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.

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 denotes the largest integer that

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,

We now write Af where Af are distinct complex numbers.

The problem becomes even more complex where an enterprise is engaged in the manufacture of a wide variety of other goods in addition to the heavy electrical equipment.

The term Afroasiatic Urheimat ( Urheimat meaning " original homeland " in German ) refers to the ' hypothetical ' place where Proto-Afroasiatic speakers lived in a single linguistic community, or complex of communities, before this original language dispersed geographically and divided into distinct languages.

* Gaussian integers: those complex numbers where both and are integers are also quadratic integers.

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

Computational fluid dynamics was started as an effort to solve for flow properties around complex objects and has rapidly grown to the point where entire aircraft can be designed using a computer, with wind-tunnel tests followed by flight tests to confirm the computer predictions.

Chapters 24 – 34, while too complex to characterize easily, are primarily concerned with prophecies of a " Messiah ", a person anointed or given power by God, and of the Messiah's kingdom, where justice and righteousness will reign.

Asymmetry can be manifested in the size of the breast, the position of the nipple-areola complex ( NAC ), the angle of the breast, and the position of the inframammary fold, where the breast meets the chest.

where are complex numbers.

where is the Gelfand representation of x defined as follows: is the continuous function from Δ ( A ) to C given by The spectrum of in the formula above, is the spectrum as element of the algebra C ( Δ ( A )) of complex continuous functions on the compact space Δ ( A ).

where ν > − 1 / 2 and z is a complex number.

where and may be taken as arbitrary complex numbers.

A decomposition reaction is the opposite of a synthesis reaction, where a more complex substance breaks down into its more simple parts.

It is now believed that this complex is mostly released from chromosome arms during prophase, so that by the time the chromosomes line up at the mid-plane of the mitotic spindle ( also known as the metaphase plate ), the last place where they are linked with one another is in the chromatin in and around the centromere.

* The idea of " the matrix " in the film The Matrix resembles a complex form of cyberspace where people are " jacked in " from birth and do not know that the reality they experience is virtual.

A complex instruction set computer ( CISC, ) is a computer where single instructions can execute several low-level operations ( such as a load from memory, an arithmetic operation, and a memory store ) and / or are capable of multi-step operations or addressing modes within single instructions.

For instance, low-end versions of complex architectures ( i. e. using less hardware ) could lead to situations where it was possible to improve performance by not using a complex instruction ( such as a procedure call or enter instruction ), but instead using a sequence of simpler instructions.

In May 1971, Hall moved into an apartment complex on Channing Way where she met Patricia Soltysik.

* Prison of Christ-In the north-east side of the complex there is The Prison of Christ, alleged by the Franciscans to be where Jesus was held.

More complex forms of monist dualism also exist, for instance in Hermeticism, where Nous " thought "-that is described to have created man-brings forth both good and evil, dependent on interpretation, whether it receives prompting from the God or from the Demon.

Hazards are routinely divided into natural or human-made, although complex disasters, where there is no single root cause, are more common in developing countries.

If we look for solutions that have the form, where C is a constant, we discover the relationship, and thus must be one of the complex numbers or.

** For example, consider the map ( which is the " realification " of the complex square function ) where U