Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual

We define and study Dunkl wavelets and the corresponding Dunkl wavelets transforms, and we prove for these transforms Plancherel and reconstruction formulas. We give as application the inversion of the Dunkl intertwining operator and its dual

Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish a central limit theorem for the estimator of the memory parameter with the minimax rate of convergence (up to a logarithm factor). The quality of the estimators are attested by simulations

Biorthogonal multiresolution analyses and decompositions of Sobolev spaces

The object of this paper is to construct extension operators in the Sobolev spaces Hk(]−∞,0]) and Hk([0,+∞[)(k≥0). Then we use these extensions to get biorthogonal wavelet bases in Hk(ℝ). We also give a construction in L2([−1,1]) to see how to obtain boundaries functions

© Hindawi Publishing Corp. BIORTHOGONAL MULTIRESOLUTION ANALYSES AND DECOMPOSITIONS OF SOBOLEV SPACES

Abstract. The object of this paper is to construct extension operators in the Sobolev spaces H k (]−∞,0]) and H k ([0,+∞[) (k ≥ 0). Then we use these extensions to get biorthogonal wavelet bases in H k (R). We also give a construction in L 2 ([−1,1]) to see how to obtain boundaries functions. 2000 Mathematics Subject Classification. 41A58, 42C15

More general constructions of wavelets on the interval

Accessible en ligne : http://www.commun-math-anal.org/vv4.htmInternational audienceIn this paper we present general constructions of orthogonal and biorthogonal multiresolution analysis on the interval. In the first one, we describe a direct method to define an orthonormal multiresolution analysis. In the second one, we use the integration and derivation method for constructing a biorthogonal multiresolution analysis. As applications, we prove that these analyses are adapted to study regular functions on the interval

Urinary lithiasis and urinary tract malformations in children: A retrospective study of 34 cases

Background: Although the association of urinary lithiasis and urinary tract malformation is not rare, their management poses challenges. The aim of this study was to evaluate the relationship between urolithiasis and malformations of the urinary system. There were 34 patients (19 males and 15 females) with a mean age of 4.8 years (range, 2 months to 14 years). All patients had urinary lithiasis with a urinary tract malformation. Abdominal pain was the most frequent clinical symptom (38%). Urinary infection was found in 7 patients (21%) and macroscopic haematuria was present in 10 patients (29%). The most frequent urinary tract malformations were megaureter (8 cases), uretero-pelvic junction obstruction (7 cases) and vesico-ureteric reflux (8 cases), but its malformative origin could not be confirmed. Treatment consisted of lithiasis extraction in 32 cases associated with specific treatment of the uropathy in 27 cases. Postoperative outcome was uneventful in all cases. In fact, urinary lithiasis and urinary tract malformation association is not rare. Indeed, 9-34% of urinary lithiasis are noted to be associated with urinary tract malformation. Positive diagnosis relies specifically on kidney ultrasound, intravenous urography, and urethrocystography. Treatment depends on the type of urinary tract malformation, localisation and size of the urinary lithiasis. Conclusion: In conclusion, urinary lithiasis and urinary tract malformation association is a frequent eventuality. Surgical intervention is the usual mode of treatment

First Detection of CTX-M-1 in Extended-Spectrum β-Lactamase-Producing Escherichia coli in Seafood from Tunisia.

International audienceThe purpose of this study was to determine the carriage rate of Escherichia coli isolates in seafood, to analyze the phenotype and genotype of antimicrobial resistance in the recovered isolates, and to characterize extended-spectrum β-lactamase (ESBL) E. coli producers. E. coli isolates were recovered from 24 (34.3%) of the 70 seafood samples analyzed, and one isolate per sample was further characterized. Antibiotic resistance was determined by the disk diffusion method in the 24 isolates, with the following results (number of resistant isolates): tetracycline (8), streptomycin (7), ampicillin (6), trimethoprim-sulfamethoxazole (4), chloramphenicol (4), ciprofloxacin (3), cefotaxime (2), and ceftazidime (2). Six isolates showed a multiresistant phenotype (including at least three families of antibiotics). Among tetracycline-resistant E. coli isolates, tet(A) was detected in five isolates and tet(B) in two isolates. The qnr(A) or aac(6')-1b-cr genes were detected in two ciprofloxacin-resistant E. coli isolates, and the sul2 gene in two trimethoprim-sulfamethoxazole-resistant isolates. ESBL-containing E. coli isolates, carrying the blaCTX-M-1 gene, were detected in 2 of the 70 seafood samples, obtained from gilt-head bream aquaculture. The ESBL isolates were typed phylogenetically and by multilocus sequence typing, and they were ascribed to lineage ST48/A and to the new ST3497/B1; these isolates carried the fimA, aer, and papGIII virulence genes. One of the ESBL-producing E. coli isolates carried an unusual class 1 integron (with the array dfr32-ereA-aadA1). Seafood could be a source of multiresistant E. coli isolates for the aquatic environment, and these could enter the food chain