It is easier to master Newton-Leibniz formula、green formula、Gauss formula and Stokesformula through one formula by using exterior product and exterior differential.

We have taken exterior differential to Maurer-Cartan form of Lie Group as symplectic structure and given the definition of Symplectic Lie group,further we have discussed the special properties of Symplectic Lie group.

The neutrino equation under the Kerr_Newman metric is separated by the exterior derivative in this paper, which provides a convenient tool for the study of the curved space quantum field theory.

The neutrino equation under the Robertson Walker metrtic is given and separated by the exterior derivative,which provides a convenient tool for the study of the curved space spinor field.

In this paper characterstic function of optics was studied and property of symplectic structre was deduced from the characteristic function by using the opertion of exterior differentiation.

The samples have output power of 1 to 2W, threshold current density (Jth) of 330 to 450A/cm2 and external differential efficiency (η d) 55％ to 78％ , lasing wavelength λ =808± 3nm, which are in good agreement with the designed requirement.

GaAs- (AlGa) As large optical cavity lasers have been fabricated using liquid phase epitaxy method and its main parameters, have been measured, such as laser pulse power, beam divergence angle, wave length and external differential quantum efficiency etc.

The laser with 100 μm line width and 1 mm cavity length has output power of 1.2 W, threshold current density ( J th ) of 410 A/cm 2 and external differential efficiency ( η d) of 62% at laser wavelength of 808 nm. The experiments on the reliability were also carried out.

The devices exhibited a peak power of 2.74W (both faces) at 1.08μ m with threshold current density of Jth=221A/cm2 and external differential quantum efficiency of η D=88％ during room－ temperature continuous－ wave lasing. The life measurements indicate that the device remain output power >1.2W after stably operating over 1000 h at 50oC.

In this paper, we construct the algebra of differential forms with exterior differential satisfying d3=0 on the two-dimensional quantum plane assuming that the homomorphism defining first-order differential calculus is linear in variables.

In this note, the essence and some supplements for the unified definition of divergence, rotation and gradient advanced by Tai have been presented based on the method of exterior differential form with an expression of vectors of tensors.

Applications of fractional exterior differential in three-dimensional space

In order to obtain the expression, the exterior differential method was presented.

An exterior differential calculus for spinor forms quite analogous to the well known tensorial Cartan calculus is developed which renders possible the direct spinorial calculation of the Weyl- and Ricci-spinors.

The vanishing of its exterior derivative must be included in the necessary and sufficient conditions for a metric to be a solution of the source-free Einstein-Maxwell equations.

Over the years a third-rank antisymmetric tensor field, derived as the exterior derivative of a potential, has been considered as a part of string theory Lagrangians.

The centre of the operator algebra generated by Hodge's star and the exterior derivative

If the ghost number is positive or zero there is a bijective correspondence between the BRST classes and those of the exterior derivative along the gauge orbits.

Finally, the BRST cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits, as in the irreducible case.

This implies construction of an exterior differentiation, a graded algebra[Figure not available: see fulltext.] of forms and partial derivatives.

A quasi-associative generalization of noncommutative differential geometry is introduced by defining a covariant exterior differentiation of forms.

They are commonly used in quantum field theory in spite of the fact that, unlike ordinary traces on matrices, they are neither cyclic nor do they commute with exterior differentiation, thus giving rise to tracial anomalies.

finitely generated algebra or a local analytic algebra A over a field k, which was defined in [9].ωA is a finitely generated module over the De Rham-algebra ΩA with an exterior differentiation d.

From such an interaction field, the gauge potential field in the internal space, one may derive a gauge force field by exterior differentiation.

A record external differential efficiency of 88% and the characteristic temperature of threshold current, 145 K, were obtained.

It is shown that both the threshold current density and the external differential quantum efficiency become N-shaped functions of temperature as the distribution of carriers in the active region changes from nonequilibrium to equilibrium one.

VCSELs with current aperture of 3 μm in diameter demonstrate single-mode lasing in 980-nm range with the threshold current of 0.6 mA, maximum output power up to 4 mW, and external differential efficiency of 68%.

This latent instability is not related to the sign of the external differential resistance, so that internal damping factors are necessary in order to prevent its development.

Under pulsed operation, where the device heating is greatly minimized, the InAs QD laser (2?×?2,000?μm2) delivered extremely high output power (both facets) of up to 1.22?W at 20?°C, at high external differential quantum efficiency of 96%.