Comparative studies of praseodymium(III) selective sensors based on newly synthesized Schiff's bases

Praseodymium ion selective polyvinyl chloride (PVC) membrane sensors, based on two new Schiff's bases 1,3-diphenylpropane-1,3-diylidenebis(azan-1-ylidene)diphenol (M₁) and N,N′-bis(pyridoxylideneiminato) ethylene (M₂) have been developed and studied. The sensor having membrane composition of PVC: o-NPOE: ionophore (M₁): NaTPB (w/w; mg) of 150: 300: 8: 5 showed best performances in comparison to M₂ based membranes. The sensor based on (M₁) exhibits the working concentration range 1.0 × 10⁻⁸ to 1.0 × 10⁻² M with a detection limit of 5.0 × 10⁻⁹ M and a Nernstian slope 20.0 ± 0.3 mV decade⁻¹ of activity. It exhibited a quick response time as <8 s and its potential responses were pH independent across the range of 3.5-8.5.The influence of the membrane composition and possible interfering ions have also been investigated on the response properties of the electrode. The sensor has been found to work satisfactorily in partially non-aqueous media up to 15% (v/v) content of methanol, ethanol or acetonitrile and could be used for a period of 3 months. The selectivity coefficients determined by using fixed interference method (FIM) indicate high selectivity for praseodymium(III) ions over wide variety of other cations. To asses its analytical applicability the prepared sensor was successfully applied for determination of praseodymium(III) in spiked water samples.     

A single-wall carbon nanotubes modified edge plane pyrolytic graphite sensor for determination of methylprednisolone in biological fluids

An electrochemical protocol based on reduction is developed to determine methylprednisolone using single-wall carbon nanotubes (SWNTs) modified edge plane pyrolytic graphite electrode (EPPGE). To obtain a good sensitivity, instrumental variables were studied using Square Wave Voltammetry (SWV). The voltammetric results indicate that SWNTs modified EPPGE remarkably enhances the reduction of methylprednisolone which leads to considerable improvement of peak current with shift of peak potential to less negative values. The voltammetric current showed a linear response for methylprednisolone concentration in the range 5-500 nM with a sensitivity of 98 nA nM⁻¹. The limit of detection was estimated to be 4.5 × 10⁻⁹ M. The developed method is used for the determination of methylprednisolone in pharmaceutical dosages and human blood plasma samples of patients undergoing treatment with methylprednisolone. The major metabolites present in blood plasma did not interfere with the present investigation as they did not exhibit reduction peak in the experimental range used. A comparison of results with high performance liquid chromatography (HPLC) indicates a good agreement.     

Riccati generalization of self-similar solutions of nonautonomous Gross-Pitaevskii equation

We present a systematic analytical approach to construct a family of self-similar waves, related through a free parameter, in quasi one-dimension Gross-Pitaevskii equation with time-varying parameters. This approach enables us to control the dynamics of dark and bright similaritons, and first- and second- order self-similar rogue waves in Bose-Einstein condensate through the modulation of time dependent trapping potential. The analysis is done for the sech²? type time-varying quadratic trapping potential for two different choices of linear potential.     

On the approximability of adjustable robust convex optimization under uncertainty

In this paper, we consider adjustable robust versions of convex optimization problems with uncertain constraints and objectives and show that under fairly general assumptions, a static robust solution provides a good approximation for these adjustable robust problems. An adjustable robust optimization problem is usually intractable since it requires to compute a solution for all possible realizations of uncertain parameters, while an optimal static solution can be computed efficiently in most cases if the corresponding deterministic problem is tractable. The performance of the optimal static robust solution is related to a fundamental geometric property, namely, the symmetry of the uncertainty set. Our work allows for the constraint and objective function coefficients to be uncertain and for the constraints and objective functions to be convex, thereby providing significant extensions of the results in Bertsimas and Goyal (Math Oper Res 35:284–305, 2010) and Bertsimas et al. (Math Oper Res 36: 24–54, 2011b) where only linear objective and linear constraints were considered. The models in this paper encompass a wide variety of problems in revenue management, resource allocation under uncertainty, scheduling problems with uncertain processing times, semidefinite optimization among many others. To the best of our knowledge, these are the first approximation bounds for adjustable robust convex optimization problems in such generality.     

Oxidation chemistry of 2'-deoxyadenosine at pyrolytic graphite electrode

The electrochemical oxidation of 2'-deoxyadenosine has been investigated in phosphate containing supporting electrolytes in pH range 2-10 at a pyrolytic graphite electrode by cyclic sweep voltammetry, spectral studies, controlled potential electrolysis and related techniques. The oxidation of 2'-deoxyadenosine occurred in a single well-defined oxidation peak (I(a)), over the entire pH range. The electrooxidation occurred by the loss of 6.0+/-0.5 e(-) per mole over the entire pH range. The kinetics of the decay of the UV-absorbing intermediates has been studied and found to follow pseudo first order kinetics having rate constant (k) in the range (5.7-7.7)x10(-4) s(-1). The major products of electrooxidation were separated by HPLC and characterized by GC-MS/MS, (1)H NMR and a tentative mechanism for electrooxidation of 2'-deoxyadenosine has been suggested.     

Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives

Estimates for second and third Maclaurin coefficients of certain bi-univalent functions in the open unit disk defined by convolution are determined. Certain special cases are also indicated.     

A PTAS for the chance-constrained knapsack problem with random item sizes

We consider a stochastic knapsack problem where each item has a known profit but a random size that is normally distributed independent of other items. The goal is to select a profit maximizing set of items such that the probability of the total size exceeding the knapsack bound is at most a given threshold. We present a Polynomial Time Approximation Scheme (PTAS) for the problem via a parametric LP reformulation that efficiently computes a solution satisfying the chance constraint strictly and achieving near-optimal profit.     

Equipment Selection Problems in Just-in-Time Manufacturing Systems

This paper is concerned with the development of a mathematical model for solving the problem of equipment selection in just-in-time (JIT) manufacturing systems. Equipment selection issues are important, particularly during the initial stages of implementing JIT. In this paper a mathematical model is proposed for capacity planning and for selecting equipment in a multi-stage JIT production system. An example situation is considered to explain the application and behaviour of the model.