Study of EIT resonances in an anti-relaxation coated Rb vapor cell

We study the sign of resonances obtained in electromagnetically induced transparency (EIT). Resonances of both kinds—bright (corresponding to enhanced absorption) and dark (corresponding to reduced absorption)—are obtained when the frequency of a probe beam is scanned. The experimental results, presented earlier, use magnetic sublevels of a hyperfine transition in the D₁ line of ⁸⁷Rb along with a magnetic field of 27 G. The atoms are contained in a vapor cell at room temperature, and with anti-relaxation coating on the walls. A quantitative theoretical model, which reproduces the experimental results quite well, is presented for the first time. The model solves the density matrix of the sublevels involved, and uses two regions—one with both the light and magnetic field, and the second without light and just a magnetic field. This ability to have both bright and dark resonances promises applications in sub- and super-luminal propagation of light.     

Synthesis of a novel, bowl-like bis γ-lactone

Synthesis of a compound with bowl-like, symmetrical molecular architecture, starting from a Diels-Alder adduct 7, derived from a reaction between 2,5-dihydro-2,5-dimethoxyfuran and 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadiene, is reported.     

Arylation of Sensitive 1-(Pyrrolidin-1-yl)-diazen-1-ium-diolate in Ionic Liquids

The purpose of this research was to investigate the stability and reactivity of 1-(pyrrolidin-1-yl)diazen-1-ium-1,2-diolate (PYRRO/NO) in dimethylformamide (DMF, as the reference solvent) and compare them to those obtained using different ionic liquids. The results of our experiments showed that PYRRO/NO is more stable (based on reactivity) in ionic liquid [EMIM][Ms] (with reaction yields up to 52%) than in DMF, that substitution products can be separated directly and quantitatively from the ionic liquid using a single flash-column separation, and that the ionic liquids can also be recovered and reused in a second iteration of the same reaction to achieve similar yields.     

Poly(γ‐glutamic acid)/Silica Hybrids with Calcium Incorporated in the Silica Network by Use of a Calcium Alkoxide Precursor

Current materials used for bone regeneration are usually bioactive ceramics or glasses. Although they bond to bone, they are brittle. There is a need for new materials that can combine bioactivity with toughness and controlled biodegradation. Sol‐gel hybrids have the potential to do this through their nanoscale interpenetrating networks (IPN) of inorganic and organic components. Poly(γ‐glutamic acid) (γ‐PGA) was introduced into the sol‐gel process to produce a hybrid of γ‐PGA and bioactive silica. Calcium is an important element for bone regeneration but calcium sources that are used traditionally in the sol‐gel process, such as Ca salts, do not allow Ca incorporation into the silicate network during low‐temperature processing. The hypothesis for this study was that using calcium methoxyethoxide (CME) as the Ca source would allow Ca incorporation into the silicate component of the hybrid at room temperature. The produced hybrids would have improved mechanical properties and controlled degradation compared with hybrids of calcium chloride (CaCl₂), in which the Ca is not incorporated into the silicate network. Class II hybrids, with covalent bonds between the inorganic and organic species, were synthesised by using organosilane. Calcium incorporation in both the organic and inorganic IPNs of the hybrid was improved when CME was used. This was clearly observed by using FTIR and solid‐state NMR spectroscopy, which showed ionic cross‐linking of γ‐PGA by Ca and a lower degree of condensation of the Si species compared with the hybrids made with CaCl₂ as the Ca source. The ionic cross‐linking of γ‐PGA by Ca resulted in excellent compressive strength and reduced elastic modulus as measured by compressive testing and nanoindentation, respectively. All hybrids showed bioactivity as hydroxyapatite (HA) was formed after immersion in simulated body fluid (SBF).     

Fibrinolytic activity of kaempferol isolated from the fruits of Lagenaria siceraria (Molina) Standley

This study was undertaken to isolate a flavonol, kaempferol, from the fruits of Lagenaria siceraria (bottle gourd) as a sole compound and to explore the fibrinolytic potential of the methanolic extract of the fruits of L. siceraria and the isolated compound using their in vitro activity. The fibrinolytic activity in terms of percentage of plasma clot liquefaction was determined by plasma clot lysis at 37°C in 24?h. The fibrinolytic activity of both substances was compared to the well-known thrombolytic agent streptokinase (30,000?IU). The percentage of fibrinolytic activity of the extract and isolated compound were found to be 54.72?±?0.7210 and 77.37?±?1.3010, respectively. Streptokinase was considered as the standard fibrinolytic enzyme for comparative purposes and had 91.46?±?0.7625% fibrinolytic activity. The conclusion drawn in our study after testing the hypothesis by experimental procedures is that in vitro fibrinolytic activity on plasma clots is an inherent property of kaempferol isolated from the fruits of L. siceraria, and its comparison with streptokinase is a new aspect for further study.     

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.     

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.