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

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 is the pertinent excerpt from the December 11 opinion of the Florida Supreme Court: However, according to Nelson Lund, one might argue that the Florida Supreme Court was discussing the " protest provisions of the Florida Election Code, whereas the issues in Bush v. Gore arose under the contest provisions.

Here, is density, u, v, and are the components of wind velocity, and is the 2-dimensional ( i. e. horizontal-component-only ) del.

Here the substitution function ( v < sub > 1 </ sub >,..., v < sub > n </ sub >) =

Here is Leibniz's argument: Let u ( x ) and v ( x ) be two differentiable functions of x.

Apollonius's genius reaches its highest heights in Book v. Here he treats of normals as minimum and maximum straight lines drawn from given points to the curve ( independently of tangent properties ); discusses how many normals can be drawn from particular points ; finds their feet by construction ; and gives propositions that both determine the center of curvature at any point and lead at once to the Cartesian equation of the evolute of any conic.

Here at Lamlash on April 25th 1829 part of the clearance ( 86 souls ) when embarking on the brig Caledonia ( 196 ton ) the Rev. A. Mackay preached from The Mound ( opposite ) formed by the departing his text " Casting all your care upon him: for he careth for you " 1st Peter ch. 5 v. 7.

Here the hessian of F < sup > 2 </ sup > at v is the symmetric bilinear form

where v < sub > x </ sub >, v < sub > y </ sub > and v < sub > z </ sub > are the Cartesian components of the velocity v. Here, H is short for Hamiltonian, and used henceforth as a symbol for energy because the Hamiltonian formalism plays a central role in the most general form of the equipartition theorem.

Here is a video showing how they are made ... " http :// www. youtube. com / watch? v = AqfWabob0-4

Here v ( the number of elements of X, called points ), b ( the number of blocks ), k, r, and λ are the parameters of the design.

Here, r is attained for x taken to be the Perron-Frobenius eigenvector v. The proof requires that values f on the other vectors are less or equal.

Here, dƒ is the exterior derivative of the function ƒ ; it is a 1-form taking argument v < sub > x </ sub >.

Here the < var > x </ var >- velocity remains constant ; it is always equal to < var > v </ var > cos < var > θ </ var >.

Here, " intent " means either purpose or " knowledge with substantial certainty ," as elucidated in Garratt v. Dailey.

He was nicknamed Tifa before reaching the age of 4 because he loved trains and would often shout " Ide lokomotifa " ( properly pronounced " Ide lokomotiva " meaning " Here comes the locomotive ") because he had problems pronouncing phoneme " v ".

Here the court distinguished the case from Balfour v Balfour on the fact that Mr and Mrs Merritt, although still married, were estranged at the time the agreement was made and therefore any agreement between them was made with the intention to create legal relations.

Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

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 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

Here k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.

Here I < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.

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 < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.

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

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here, R < sub > ij </ sub > is the Ricci tensor.

# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.

Here n is the number of electrons / mole product, F is the Faraday constant ( coulombs / mole ), and ΔE is cell potential.

which is natural in the variable N. Here the functor Hom ( N, F –) is the composition of the Hom functor Hom ( N, –) with F. This isomorphism is the unique one which respects the limiting cones.

Here, F means " draw forward ", + means " turn right 60 °", and − means " turn left 60 °".

Here, intense solar radiation by day, which raises the surface when dry to a temperature approaching 27 ° C ( 80 ° F ), alternates with severe frost by night.

Here one starts with some covariant additive functor F and some module X.

Here E and F ( or equivalently, G and ) are real constants which depend on the initial conditions.

The Gang's All Here " w. D. A. Esrom m. Theodore F. Morse & Arthur Sullivan

Here F = J + I, where I is the nuclear spin.

Here we show that the size of the ( sub ) tree rooted at any node x of degree d in the heap must have size at least F < sub > d + 2 </ sub >, where F < sub > k </ sub > is the kth Fibonacci number.

Here, Bragg was stationed with three future Union Army generals that he came to consider close friends: George H. Thomas and John F. Reynolds ( both of whom were lieutenants who reported to Bragg ) and William T. Sherman.

Here h is the zero-field height ( or unreduced height ) of the barrier, e is the elementary positive charge, F is the barrier field, and ε < sub > 0 </ sub > is the electric constant.

* Cairns, J. F., Here I stand: statements, 1966

Here the sign of the distances is taken negative if and only if the line segment DX ( X = F, G, H ) lies completely outside the triangle.

:: 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.

A second type of short octave used the keys B C # D # C D E F # G to play the G major scale G A B C D E F # G. Here, the " exotic " bass notes C # and D # are sacrificed to obtain the more essential A and B.

Here, E played C, the front half of the F # key played D, and the ( less accessible ) rear half played F #.

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

for any torsion sheaf F. Here j is any open immersion of X into a scheme Y with a proper morphism g to S ( with f = gj ), and as before the definition does not depend on the choice of j and Y. Cohomology with compact support is the special case of this with S a point.

Here is a list of Farnborough Town and Farnborough F. C.