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One must keep in mind that the Jacobian determinant (J k_x,k_y,k_z)) given by Eq. (15) is zero for special points ({bf k}= k_x, k_y, k_z)), where (nabla _{bf k}varepsilon ({bf k})=0).
This is the case for the (Gamma -point and usually for points on the Brillouin zone boundary [19], and even the transformation (14) could be not continuously differentiable for special points.
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For special point defects such as oxygen vacancies or interstitials, the local stress in their vicinity could become dominant given an adequate concentration.
They propose a method for generating sets of special points in the Brillouin zone.
Our bounds for the extreme inner products of special points in such designs allow new lower bounds on the minimum possible odd cardinality.
For these special points the Jacobian (Jleft( k_{x},k_{y},k_{z}right)) is zero, and the reverse transformation involving (widetilde{J}left( epsilon,vartheta,varphi right)) is not defined in a rigorous mathematical interpretation.
This submembrane (cortical) cytoskeleton of muscle cells is generally similar to the cortical cytoskeleton of nonmuscle cells, except for in several special points, that is in the projection of Z-disc and M-line on the membrane.
Pack, J. D. & Monkhorst, H. J. Special points for Brillouin-zone integrations.
Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations.
McAlpine awarded the song five out five stars, and gave it "special points" for its "faux-classical synth solo" in the middle.
But he also implies that Gov. Christie deserves special points for the fact that he is not particularly Islamophobic by the standards of contemporary conservatives and would prefer less harsh drug laws -- though again, none of this is based on anything Springsteen has ever said or done.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com