Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Decomposition of Boolean Functions – Recognizing a Good Solution by Traces

The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Some Applications of the Graphic Method

There are discussed three groups of problems which are solved with the help of the graphic method.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

The role of amyloid precursor protein in neuronal and non-neuronal cell lines

Models of Alzheimer’s disease (AD) have provided useful insights into the pathogenesis and mechanistic pathways that lead to its development. One emerging idea about AD is that it may be described as a hypometabolic disorder due to the reduction of glucose uptake in AD brains. Inappropriate processing of Amyloid Precursor Protein (APP) is considered central to the initiation and progression of the disease. Although the exact role of APP misprocessing is unclear, it may play a role in neuronal metabolism before the onset of neurodegeneration. To investigate the potential role of APP in neuronal metabolism, the SHSY5Y neuroblastoma cell line was used to generate cell lines that stably overexpress wild type APP695 or express Swedish mutated-APP observed in familial AD (FAD), both under the control of the neuronal promoter, Synapsin I. The effects of APP on glucose uptake, cellular stress and energy homeostasis were studied extensively. It was found that APP-overexpressing cells exhibited decreased glucose uptake with changes in basal oxygen consumption in comparison to control cell lines. Similar studies were also performed in fibroblasts taken from FAD patients compared with control fibroblasts. Previous studies found FAD-derived fibroblasts displayed altered metabolic profiles, calcium homeostasis and oxidative stress when compared to controls. As such, in this study fibroblasts were studied in terms of their ability to metabolise glucose and their mitochondrial function. Results show that FAD-derived fibroblasts demonstrate no differences in mitochondrial function, or response to oxidative stress compared to control fibroblasts. However, control fibroblasts treated with Aβ1-42 demonstrated changes in glucose uptake. This study highlights the importance of APP expression within non-neuronal cell lines, suggesting that whilst AD is considered a brain-associated disorder, peripheral effects in non-neuronal cell types should also be considered when studying the effects of Aβ on metabolism.

Stabilization of catalyst particles against sintering on oxide supports with high oxygen ion lability exemplified by Ir-catalyzed decomposition of N2O

Iridium nanoparticles deposited on a variety of surfaces exhibited thermal sintering characteristics that were very strongly correlated with the lability of lattice oxygen in the supporting oxide materials. Specifically, the higher the lability of oxygen ions in the support, the greater the resistance of the nanoparticles to sintering in an oxidative environment. Thus with γ-Al2O3 as the support, rapid and extensive sintering occurred. In striking contrast, when supported on gadolinia-ceria and alumina-ceria-zirconia composite, the Ir nanoparticles underwent negligible sintering. In keeping with this trend, the behavior found with yttria-stabilized zirconia was an intermediate between the two extremes. This resistance, or lack of resistance, to sintering is considered in terms of oxygen spillover from support to nanoparticles and discussed with respect to the alternative mechanisms of Ostwald ripening versus nanoparticle diffusion. Activity towards the decomposition of N2O, a reaction that displays pronounced sensitivity to catalyst particle size (large particles more active than small particles), was used to confirm that catalytic behavior was consistent with the independently measured sintering characteristics. It was found that the nanoparticle active phase was Ir oxide, which is metallic, possibly present as a capping layer. Moreover, observed turnover frequencies indicated that catalyst-support interactions were important in the cases of the sinter-resistant systems, an effect that may itself be linked to the phenomena that gave rise to materials with a strong resistance to nanoparticle sintering.

Photocatalytic decomposition of organophosphonates and fluorophenols in irradiated titanium dioxide suspensions

Dimethyl methyl phosphonate (DMMP), diethyl methyl phosphonate (DEMP), and fluorophenols undergo rapid decomposition upon TiO$\sb2$ catalyzed photooxidation in air saturated aqueous solution. The degradation rates of DMMP were determined over a range of temperatures, under solar and artificial irradiation with and without simultaneous sonication. Solar illumination is effective for the degradation and the use of low energy of sonication increases the rate of mineralization. The surface area and the type of TiO$\sb2$ dramatically affect the photoactivity of the catalyst. A number of intermediate products are formed and ultimately oxidized to phosphate and carbon dioxide. Possible reaction mechanisms and pathways for DMMP and DEMP are proposed. The Langmuir-Hinshelwood kinetic parameters for the photocatalysis of fluorophenols suggest modestly different reactivity for each isomer. The adsorption constant is largest for the ortho isomer consistent with the adsorption onto TiO$\sb2$ through both hydroxyl and fluoride groups to form a chelated type structure. ^

Belowground decomposition of mangrove roots in Florida coastal everglades

Mangrove root decomposition rates were measured by distributing mesh bags containing fine root material across six sites with different soil fertility and hydroperiod to compare ambient differences to substrate quality. Roots from a site with lower soil phosphorus concentration were used as a reference and compared to ambient roots at five other sites with increased phosphorus concentration. Four mesh bags of each root type (ambient versus reference), separated into four 10-cm replicate intervals, were buried up to 42 cm depth at each site and incubated for 250 d (initiation in May 2004). Mass loss of ambient mangrove roots was significant at all study sites and ranged from 17% to 54%; there was no significant difference with depth at any one site. Reference decomposition constants (−k) ranged from 0.0012 to 0.0018 d−1 among Taylor Slough sites compared to 0.0023–0.0028 d−1 among Shark River sites, indicating slower decomposition rates associated with lower soil phosphorous and longer flood duration. Reference roots had similar decomposition rates as ambient roots in four of the six sites, and there were no significant correlations between indices of root substrate quality and decomposition rates. Among these distinct landscape gradients of south Florida mangroves, soil environmental conditions have a greater effect on belowground root decomposition than root substrate quality.

