Thresholded covering algorithms for robust and max–min optimization

In a two-stage robust covering problem, one of several possible scenarios will appear tomorrow and require to be covered, but costs are higher tomorrow than today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? We consider the \(k\) -robust model where the possible scenarios tomorrow are given by all demand-subsets of size \(k\) . In this paper, we give the following simple and intuitive template for \(k\) -robust covering problems: having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat. We show that this template gives good approximation algorithms for \(k\) -robust versions of many standard covering problems: set cover, Steiner tree, Steiner forest, minimum-cut and multicut. Our \(k\) -robust approximation ratios nearly match the best bounds known for their deterministic counterparts. The main technical contribution lies in proving certain net-type properties for these covering problems, which are based on dual-rounding and primal–dual ideas; these properties might be of some independent interest. As a by-product of our techniques, we also get algorithms for max–min problems of the form: “given a covering problem instance, which \(k\) of the elements are costliest to cover?” For the problems mentioned above, we show that their \(k\) -max–min versions have performance guarantees similar to those for the \(k\) -robust problems.     

Activation-controlled outer-sphere electron transfer reactions: reduction of heteropoly 11-tungstovanadophosphate and heteropoly 10-tungstodivanado phosphate by thiourea in aqueous acid medium

The kinetics of reduction of heteropoly 11-tungstovanadophosphate, [PV^VW₁₁O₄₀]⁴⁻, (HPA1) and heteropoly 10-tungstodivanadophosphate, [PV^VV^VW₁₀O₄₀]⁵⁻, (HPA2) by thiourea has been investigated in HClO₄/phthalate/acetate buffer solutions spectrophotometrically at 25 °C in aqueous medium. The stoichiometry of the reaction is 1:1 in both cases. The HPAs are converted into the corresponding one-electron reduced heteropoly blues, namely, [PV^IVW₁₁O₄₀]⁵⁻ and [PV^IVV^VW₁₀O₄₀]⁶⁻, and thiourea is oxidised to formamidine disulphide. The reaction shows first-order dependence in both [HPA] and [thiourea] at constant pH. The rate–pH profile shows the participation of both the neutral and deprotonated forms of thiourea in the reaction. The reaction proceeds through an outer sphere electron transfer mechanism in which activation-controlled electron transfer is the rate-determining step. Self-exchange rate constants for the couples [PV^VW₁₁O₄₀]⁴⁻/[PV^IVW₁₁O₄₀]⁵⁻, [PV^VV^VW₁₀O₄₀]⁵⁻/[PV^IVV^VW₁₀O₄₀]⁶⁻ and H₂NCSNH₂/H₂NCS^·+NH₂ have been evaluated by Marcus theory.     

Cascade synthesis of bis-N-sulfonylcyclobutenes via Cu(I)/Lewis acid-catalyzed (3 + 2)/(2 + 2) cycloadditions: observation of aggregation-induced emission enhancement from restricted C=N photoisomerization

A remarkable role of Lewis acid additives in syntheses of bis-N-sulfonylcyclobutenes via copper(I) catalyzed (3 + 2)/(2 + 2) cycloaddition cascade of sulfonyl azides and terminal alkynes is described. In addition, these cyclobutenes display a unique aggregation-induced emission enhancement (AIEE), reported for the first time, arising predominantly from restricted rotation in C=N photoisomerization in the solid state.     

Normal Approximations for Descents and Inversions of Permutations of Multisets

Normal approximations for descents and inversions of permutations of the set {1,2,…,n} are well known. We consider the number of inversions of a permutation π(1),π(2),…,π(n) of a multiset with n elements, which is the number of pairs (i,j) with 1≤i<j≤n and π(i)>π(j). The number of descents is the number of i in the range 1≤i<n such that π(i)>π(i+1). We prove that, appropriately normalized, the distribution of both inversions and descents of a random permutation of the multiset approaches the normal distribution as n→∞, provided that the permutation is equally likely to be any possible permutation of the multiset and no element occurs more than α n times in the multiset for a fixed α with 0<α<1. Both normal approximation theorems are proved using the size bias version of Stein’s method of auxiliary randomization and are accompanied by error bounds. This work was supported by a research fellowship from the Sloan Foundation.     

Blue luminescence from the InGaN multiple quantum wells

We have fabricated very high-quality In_0.13Ga_0.87N/GaN multiple quantum wells with thickness as small as on (0 0 0 1) sapphire substrate using metal organic chemical vapour deposition (MOCVD). We have investigated these ultra-thin multiple quantum wells by continuous wave (cw) and time resolved spectroscopy in the picosecond time scales in a wide range of temperatures from 10 K to 290 K. In the luminescence spectrum at 10 K we observed a broad peak at 3.134 eV which was attributed to the quantum wells emission of InGaN. The full-width at half-maximum of this peak was 129 meV at 10 K and the broadening at low temperatures which was mostly inhomogeneous was thought to be due to compositional fluctuations and interfacial disorder in the alloy. The ultra narrow width of the quantum well was found to have a very profound effect in increasing the emission linewidth. We also observed an intense and narrow peak at 3.471 eV due to the GaN barrier. The temperature dependence of the luminescence was studied. The peak positions and intensities of the different peaks were obtained after a careful Lorentzian analysis. The activation energy of the InGaN quantum well emission peak was estimated as 69 meV. The lifetime of the quantum well emission was found to be 720 ps at 10 K. The results were explained by considering the localization of the excitons due to potential fluctuations. At higher temperatures the non-radiative recombination was found to be very dominant.     

Michael addition of indoles to β-nitrostyrenes catalyzed by HY zeolite under solvent-free conditions

Michael addition of indoles to β-nitrostyrenes is reported using HY zeolite as catalyst under mild reaction conditions. This methodology allows the synthesis of various indole derivatives in good to high yields at 50 °C under solvent-free conditions. The short reaction time and achieving high yield of the desired products are the main advantages of the present work. The catalyst can be easily recovered and reused for six successive runs without considerable changes in yields. This Michael addition catalyzed by HY zeolite is operationally simple and can be considered as a greener protocol as it avoids the use of corrosive acids and toxic reagents.     

Highly Selective “Turn‐On” Fluorescent and Colorimetric Sensing of Fluoride Ion Using 2‐(2‐Hydroxyphenyl)‐2,3‐dihydroquinolin‐4(1 H)‐one based on Excited‐State Proton Transfer

A simple, highly selective and sensitive colorimetric system for the detection of fluoride ion in an aqueous medium has been developed using 2‐(2‐hydroxyphenyl)‐2,3‐dihydroquinolin‐4(1 H)‐one. This system allows selective “turn‐on” fluorescence detection of fluoride ion, which is found to be dependent upon guest basicity. An excited‐state proton transfer is proposed to be the signaling mechanism, which is rationalized by DFT and TD‐DFT calculations. The present sensor can also be applied to detect fluoride levels in real water samples.