Rockenbauer has further explained the relativistic

Dirac equation and how it gave a perfect description of the electromagnetic properties of an electron in his study.

are the 4 x 4

Dirac [gamma]-matrices where [I.sub.2] and 0 are the 2 x 2 identity and null matrices respectively, and |[psi]> is the four component

Dirac [6,7] wave-function, h is the normalized Planck constant, c is the speed of light in vacuum, i = [square root of -1], and:

By comparing the second-order differential equation that has been obtained from

Dirac equation with Schrodinger equation for the well-known potential such as Scarff-II, Poshel-Teller, Morse, 3D-oscillator, and shift-oscillator potentials, the gauge field potential can be written based on the well-known superpotentials that are related to the mentioned potentials.

In the previous work [9], it was shown that D'Eath and Halliwell's [2] quantization of the

Dirac field in the closed FRW cosmology satisfies requirements similar to those just mentioned in the scalar field context; namely, the complex structure chosen in [2] is invariant under the symmetries of the field equations (which of course include SO(4), the isometry group of the spatial sections) and admits a unitary implementation of the dynamics.

Current [I.sub.DS] versus concentration of IgE is plotted at a constant gate voltage near the

Dirac point.

The study showed how this naturally leads to the formation of stacked sets of topological surface states and 3D

Dirac fermions in the transition-metal dichalcogenides.

Soon after

Dirac presented his relativistic electron theory, (6,7) O.

The inverse problem and the spectral properties of

Dirac operators were investigated in detail by many authors [1, 2, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 29, 30, 31, 32].

In the wake of developments in science and technology, the (1 + 1)-dimensional nonlinear

Dirac (NLD) equations have emerged as useful models in many physical problems, such as Bose-Einstein condensates in honeycomb optical lattices [4] and the gap solitons in nonlinear optics [5].

[36] proposed a combination of the wavelet, DCT, and

DIRAC for EEG artifact removals, while their results could not tell how effective the method was in a qualitative manner.

One of the main aims of Clifford analysis is to study the function-theoretical properties of the null-solutions of the

Dirac operator which is invariant under rotations but not under reflections [7].

Addressing the needs of emergency and first responders, Lawrence Livermore National Laboratory and

Dirac Solutions Inc.

Cuatro desarrollos teoricos que, a juicio de Colyvan, auspician el despliegue de (a) y (b), son: (i) la teoria de la gravitacion newtoniana, la cual, prima facie, caracteriza galaxias con cantidades inconsistentes de masa; (ii) la oceanografia descriptiva, que parece postular oceanos de profundidad finita e infinita; (iii) el calculo temprano, con sus cantidades infinitesimales fluctuantes; y (iv) la teoria cuantica de

Dirac, que incorpora una tecnica de normalizacion de vectores basada en la integracion de funciones inconsistentes.

Euclidean Clifford analysis offers a function theory with the

Dirac operator, which is an elegant generalization to higher dimensions of holomorphic functions in the complex plane.