Here ℓ is the rank of the covariance matrix.

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 are suggestions for the frankfurter trimmings: 1.

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.

Here Acts 12: 21-23 is largely parallel to Antiquities 19. 8. 2 ; ( 2 ) the cause of the Egyptian pseudo-prophet in Acts 21: 37f and in Josephus ( War 2. 13. 5 ; Antiquities 20. 8. 6 ); ( 3 ) the curious resemblance as to the order in which Theudas and Judas of Galilee are referred to in both ( Acts 5: 36f ; Antiquities 20. 5. 1 ).

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 the expression has the value 1 if m = 0 and 0 otherwise ( Iverson bracket ).

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 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 the server, 192. 168. 1. 1, specifies the IP address in the YIADDR ( Your IP Address ) field.

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 Oscan, Greek, and Latin languages were in contact with one another ; according to Aulus Gellius 17. 17. 1, Ennius referred to this heritage by saying he had " three hearts " ( Quintus Ennius tria corda habere sese dicebat, quod loqui Graece et Osce et Latine sciret ).

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, according to an allegorical parable, " The Choice of Heracles ", invented by the sophist Prodicus ( c. 400 BC ) and reported in Xenophon's Memorabilia 2. 1. 21-34, he was visited by two nymphs — Pleasure and Virtue — who offered him a choice between a pleasant and easy life or a severe but glorious life: he chose the latter.

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.

# 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 the last product means that a first electron, r < sub > 1 </ sub >, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus.

Here, there are four energy levels, energies E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, E < sub > 4 </ sub >, and populations N < sub > 1 </ sub >, N < sub > 2 </ sub >, N < sub > 3 </ sub >, N < sub > 4 </ sub >, respectively.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

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

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

Here ε is known as the relative permittivity tensor or dielectric tensor.

Here is a notational shortcut for tensor contraction with the metric tensor.

Here T is the stress – energy tensor, G is the Einstein tensor, and c is the speed of light,

Here is the operator which symmetrizes or antisymmetrizes a tensor, depending on whether the Hilbert space describes particles obeying bosonic or fermionic statistics.

Here R is the Riemann curvature tensor.

( Here ⊗ refers to the tensor product over K and id is the identity function.

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

Here a metric ( or Riemannian ) connection is a connection which preserves the metric tensor.

Here is the relativistic rest energy density of the fluid, is the fluid pressure, is the four-velocity of the fluid, and is the Minkowski metric tensor with signature.

Here the tensor product is the usual tensor product of vector spaces, and the mapping object is the vector space of linear maps from one vector space to another.

Here, the Einstein notation is used, so repeated indices indicate summation over indices and contraction with the metric tensor serves to raise and lower indices:

Here, and are the symmetric and alternating tensor product spaces.

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

Here is the absolute value of the determinant of the metric tensor g < sub > ij </ sub >.

Here, is the absolute value of the determinant of the matrix representation of the metric tensor on the manifold.