This is a technical appendix to “Adaptive estimation of covariance matrices via Cholesky decomposition (arXiv:1010.1445). AMS 2000 subject classifications: Primary 62H12; secondary 62F35, 62J05.

We prove one decomposition theorem of complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets. 2000 Mathematics Subject Classification. Primary 32W20, 32U15

The primary decomposition theorem due to Krohn and Rhodes KR which has been considered as one of the fundamental results in the theory of automata and semigroups states that every automaton is homomorphic to a cascaded de composition wreath product of simpler automata of two kinds reset automata and permutation automata If the automaton is non counting and correspond ingly its transformation se...

Amazonian forest fragments and secondgrowth forests often differ substantially from undisturbed forests in their microclimate, plant-species composition, and soil fauna. To determine if these changes could affect litter decomposition, we quantified the mass loss of two contrasting leaf-litter mixtures, in the presence or absence of soil macroinvertebrates, and in three forest habitats. Leaf-lit...

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

Fine root decomposition represents a large carbon (C) cost to plants, and serves as a potential soil C source, as well as a substantial proportion of net primary productivity. Coarse roots differ markedly from fine roots in morphology, nutrient concentrations, functions, and decomposition mechanisms. Still poorly understood is whether a consistent global pattern exists between the decomposition...

By making use of some rather elementary techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Lauricella’s hypergeometric function F (r) A in r variables (r = 2, 3, 4, . . .) and also with other multiple hypergeometric functions. Alternative derivations of some of these decomposition formulas by means of (for ex...

We describe a new approach to the canonical decompositions of 3–manifolds along tori and annuli due to Jaco–Shalen and Johannson (with ideas from Waldhausen) — the so-called JSJ–decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus–torus theorems, and the theory of Seifert fibrations does not need to be developed i...

The cell suppression problem (CSP) is one of the most widely applied methods for tabular data protection. Given a set of primary cells to be protected, CSP aims at finding a set of secondary cells to be additionally removed to guarantee that estimates of values of primary cells fall out of a predefined protection interval. From a computational point of view, CSP is very challenging even for tab...

We discuss features extracted from a wavelet packet decomposition for image classification. Statistical features computed from wavelet packet coefficients are compared to structural features which are derived from an image dependent wavelet packet decomposition subband structure. Primary application area is the classification of pit pattern structures in zoom-endoscopic colon imagery, while res...