Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.

Special functions of Weyl groups and their continuous and discrete orthogonality

Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev. Elles sont en lien avec des polynômes orthogonaux à plusieurs variables associés aux algèbres de Lie simples, par exemple les polynômes de Jacobi et de Macdonald. Elles ont plusieurs propriétés remarquables, dont l'orthogonalité continue et discrète. En particulier, il est prouvé dans la présente thèse que les fonctions $S^s$ et $S^l$ caractérisées par certains paramètres sont mutuellement orthogonales par rapport à une mesure discrète. Leur orthogonalité discrète permet de déduire deux types de transformées discrètes analogues aux transformées de Fourier pour chaque algèbre de Lie simple avec racines des longueurs différentes. Comme les polynômes de Tchebyshev, ces quatre familles des fonctions ont des applications en analyse numérique. On obtient dans cette thèse quelques formules de <<cubature>>, pour des fonctions de plusieurs variables, en liaison avec les fonctions $C$, $S^s$ et $S^l$. On fournit également une description complète des transformées en cosinus discrètes de types V--VIII à $n$ dimensions en employant les fonctions spéciales associées aux algèbres de Lie simples $B_n$ et $C_n$, appelées cosinus antisymétriques et symétriques. Enfin, on étudie quatre familles de polynômes orthogonaux à plusieurs variables, analogues aux polynômes de Tchebyshev, introduits en utilisant les cosinus (anti)symétriques.

Enterobacter sakazakii in Dried Infant Formulas and Milk Kitchens of Maternity Wards in Sao Paulo, Brazil

This study was the first conducted in Brazil to evaluate the presence of Enterobacter sakazakii in milk-based powdered infant formula manufactured for infants 0 to 6 months of age and to examine the conditions of formula preparation and service in three hospitals in Sao Paulo State, Brazil. Samples of dried and rehydrated infant formula, environments of milk kitchens, water, bottles and nipples, utensils, and hands of personnel were analyzed, and E. sakazakii and Enterobacteriaceae populations were determined. All samples of powdered infant formula purchased at retail contained E. sakazakii at <0.03 most probable number (MPN)/100 g. In hospital samples, E. sakazakii was found in one unopened formula can (0.3 MPN/100 g) and in the residue from one nursing bottle from hospital A. All other cans of formula from the same lot bought at a retail store contained E. sakazakii at <0.03 MPN/100 g. The pathogen also was found in one cleaning sponge from hospital B. Enterobacteriaceae populations ranged from 10(1) to 10(5) CFU/g in cleaning aids and <5 CFU/g in all formula types (dry or rehydrated), except for the sample that contained E. sakazakii, which also was contaminated with Enterobacteriaceae at 5 CFU/g. E. sakazakii isolates were not genetically related. In an experiment in which rehydrated formula was used as the growth medium, the temperature was that of the neonatal intensive care unit (25 C), and the incubation time was the average time that formula is left at room temperature while feeding the babies (up to 4 h), a 2-log increase in levels of E. sakazakii was found in the formula. Visual inspection of the facilities revealed that the hygienic conditions in the milk kitchens needed improvement. The length of time that formula is left at room temperature in the different hospitals while the babies in the neonatal intensive care unit are being fed (up to 4 h) may allow for the multiplication of E. sakazakii and thus may lead to an increased health risk for infants.

Study of sunless tanning formulas using molted snake skin as an alternative membrane model

Sunless tanning formulas have become increasingly popular in recent years for their ability to give people convincing tans without the dangers of skin cancer. Most sunless tanners currently on the market contain dihydroxyacetone (DHA), a keto sugar with three carbons. The temporary pigment provided by these formulasis designed to resemble a UV-induced tan. This study evaluated the effectiveness of carbomer gels and cold process self emulsifying bases on skin pigmentation, using different concentrations of a chemical system composed of DHA and N-acetyl tyrosine, which are found in moulted snake skins and their effectiveness was tested by Mexameter (R) MX 18. Eight different sunless tanning formulas were developed, four of which were gels and four of which were emulsions (base, base plus 4.0%, 5.0% and 6.0% (w/w) of a system of DHA and N-acetyl tyrosine). Tests to determine the extent of artificial tanning were done by applying 30 mg cm(-2) of each formula onto standard sizes of moulted snake skin (2.0 cm x 3.0 cm). A Mexameter (R) MX 18 was used to evaluate the extent of coloration in the moulted snake skin at T(0) (before the application) and after 24, 48, 72, 168, 192 and 216 h. The moulted snake skins can be used as an alternative membrane model for in vitro sunless tanning efficacy tests due to their similarity to the human stratum corneum. The DHA concentration was found to influence the initiation of the pigmentation in both sunless tanning systems (emulsion and gel) as well as the time required to increases by a given amount on the tanning index. In the emulsion system, the DHA concentration also influenced the final value on the tanning index. The type of system (emulsion or gel) has no influence on the final value in the tanning index after 216 h for samples with the same DHA concentration.

