The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods

The support operators method of discretizing partial differential equations produces discrete analogs of continuum initial boundary value problems that exactly satisfy discrete conservation laws analogous to those satisfied by the continuum system. Thus, the stability of the method is assured, but currently there is no theory that predicts the accuracy of the method on nonuniform grids. In this paper, we numerically investigate how the accuracy, particularly the accuracy of the fluxes, depends on the definition of the inner product for discrete vector fields. We introduce two different discrete inner products, the standard inner product that we have used previously and a new more accurate inner product. The definitions of these inner products are based on interpolation of the fluxes of vector fields. The derivation of the new inner product is closely related to the use of the Piola transform in mixed finite elements. Computing the formulas for the new accurate inner product requires a nontrivial use of computer algebra. From the results of our numerical experiments, we can conclude that using more accurate inner product produces a method with the same order of convergence as the standard inner product, but the constant in error estimate is about three times less. However, the method based on the standard inner product is easier to compute with and less sensitive to grid irregularities, so we recommend its use for rough grids.     

Computer arithmetic for probability distribution variables

The uncertainty in the variables and functions in computer simulations can be quantified by probability distributions and the correlations between the variables. We augment the standard computer arithmetic operations and the interval arithmetic approach to include probability distribution variable (PDV) as a basic data type. Probability distribution variable is a random variable that is usually characterized by generalized probabilistic discretization. The correlations or dependencies between PDVs that arise in a computation are automatically calculated and tracked. These correlations are used by the computer arithmetic rules to achieve the convergent approximation of the probability distribution function of a PDV and to guarantee that the derived bounds include the true solution. In many calculations, the calculated uncertainty bounds for PDVs are much tighter than they would have been had the dependencies been ignored. We describe the new PDV Arithmetic and verify the effectiveness of the approach to account for the creation and propagation of uncertainties in a computer program due to uncertainties in the initial data.     

Suggested guidelines for rating cardiac disability in workers' compensation. Medical and Chiropractic Advisory Committee to the Administrative Director of the California Division of Industrial Accidents

Cardiac disability ratings in workers' compensation cases currently lack any consistent scientific basis, with varying medical evidence used by different examiners in the same case. Opinions about the extent of disability may differ with the same patient, delaying resolution and the delivery of benefits. We describe guidelines for determining cardiac impairment and suggest a schedule for rating disability based on evidence. Our experience is in California, but arriving at equitable ratings for disability purposes is a nationwide challenge. Exercise stress testing provides the best reproducible data to test the heart's ability to do work. When exercise stress testing is not possible or adequate, alternative or supplemental testing is necessary. Certain conditions, such as hypertension, arrhythmias, coronary artery spasm, and a history of coronary artery operations or myocardial infarction, may affect "cardiac disability" but may not necessarily be reflected in exercise testing.     

A newly identified polymorphism in the apolipoprotein E enhancer gene region is associated with Alzheimer's disease and strongly with the epsilon 4 allele

Apolipoprotein E allele 4 (apoE epsilon 4) is a major risk factor for late-onset AD. Inheritance of this allele is associated with an earlier age of onset of dementia in individuals with AD. It is unknown whether other polymorphisms in the apoE gene may influence the effect of apoE epsilon 4 on AD. We screened portions of the promoter enhancer element and of the apoE receptor binding domain for other polymorphisms that could affect risk of AD. In particular, a C/G polymorphism at position +113 of the apoE mRNA in the apoE intron 1 enhancer element (IE1) has been recently identified. We found no other polymorphisms. We studied the relationship of the two alleles of the IE1 polymorphism with AD and found an apparent association between IE1 G and AD (n = 94; p = 0.0515). However, the IE1 G allele is also closely associated with apoE epsilon 4 (p < 0.0001). When the presence of apoE epsilon 4 is covaried, the association between the IE1 G allele and AD is no longer statistically significant (odds ratio = 1.29, 95% confidence interval: 0.44, 3.78). In contrast, epsilon 4 is still highly associated with AD when IE1 G is controlled for (odds ratio = 5.91, 95% confidence interval: 3.29, 10.63). Furthermore, there is no significant association between the age of onset of dementia and the inheritance of the G allele. We believe that the apparent association between IE1 G and AD is a consequence of the association between the epsilon 4 and IE1 G alleles.     

