Here-p-is-a-vector-of-prices-and-X-is-a-vector-o

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Here and p

Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in blue , and secret values in boldface red :

Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion

beautiful whelks, a penny a lot .” “ Here ‘ s ha ‘ p ‘ orths ,” shouts the perambulating confectioner.

Here, the sum is taken over all different states under permutations p acting on N elements.

Here, sgn ( p ) is the signature of each permutation ( i. e. + 1 if p is composed of an even number of transpositions, and − 1 if odd.

This is an approximate equation that is derived from the incompressible Navier-Stokes equations ( written in spherical coordinate system ) and describes the motion of the radius of the bubble R as a function of time t. Here, μ is the viscosity, p the pressure, and γ the surface tension.

Here the random vector is the vector r of random returns on the individual assets, and the portfolio return p ( a random scalar ) is the inner product of the vector of random returns with a vector w of portfolio weights — the fractions of the portfolio placed in the respective assets.

Here she was probably being worshipped before Zeus arrived in the Aegean, but certainly in Minoan-Mycenaean times ( Burkert 1985 p 171 ; Nilsson 1950: 53 ).

Here p is the momentum of the particle, m is the mass of the particle, E is the kinetic energy of the particle, and ħ is the reduced Planck's constant.

Here q is the coordinate and p is the momentum, mv.

Here, Szpilman !’ A hand grabbed me by the collar, and I was flung back and out of the police cordon .

( 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 there are two equations μ < sub > sol </ sub >( T, p )

Here I < sub > p </ sub > denotes a p × p identity matrix.

Here a refined theory of ( in effect ) a right adjoint to reduction mod p — the Néron model — cannot always be avoided.

Here " l " stands for any prime number different from p, where p is the characteristic of F < sub > q </ sub >.

Here and is

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.

Here and vector

Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).

Here are the point coordinates in the canonical system, whose origin is the center of the ellipse, whose-axis is the unit vector coinciding with the major axis, and whose-axis is the perpendicular vector coinciding with the minor axis.

Here is the Jones vector ( is the imaginary unit with ).

Here a rank 1 tensor ( matrix product of a column vector and a row vector ) is the same thing as a rank 1 matrix of the given size.

Here is the tensor derivative of the velocity vector, equal in Cartesian coordinates to the component by component gradient.

Here is a-dimensional vector, is the known-dimensional mean vector, is the known covariance matrix and is the quantile function for probability of the chi-squared distribution with degrees of freedom.

Here the first three vectors are linearly independent ; but the fourth vector equals 9 times the first plus 5 times the second plus 4 times the third, so the four vectors together are linearly dependent.

Here the numerator is a symmetric matrix while the denominator is a number, the squared magnitude of v. This is a reflection in the hyperplane perpendicular to v ( negating any vector component parallel to v ).

Here one is working with a vector space over the complex numbers.

Here, each vector Y < sub > j </ sub > of the f ' basis is a linear combination of the vectors X < sub > i </ sub > of the f basis, so that

Here is a known vector, and is an unknown vector of numbers x < sub > i </ sub > yet to be determined.

Here + is addition either in the field or in the vector space, as appropriate ; and 0 is the additive identity in either.

Here the vectors are elements of a given vector space V over a field K, and the coefficients are scalars in K.

Here one considers a modification of the directional derivative by a certain linear operator, whose components are called the Christoffel symbols, which involves no derivatives on the vector field itself.

:: Here, as in the classical theory V is a braided vector space of dimension n spanned by the E ´ s, and σ ( a so-called cocylce twist ) creates the nontrivial linking between E ´ s and F ´ s.

Here, represents a vector of states and represents the corresponding flux tensor.

* The dimension of the – vector space is the same for all prime ideals of R .< ref > Here, is the residue field of the local ring .</ ref >

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