Impact of Vegetable Preparation Method and Taste-Test on Vegetable Preference for First Grade Children in the United States

How children rate vegetables may be influenced by the preparation method. The primary objective of this study was for first grade students to be involved in a cooking demonstration and to taste and rate vegetables raw and cooked. First grade children of two classes (N= 52: 18 boys and 34 girls (approximately half Hispanic) that had assented and had signed parental consent participated in the study. The degree of liking a particular vegetable was recorded by the students using a hedonic scale of five commonly eaten vegetables tasted first raw (pre-demonstration) and then cooked (post-demonstration). A food habit questionnaire was filled out by parents to evaluate their mealtime practices and beliefs about their child’s eating habits. Paired sample t-tests revealed significant differences in preferences for vegetables in their raw and cooked states. Several mealtime characteristics were significantly associated with children’s vegetable preferences. Parents who reported being satisfied with how often the family eats evening meals together were more likely to report that their child eats adequate vegetables for their health (p=0.026). Parents who stated that they were satisfied with their child’s eating habits were more likely to report that their child was trying new foods (p<.001). Cooking demonstrations by nutrition professionals may be an important strategy that can be used by parents and teachers to promote vegetable intake. It is important that nutrition professionals provide guidance to encourage consumption of vegetables for parents so that they can model the behavior of healthy food consumption to their children.

Photocatalytic decomposition of organophosphonates fluorophenols in irradiated titanium dioxide suspensions

Dimethyl methyl phosphonate (DMMP), diethyl methyl phosphonate (DEMP), and fluorophenols undergo rapid decomposition upon TiO2 catalyzed photooxidation in air saturated aqueous solution. The degradation rates of DMMP were determined over a range of temperatures, under solar and artificial irradiation with and without simultaneous sonication. Solar illumination is effective for the degradation and the use of low energy of sonication increases the rate of mineralization. The surface area and the type of TiO2 dramatically affect the photoactivity of the catalyst. A number of intermediate products are formed and ultimately oxidized to phosphate and carbon dioxide. Possible reaction mechanisms and pathways for DMMP and DEMP are proposed. The Langmuir- Hinshelwood kinetic parameters for the photocatalysis of fluorophenols suggest modestly different reactivity for each isomer. The adsorption constant is largest for the ortho isomer consistent with the adsorption onto TiO2 through both hydroxyl and fluoride groups to form a chelated type structure.

A comparison of the Kodaly method and the traditional method to determine pitch accuracy in grade 6 choral sight-singing

The purpose of this study was to determine which of the two methods is more appropriate to teach pitch discrimination to Grade 6 choral students to improve sight-singing note accuracy. This study consisted of three phases: pre-testing, instruction and post-testing. During the four week study, the experimental group received training using the Kodaly method while the control group received training using the traditional method. The pre and post tests were evaluated by three trained musicians. The analysis of the data utilized an independent t-test and a paired t-test with the methods of teaching (experimental and control) as a factor. Quantitative results suggest that the experimental subjects, those receiving Kodaly instruction at post-treatment showed a significant improvement in the pitch accuracy than the control group. The specific change resulted in the Kodaly method to be more effective in producing accurate pitch in sight-singing.

Validation of an Analytical Method for the Identification of SmartWater CSI Forensic Marking Technology

SmartWater is a chemical taggant used as a crime deterrent. The chemical taggant is a colorless liquid that fluoresces yellow under ultra-violet (UV) light and contains distinctive, identifiable and traceable elemental composition. For instance, upon a break and entry scenario, the burglar is sprayed with a solution that has an elemental signature custom-made to a specific location. The residues of this taggant persist on skin and other objects and can be easily recovered for further analysis. The product has been effectively used in Europe as a crime deterrent and has been recently introduced in South Florida. In 2014, Fourt Lauderdale Police Department reported the use of SmartWater products with a reduction in burglaries of 14% [1]. The International Forensic Research Institute (IFRI) at FIU validated the scientific foundation of the methods of recovery and analysis of these chemical tagging systems using LA-ICP-MS. Analytical figures of merit of the method such as precision, accuracy, limits of detection, linearity and selectivity are reported in this study. Moreover, blind samples were analyzed by LA-ICP-MS to compare the chemical signatures to the company’s database and evaluate error rates and the accuracy of the method. This study demonstrated that LA-ICP-MS could be used to effectively detect these traceable taggants to assist law enforcement agencies in the United States with cases involving transfer of these forensic coding systems.