pK determination. A mean field, Poisson-Boltzmann approach

A model describing dissociation of monoprotonic acid and a method for the determination of its pK value are presented. The model is based on a mean field approximation. The Poisson-Boltzmann equation, adopting spherical symmetry, is numerically solved, and the solution of its linearized form is written. By use of the pH values of a dilution experiment of galacturonic acid as the entry data, the proposed method allowed estimation of the value of pK = 3.25 at a temperature of 25 degrees C. Values for the complex dimensions and dissociation degree are calculated using experimental pH values for solution concentration values ranging from 0.1 to 60 mM. The present analysis leads to the conclusion that the Poisson-Boltzmann equation or its linear form is equally suited for the description of such systems.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Synthetic control chart for monitoring the pprocess mean and variance

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control the process mean and variance. During the first stage, one item of the sample is inspected; if its value X, is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the statistic T = Sigma [x(i) - mu(0) + xi sigma(0)](2) is computed taking into account all items of the sample. The design parameter is function of X-1. When the statistic T is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on Conforming Run Length (CRL). The CRL is the number of samples taken from the process since the previous nonconforming sample until the occurrence of the next nonconforming sample. If the CRL is sufficiently small, then a signal is generated. A comparative study shows that the SyTS chart and the joint X and S charts with double sampling are very similar in performance. However, from the practical viewpoint, the SyTS chart is more convenient to administer than the joint charts.

X charts with supplementary samples to control the mean and variance

A standard X chart for controlling a process takes regular individual observations, for instance every half hour. This article proposes a modification of the X chart that allows one to take supplementary samples. The supplementary sample is taken (and the (X) over bar and R values computed) when the current value of X falls outside the control limits. With the supplementary sample, the signal of out-of-control is given by an (X) over bar value outside the (X) over bar chart's control limits or an R value outside the R chart's control limit. The proposed chart is designed to hold the supplementary sample frequency, during the in-control period, as low as 5% or less. In this context, the practitioner might prefer to verify an out-of-control condition by simply comparing the (X) over bar and R values with the control limits. In other words, without plotting the (X) over bar and R points. The X chart with supplementary samples has two major advantages when compared with the standard (X) over bar and A charts: (a) the user will be plotting X values instead of (X) over bar and R values; (b) the shifts in the process mean and/or changes in the process variance are detected faster.

Monitoring the process mean and variance using a synthetic control chart with two-stage testing

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mean-field description of collapsing and exploding Bose-Einstein condensates

Numerical simulations based on the time-dependent mean-field Gross-Pitaevskii equation was performed to explain the dynamics of collapsing and exploding Bose-Einstein condensates (BEC) of 85Rb atoms. The atomic interaction was manipulated by an external magnetic field via a Feshbach resonance. On changing the scattering length of atomic interaction from a positive to a large negative value, the condensate collapsed and ejected atoms via explosion.

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co)variances with age adequately and larger breeding value accuracies can be expected using this model. © South African Society for Animal Science.

Study of pK Values and Effective Dielectric Constants of Ionizable Residues in Pentapeptides and in Staphylococcal Nuclease (SNase) Using a Mean-Field Approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Total energy value and percentage contribuition of calories from macronutrients in the diet of elderly individuals from Fortaleza, state of Ceara, Brazil

