Here | u | and | v | denote the length of the strings respectively.

Here we denote with the Bernoulli number of the second kind ( only because the historical reason of formation of this article ) which differ from the first kind only for the index 1.

Here a < sub > 1 </ sub >, ..., a < sub > m </ sub > denote the rows of the matrix A.

( Here V0, V1, and V2 denote verbs and Ny denotes a noun.

Here we denote a pair of corresponding lower and upper adjoints by f < sup > ∗</ sup > and f < sub > ∗</ sub >, respectively.

Here a and l denote radius and length of the wire, and Y is a constant that depends on the distribution of the current in the wire: Y =

Here ε and µ denote dielectric constant and magnetic permeability of the medium the conductors are embedded in.

Here, ran and dom denote the range and the domain, respectively.

Here the chain rule has been applied, and the subscripts denote partial derivatives (, ).

Here, the term energy is used in the generalized sense of signal processing to denote a variance of the signal.

Here the vertical bars denote the absolute value.

Here FG: D → D and GF: C → C, denote the respective compositions of F and G, and I < sub > C </ sub >: C → C and I < sub > D </ sub >: D → D denote the identity functors on C and D, assigning each object and morphism to itself.

Here d < sub > X </ sub > and d < sub > Y </ sub > denote the metrics on X and Y respectively.

Here, let R < sup > n + 1 </ sup > denote the real coordinate space of n + 1 dimensions, and regard the landscape to be painted as a hyperplane in this space.

Here we denote transpose by an apostrophe.

Here " T +" or " T −" denote that the result of the test is positive or negative, respectively.

Here, it has to be noted that the military manuals of Asclepiodotus and Aelian use the term lochos to denote a file in the phalanx.

Here, we use to denote the braiding map associated to the permutation ( represented as a product of disjoint cyclic permutations ).

Here let denote the Riemann tensor, regarded as a tensor in.

Here,, and will be used to denote the initial velocity, the velocity along the direction of < var > x </ var > and the velocity along the direction of < var > y </ var >, respectively.

Here there may be an analogy with cancer: we can detect cancers by their rapidly accelerating growth, determinable only when related to the more normal rate of healthy growth.

Here the Pennsylvania militia skirmished with the British, but soon fled.

Here I am face to face with the primeval stuff ''.

Here, as in all sectors of the economy, quality and justice are both dependent on the right of the individual to deal directly with his employer if he so chooses.

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 they are, with my comments and judgments.

Here he put a small man, whose missing hands might have left his function doubtful, until comparison with the first sketches showed that when the artist came back to the beginning, this was to be the closing figure of the party of `` forty-niners '', and was to hold a basket.

Here P represents the value of the stream in state P and Q the cost of operating the stage with conditions Q.

Here the absent sitter makes a `` date '' with a communicator ( someone close to him who is deceased ), asking him to `` come in '' at a certain hour, when a channel will be open for him.

Here I was accompanied by Mrs. Okamoto ( Fumio's mother ), her son, Mr. Washizu ( a prospective student with whom I have been corresponding for more than a year ), and Mr. Nishima, one of the science teachers.

Here again it was vacation time and there were many things I could not see, but I was able to visit with a professor who is famous in Japanese circles and be guided through the grounds by his assistant.

And, Here, I'll take this, I was before her, you wait on me now or I don't bother with it, see!!

Here and there on work table or pedestal stood a shape with a sheet or a tarpaulin draped over it.

Here was a man with an enormous gift for living as well as thinking.

Here was another human who understood the stupidity of quarreling with the inevitable.

Here he often met with the elderly Aristide Cavaillé-Coll.

Here Alexios III eventually surrendered, with Euphrosyne, to Marquis Boniface of Montferrat, who was establishing himself as ruler of the Kingdom of Thessalonica.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Here he hired the famous condottiero Braccio da Montone with the task of reducing the resistance of the other pretender, Louis III of Anjou, and his forces led by Muzio Attendolo Sforza.

Here she repudiated her earlier adoption of Alfonso and, with support from Martin V, named Louis III as her heir instead.

Here Hume tackles the problem of how liberty may be reconciled with metaphysical necessity ( otherwise known as a compatibilist formulation of free will ).

Here we can store 6 elements they are stored linearly but starting from first row linear then continuing with second row.

Here for nearly four years he labored with the greatest perseverance and industry.

Here Salieri returned to his collaboration with the young Boccherini who crafted an original plot.

Here, there is a two-manual and pedal board electric organ, with speakers at the front and sides of the church.