Stochastic boundary value problems: a white noise functional approach

Summary We give a program for solving stochastic boundary value problems involving functionals of (multiparameter) white noise. As an example we solve the stochastic Schrödinger equation {ie391-1} whereV is a positive, noisy potential. We represent the potentialV by a white noise functional and interpret the product of the two distribution valued processesV andu as a Wick productV u. Such an interpretation is in accordance with the usual interpretation of a white noise product in ordinary stochastic differential equations. The solutionu will not be a generalized white noise functional but can be represented as anL ¹ functional process.     

Summary of reference materials for the determination of the nutrient composition of foods

Certified reference materials (CRMs) play a critical role in validating the accuracy of nutrient data for food samples. A number of available food CRMs of differing matrix composition have assigned concentrations for various nutrients, along with associated uncertainty intervals (UIs) for those values. These CRMs have been used extensively in the United States Department of Agriculture’s (USDA) ongoing National Food and Nutrient Analysis Program (NFNAP) to monitor the accuracy of assays of key foods and nutrients consumed in the United States. A total of 690 assigned values for individual nutrients, including proximates, vitamins, macroelements, microelements, fatty acids, amino acids, and selected phytochemicals (e.g., carotenoids), were compiled from the certificates of analysis for 63 CRMs, and the specified UI in each case was expressed as a percentage of the assigned certified or reference concentration. Across all nutrients, 63.5% of the UIs were less than 10% of the assigned value, 25.5% were 10–20%, and 11% were greater than 20% of the assigned value. The UIs for proximates, minerals, and trace elements were most consistently less than 10% of the assigned value. The relative uncertainties were significantly higher for vitamins, suggesting greater challenges in measuring and certifying these components. These high UIs (greater than 10% assigned value) in the best available reference materials are likely to be indicative of the precision and accuracy that can be obtained by current measurement systems for these components. These data suggest that care must be taken in choosing CRMs to monitor food composition analysis, including evaluating what levels of uncertainty are required in assigned values and which analytical measurement systems for food components need closer examination and improvement. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Presented at ‘BERM-10’, April 2006, Charleston, SC, USA.     

On the riemann problem for a prototype of a mixed type conservation law

We study the system of conservation laws given by With initial value The system is elliptic when u² + v² < ρ² and hyperbolic when u² + v² ≧ ρ². Following Liu's construction it is found that the system always has a weak solution which however is not necessarily unique.     

The electrochemical reduction of an unsaturated mixed-metal cluster anion: Synthesis and x-ray crystal structure of [(Ph3P)2N][{Os3H(CO)10}2Ag]

The unsaturated mixed-metal cluster anion [{Os₃H(CO)₁₀}₂Ag]^? has been prepared by the reaction of [(Ph₃P)₂N][Os₃H(CO)₁₁] with Ag[PF₆], and the anion has been shown by an X-ray analysis to consist of an Ag^I atom linking together two “Os₃H(CO)₁₀” fragments. The electrochemistry of this complex has been investigated and it has been shown to undergo two one-electron reductions.     

A Web-Based, Calculator-Skills Tutorial and Self-Test for General Chemistry Students

We describe the creation and utilization of a collection of Internet-based materials as supplemental instruction for students enrolled in the first-semester course of a general chemistry sequence. These tutorial and self-assessment materials are intended for asynchronous use as a review of mathematical concepts and skills including functional performance with calculators.     

Erratum to: “The Schrödinger–Maxwell system with Dirac mass” [Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (5) (2007) 773–793]

We correct the proof of [G.M. Coclite, H. Holden, The Schrödinger–Maxwell system with Dirac mass, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (5) (2007) 773–793, Lemma 4.1].     

Long-term stability of nutrients in a frozen mixed food control material

A mixed food homogenate was prepared as a quality control material for two multi-center clinical feeding trials. Approximately 100 kg of homogenized human diet material was prepared under controlled conditions to maintain the stability of lipid components. More than 4,800 20-25 g aliquots were prepared and stored at -60 degrees C in glass jars with Teflon-lined lids. The homogeneity of the composite was validated by analysis of moisture and total fat in aliquots taken throughout the dispensing sequence. A portion of the material was reserved at the National Institute of Standards and Technology and further characterized as SRM 1544-Fatty Acids in Diet Composite. Moisture, protein, ash, total lipid, fatty acids, cholesterol, sodium, potassium, calcium, and magnesium were assayed as part of routine quality-control analyses. Components were analyzed over a total time period ranging from 29 months (minerals) to 60 months (moisture), and up to 319 values per nutrient were generated. Results for all components assayed were stable over the time period studied. For example, moisture (n = 319; 60 months) ranged from 70.66 to 72.58 g/100 g with a mean, standard deviation (SD), and relative standard deviation (RSD) of 71.90, 0.27, and 0.4%, respectively. The range, mean, SD, and RSD for cholesterol (mg/100 g; n = 98; 49 months) were 13.54-17.96, 15.14, 0.64, and 4%.     

The Table of Standard Atomic Weights—An exercise in consensus

The present Table of Standard Atomic Weights (TSAW) of the elements is perhaps one of the most familiar data sets in science. Unlike most parameters in physical science whose values and uncertainties are evaluated using the “Guide to the Expression of Uncertainty in Measurement” (GUM), the majority of standard atomic-weight values and their uncertainties are consensus values, not GUM-evaluated values. The Commission on Isotopic Abundances and Atomic Weights of the International Union of Pure and Applied Chemistry (IUPAC) regularly evaluates the literature for new isotopic-abundance measurements that can lead to revised standard atomic-weight values, A_r°(E) for element E. The Commission strives to provide utmost clarity in products it disseminates, namely the TSAW and the Table of Isotopic Compositions of the Elements (TICE). In 2016, the Commission recognized that a guideline recommending the expression of uncertainty listed in parentheses following the standard atomic-weight value, for example, A_r°(Se) = 78.971(8), did not agree with the GUM, which suggests that this parenthetic notation be reserved to express standard uncertainty, not the expanded uncertainty used in the TSAW and TICE. In 2017, to eliminate this noncompliance with the GUM, a new format was adopted in which the uncertainty value is specified by the “±” symbol, for example, A_r°(Se) = 78.971 ± 0.008. To clarify the definition of uncertainty, a new footnote has been added to the TSAW. This footnote emphasizes that an atomic-weight uncertainty is a consensus (decisional) uncertainty. Not only has the Commission shielded users of the TSAW and TICE from unreliable measurements that appear in the literature as a result of unduly small uncertainties, but the aim of IUPAC has been fulfilled by which any scientist, taking any natural sample from commerce or research, can expect the sample atomic weight to lie within A_r°(E) ± its uncertainty almost all of the time.