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The common notation for the divergence ∇· F is a convenient mnemonic, where the dot denotes an operation reminiscent of the dot product: take the components of ∇ ( see del ), apply them to the components of F, and sum the results.
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common and notation
though this is something of a ( fairly common ) abuse of notation.
The common notation of chain rule is due to Leibniz.
Such notation involving operators is common in physics and algebra.
If certain coordinate systems are used, for instance, polar-toroidal coordinates ( common in plasma physics ) using the notation ∇ × F will yield an incorrect result.
In this system, the number ten may be written as " A ", " T " or " X ", and the number eleven as " B " or " E " ( another common notation, introduced by Sir Isaac Pitman, is to use a rotated " 2 " for ten and a reversed " 3 " for eleven ).
The greatest common divisor is often written as GCD ( a, b ) or, more simply, as ( a, b ), although the latter notation is also used for other mathematical concepts, such as two-dimensional vectors.
In RPN, the operator is placed after its operands, as opposed to the more common infix notation where the operator is placed between its operands.
In common mathematical notation, the digit string can be of any length, and the location of the radix point is indicated by placing an explicit " point " character ( dot or comma ) there.
Historically, several number bases have been used for representing floating-point numbers, with base 2 ( binary ) being the most common, followed by base 10 ( decimal ), and other less common varieties, such as base 16 ( hexadecimal notation ), as well as some exotic ones like 3 ( see Setun ).
Many people in cultures which have notation still learn by ear and ear training, often through a musicianship course at a music conservatory or college, is common practice among those who use notation extensively.
A remark on the notation: Because it is common to consider several congruence relations for different moduli at the same time, the modulus is incorporated in the notation.
This would have been clearer if the notation a < sub > n </ sub > b had been used, instead of the common traditional notation.
In everyday usage infix notation is the most common, however other notations also exist, such as the prefix and postfix notations.
These peculiarities are the most common in the plays of Plautus, and their notation should make initial readings a bit easier.
Unlike more common systems for transliterating Arabic, SATTS does not provide the reader with any more phonetic information than standard Arabic orthography does ; that is, it provides the bare Arabic alphabetic spelling with no notation of short vowels, doubled consonants, etc.
Gibbs introduced the now common notation for the dot product and the cross product of two vectors, and he was largely responsible for the development of the vector calculus techniques still used today in electrodynamics and fluid mechanics.
Siteswap is by far the most common juggling notation.
A common alternative notation is and for positive semidefinite and positive definite matrices, respectively .</ ref > The notion comes from functional analysis where positive-semidefinite matrices define positive operators.
It is common to score music for the whistle using standard musical notation.
Abc notation is the most common means of electronic exchange of tunes.
common and for
John Adams asserted in the Continental Congress' Declaration of Rights that the demands of the colonies were in accordance with their charters, the British Constitution and the common law, and Jefferson appealed in the Declaration of Independence `` to the tribunal of the world '' for support of a revolution justified by `` the laws of nature and of nature's God ''.
`` we the People of the United States, in order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common Defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America ''.
This almost trivial example is nevertheless suggestive, for there are some elements in common between the antique fear that the days would get shorter and shorter and our present fear of war.
During the decade that followed, the common man, as that piece put it, grew uncomfortable as the Voice of God and fled from behind Saint Woodrow ( Wilson ) only to learn from Science, to his shocked relief that after all there was no God he had to speak for and that he was just an animal anyhow -- that there was a chemical formula for him, and that too much couldn't be expected of him.
The men who speculate on these institutions have, for the most part, come to at least one common conclusion: that many of the great enterprises and associations around which our democracy is formed are in themselves autocratic in nature, and possessed of power which can be used to frustrate the citizen who is trying to assert his individuality in the modern world ''.
Now this concern for the freedom of other peoples is the intellectual and spiritual cement which has allied us with more than forty other nations in a common defense effort.
A common meeting ground is desirable for those nations which are prepared to assist in the development effort.
It purported to be a reasonably serious attempt at a treatment of jazz musicians, their aims, their problems -- the tug-of-war between the `` pure '' and the `` commercial '' -- and seemed a promising vehicle, for the two men shared a common interest in jazz.
The headquarters of Morgan was on a farm, said to have been particularly well located so as to prevent the farmers nearby from trading with the British, a practice all too common to those who preferred to sell their produce for British gold rather than the virtually worthless Continental currency.
For a time it appeared that a common European army might be created, but the project for a European Defense Community was rejected by the French National Assembly in 1954.
By comparison, Stone Harbor bird sanctuary's allies seem less formidable, for aside from the Audubon Society, they are mostly the snowy, common and cattle egrets and the Louisiana, green, little blue and black-crowned herons who nest and feed there.
