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.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.

Drying of persimmon: Mathematical model for diffusivity as a simultaneous function of moisture content and shrinkage

Fresh persimmon has a high moisture content (about 85% wet basis) making it highly perishable and requiring adequate drying conditions to obtain an acceptable dehydrated product. Drying kinetics of persimmon cv. Rama Forte was studied in a fixed bed dryer at temperatures ranging from 50 to 80 degreesC and air velocity of 0.8 m/s. Shrinkage during drying was described by a linear correlation with respect to water content. Evaluation of effective diffusivity as a function of moisture content, with undergoing shrinkage during drying was based on Fourier series solution of Fick's diffusion equation. Effective diffusivity values at moisture contents between 0.09 - 4.23 kg water/kg dry matter were found to be in the range of 2.6 x 10(-10) m(2)/s to 5.4 x 10(-10) m(2)/s, and its dependence on air drying temperature was represented by an Arrhenius type equation. Activation energy increased with decreasing water content in persimmons.

Disturbances in beta-cell function in impaired fasting glycemia

In a cross-sectional study, we assessed beta-cell function and insulin sensitivity index (ISI) with hyperglycemic clamps (10 mmol/l) in 24 subjects with impaired fasting glycemia (IFG, fasting plasma glucose [FPG] between 6.1 and 7.0 mmol/l), 15 type 2 diabetic subjects (FPG >7.0 mmol/l), and 280 subjects with normal fasting glycemia (NFG, FPG <6.1 mmol/l). First-phase insulin release (0-10 min) was lower in IFG (geometric mean 541 pmol/l (.) 10 min; 95% confidence interval [CI] 416-702 pmol/l (.) 10 min) and in type 2 diabetes (geometric mean 376 pmol/l (.) 10 min; 95% CI 247-572 pmol/l (.) 10 min) than NFG (geometric mean 814 pmol/l (.) 10 min; 95% CI 759-873 pmol/l (.) 10 min) (P < 0.001). Second-phase insulin secretion (140-180 min) was also lower in IFG (geometric mean 251 pmol/l; 95% CI 198-318 pmol/l; P = 0.026) and type 2 diabetes (geometric mean 157 pmol/l; 95% CI 105-235 pmol/l; P < 0.001) than NFG (geometric mean 295 pmol/l; 95% CI 276-315 pmol/l): IFG and type 2 diabetic subjects had a lower ISI (0.15 +/- 0.02 and 0.16 +/- 0.02 mumol/kg fat-free mass [FFM]/min/ pmol/l, respectively) than NFG (0.24 +/- 0.01 mumol/kg FFM/min/pmol/l, P < 0.05). We found a stepwise decline in first-phase (and second-phase) secretion in NFG subjects with progressive decline in oral glucose tolerance (P < 0.05). IFG subjects with impaired glucose tolerance (IGT) had lower first-phase secretion than NFG subjects with IGT (P < 0.02), with comparable second-phase secretion and ISI. NFG and IFG subjects with a diabetic glucose tolerance (2-h glucose >11.1 mmol/l) had a lower ISI than their respective IGT counterparts (P < 0.05). We conclude that the early stages of glucose intolerance are associated with disturbances in beta-cell function, while insulin resistance is seen more markedly in later stages.

Designing a modified Hopfield network to solve an Economic Dispatch problem with nonlinear cost function

Economic Dispatch (ED) problems have recently been solved by artificial neural networks approaches. In most of these dispatch models, the cost function must be linear or quadratic. Therefore, functions that have several minimum points represent a problem to the simulation since these approaches have not accepted nonlinear cost function. Another drawback pointed out in the literature is that some of these neural approaches fail to converge efficiently towards feasible equilibrium points. This paper discusses the application of a modified Hopfield architecture for solving ED problems defined by nonlinear cost function. The internal parameters of the neural network adopted here are computed using the valid-subspace technique, which guarantees convergence to equilibrium points that represent a solution for the ED problem. Simulation results and a comparative analysis involving a 3-bus test system are presented to illustrate efficiency of the proposed approach.

