Let 袚 be a finite group acting topologically freely on a smooth closed manifold M , and suppose that we are given a nonlocal elliptic operator 1 $$ A = \\sum\\limits_{g \\in \\Gamma } {T\\left( g ight)A\\left( g ight):C^\\infty \\left( {M,\\mathbb{C}^n } ight) ...
The index formula for the Hecke group H_5Mathematics - Group Theory11F06The present article gives the index formula of the principal congruence subgroups of the Hecke group H_5doi:10.48550/arXiv.1401.0775Lang, Cheng LienLang, Mong Lung
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That paper also gave an incorrect, although sufficiently accurate, procedure for calculating the group refractive index. Here we describe the results of a more rigorous derivation of the group index that takes proper account of the Lorentz-Lorenz formula, and we demonstrate that deviations from the...
In cell A5, enter the formula:=ds1.group (int ($$group_ result_ Sequence-1)/5), extending vertically, with left parent set to A4 and set the parent cell of B5 to A5 ( or the default). Explanation: the meaning of the formula is to group every 5 records in the parent shipmethod...
(*strict equality*)|EPathPofexp|EPLamofexp|EAppFormulaofexp*exp(*path equality*)|EI|EDirofdir|EAndofexp*exp|EOrofexp*exp|ENegofexp(*CCHM interval*)|ETranspofexp*exp|EHCompofexp*exp*exp*exp(*Kan operations*)|EPartialofexp|EPartialPofexp*exp|ESystemofexpSystem.t(*partial functions*...
Wang, H.: L 2 -index formula for proper cocompact group actions, preprint. http://arxiv.org/abs/1106.4542H. Wang, L2-index formula for proper cocompact group actions. J. Noncom- mut. Geom. 8 (2014), no.2, 393-432.Wang, H.: L2-index formula for proper cocompact group actions,...
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Add formula:SUM_AGG(Volume)/TOTAL(SUM_AGG(Volume),1,"sum") , use the Volume summarized in groups to obtain the proportion of the total volume, name the calculation index as "proportion in group", and click "OK". As shown in the figure below: Note: the field in the formula needs to...
Drag the data columns from ds1 into the table, and enter the formula SUM(D2) in cell D3, and SUM(D3) in cell D4, as shown in the following figure. Left Parent Cell Setting Set the left parent cell of cells B3 and D3 to B2, and cells A4 and D4 to A2. Taking the left pa...