A method for the calculation of eigenfunction expansions

In this paper, a method is presented for the calculation of the coefficients of the series expansion of a function f(t), in the base orthonormal set made up by the eigenfunctions of the self-adjoint operator $\text{L: L(x(t)) = (}\text{d}\text{dt}\text{)( p(t)(}\text{dx(t)}\text{dt}\text{))?q(t)x(t)}$. We show that the values of the numbers $\text{t}\text{}$x_k> can be obtained by solving the differential equation L + λ) y(t) = Kf(t), in the interval of definition, for each of the eigenvalues λ of L and by using as initial conditions those which determine one of its associated orthonormal functions. This makes the method specially interesting for its implementation on a hybrid computer: One advantage of the proposed method is that the analysis of f(t) does not require the simultaneous presence of the functions of the base set and the problem signal, thus eliminating both the problems of the synchronized generation of signals and the need for storing it in memory.     

Mass balance assessment for mercury in Lake Champlain

A mass balance model for mercury in Lake Champlain was developed in an effort to understand the sources, inventories, concentrations, and effects of mercury (Hg) contamination in the lake ecosystem. To construct the mass balance model, air, water, and sediment were sampled as a part of this project and other research/monitoring projects in the Lake Champlain Basin. This project produced a STELLA-based computer model and quantitative apportionments of the principal input and output pathways of Hg for each of 13 segments in the lake. The model Hg concentrations in the lake were consistent with measured concentrations. Specifically, the modeling identified surface water inflows as the largest direct contributor of Hg into the lake. Direct wet deposition to the lake was the second largest source of Hg followed by direct dry deposition. Volatilization and sedimentation losses were identified as the two major removal mechanisms. This study significantly improves previous estimates of the relative importance of Hg input pathways and of wet and dry deposition fluxes of Hg into Lake Champlain. It also provides new estimates of volatilization fluxes across different lake segments and sedimentation loss in the lake.     

Measuring acceptance of milk and milk substitutes among younger and older children

Appropriate nutrient-dense foods and beverages are crucial for children for proper growth and development and to develop healthful lifelong habits. This study investigated children's (ages 8 to 16 y old) perception of sensory intensity, attribute liking and overall liking of unflavored and chocolate lactose-free cow's milk and soy beverages. Products were not identified as to whether they were soy or milk. Children showed greater acceptance of lactose-free cow's milk compared to milk substitute beverages, within flavor category. No differences in acceptance emerged by ethnic group (Caucasian, African American, Hispanic), but a large difference emerged by age group. All product acceptance differences perceived by older children reoccurred among the younger children and in the same direction, but the older children used a larger range of numbers, especially at the lower end, rather than at the higher end of acceptance. The effect of age is not a simple scaling bias but may suggest a reduced criticism by younger respondents of less-acceptable products.     

Effect of androgen treatment during foetal and/or neonatal life on ovarian function in prepubertal and adult rats

We investigated the effects of different windows of testosterone propionate (TP) treatment during foetal and neonatal life in female rats to determine whether and when excess androgen exposure would cause disruption of adult reproductive function. Animals were killed prepubertally at d25 and as adults at d90. Plasma samples were taken for hormone analysis and ovaries serial sectioned for morphometric analyses. In prepubertal animals, only foetal+postnatal and late postnatal TP resulted in increased body weights, and an increase in transitory, but reduced antral follicle numbers without affecting total follicle populations. Treatment with TP during both foetal+postnatal life resulted in the development of streak ovaries with activated follicles containing oocytes that only progressed to a small antral (smA) stage and inactive uteri. TP exposure during foetal or late postnatal life had no effect upon adult reproductive function or the total follicle population, although there was a reduction in the primordial follicle pool. In contrast, TP treatment during full postnatal life (d1-25) resulted in anovulation in adults (d90). These animals were heavier, had a greater ovarian stromal compartment, no differences in follicle thecal cell area, but reduced numbers of anti-Mullerian hormone-positive smA follicles when compared with controls. Significantly reduced uterine weights lead reduced follicle oestradiol production. These results support the concept that androgen programming of adult female reproductive function occurs only during specific time windows in foetal and neonatal life with implications for the development of polycystic ovary syndrome in women.     