Objective: Describe the total energy value and percentage contribution of calories from macronutrients in the diet of elderly individuals living in Fortaleza/CE. Methods: This is a population-based, cross-sectional domiciliary study, which included 458 elderly individuals (66.6% women). The variables evaluated were total energy value (TEV) and the percentage contribution of calories from proteins, carbohydrates, and lipids. The results are shown as mean, standard deviation, and percentile distribution (P5, P10, P25, P50, P75, P90, P95). The Student's t-test and analysis of variance (one-way ANOVA) with LSD post-hoc tests were used to determine the statistical significance of means between two groups and among three or more groups, respectively. Results: When comparing the mean values of TEV among categories of socioeconomic and demographic variables, statistically significant differences were found between women for ethnicity, years of schooling and socioeconomic level. Among men, differences were found for years of schooling and socioeconomic level. The mean energy value of men's diet was significantly higher than that of women (1475.8 kcal and 1236.4 kcal, respectively). The mean values of calorie percentage contribution from proteins, carbohydrates, and lipids were similar between men and women. Conclusion: The elderly of this study showed significant differences in mean values of TEV between sexes and between the categories years of schooling and socioeconomic level. Women also showed significant differences between the ethnic categories. The mean relative contribution of macronutrients in TEV was similar between genders and age groups.

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

What is the diagnostic value of ultrasonography compared to physical evaluation in patients with idiopathic carpal tunnel syndrome?

[EN] OBJECTIVE: Our hypothesis is that sonography performed by the rheumatologist in patients with suspected carpal tunnel syndrome (CTS) has higher diagnostic value compared to physical evaluation. METHODS: Adult patients with suspected idiopathic CTS, defined by sensory symptoms over the distribution of the median nerve with or without positive results with the Phalen and/or the Tinel's maneuvers were included. The diagnosis of CTS was indicated by typical symptoms daily for at least 3 months and a positive nerve conduction study. One rheumatologist unaware of the clinical and electrodiagnostic results performed an ultrasound examination of the median nerve for the area ranging from the inlet to the outlet of the carpal tunnel. Mean cross-sectional area at each level, flattening ratio and bowing of flexor retinaculum were obtained. RESULTS: Sixty-eight patients with 105 affected wrists were examined. Tinel's and Phalen's signs had a closer sensitivity (73% and 67% respectively) and specificity (40% and 30% respectively). The best swelling nerve cut-off by sonography was 9.7 mm2 at the tunnel inlet, with a sensitivity of 86%, a specificity of 48% and accuracy of 77%. A 100% positive predictive value was reached with a cross-sectional area of 13 mm2, involving 33 hands (31% of the whole sample). Maximal cross sectional area and the measurement of flexor retinaculum had an accuracy of 72% and 73% respectively. Combination of physical maneuvers and sonography not yielded more accuracy than cross-sectional area itself. CONCLUSION: In patients with clinical history of idiopathic CTS and positive nerve conduction study, sonography performed by the rheumatologist has higher diagnostic value than physical maneuvers.

Limited value of ultrasound assessment in patients with poor outcome after carpal tunnel release surgerys

[EN] OBJECTIVE: To determine the value of ultrasonography in the assessment of patients with idiopathic carpal tunnel syndrome (CTS) and poor outcome after carpal tunnel release. METHODS: A total of 88 consecutive patients with CTS (104 hands) underwent open surgical release of the median nerve. Ultrasound (US) examination was performed blind to any patient's data. The median nerve area at tunnel inlet and outlet, the retinaculum distance, and the flattening ratio were measured. The main outcome variable was the patient's overall satisfaction using a five-point Likert scale (1 = worse, 2 = no change, 3 = slightly better, 4 = much better, 5 = cured) at 3 months postoperatively. Pre- and postoperative ultrasonographic findings in relation to clinical outcome were analysed. RESULTS: Improvement (scores 4 or 5 on the Likert scale) was recorded in 75 hands (72%). After carpal tunnel release, the cross-sectional area at tunnel inlet decreased from a mean of 14.2 to 13.3 mm2 in the group with clinical improvement and also from a mean of 12.5 to 11.6 mm2 in the group with no change or slight improvement. No significant changes in the cross-sectional area at tunnel outlet, retinaculum distance, and flattening ratio were observed. CONCLUSION: Reduction of the median nerve cross-sectional area at tunnel inlet at 3 months after carpal tunnel release was similar in patients reporting cure or great improvement and in those with slight or no improvement. Ultrasonography is of limited value in assessment of patients with poor outcome after median nerve release.

On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.