Higher complexity (mathsf L _t -formulas arise in considerations of topological betweenness notions in Hausdorff continua—this being taken up in [3, 4].
Higher complexity (mathsf L _t -formulas arise in considerations of topological betweenness notions in Hausdorff continua—this being taken up in [3, 4]. (ii) When centroids exist in antisymmetric, weakly disjuctive (tau )-basic relations, they are unique, by Theorem 5.0.6.
For χ2-distributed inverse temperature, we obtain a generalized fluctuation theorem based on q-exponentials, whereas for other temperature distributions more complicated formulae arise.
In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33].
In practical applications of the formula, problems arise in finding the appropriate numerical values of power-to-heat ratios.
Third, cross-meshed series with (overline{Delta m/z}) values not matching any molecular formula can arise if the atoms of the homologue units do not form subsets.
Already in the late parts of the Ṛgveda (10.90.9), we hear that the verses (ṛk), the songs (sāma), and the ritual formulas (yajus) arose from the primordial sacrifice offered by the gods.
This formula, which arises from a spectral decomposition of the graph Laplacian associated with the full process, gives an explicit criterion for choosing the k most important edges in the graph, for any 0 < k < m.
To this end, two classes of solution schemes for the coupled problem are considered: (i) Global product formula algorithm arising from operator split which leads to a two step solution procedure, and (ii) an implicit coupled algorithm which employs simultaneous solution of the coupled system of equations.
