Here is called a spherical harmonic function of degree ℓ and order m, is an associated Legendre polynomial, N is a normalization constant, and θ and φ represent colatitude and longitude, respectively.

Here L is the orbital angular momentum, n, ℓ and m are the principal, azimuthal and magnetic quantum numbers respectively.

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 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 χ is not a number as before but a tensor of rank 2, the electric susceptibility tensor.

Here he stepped at once into the foremost rank as a preacher, and his church was thronged with thoughtful men of all classes in society and of all shades of religious belief.

Here he established himself by rapidly rising through the ranks, and, after a military campaign against El Salvador, held the rank of colonel at the age of 28.

* Generic rank 2 distributions on 5-manifolds: Here G =

Here is a list of current-model CCM skates, as listed by rank of performance:

Here is a list of current-model CCM sticks, as listed by rank of performance

Here the rank of Q < sub > i </ sub > should be interpreted as meaning the rank of the matrix B < sup >( i )</ sup >, with elements B < sub > j, k </ sub >< sup >( i )</ sup >, in the representation of Q < sub > i </ sub > as a quadratic form:

Here he threw himself heart and soul into the cause of the French Revolution, and took part under Dumouriez and Pichegru in the campaigns of 1792 and 1793, and was soon promoted to the rank of brigadier-general.

Here he followed revivalist principles by preaching to all people willing to listen, regardless of religious denomination or social rank ; attracting note as a populist pulpit orator, religious author and scholar, and a friendly counsellor.

Here, electors may rank all candidates in the order of their preference.

Here, the verb + has a rank of 0 0 0, the left argument has a rank of 0, and the right argument has a rank of 1 ( with a dimension of 3 ).

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.

As explained above, Gaussian elimination writes a given m × n matrix A uniquely as a product of an invertible m × m matrix S and a row-echelon matrix T. Here, S is the product of the matrices corresponding to the row operations performed.

Here D is a traceless matrix such that αDe gives the derivative of e with respect to z.

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

Here the t denotes the matrix transpose.

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, || ||< sub > 2 </ sup > is the matrix 2-norm, c < sub > n </ sub > is a small constant depending on n, and ε denotes the unit round-off.

* the algebra of all n-by-n matrices over the field ( or commutative ring ) K. Here the multiplication is ordinary matrix multiplication.

Here M < sup > T </ sup > denotes the transpose of the matrix M. One can easily verify that the set of all such matrices forms a group.

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( Here and are matrices the same size as ( is the identity matrix ); and is the square root of − 1 ).

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

Here, is the Hankel matrix of the sequence.

Here ω < sup > α </ sup >< sub > β </ sub > defines a k × k matrix of one-forms on U. In fact, given any such matrix the above expression defines a connection on E restricted to U. This is because ω < sup > α </ sup >< sub > β </ sub > determines a one-form ω with values in End ( E ) and this expression defines ∇ to be the connection d + ω, where d is the trivial connection on E over U defined by differentiating the components of a section using the local frame.

Here dt is the matrix of one-forms obtained by taking the exterior derivative of the components of t.

Here it is assumed that the mixing matrix is square ().

Here π < sub > n </ sub > is a homotopy group, GL ( R ) is the direct limit of the general linear groups over R for the size of the matrix tending to infinity, B is the classifying space construction of homotopy theory, and the < sup >+</ sup > is Quillen's plus construction.

Here, we only describe the method based on the computation of the eigenvectors and eigenvalues of the rotation matrix.