Some convergence results on quadratic forms for random fields and application to empirical covariances

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (J. Contemp. Math. Anal. 34(2):1?C15) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example of quadratic forms. We show that it is possible to obtain a Gaussian limit when the spectral density is not in L ². Therefore the dichotomy observed in dimension d?=?1 between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in d?>?1.     

Isolated boundary singularities of semilinear elliptic equations

Given a smooth domain ${\Omega\subset\mathbb{R}^N}$ such that ${0 \in \partial\Omega}$ and given a nonnegative smooth function ?? on ???, we study the behavior near 0 of positive solutions of ???u?=?u ^q in ?? such that u =? ?? on ???\{0}. We prove that if ${\frac{N+1}{N-1} < q < \frac{N+2}{N-2}}$ , then ${u(x)\leq C |x|^{-\frac{2}{q-1}}}$ and we compute the limit of ${|x|^{\frac{2}{q-1}} u(x)}$ as x ?? 0. We also investigate the case ${q= \frac{N+1}{N-1}}$ . The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains.     

Sharply k-Transitive Permutation Groups Viewed as Galois Groups

The classification of finite sharply k-transitive groups was achieved by the efforts of Jordan (1873), Dickson (1905), and Zassenhaus (1936). Likewise for other families of finite groups, one expects that they are realizable as Galois groups over the field of rational numbers \mathbbQ{\mathbb{Q}}. In this article, we study some properties of the polynomials f ? \mathbbQ[x]{f \in \mathbb{Q}[x]} such that the Galois group Gal(f) acts sharply k-transitively on its roots.     

Real Interpolation of Generalized Besov-Hardy Spaces and Applications

In this paper we consider generalized Hardy spaces which include classical Hardy spaces and Hardy-Lorentz spaces as special cases. We give real interpolation results for such spaces. As applications, we solve an interpolation problem for Besov spaces of generalized smoothness and prove the boundedness of pseudodifferential operators acting both in these spaces and in the local Hardy spaces. For the latter spaces, we also obtain wavelet decompositions.     

Budgeted matching and budgeted matroid intersection via the gasoline puzzle

Many polynomial-time solvable combinatorial optimization problems become NP-hard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximum-weight matching and maximum-weight matroid intersection with one additional budget constraint. We present the first polynomial-time approximation schemes for these problems. Similarly to other approaches for related problems, our schemes compute two solutions to the Lagrangian relaxation of the problem and patch them together to obtain a near-optimal solution. However, due to the richer combinatorial structure of the problems considered here, standard patching techniques do not apply. To circumvent this problem, we crucially exploit the adjacency relations on the solution polytope and, surprisingly, the solution to an old combinatorial puzzle.     

Consensus of partitions : a constructive approach

Given a profile (family) ?? of partitions of a set of objects or items X, we try to establish a consensus partition containing a maximum number of joined or separated pairs in X that are also joined or separated in the profile. To do so, we define a score function, S _?? associated to any partition on X. Consensus partitions for ?? are those maximizing this function. Therefore, these consensus partitions have the median property for the profile and the symmetric difference distance. This optimization problem can be solved, in certain cases, by integer linear programming. We define a polynomial heuristic which can be applied to partitions on a large set of items. In cases where an optimal solution can be computed, we show that the partitions built by this algorithm are very close to the optimum which is reached in practically all the cases, except for some sets of bipartitions.     

Radon Transform on the Torus

We consider the Radon transform on the (flat) torus \mathbbTⁿ = \mathbbRⁿ/\mathbbZⁿ{\mathbb{T}^{n} = \mathbb{R}^{n}/\mathbb{Z}^n} defined by integrating a function over all closed geodesics. We prove an inversion formula for this transform and we give a characterization of the image of the space of smooth functions on \mathbbTⁿ{\mathbb{T}^{n}} .     

MEKC Determination of Nilutamide in Human Serum Using Sweeping in High Salt Sample Matrix

The determination of the antiandrogen drug nilutamide in human serum by MEKC using flutamide as an internal standard is described. Several parameters influencing the separation, such as the running electrolyte composition concerning the micelle concentration and pH, are discussed. MEKC separation was achieved within 7 min using 50 mM sodium borate pH 9.0 with the addition of 50 mM sodium dodecylsulfate at +20 kV. The proposed method was applied to determination of nilutamide in spiked human serum samples after protein precipitation with acetonitrile. The increasing of sensitivity for determination of nilutamide in serum was done by sweeping in a high salt concentration sample matrix when the injection of a larger volume of sample diluted in 150 mM NaCl was applied. The limit of detection after the preconcentration step for nilutamide was 26 ??g L^?1.     

Mercury characterisation in urban particulate matter

A five-step sequential extraction procedure was proposed in order to assess the distribution of mercury (Hg) forms in urban particulate matter (PM): exchangeable, HCl-soluble, organic-bound, elemental and other slightly soluble Hg species, mercury(II) sulphide (HgS), and residual Hg. This process was applied to the analysis of urban dust samples collected at locations in Prague (Czech Republic) with high traffic density. In addition to sequential extractions, thermal desorption analysis was performed. The differences in Hg concentrations between untreated and thermally treated samples were indicated as the thermally releasable amount of Hg. For the study of PM-adsorbing capacity, Hg vapours were passed through the samples as long as the enrichment of materials was observed. The retained elemental Hg was readily released by thermal desorption. All Hg analyses were based on the highly sensitive pyrolysis technique of atomic absorption spectrometry using the mercury analyser AMA-254.     

The time-dependent von K��rm��n plate equation as a limit of 3d nonlinear elasticity

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of h, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von Kármán plate equation.