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外微分     
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  exterior differential
     Applications of Fractional Exterior Differential in Three-Dimensional Space
     分数外微分在三维空间中的应用
短句来源
     Application of exterior differential in field theory
     外微分在场论中的应用
短句来源
     TEACHING DISCUSSION ABOUT SUBSUMING THE FOUR FAMOUS FORMULAS OF CALCULUS BY USING EXTERIOR PRODUCT AND EXTERIOR DIFFERENTIAL
     利用外积、外微分统一微积分中四大公式的教学探讨
短句来源
     It is easier to master Newton-Leibniz formula、green formula、Gauss formula and Stokesformula through one formula by using exterior product and exterior differential.
     利用外积、外微分将牛顿·莱布尼兹公式、格林公式、奥·高公式和斯托克斯公式可用一个公式表示,便于掌握。
短句来源
     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.
     以李群的Maurer-Cartan形式的外微分为辛结构,给出了辛李群的概念,进而讨论了辛李群的特殊性质。
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  exterior derivative
     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.
     利用外微分分离了Kerr_Newman度规下的中微子方程,为弯曲时空量子场论的研究提供了方便
短句来源
     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.
     利用外微分给出了Robertson-Walker度规下的中微子方程并分离了该方程,为弯曲时空旋量场的研究提供了方便.
短句来源
  exterior differentiation
     Application of Exterior Differentiation in Electrodynamics
     外微分在电动力学中的应用
短句来源
     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.
     本文研究光学特征函数,利用外微分运算,由光学特征函数导出了光的辛结构性质。
短句来源
  external differential
     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.
     腔面未镀膜情况下,测试10支条宽100μm,腔长1mm的激光器样品,连续输出功率超过1W,阈值电流密度为330~490A/cm2,外微分量子效率为55%~78%,中心发射波长为(808±3)nm。
短句来源
     The lowest threshold current and peak wavelength are 92 mA and849.2 nm, respectively. The external differential quantum efficiency is 11%.
     最低阈电流92mA、激射波长849.2nm,外微分量子效率11%.
短句来源
     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.
     用液相外延法研制了GaAs-(AlGa)As大光腔激光器,并给出它的一些主要参数如脉冲光功率、光束发散角、波长、外微分量子效率等的测试结果.
短句来源
     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.
     对于条宽 1 0 0 μm、腔长 1 mm腔面未镀膜的激光器 ,连续输出光功率为 1 .2 W,阈值电流密度为 41 0 A/cm2 ,外微分量子效率为 62 % ,并进行了可靠性实验。
短句来源
     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.
     器件为条宽100μm,腔长1600μm未镀膜激器。 室温阈值电流密度为221A/cm2,激射波长为1.08μm,连续波工作最大光功率输出为2.74W(双面),外微分效率为88%,经50oC,1000h老化,仍有>1.2W的光功率输出。
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  exterior differential
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.
      
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  exterior derivative
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.
      
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  exterior differentiation
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.
      
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  external differential
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%.
      
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