Stability of vitamin A during storage of enteral feeding formulas

Vitamin A (13-cis-retinol, all-trans-retinol and total carotenes) content was evaluated in 15 samples of enteral feeding formulas during 3-6,9 and 12 months of storage in closed containers, protected from light and at room temperature (22-30 degrees C). All formulas were nutritionally complete and/or recommended for different diseases. Equivalent batches were also evaluated after preparation and refrigerated storage for 24 h. Nutrient content did not decrease during both storage scenarios. Stability of vitamin A in the enteral feeding formulas, as determined in this study, is probably due to production and storage conditions, e.g. absence of oxygen in contact with the packaged product, the technological process used in the microencapsulation of vitamins, and protected storage in the absence of light and at a temperature maximum of 30 degrees C. (C) 2010 Elsevier Ltd. All rights reserved.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Osmolality of preterm formulas suplemented with monprotein energy supplements

Background: Addition of energy supplements to preterm formulas is an optional strategy to increase the energy intake in infants requiring fluid restriction, in conditions like bronchopulmonary dysplasia. This strategy may lead to an undesirable increase in osmolality of feeds, the maximum recommended safe limit being 400 mOsm/kg. The aim of the study was to measure the changes in osmolality of several commercialized preterm formulas after addition of glucose polymers and medium-chain triglycerides. Methods: Osmolality was measured by the freezing point depression method. Six powdered formulas with concentrations of 14 g/100 ml and 16 g/100 ml, and five ready-to-feed liquid formulas were analyzed. All formulas, were supplemented with 10% (low supplementation) or 20% (high supplementation) of additional calories, respectively, in the form of glucose polymers and medium chain triglycerides, maintaining a 1:1 glucose:lipid calorie ratio. Inter-analysis and intra-analysis coefficients of variation of the measurements were always < 3.9%. Results: The mean osmolality (mOsm/kg) of the non-supplemented formulas varied between 268.5 and 315.3 mOsm/kg, increasing by 3–5% in low supplemented formulas, and by 6–10% in high supplemented formulas. None of the formulas analyzed exceeded 352.8 mOsm/kg. Conclusion: The supplementation of preterm formulas with nonprotein energy supplements with up to 20% additional calories did not exceed the maximum recommended osmolality for neonatal feedings.

Fractional calculus: a survey of useful formulas

This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.

Osmolality of Elemental and Semi-Elemental Formulas Supplemented with Nonprotein Energy Supplements

Elemental and semi-elemental formulas are used to feed infants with short bowel syndrome, who may not be able to tolerate feeds of more than 310 mOsm kg(-1). The present study aimed to measure the osmolality of elemental and semi-elemental formulas at different concentrations, with and without the addition of nonprotein energy supplements.

Assessment of adult formulas for glomerular filtration rate estimation in children.

BACKGROUND: Estimated glomerular filtration rate (eGFR) is an important diagnostic instrument in clinical practice. The National Kidney Foundation-Kidney Disease Quality Initiative (NKF-KDOQI) guidelines do not recommend using formulas developed for adults to estimate GFR in children; however, studies confirming these recommendations are scarce. The aim of our study was to evaluate the accuracy of the new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula, the Modification of Diet in Renal Disease (MDRD) formula, and the Cockcroft-Gault formula in children with various stages of chronic kidney disease (CKD). METHODS: A total of 550 inulin clearance (iGFR) measurements for 391 children were analyzed. The cohort was divided into three groups: group 1, with iGFR >90 ml/min/1.73 m(2); group 2, with iGFR between 60 and 90 ml/min/1.73 m(2); group 3, with iGFR of <60 ml/min/1.73 m(2). RESULTS: All formulas overestimate iGFR with a significant bias (p < 0.001), present poor accuracies, and have poor Spearman correlations. For an accuracy of 10 %, only 11, 6, and 27 % of the eGFRs are accurate when using the MDRD, CKD-EPI, and Cockcroft-Gault formulas, respectively. For an accuracy of 30 %, these formulas do not reach the NKF-KDOQI guidelines for validation, with only 25, 20, and 70 % of the eGFRs, respectively, being accurate. CONCLUSIONS: Based on our results, the performances of all of these formulas are unreliable for eGFR in children across all CKD stages and cannot therefore be applied in the pediatric population group.

Chebyshev-type quadrature formulas for new weight classes

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.

Additional compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Compact expressions, complete through second order in electrical and/or mechanical anharmonicity, are given for the dynamic dipole vibrational polarizability and dynamic first and second vibrational hyperpolarizabilities. Certain contributions not previously formulated are now included

Explicit ruin formulas for models with dependence among risks

We show that a simple mixing idea allows one to establish a number of explicit formulas for ruin probabilities and related quantities in collective risk models with dependence among claim sizes and among claim inter-occurrence times. Examples include compound Poisson risk models with completely monotone marginal claim size distributions that are dependent according to Archimedean survival copulas as well as renewal risk models with dependent inter-occurrence times.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.