The effect of vitamin concentrates on the flavor of pasteurized fluid milk

Fluid milk consumption in the United States continues to decline. As a result, the level of dietary vitamin D provided by fluid milk in the United States diet has also declined. Undesirable flavor(s)/off flavor(s) in fluid milk can negatively affect milk consumption and consumer product acceptability. The objectives of this study were to identify aroma-active compounds in vitamin concentrates used to fortify fluid milk, and to determine the influence of vitamin A and D fortification on the flavor of milk. The aroma profiles of 14 commercial vitamin concentrates (vitamins A and D), in both oil-soluble and water-dispersible forms, were evaluated by sensory and instrumental volatile compound analyses. Orthonasal thresholds were determined for 8 key aroma-active compounds in skim and whole milk. Six representative vitamin concentrates were selected to fortify skim and 2% fat pasteurized milks (vitamin A at 1,500–3,000 IU/qt, vitamin D at 200–1,200 IU/qt, vitamin A and D at 1,000/200–6,000/1,200 IU/qt). Pasteurized milks were evaluated by sensory and instrumental volatile compound analyses and by consumers. Fat content, vitamin content, and fat globule particle size were also determined. The entire experiment was done in duplicate. Water-dispersible vitamin concentrates had overall higher aroma intensities and more detected aroma-active compounds than oil-soluble vitamin concentrates. Trained panelists and consumers were able to detect flavor differences between skim milks fortified with water-dispersible vitamin A or vitamin A and D, and unfortified skim milks. Consumers were unable to detect flavor differences in oil-soluble fortified milks, but trained panelists documented a faint carrot flavor in oil-soluble fortified skim milks at higher vitamin A concentrations (3,000–6,000 IU). No differences were detected in skim milks fortified with vitamin D, and no differences were detected in any 2% milk. These results demonstrate that vitamin concentrates may contribute to off flavor(s) in fluid milk, especially in skim milk fortified with water-dispersible vitamin concentrates.     

Parents’ and Children's Acceptance of Skim Chocolate Milks Sweetened by Monk Fruit and Stevia Leaf Extracts

Chocolate milk increases milk consumption of children, but high sugar content raises health concerns. Interest in sugar reduction and parents’ preference for natural sweeteners necessitates further research on natural nonnutritive sweeteners. However, it is important to maintain consumer acceptability, especially for children, while reducing sugar in chocolate milk. The objectives of this study were to identify the sweetness intensity perception of stevia leaf (STV) and monk fruit (MK) extracts in skim chocolate milk (SCM), to evaluate STV and MK as the sole or partial sweetener source for SCM for young adults (19 to 35 y) and children (5 to 13 y), and to determine if information on natural nonnutritive sweeteners impacted parents’ acceptability of SCM. Power function and 2‐alternative forced choice studies were used to determine the iso‐sweetness of nonnutritive sweeteners to a sucrose control in SCM (51.4 g/L, SUC control). Young adults (n = 131) evaluated 9 different SCM (SUC control, STV, MK, STV:sucrose blends, or MK:sucrose blends) in a completely randomized 2‐d test. Children (n = 167) evaluated SUC control SCM and SCM with 39.7 g/L sucrose and 46 mg/L MK (MK25) or 30 mg/L STV (STV25). Parents evaluated SUC control, MK25, and STV25 in a balanced crossover design with a 40‐d wait time between primed or unprimed ballots. Chocolate milks solely sweetened by nonnutritive sweeteners were less acceptable compared with SUC control by young adults. MK25 and STV25 were acceptable by young adults and children. The presentation of chocolate milk label information had different effects on parental acceptance. Traditional parents preferred sucrose sweetened SCM, and label conscious parents preferred SCM with natural nonnutritive sweeteners.