In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

Here the sum is extended over all ( k, j ) with and with

Here, overall cost and benefit to society is defined as the sum of the economic benefits and costs for all parties involved.

Here, dq < sub > k </ sub >/ T represents a very small exchange of heat energy at temperature T. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.

Here, addition involves summing the points in the respective lines of the parents: if the sum is an even number, then the resulting figure's line will have two points, and if the sum is odd then the line will have one point.

( Here the term κ-additive means that, for any sequence A < sub > α </ sub >, α < λ of cardinality λ < κ, A < sub > α </ sub > being pairwise disjoint sets of ordinals less than κ, the measure of the union of the A < sub > α </ sub > equals the sum of the measures of the individual A < sub > α </ sub >.

( Here, the product is taken over all primes p ; in the following, a sum or product taken over p always represents a sum or product taken over a specified set of primes, unless noted otherwise.

Here the maps i: A ∩ B ↪ A, j: A ∩ B ↪ B, k: A ↪ X, and l: B ↪ X are inclusion maps and denotes the direct sum of abelian groups.

Here we wrote τ ( χ ) for the Gauss sum

Here we sum over the i regions into which µ-space is divided.

Here γ is the famous Euler – Mascheroni constant, which has a similar definition involving a sum over all integers ( not just the primes ).

Here is the Dedekind sum

Here at + b is the trend line, so the sum of squared deviations from the trend line is what is being minimised.

Here is the Legendre symbol, which is a quadratic character mod p. An analogous formula with a general character χ in place of the Legendre symbol defines the Gauss sum G ( χ ).

" Here, parity refers to the XOR sum of all the bits.

Here, if he wishes, the Briton may, for the small sum of half a dollar, stupefy himself with food.

" When the Governor-General wasn't forthcoming with the sum, she elected to stay ; commenting that unlike in Paris, " Here, I reign like Josephine wife ; I hold first place.

Here, B < sub > n </ sub > are the Bernoulli numbers, ζ ( z ) is Riemann's zeta function and σ < sub > p </ sub >( n ) is the divisor sum function, the sum of the p < sup > th </ sup > powers of the divisors of n. In particular, one has

Here the definition of geo-strategy is used in a more limited regional frame wherein the sum of geographic factors interact to influence or to give advantage to one adversary, or intervene to modify strategic planning as well as political and military venture.

( Here, the graph Γ ( T ) is a linear subspace of the direct sum, defined as the set of all pairs, where x runs over the domain of T ).

" Here the sum of both the first and second distich is 5699.

Here, on the hottest day, it is cool beneath the stone and fresh from the water flowing in the sluices at the bottom of the vaults.

Here in these little rooms -- or stages arched open to the sky and river -- they choose a few lines out of the hundreds they may know and sing them according to one of the modes into which Persian music is divided.

Here, on a desk, is a stack of pamphlets representing the efforts of some of the best men of the day to penetrate these questions.

Here, if anywhere, it is not wholly incontrovertible.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Here an important caveat is in order.

Here, then, is what Swift would have called a modest proposal by way of a beginning.

But this we know: Here is a great life that in every area of American politics gives the American people occasion for pride and that has invested the democratic process with the most decent qualities of honor, decency, and self-respect.

Here is a word of advice when you go shopping for your pansy seeds.

Here then is our problem: aircraft are vital to winning a war today because they can perform those missions which a missile is totally incapable of performing ; ;

Here is truly a `` Great Recording of the Century '', and its greatness is by no means diminished by the fact that it is not quite perfect.

Here is an original kedgeree recipe from the Family Club's kitchen:

Here is the promise of a vacation trip they can afford.

Here is where things stand today:

Here the Af distance is 2.44 Aj.

Here the pulmonary vein, as in type 2,, is noted to draw away from the bronchus, and to follow a more direct, independent course to the hilum ( figs. 23, 24 ).

Here the number of trials is a random variable, not a fixed number.

Here there is a specific preventive component which applies in a more generalized sense to any casework situation.

( Here an entry is a form plus the information that pertains to it.

Here again, in the written language it is possible to help the reader get his stresses right by using underlining or italics, but much of the time there is simply reliance on his understanding in the light of context.

Here is the best short explanation of the origins of the Cold War that has been written.