where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.

where and denotes the portfolio value at time t.

respectively, where e < sub > x </ sub >, e < sub > y </ sub >, e < sub > z </ sub > denotes the cartesian basis vectors ( all are orthogonal unit vectors ) and A < sub > x </ sub >, A < sub > y </ sub >, A < sub > z </ sub > are the corresponding coordinates, in the x, y, z directions.

where denotes the complex conjugate of.

denotes the rank-one operator that maps the ket to the ket ( where is a scalar multiplying the vector ).

Just as kets and bras can be transformed into each other ( making into ) the element from the dual space corresponding with is where A < sup >†</ sup > denotes the Hermitian conjugate ( or adjoint ) of the operator A.

where Z denotes J, Y, H < sup >( 1 )</ sup >, or H < sup >( 2 )</ sup >.

where C < sub > α </ sub > denotes I < sub > α </ sub > or e < sup > απi </ sup > K < sub > α </ sub >.

where ε denotes the Levi-Civita symbol, the metric tensor is used to lower the index on F, and the Einstein summation convention implies that repeated indices are summed over.

where denotes the length of a string p.

where J denotes the Jacobian matrix of partial derivatives of ƒ and is the induced norm on the matrix.

for every automorphism φ of G ( where φ ( H ) denotes the image of H under φ ).

where denotes the vector cross product and square brackets denote evaluation in the rotating frame of reference.

This functional relationship is often denoted y = f ( x ), where f denotes the function.

The common notation for the divergence ∇· F is a convenient mnemonic, where the dot denotes an operation reminiscent of the dot product: take the components of ∇ ( see del ), apply them to the components of F, and sum the results.

where the star denotes complex conjugation.

A *( B *( C * D )) where A, B, C, D are partially transparent image layers and "*" denotes a compositing operator ( with the left layer on top of the right layer ).

With this view it turns out that the extractor property is equivalent to: for any source of randomness that gives bits with min-entropy, the distribution is-close to, where denotes the uniform distribution on.

In mathematics and abstract algebra, a group is the algebraic structure, where is a non-empty set and denotes a binary operation called the group operation.

where ζ denotes the Riemann zeta function ( see Lehmer ; one approach to prove the inequality is to obtain the Fourier series for the polynomials B < sub > n </ sub >).

where denotes the largest integer that is not greater than x.

where denotes Newton's gravitational constant,

The Catholics had the largest cemetery, near the Neversink River where Main Street ran south ; ;

The largest true alphabet where each letter is graphically independent is probably Georgian, with 41 letters.

Only small, isolated sections are left standing with the largest portion lying in a pile of rubble that stretches the length of where the aqueducts once stood.

The aorta (; from Greek ἀορτή-aortē, from ἀείρω-aeirō " I lift, raise ") is the largest artery in the body, originating from the left ventricle of the heart and extending down to the abdomen, where it bifurcates into two smaller arteries ( the common iliacs ).

The main occupation of the islanders is fishing and this is where the largest tuna fishery in Sicily can be found.

The Liberals now found themselves with 59 members holding the balance of power in a Parliament where Labour was the largest party but lacked an overall majority.

In the first millennium AD, an urban tradition developed in the Khmer region of Cambodia, where Angkor grew into one of the largest cities ( in area ) of the world.

Only ethnic dominance, the case where the largest ethnic group comprises a majority of the population, increased the risk of civil war.

Their classification is divided into the small and large rank cases, where the rank is the largest rank of an odd abelian subgroup normalizing a nontrivial 2-subgroup, which is often ( but not always ) the same as the rank of a Cartan subalgebra when the group is a group of Lie type in characteristic 2.

One of the largest and oldest summer leagues in the United States is found in the Northern Virginia area where teams from 47 pools compete against each other every summer.

The largest massacre was at Antioch, where 5, 000 Druze religious leaders were killed, followed by that of Aleppo.

For bassists with smaller hands, the large spaces between pitches may present a significant challenge, especially in the lowest range, where the spaces between notes are largest.

Detroit was ( and still is ) the largest city bordering Canada, where alcohol remained legal during Prohibition.

The industry is concentrated mainly in Guayaquil, the largest industrial center, and in Quito where in recent years the industry has grown considerably, this city is also the largest business center of the country.

For cases where electrons are shared ( covalent bonds ) between atoms with large differences in electronegativity, the electron is assigned to the atom with the largest electronegativity in determining the oxidation state.

One of the country's largest sheep stations, located near where Butler lived, is named " Erewhon " in his honour.

The Duchy of Aquitaine was the largest and richest province of France ; Poitou ( where Eleanor spent most of her childhood ) and Aquitaine together were almost one-third the size of modern France.

The number of normalized floating point numbers in a system F ( B, P, L, U ) ( where B is the base of the system, P is the precision of the system to P numbers, L is the smallest exponent representable in the system, and U is the largest exponent used in the system ) is:

It was the largest party in Dáil Éireann at every general election from the 1932 general election until the 2011 general election, when it suffered the worst defeat of a sitting government in the history of the Irish state, a loss described as " historic " in its proportions, where it saw its electoral support base diminished by 75 %, as a reaction to the intervention, and in the running of the Irish economy, of the International Monetary Fund and the European Central Bank in November 2010.

Virginia, the largest colony, deserved recognition, and New England — where the fighting began — realized it needed Southern support.

In his opinion, those born between the periods of 1947-1966 were the Baby Boomers, where in Canada they were the largest boom of the industrialized world ( relative to population ).

Following the bird's extinction, remains of the Great Auk increased dramatically in value, and auctions of specimens created intense interest in Victorian Britain, where 15 specimens are now located, the largest number of any country.