So be it -- then we must embark on a crash program for 200-megaton bombs of the common or hydrogen variety, and neutron bombs, which do not exist but are said to be the coming thing.
for what had happened on the common was only terror and flight ; ;
Such payments shall be made to small domestic producers of lead as long as the market price for common lead at New York, New York, as determined by the Secretary, is below 14-1/2 cents per pound, and such payments shall be 75 per centum of the difference between 14-1/2 cents per pound and the average market price for the month in which the sale occurred as determined by the Secretary.
Leasing a car is not as common or as popular as renting a car in Europe, but for long periods it will be unquestionably more economical and satisfactory.
The common codes, for religious action as such and in their ethical aspects for everyday moral behavior, bind the devotees together.
While other conditions might be even more effective in bringing about a change from immobility to mobility in Kohnstamm reactivity, it is our hypothesis that all such conditions would have as a common factor the capacity to induce an attitude in the subject which enabled him to divorce himself temporarily from feelings of responsibility for his behavior.
Law became a conscious process, something more than simply doing justice and looking to local customs and a common morality for applicable norms.
He is a trustee for the common good, however feeble the safeguards which the positive or municipal law of property provides against his misuse of that share of the common fund, wisely or unwisely, entrusted to his keeping.
a common habit or uniform prescribed for all citizens ; ;
common and divergence
This divergence between American English and British English once caused George Bernard Shaw to say that the United States and United Kingdom are " two countries divided by a common language "; a similar comment is ascribed to Winston Churchill.
One common practice ( not discussed above ) is to handle that divergence via Dirac delta and Dirac comb functions.
Ethnicity, being largely developed by a divergence in geography, language, culture, genes and similarly, point of view, has the potential to be countered by a common source of information.
Dialectology treats such topics as divergence of two local dialects from a common ancestor and synchronic variation.
He declared that the first work worthy to be called opéra-comique was Philidor's 1759 Blaise le savetier, and he described the gradual divergence of Italian and French notions of comic opera, with verve, imagination and gaiety from Italian composers, and cleverness, common sense, good taste and wit from the French composers.
There are several theories about what Hellenic dialect groups may have existed between the divergence of early Greek-like speech from the common Proto-Indo-European language.
Roughly speaking, high sequence identity suggests that the sequences in question have a comparatively young most recent common ancestor, while low identity suggests that the divergence is more ancient.
The first may be more accurately called a " diverging universe " whereby two versions of the universe share a common history up to a point of divergence.
By applying a molecular clock to the amount of mitochondrial DNA sequence divergence between the two, it was estimated that Troglodytes pacificus and Troglodytes troglodytes last shared a common ancestor approximately 4. 3 million years ago, long before the glacial cycles of the Pleistocene, thought to have promoted speciation in many avian systems inhabiting the boreal forest of North America.
This is due to a pseudogene's shared ancestry with a functional gene: in the same way that Darwin thought of two species as possibly having a shared common ancestry followed by millions of years of evolutionary divergence ( see speciation ), a pseudogene and its associated functional gene also share a common ancestor and have diverged as separate genetic entities over millions of years.
In northern Iran, there is a region of range overlap with the Red-headed Bunting and natural hybrids are common although molecular data indicates that there is considerable genetic divergence between the two species.
However, this film then follows the common divergence from Shaw's plot when she returns to Love at the end.
Lumpers are more willing to admit techniques like mass lexical comparison or lexicostatistics, and mass typological comparison, and to tolerate the uncertainty of whether relationships found by these methods are the result of linguistic divergence ( descent from common ancestor ) or language convergence ( borrowing ).
St. Thomas definitively expressed the doctrine that, after some controversies between Scotists and Thomists upon minor points and subtleties, and with some divergence of opinion upon unimportant details, is now the common teaching of Catholic theologians and philosophers.
The most common type of variational Bayes, known as mean-field variational Bayes, uses the Kullback – Leibler divergence ( KL-divergence ) of P from Q as the choice of dissimilarity function.
The three described varieties in C. comosum could be an example of this convergent evolution of leaf shape among the forest-dwelling varieties from species of disparate origin, leading to the species C. comosum being polyphyletic, instead of the traditional view of morphological divergence among the varieties within the species with the assumption of a common origin ( monophyly ).
The ancient common origin and more recent divergence of Russian and Ukrainian make it difficult to establish the degree of mixing in a vernacular of this sort.
This could explain the divergence from a common ancestor of Galápagos tortoises and mockingbirds, and of the rheas which remained distinct species with their overlapping territories.
Legislative independence has been paralleled by a growing divergence between Australian and English common law in the last quarter of the 20th century.
In 1978, the High Court declared that it was no longer bound by decisions of the Judicial Committee of the Privy Council, the last appeals to the Privy Council were abolished by the Australia Acts of 1986, and there is now a measure of divergence between the two common law systems.
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.
Dialectology treats such topics as divergence of two local dialects from a common ancestor and synchronic variation.
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