they were only able to perform the calculation when the theory contains one less flavor of chiral matter than the number of colors in the special unitary gauge group, because in the presence of fewer flavors an unbroken nonabelian gauge symmetry leads to an infrared divergence and in the case of more flavors the contribution in equal to zero.

KL divergence is a special case of a broader class of divergences called f-divergences.

In this case, divergence is facilitated by the absence of gene flow, which tends to keep populations genetically similar.

In this case, divergence occurs despite limited interbreeding where the two diverging groups come into contact.

A few standards also have English versions, but in case of any divergence of interpretation, the Chinese text shall prevail.

Note that Green's first identity above is a special case of the more general identity derived from the divergence theorem by substituting:

In the case of divergent evolution, similarity is due to the common origin, such as divergence from a common ancestral structure or function has not yet completely obscured the underlying similarity.

This " divergence problem " was solved in the case of quantum electrodynamics during the late 1940s and early 1950s by Hans Bethe, Tomonaga, Schwinger, Feynman, and Dyson, through the procedure known as renormalization.

The divergence between total product-values and total production prices on the whole was, Marx believed, probably not so very large, in an open, competitive market within the domestic economy, where enormous price-value discrepancies were ordinarily impossible to maintain commercially for any length of time ( among other things because in that case people would exchange very large amounts of work for very small amounts of work ; they might be prepared to do that for some products, but not for most of them, because they simply could not afford to do so ).

* stable: in the case of hydrostatic equilibrium of a ball of perfect fluid ( e. g. in a model of a stellar interior ), the expansion, shear, and vorticity all vanish, and a radial divergence in the acceleration vector ( the necessary body force on each blob of fluid being provided by the pressure of surrounding fluid ) counteracts the Raychaudhuri scalar, which for a perfect fluid is.

Some linguists believe the case for either interpretation is about equally strong ; they have been called the " skeptics ".

However, as is often the case with the interpretation of scripture, there is dispute on this matter.

ECMA and ISO require that all patents essential to implementation be made available under " reasonable and non-discriminatory ( RAND ) terms ", but interpretation of this has led to much controversy, particularly in the case of Mono.

One reason for the popularity of the dissociation constant in biochemistry and pharmacology is that in the frequently encountered case where x = y = 1, K < sub > d </ sub > has a simple physical interpretation: when = K < sub > d </ sub >, = or equivalently /(+)= 1 / 2.

Their sentences were supposed to be simple interpretations of the traditional customs, but effectively it was an activity that, apart from formally reconsidering for each case what precisely was traditionally in the legal habits, soon turned also to a more equitable interpretation, coherently adapting the law to the newer social instances.

Other support in the authorities also exists for this interpretation of the standards enunciated in the findings presented to the House of Lords regarding M ' Naghten's case:

The complexity penalty has a Bayesian interpretation as the negative log prior probability of,, in which case is the posterior probabability of.

However, some courts ( such as German courts ) have less emphasis on the particular facts of the case than common law courts, but have more emphasis on the discussion of various doctrinal arguments and on finding what the correct interpretation of the law is.

Clark Warburton is credited with making the first solid empirical case for the monetarist interpretation of business fluctuations in a series of papers from 1945 .< sup > p.

Cases which raise serious questions of interpretation and application of the European Convention on Human Rights, a serious issue of general importance, or which may depart from previous case law can be heard in the Grand Chamber if all parties to the case agree to the Chamber of the Court relinquishing jurisdiction to the Grand Chamber.

The vialis case in Eskimo – Aleut languages has a similar interpretation, used to express movement using a surface or way.

The term is widely needed to support the more esoteric requirements of a number of disciplines including in philosophy when a concept is not available ; in biology when a genus is not available ; in law when a special and unique interpretation of a case or authority will be needed on-the-fly ; in town-planning where there is no existing use-case ; in intellectual property rights where there is no defining characteristic ; and in politics and societal norms where there is no real authority perceived.

In 3rd edition, to tie the game into the World of Darkness line, this was the case because those were the beliefs ; other editions distance themselves from this interpretation, simply taking place in a world where those beliefs happen to be true.

The judge hears all the witnesses and any other evidence presented by the parties of the case, assesses the credibility and arguments of the parties, and then issues a ruling on the matter at hand based on his or her interpretation of the law and his or her own personal judgment.

Especially in the case of full rank, see the section below on Geometric interpretation.

Despite the common interpretation, the location was not midway between the national seats of DC and of the Italian Communist Party ( PCI ) in Rome ( in this case to symbolize the end of the Historic Compromise, the alliance between DC and PCI sought by Moro ), but towards the Tiber River, near the Ghetto.

Federal courts must defer to state courts in their the interpretation of state laws, and sometimes " certify " a question of state law in a case pending before it to the highest state court in the state, if state law is unsettled on the issue.

Because no postcranial remains ( bones below the skull ) have been discovered, it is as of yet unknown whether Sahelanthropus tchadensis was indeed bipedal or two-footed, although claims for an anteriorly placed foramen magnum suggests that this may have been the case, some paleontologists have disputed this interpretation of the basicranium.

V. Yatsko's interpretation ( Y-interpretation ) can be effectively used to compute threshold values in case it is necessary to distinguish subsets within a set of objects ( e. g. successful / unsuccessful applicants, developed / underdeveloped regions, etc.

When a vector field represents force, the line integral of a vector field represents the work done by a force moving along a path, and under this interpretation conservation of energy is exhibited as a special case of the fundamental theorem of calculus.

the remaining flesh of the animal ( in later rabbinical interpretation as one of the twenty four priestly gifts ) was later consumed by the priest and his family, except when the priest himself was the offerer ( such as in community offerings, and in the case of the Day of Atonement ), when it would be burnt outside the sanctuary.

However, the V-T Theory does not provide an entirely satisfactory framework of interpretation as clearly shown in the case of modern English with its universal ' you ' instead of a grammatical V-T binary system.