Synthesis and applications of novel bis(ammonium) chiral ionic liquids derived from isomannide

Carbohydrate-based novel bis(ammonium) chiral ionic liquids have been synthesized by following a straightforward protocol using isomannide as the substrate. Their applications in chiral discrimination and optical resolution of racemates have been established.     

Temperature sensing behaviour of the stark sublevels

The temperature dependence of the fluorescence intensity ratio of the two stark components of (4)S(3/2)-->(4)I(15/2) transition using 800 nm radiation from a Ti-sapphire laser pumped by the second harmonic of Nd:YVO(4) laser has been augmented in Er(3+) doped tellurite glass. It is emphasized that even the two stark components of (4)S(3/2)-->(4)I(15/2) transition may be utilized to monitor the temperature within 300-550 K with its appreciable sensitivity.     

Convenient photooxidation of alcohols using dye sensitised zinc oxide in combination with silver nitrate and TEMPO

A novel photooxidative system using dye sensitised zinc oxide in combination with silver nitrate and 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO) in an aqueous solution is described. Under visible light irradiation the selective oxidation of alcohols to their corresponding aldehydes and ketones was effected in good to excellent yields.     

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.     

A stable numerical inversion of Abel's integral equation using almost Bernstein operational matrix

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel's type integral equation. The aim of this communication is to modify the stable algorithm proposed in [Singh VK, Pandey RK, Singh OP. New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials. Applied Mathematical Sciences 2009;3(5):241–255] which is based on normalized Bernstein polynomial approximation of the projected intensity profile. So, first we construct an orthonormal family of polynomials of degree 5 from the 5th degree Bernstein polynomials B_i5 and use them as a basis to approximate the projected intensity profile. Then, a 6×6 matrix P, named as almost Bernstein operational matrix of integration is constructed and used to reduce the integral equation to a system of algebraic equation which can be solved easily. The method is quite accurate and stable even though the approximations are performed by polynomials of degree 5, as illustrated by applying the method to intensity data with and without random noise to invert and compare it with those obtained by the other methods or with the known analytical inverse. Thus it is good method for applying to experimental intensities distorted by noise.     

One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems

Non-overlapping domain decomposition (DD) methods with complex first order Robin-type transmission conditions (TCs) provide an efficient iterative solution for Maxwell’s equation. Unfortunately, the first order TCs do not effectively account for some eigenmodes of the system matrix, which limits the scalability of the methods. In this work, we examine two TCs with a second order transverse derivative to improve the method’s performance. A detailed convergence analysis of the two TCs is presented. We then investigate the use of the two second order TCs in non-conformal and non-overlapping one way DD methods. Numerical results illustrate the effectiveness of the proposed methods on some model problems and on several problems of practical interest.     

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.     

A stable algorithm for numerical evaluation of Hankel transforms using Haar wavelets

The purpose of the paper is to propose a stable algorithm for the numerical evaluation of the Hankel transform F _n (y) of order n of a function f(x) using Haar wavelets. The integrand \(\sqrt x f(x)\) is replaced by its wavelet decomposition. Thus representing F _n (y) as a series with coefficients depending strongly on the local behavior of the function \(\sqrt x f(x)\), thereby getting an efficient and stable algorithm for their numerical evaluation. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithm.     

Naturally occurring aristolactams, aristolochic acids and dioxoaporphines and their biological activities

Aristolactams, having a phenanthrene chromophore are a small group of compounds mainly found in the Aristolochiaceae together with the aristolochic acids and 4,5-dioxoaporphines. In this report, these three important classes of natural products are reviewed and classified on the basis of their oxygenation pattern. In addition the biological activities of these compounds and their general chemistry are discussed.     

A comparative study of FIR and FL based temperature sensing schemes: an example of Pr3+

Temperature sensing schemes based on fluorescence intensity ratio and fluorescence lifetimes have been compared on the basis of experimental and theoretical approaches, taking Pr³⁺ as an example. The responses of the two techniques based on their sensitivities has also been discussed. PACS 42.70.Ce