Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

Kinetics of Oxidation of 4-Oxoacids by <Emphasis Type="Italic">N</Emphasis>-Chlorosaccharin in Aqueous Acetic Acid Medium

The oxidation kinetics of substituted and unsubstituted 4-oxoacids (S) by N-chlorosaccharin (NCSA) have been studied in aqueous acetic acid media. The reaction follows first-order kinetics in each of the 4-oxoacids, NCSA and H⁺. The effect of changes in the electronic nature of the substrate reveals that positive charge develops in the transition state. Based on the kinetic results and product analysis, a suitable mechanism has been proposed for the reaction of NCSA with 4-oxoacids.     

Kinetics and mechanism of oxidation of 4-oxoacids by N-bromosuccinimide in aqueous acetic acid medium

Kinetics and mechanism of oxidation of substituted and unsubstituted 4-oxoacids (S) by N-bromosuccinimide (NBS) in aqueous acetic acid medium have been studied potentiometrically. The reaction follows first-order kinetics, each in 4-oxoacids, NBS and H⁺. The effect of changes in the electronic nature of the substrate reveals that there is a development of positive charge in the transition state. Based on the kinetic results and the product analysis, a suitable mechanism has been proposed for the reaction of NBS with 4-oxoacids.     

Exact Solution of a(2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a(2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function grrproposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum.Grav. 6(1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.     

Exact interior solutions in 2+1-dimensional spacetime

An exact formulation of two-dimensional chiral hydrodynamics with diffeomorphism and conformal anomalies is provided. The constitutive relation involving the stress tensor is computed. It reveals a one parameter class of solutions which is a new result. For a particular value of this parameter, the results found in the gradient expansion scheme are reproduced. Moreover, the constitutive relation is analogous to the corresponding relation for an ideal fluid, appropriately modified to include the chirality property, which has also been derived here.     

Time-optimal control of a parabolic system with time lags given in the integral form

In this paper the time-optimal control problem for a distributedparabolic system in which time lags appear in the integral formboth in the state equation and in the boundary condition ispresented. The particular properties of the optimal controlare discussed.     

Higher dimensional global monopole in Brans-Dicke theory

The gravitational field of a higher dimensional global monopole in the context of Brans-Dicke theory of gravity is investigated. The space time metric and the scalar field generated by a global monopole are obtained using the weak field approximation. Finally, the geodesic of a test particle due to the gravitational field of the monopole is studied.     

Electrochemical Studies on Effects of Psychostimulants,Opioids and Alcohol Intake Towards Level of Hydrogen Peroxide in the Brain Striatum

Hydrogen peroxide (H₂O₂) was the main types of many peroxides produced in living mammalian cells that consumed oxygen. In the brain, the main source of H₂O₂ was the superoxide dismutase (SOD)‐catalyzed reaction in mitochondria. However, the level of H₂O₂ would be elevated through administration of control drugs and alcohol by dopamine metabolism of monoamine oxidase. In this study, a H₂O₂ microsensor was used to investigate the level of H₂O₂ in the brain striatum after administration of methamphetamine (MAP), morphine (MrP) or ethanol (Eth). The placement of microsensor in the brain was done at coordinates A/P 1.1 from bregma, M/L+2.6 and D/V‐1.5. A working potential of +0.05 V vs. Ag/AgCl was applied. The H₂O₂ concentration was measured direct from the current generated by its catalytic reaction at the electro active surface of the electrode. A significant increase of H₂O₂ level was observed after 7 successive injections of the controlled drugs or alcohol. The initial measurement of H₂O₂ is essential as excess dosage of H₂O₂ during treatment will contribute to the formation of neurotoxin oxygenated radicals. The H₂O₂ was the precursor of O_2? and OH radicals. Thus, this study provided a mean to monitor H₂O₂ level in the brain.