The Development of a Unique Buffered Matrix Aspirin Tablet

Aspirin is used widely as an analgetic, antipyretic, and antirheumatic agent. The major disadvantage of aspirin therapy is gastrointestinal irritation caused by direct contact of the solid aspirin crystals and the gastric mucosa which causes gastrointestinal bleeding. Buffered aspirin tablets have been developed to reduce gastrointestinal bleeding. However, these multilayer tablets have proven to be, at times, ineffective.

A compressed buffered aspirin tablet was formulated which was composed of aqueous-based polymer coated aspirin crystals, a buffering system, a hydrophilic gel-forming matrix material, a binder, and a hydrophobic lubricant. The aspirin crystals were coated with an aqueous-based polymer to reduce aspirin degradation caused by the tablet components. The Glatt GPCG5 fluid bed with a top spray apparatus was used to coat 3 to 6 percent wt./wt. polymer onto aspirin crystals.

The coated aspirin crystals were incorporated with the tablet components and directly compressed using conventional tablet technology and equipment. Aspirin was released rapidly from the eroding matrix. Erosion was achieved due to the gel formation of Methocel K100LV which protects the tablet interior from dissolving and disintegrating upon initial wetting and hydration. The buffering system created a microenvironment of pH 5 within and around the eroding tablet matrix to aid in increasing aspirin solubility. The prototype formulation was scaled-up to large processing equipment and tablet stability was evaluated.     

AN APPARATUS FOR DETERMINING THE ANNEALING CONSTANTS OF GLASS1

An apparatus is described by means of which annealing data on glass may be rapidly and accurately obtained. Essentially, the apparatus consists of a mechanical means straining the glass, an optical means of measuring the stresses, and a means of heating the sample uniformly while making the measurement. The results are consistent and expressed in definite terms. The specimens for test may be quite small. The apparatus may be used for control purposes in place of measuring softening temperatures.     

Differential Scanning Calorimetry of Ampicillin-Dextrose Mixture

The possible interaction of anhydrous ampicillin and ampicillin trihydrate with anhydrous dextrose, in the solid state, was investigated by comparing the thermal behavior, using differential scanning calorimetry, of physical mixtures of the respective original components in different molar ratios. Anhydrous dextrose was found to form complexes with anhydrous ampicillin and ampicillin trihydrate. These complexes were found to be dependent on the molar ratios of the mixture components. The stoichiometries of these complexes were determined from the enthalpy change of the DSC transitions of the mixtures and were found to be 1:1, 2:3 and 1:3 molar complexes between ampicillin, anhydrous and trihydrate, and anhydrous dextrose. Complexed ampicillin was found to decompose at markedly lower temperatures than uncomplexed ampicillin.     

Psychology, education, and schooling: Social policy implications in the lives of children and youth.

Offers a broad perspective on the problems that face schools and related areas of interface between professional and academic psychology, educators, and the public. School psychology is discussed as a practice that has historically received too little attention. One result is the growth of problems affecting consumers and the psychology community. These are discussed in a broader perspective of the economy, social justice, the generation gap, and the growing trend of punitiveness toward children and youth. Suggestions for social policy planning are offered. (7 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Differential Scanning Calorimetry of Ampicillin-Aspartame Mixture

The possible interaction of anhydrous and trihydrate ampicillin with aspartame, in the solid state, was investigated by comparing the thermal behavior of physical mixtures of the respective original components in different molar ratios, using differential scanning calorimetry. Aspartame was found to form complexes with anhydrous ampicillin and ampicillin trihydrate. These complexes were found to be dependent on the molar ratios of the mixture components. One of the complexes between anhydrous and trihydrate ampicillin and aspartame, as determined from the enthalpy change of the DSC transitions of the mixtures, was found to have a 2:1 molar ratio.