EFFECT OF AN LH-RH ANALOG ON CAT TESTIS AND ADRENAL-CORTEX FUNCTION

The LH-RH analog LH-RH-A (des-Gly10,[D-Trp6]-LH-RH ethylamide) was administered in pharmacological doses (20-mu-g/kg, sc) to adult male cats for 15 days and its effect on testis and adrenal function was determined. Daily administration of the analog promoted a 3-fold increase in plasma testosterone levels after 7 days, indicating a stimulatory effect of LH-RH-A (mean +/- SD for 6 treated cats, 1.88 +/- 0.35 vs 0.51 +/- 0.08 ng/ml for 6 control cats). After 15 days the LH-RH-A-treated group exhibited a similar plasma testosterone concentration as the control group (mean +/- SD, 0.96 +/- 0.35 ng/ml vs 0.88 +/- 0.39 ng/ml, respectively), similar testicular and adrenal weights and no significant differences in the spermatogenic process. However, semiquantitative analysis of the zona fasciculata of the adrenals from the LH-RH-A-treated group showed a significant accumulation of a substance not stained by hematoxylin-eosin or Schiff periodic acid (mean +/- SD of index of accumulation was 3.50 +/- 0.4 for treated cats vs 2.20 +/- 0.3 for control cats). The present results show that pharmacological doses of LH-RH-A have an effect on the adrenal cortex of cats without modifying spermatogenesis or plasma testosterone levels.

Appraisal of the chelipeds size on Hepatus-pudibundus (Herbst, 1785) (Crustacea, Calappidae) in function of sex and maturation

This paper appraises the influence of chelipeds on sexual and maturation phasis of the crab Hepatus pudibundus (Herbst, 1785), collected in Ubatuba (SP) region. The allometric constants obtained from the regression (carapace width X cheliped weight) adjusted to a power function (Y=aX(b)) were analysed. It was verified that males show larger chelipeds than females. The mean percentage of the chelipeds weight differs in sex and maturation.

On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

THE GREEN-FUNCTION IN THE BLOCH-NORDSIECK MODEL FOR QED(3)

The electron Green's function is obtained in the Bloch-Nordsieck approximation of three-dimensional QED. Dimensional regularization is used in the intermediate stages of calculation.

Long-term accumulation of uranium in bones of Wistar rats as a function of intake dosages

Groups of Wistar rats were fed with ration doped with uranyl nitrate at concentration A ranging from 0.5 to 100 ppm, starting after the weaning period and lasting until the postpuberty period when the animals were sacrificed. Uranium in the ashes of bones was determined by neutron activation analysis. It was found that the uranium concentration in the bones. as a function of A, exhibits a change in its slope at similar to20 ppm-a probable consequence of the malfunctioning of kidneys. The uranium transfer coefficient was obtained and an analytical expression was fitted into the data. thus allowing extrapolation down to low doses. Internal and localized doses were calculated. Absorbed doses exceeded the critical dose. even for the lowest uranium dosage.

K-bi-Lipschitz equivalence of real function-germs

In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to K-bi-Lipschitz equivalence, is finite.

Charge distribution and calcium affinity of sulfated alpha-L-galactans from ascidians. Comparison between linear and highly branched polymers

Calcium binding and charge distribution on highly branched and linear sulfated L-galactans from ascidians have been studied using a metallochromic indicator and conductimetric titrations. The distance between charged groups of the linear and highly branched galactans does not vary despite their marked differences in sulfate/total sugar molar ratios. These results indicate that the sulfated L-galactose units are concentrated in the central polysaccharide core and not intercalated among non-sulfated units. This inference is consistent with the chemical studies of these galactans. Surprisingly, calcium affinity increases with increasing amounts of non-sulfated sugar branches in the molecule. Thus, calcium binding in these polymers is not a simple function of availability of anion binding sites but a more complex calcium-polysaccharide interaction. (C) 1998 Elsevier B.V. Ltd. All rights reserved.