The method exploits infinitesimal

unitary transformation steps, from which renormalization-group-like flow equations are derived to produce the effective Hamiltonian.

Following this idea, Huarng and Yeh [17] introduced an outstanding

unitary transformation for low-complexity DOA estimation with real-valued computation.

Alhaidari [11-13] applies a

unitary transformation to Dirac equation such that the resulting second-order differential equation becomes Schroodinger-like equation so that comparison with the well-known nonrelativistic problems is transparent.

The link consists of a (constant)

unitary transformation of the [[beta].sup.[mu]] matrices and a projection onto a lower-dimensional subspace.

We have shown via a careful error analysis that it is possible to do this deflation via a structure preserving real orthogonal or

unitary transformation as well as with a Schur complement approach.

QFT can be used in novel image encryption and decryption [17], where the quantum bit numbers of the quantum state |x) are m, [U.sub.QFT] is a unitary operator, and QFT is a [2.sup.m]-dimensional

unitary transformation [18,19].

In this formulation the real part of the dielectric constant [[epsilon].sup./] will lead to an expression for the change in Curie temperature ([T.sub.c]) by the presence of electric field.We make use of

unitary transformation discussed in previous studies [4] which render the most significant first order dipole moment to effect the Curie temperature ([T.sub.c]) with the applied electric field.

When anyons move around each other along braided paths, the motion changes the pattern of the anyons' interactions with each other--a change physicists call a

unitary transformation. This transformation alters what will happen if two anyons collide, so by bumping anyons into each other it's possible to tell that they have moved.

Assume that U is a

unitary transformation that clones, in that U(|a0>) = |aa> for all quantum states |a>.

For example, the

unitary transformation that inverts the amplitude of each basis state is modeled as follows:

The nonrelativistic approximation can be obtained by using the well-known Foldy-Wouthuysen

unitary transformation (FWUF) [45] and by neglecting the spin degree of freedom the nonrelativistic Hamiltonian is given as [25, 26]

He uses a

unitary transformation which yields wave functions which do not undergo Coulomb forces.