On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Chaotic Kabanov formula for the Azéma martingales

We derive the chaotic expansion of the product of nth- and first-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integrals, polynomials and Wick products, that characterize the Wiener and Poisson processes.

Control of Concrete Deterioration Due to Trace Compounds in Deicers, HR-299, 1992

This report describes the research completed under the research contract entitled "Development of a Conductometric Test for Frost Resistance of Concrete" undertaken for the Iowa Highway Research Board. The objective of the project was to develop a test method which can be reasonably and rapidly performed in the laboratory and in the field to predict, with a high degree of certainty, the behavior of concrete subjected to the action of alternate freezing and thawing. The significance of the results obtained, and recommendations for use and the continued development of conductometric testing are presented in this final report. In this project the conductometric evaluation of concrete durability was explored with three different test methods. The test methods and procedures for each type of test as well as presentation of the results obtained and their significance are included in the body of the report. The three test methods were: (1) Conductometric evaluation of the resistance of concrete to rapid freezing and thawing, (2) Conductometric evaluation of the resistance of concrete to natural freezing and thawing, and (3) Conductometric evaluation of the pore size distribution of concrete and its correlation to concrete durability. The report also includes recommendations for the continued development of these test methods.

Effects of Deicing Salt Trace Compounds on Deterioration of Portland Cement Concrete, HR-271, 1987

A study was made of the detrimental effects of trace amounts of calcium sulfate (occurring naturally in halite deposits used for deicing) on portland cement concrete pavements. It was found that sulfate introduced as gypsum with sodium chloride in deicing brines can have detrimental effects on portland cement mortar. Concentrations of sulfate as low as 0.5% of the solute rendered the brine destructive. Conditions of brine application were critical to specimen durability. The mechanisms of deterioration were found to be due to pore filling resulting from compound formation and deposition. A field evaluation of deteriorating joints suggests that the sulfate phenomena demonstrated in the laboratory also operates in the field. A preliminary evaluation was made of remedies: limits on sulfates, fly ash admixtures, treatment of existing pavement, and salt treatments. This report gives details of the research objectives, experimental design, field testing, and possible solutions. Recommendations for further study are presented.

Control of Concrete Deterioration Due to Trace Compounds in Deicers, HR-299 Phase I, 1988

This report presents the results of research on the influence of trace compounds from rock salt deicers on portland cement mortar and concrete. An evaluation of the deicers in stock throughout the state showed that about ninety-five percent contained enough sulfate to cause accelerated deterioration of concrete. Of the impurities found in rock salts, sulfate compounds of calcium and magnesium were found to be equally deleterious. Magnesium chloride was found to be innocuous. Introduction of fly ash eliminated the damage to portland cement mortar caused by sulfates. When used with frost resistant Alden aggregate in fly ash concrete and exposed to a variety of deicer brine compositions, the concrete did not deteriorate after exposure. With the exception of a high calcium brine, the behavior of the frost-prone Garrison aggregate was independent of deicer treatment; the high calcium brine reduced frost damage with this aggregate. Two approaches to reducing sulfate deterioration from deicers are suggested as (1) limiting the amount of sulfate to about 0.28 percent, and (2) making concrete sulfate-resistant by using fly ash. Techniques for making existing concrete deicer-sulfate-resistant are essential to a practical solution.

Control of Concrete Deterioration Due to Trace Compounds in Deicers, Phase II, HR-299, 1989

This report presents results of research on ways to reduce the detrimental effects of sulfate-tainted rock salt deicers on portland cement concrete used for highway pavements. Repetitious experiments on the influence of fly ash on the mortar phase of concrete showed significant improvement in resistance to deicing brines is possible. Fifteen to twenty percent by weight of fly ash replacement for portland cement was found to provide optimum improvement. Fly ashes from five sources were evaluated and all were found to be equally beneficial. Preliminary results indicate the type of coarse aggregate also plays an important role in terms of concrete resistance to freeze-thaw in deicing brines. This was particularly true for a porous ferroan dolomite thought to be capable of reaction with the brine. In this case fly ash improved the concrete, but not enough for satisfactory performance. An intermediate response was with a porous limestone where undesirable results were observed without fly ash and adequate performance was realized when 15% fly ash was added. The best combination for making deicer-resistant concrete was found to be with a non-porous limestone. Performance in brines was found to be adequate without fly ash, but better when fly ash was included. Consideration was given to treating existing hardened concrete made with poor aggregate and no fly ash to extend pavement life in the presence of deicers, particularly at joints. Sodium silicate was found to improve freeze-thaw resistance of mortar and is a good candidate for field usage because of its low cost and ease of handling.

Combined Serum Creatinine and Cystatin C Schwartz Formula Predicts Kidney Function Better than the Combined CKD-EPI Formula in Children.

Background: The combined serum creatinine (SCreat) and cystatin C (CysC) CKD-EPI formula constitutes a new advance for glomerular filtration rate (GFR) estimation in adults. Using inulin clearances (iGFRs), the revised SCreat and the combined Schwartz formulas, this study aims to evaluate the applicability of the combined CKD-EPI formula in children. Method: 201 iGFRs for 201 children were analyzed and divided by chronic kidney disease (CKD) stages (iGFRs ≥90 ml/min/1.73 m(2), 90 > iGFRs > 60, and iGFRs ≤59), and by age groups (<10, 10-15, and >15 years). Medians with 95% confidence intervals of bias, precision, and accuracies within 30% of the iGFRs, for all three formulas, were compared using the Wilcoxon signed-rank test. Results: For the entire cohort and for all CKD and age groups, medians of bias for the CKD-EPI formula were significantly higher (p < 0.001) and precision was significantly lower than the solely SCreat and the combined SCreat and CysC Schwartz formulas. We also found that using the CKD-EPI formula, bias decreased and accuracy increased while the child age group increased, with a better formula performance above 15 years of age. However, the CKD-EPI formula accuracy is 58% compared to 93 and 92% for the SCreat and combined Schwartz formulas in this adolescent group. Conclusions: The performance of the combined CKD-EPI formula improves in adolescence compared with younger ages. Nevertheless, the CKD-EPI formula performs more poorly than the SCreat and the combined Schwartz formula in pediatric population. © 2013 S. Karger AG, Basel.

Atmospheric deposition and migration of artificial radionuclides in Alpine soils (Val Piora, Switzerland) compared to the distribution of selected major and trace elements.

Artificial radionuclides ((137)Cs, (90)Sr, Pu, and (241)Am) are present in soils because of Nuclear Weapon Tests and accidents in nuclear facilities. Their distribution in soil depth varies according to soil characteristics, their own chemical properties, and their deposition history. For this project, we studied the atmospheric deposition of (137)Cs, (90)Sr, Pu, (241)Am, (210)Pb, and stable Pb. We compared the distribution of these elements in soil profiles from different soil types from an alpine Valley (Val Piora, Switzerland) with the distribution of selected major and trace elements in the same soils. Our goals were to explain the distribution of the radioisotopes as a function of soil parameters and to identify stable elements with analogous behaviors. We found that Pu and (241)Am are relatively immobile and accumulate in the topsoil. In all soils, (90)Sr is more mobile and shows some accumulations at depth into Fe-Al rich horizons. This behavior is also observed for Cu and Zn, indicating that these elements may be used as chemical analogues for the migration of (90)Sr into the soil.

Issue review : school formula funding -- supplementary weightings.

Supplementary weightings for school districts are estimated to generate approximately 63.9 million dollars in funding in fiscal year 2011. This issue review provides an overview of all supplementary weightings currently available to school districts and examines the total funding amounts from fiscal year 2003 through fiscal year 2011.