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 C is either empty or Prikry generic over K ( so it has order type ω and is cofinal in κ ) and unique except up to a finite initial segment.

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 ω = 2πf is the angular frequency ( and f the frequency ), and i = is the imaginary unit, so that I is a phasor.

Here the Hilbert space is L < sup > 2 </ sup >( R ), the space of square integrable functions on R, and the energy operator H is defined by ( assuming the units are chosen such that &# 8463 ; = m = ω = 1 )

Here n ( G ) is the order of G, α ( G ) is the independence number, ω ( G ) is the clique number, and χ ( G ) is the chromatic number.

Here ω ( Y ) is the-valued function obtained by duality from pairing the one-form ω with the vector field Y, and X ( ω ( Y )) is the Lie derivative of this function along X.

Here, d < sub > F </ sub > is called the degree ( or dimension ) of F. It is given by < ref > While the ω < sub > i </ sub > are not uniquely defined by F, Selberg's result shows that their sum is well-defined .</ ref >

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 d is the spacing between diffracting planes, is the incident angle, n is any integer, and λ is the wavelength of the beam.

Here the grape is known as Melon d ' Arbois or Gamay blanc and is sometimes blended with Savagnin.

Here ∂ is a rounded d called the partial derivative symbol.

Here later François-René de Chateaubriand worked on his Mémoires d ' Outre-Tombe as the guest of duchesse Claire de Duras.

As Penman explains: '“ After I ’ d finished Here Be Dragons, I knew I wanted to continue the story .... At first I ’ d planned to write one book in which Simon de Montfort would share top billing with Llewelyn Fawr ’ s grandson, Llewelyn ap Gruffydd, who later wed Simon ’ s daughter.

Here, volunteer vessels record position, depth and time data using their standard navigation instruments, and then the d ata is processed on the server for speed of sound, tidal and other corrections.

Here again, in a position where he could observe and review affairs, he performed valuable service, especially under the presidency of the duc d ' Audiffred Pasquier, who was glad to have Sorel's advice in the most serious crises of internal politics.

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.

:" Le réseau d ' ici " ( The Network from Here )

Inscription in ledger-line: hic jacet d ( omin ) a Emma mater Venerabilissimi patris et domini D ( omi ) ni Joh ( ann ) is Stafford dei gra ( tia ) Cantuariensis Archiepi ( scopi ) qu ( a ) e obiit quinto die mensis Septembris anno d ( omi ) ni Mille ( n ) simo ccc. mo quadra ( gen ) s ( i ) mo vi. o cui ( us ) anime p ( ro ) piciet ( ur ) de ( us ) am ( en ) (" Here lies Lady Emma mother of the most venerable father and lord, Lord John Stafford by the grace of God Archbishop of Canterbury who died on the 5th day of the month of September in the one thousandth three hundredth and sixth year of our Lord on whose soul may God look with favour amen "

Here d < sub > X </ sub > and d < sub > Y </ sub > denote the metrics on X and Y respectively.

Here d < sub > H </ sub > denotes Hausdorff distance between subsets in M and the isometric embedding is understood in the global sense, i. e. it must preserve all distances, not only infinitesimally small ones ; for example no compact Riemannian manifold of negative sectional curvature admits such an embedding into Euclidean space.

Here, A is the vector potential and d represents the gauge-covariant derivative, and F the field strength or curvature form on the fiber bundle.

Here, more fortunate than the husband of Bathsheba, the duc d ' Agénois was only wounded, and returned to the court in glory.

Here his style combined something of Filippo Lippi with its original elements, and he received co-operation from Giusto d ' Andrea.

Here, d is the exterior derivative of the a < sup > th </ sup > component of x, which is a scalar field ( so this isn't a pure abstract index notation ).

In mathematical morphology, binary images are subsets of an Euclidean space R < sup > d </ sup > or the integer grid Z < sup > d </ sup >, for some dimension d. Here are some examples of widely used structuring elements ( denoted by B ):

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, 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.