Heat-kernels and functional determinants on the generalized cone

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions thereby placed on the $A_{5/2}$ coefficient. The computation of functional determinants is also addressed. General formulas are given and known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.

The Number of Symbol Comparisons in QuickSort and QuickSelect

International audienceWe revisit the classical QuickSort and QuickSelect algo-rithms, under a complexity model that fully takes into account the ele-mentary comparisons between symbols composing the records to be pro-cessed. Our probabilistic models belong to a broad category of informa-tion sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources. We establish that, under our conditions, the average-case complexity of QuickSort is O(n log 2 n) [rather than O(n log n), classically], whereas that of QuickSelect remains O(n). Explicit expressions for the implied constants are provided by our combinatorial–analytic methods