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 N < sub > x </ sub > is the number of x atoms per volume, λ the electron escape depth, θ the analyzer angle, T the transmission of the analyzer, I ( t ) the electron excitation flux at depth t, dΩ the solid angle, and δt is the thickness of the layer being probed.

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.

Music critic Jon Savage pinpointed Be Here Now as the moment where Britpop ended ; Savage said that while the album " isn't the great disaster that everybody says ," he noted that " t was supposed to be the big, big triumphal record " of the period.

Here u ( x, t ) is the temperature of the rod at position x and time t and α is a constant that depends on how fast heat diffuses through the rod.

* The ' I Didn ’ t Know The Way To Kings Cross When I First Came Here But Look At Me Now ' Book By William Rushton, Author, Artist And Beer-Drinker Extrodinary William Rushton ( New England Library, 1966 )

Here the t denotes the matrix transpose.

Here A < sub >–</ sub > and A < sub >+</ sub > are the absorbances of LCP or RCP, respectively ; ω is the modulator frequency – usually a high acoustic frequency such as 50 kHz ; t is time ; and δ < sub > 0 </ sub > is the time-dependent wavelength shift.

Here G is final average grain size, G < sub > 0 </ sub > is the initial average grain size, t is time, m is a factor between 2 and 4, and K is a factor given by:

Cooder says, " Here is some music for a place you don ’ t know, up a road you don ’ t go.

So my agent found Alice Doesn ’ t Live Here Anymore.

Here is a quoted text from PA web site: “ The Press Association supplies services to every national and regional daily newspaper, major broadcasters, online publishers and a wide range of commercial organisations .” Overall, in a system where all different media organizations gather their stories from the same source, then we can ’ t really call that system pluralist.

Here she is, blessed with a gift, with the opportunity to rock and give and she's running on some bulls ** t?

Here N ( t ) is the quantity at time t, and N < sub > 0 </ sub >

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

Here, the right hand side is clearly not convergent for any non-zero value of t. However, by truncating the series on the right to a finite number of terms, one may obtain a fairly good approximation to the value of for sufficiently small t. Substituting and noting that results in the asymptotic expansion given earlier in this article.

Producer Susskind and actor Harvey Keitel would work together again on Martin Scorsese's Alice Doesn ’ t Live Here Anymore ( 1974 ).

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 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 are suggestions for the frankfurter trimmings: 1.

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

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, 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.

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 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.