Fractionation and Bioaccessibility of Manganese,Copper, Zinc,Cadmium, and Lead in Commercial Vegetable and Rice Baby Foods Using Inductively Coupled Plasma - Mass Spectrometry (ICP-MS) with Central Composite Design (CCD)

Abstract

Herein the bioaccessibility of Mn, Cu, Zn, Cd, and Pb, selected from essential and toxic elements, was determined in commercially sold vegetable purees intended for infant and toddler consumption. Chemical fractionation studies using water, acetone, diethyl ether, chloroform:methanol, and n-hexane were employed to predict the importance of the protein and lipid parts of a matrix to assess the bioaccessibility data. In addition, in-vitro gastrointestinal digestion was performed to determine the bioaccessibility of the elements using a five level, three factor central composite design (CCD) to maximize the elemental solubility. The total elemental concentrations in all of the fractions were determined by inductively coupled plasma – mass spectrometry (ICP-MS). Based on the consumption of one jar of vegetable/rice-based baby food, Zn was 1.3% of the recommended dietary allowance and Mn was 4.2% of the adequate intake level, while Cu was almost 100% of the adequate intake level. Additionally, Pb was always below the detection limit and Cd was sometimes under the detection limit for the percent bioaccessibility. However, in some samples, Cd was as high as 80% of the tolerable weekly intake level depending on the body weight.     

Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1

The solution of a generalized non-relativistic Schrödinger equation with radial potential energy V(r)=V ₀(r/a ₀)^2–2 is presented. After reviewing the general properties of the radial ordinary differential equation, power series solutions are developed. The Green's function is constructed, its trace and the trace of its first iteration are calculated, and the ability of the traces to provide upper and lower bounds for the ground eigenvalue is examined. In addition, WKB-like solutions for the eigenvalues and eigenfunctions are derived. The approximation method yields valid eigenvalues for large quantum numbers (Rydberg states).     

Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Phase-fixed double-group 3-Γ symbols. IV. Real 3-Γ symbols and coupling coefficients for the group hierarchies T* ⊃ C 3 * and T* ⊃ C 2 *

We present sets of real 3- symbols which correspond to explicitly given irreducible matrix representations for the two double group hierarchies T* C ₃ ^* and T* C ₂ ^* . They fit into the formalism exposed in a previous paper [1] on the general theory of 3- symbols and coupling coefficients and illustrate much of the discussion in a subsequent one [2] treating the particular properties of the double groups.     

Anaerobic reduction of a sulfonated azo dye, Congo Red, by sulfate-reducing bacteria

The capacity for anaerobic decolorization of a sulfonated azo dye, Congo Red, by a strain of a sulfate-reducing bacterium was evaluated. After optimizing the growth rate of the bacteria on a simple carbon source and terminal electron acceptor pair, lactate and sulfate, respectively, the effect of the dye concentration on their growth rate was analyzed. The decolorization rate was affected by the dye concentration in the growth medium. The azo-bond cleavage mechanism of reductive decolorization with the formation of benzidine was consistent with the results, as this metabolite was identified by high-performance liquid chromatography. Several fractions of the culture medium, including lysed cell extracts, were examined for the capacity to reduce the azo dye. This reduction capacity was found in the culture medium in which the cells had previously grown. The results showed that the mechanism of reductive decolorization of this sulfonated azo dye was extracellular and nonenzymatic, consistent with the production of sulfide anion by the microorganisms while growing on lactate and sulfate. The sulfide anions were the cause of the reduction leading to the disappearance of color in the medium. To increase the rate of decolorization, the presence of ferrous ion was also necessary together with the lactate and sulfate substrates.     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

Rates of convergence of α-stable random motions

The rate-of-convergence problem in the central limit theorem is considered for -stable distributions on the noncommutative group of motions in ^d. The method used here is based on the theory of probability metrics.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.