Yes,covariant derivative on fermions.a new froof of positive mass theorem.

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By dirac operator, you mean the covariant derivative on fermions?

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Furthermore, under the assumption that the covariant derivative of the sectionssatisfies the Lipschitz condition with L-average along the geodesic, the estimates of the radiiof convergence balls of Newton\'s method and uniqueness balls of singular points around thesingular points of sections on Riemannian manifolds are given.

當(dāng)截面的協(xié)變導(dǎo)數(shù)滿足沿著測地線的關(guān)于取正值非減可積函數(shù)L-平均的Lipschitz條件條件時自拍偷拍2018，本文給出關(guān)于截面的Newton法的收斂球半徑的估計日本黄页网战，及在奇異點附近的關(guān)于截面的奇異點的唯一性球的半徑的估計。

In Riemannian manifolds, one studies Riemannian metric, covariant derivative, Riemannian connection, basic properties of the Riemann curvature tensor, curvature forms etc.

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Under the assumptionthat the covariant derivative of the sections satisfies the Lipschitz condition with L-averagealong the piecewise geodesic, a unified convergence criterion for Newton\'s method and theradii of the uniqueness balls of singular points around the initial points of sections are es-tablished.

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The inconsistencies of dimensional reduction and naive dimensional regularization in dealing withChern-Simons-matter theory are analyzed.The consistent dimensional regularization combiningwith higher covariant derivative regularization is adopted to consider Chern-Simons field theorycoupled to complex scalar and spinor field.All the local parts of one-loop two-point functionsand three-point functions are computed.Slavnov-Taylor identity is combined with these explicitcalculation results to give the one-loop local effective action.The finite gauge invariant quantumcorrection is shown and finite wave function renormalization constant for each field is defined.Thelocal part of one-loop three gauge field vertex is especially evaluated and it is verified that thereexists a renormalization choice compatible with BRST symmetry.

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Physics concepts, theorems as well as principles are primary content of physics learning, those knowledge take on the forms by proposition . In chapter 3, the study revealed that physics proposition are mainly obtained by reasoning (inductive reasoning such as tallying method, differentiation method and covariant method, deductive reasoning such as negative expression of hypothetical inference, affirmative expression of hypothetical inference ).Then by the means of experiment, the different condition needed when applying those reasoning was explored.

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In product qualiy judgement of sample Lests, when the objective indicators get its values required destructive tasting, it is usually use the covariant index from non-destructive testing to forecast.

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Vector analysis, Dyads, index notation, covariant and contravariant derivatives, Christoffel symbols, Riemann tensor, hydro-dynamical field equation.

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According to Lorentz transformation,the relativistic covariant of electromagnetic field tensor and 4-dimension forces,and the relativistic invariance of electric charge,it can be directly proved that a moving magnetic monopole will be acted- by a magnetic Lorentz force ,and that the magnetic Lorentz force has the same accuracy as the Coulomb low.

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