Calculus of variations on time scales: weak local piecewise Crd solutions with variable endpoints

A nonlinear calculus of variations problem on time scales with variable endpoints is considered. The space of functions employed is that of piecewise rd-continuously Δ-differentiable functions (C¹_prd). For this problem, the Euler-Lagrange equation, the transversality condition, and the accessory problem are derived as necessary conditions for weak local optimality. Assuming the coercivity of the second variation, a corresponding second order sufficiency criterion is established.     

New Biomimetic Catalysts for the Electrochemical Processes on the Basis of Redox-Active Macrocyclic Frame Structures

Abstract

Efficient catalytic systems mimicking the action of metalloenzymes based on cyclic frame structures containing phosphorus, nitrogen, and sulfur coordinating atoms for hydrogen oxidation or reduction under mild conditions are proposed.     

An alternative Route to (±)-Warburganal Synthon

The transformation of the ketone (1) to the unsaturated diester (11) a potential intermediate for the warburganal (12) is described. The Wittig reaction of theketone (1) with methylenetriphenylphosphorane afforded the olefin (2) which reacts with Woodward's reagent (MeCOOAg, I₂ and MeCOOH and H₂O) to give the diol (13). This on heating with dimethylsulfoxide afforded the tetralin (14)     

Vendor managed inventory for environments with stochastic product usage

We develop technology to plan delivery routes for the supply of blood products to hospitals by a blood bank. The technology produces low cost, robust plans that hedge against the natural uncertainty associated with blood product usage at hospitals. The technology relies on sampling-based approaches involving integer programming and variable neighborhood search. An extensive computational study shows the efficacy of the two approaches and highlights the impact of product usage uncertainty on the resulting delivery plans.