Stable Convergence of Multiple Wiener-Itô Integrals

We prove sufficient conditions ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Note that stable convergence is stronger than convergence in distribution. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a version of the correspondence between “abstract” and “concrete” filtered Wiener spaces, in a spirit similar to that of Üstünel and Zakai (J. Funct. Anal. 143, 10–32, [1997]).     

Prediction of Henry's constants of xenon in cyclo-alkanes from molecular dynamics simulations

Using the molecular dynamics (MD) method, we demonstrate that intermolecular nuclear magnetic resonance (NMR) chemical shifts can be used to evaluate and develop intermolecular potentials for cross-interactions for use in solubility studies. The calculation of chemical shifts in MD is an order of magnitude more efficient than solubilities, which makes it an attractive tool for fine-tuning potential models. We examine the average Xe chemical shifts in cyclo-alkanes over a range of temperatures to develop a suitable potential model for the cross-interactions between Xe and a series of cyclo-alkanes. Our results clearly demonstrate that potential models that show better agreement with experiments for chemical shift, invariably lead to better agreement with experiment for Henry's constant and solubility of gases in solvents.     

Mononuclear lanthanide single-molecule magnets based on polyoxometalates

[ErW10O36]9- is the first polyoxometalate behaving as a single-molecule magnet (SMM). It shows frequency-dependent out-of-phase magnetization and a thermally activated single relaxation process with an effective barrier of 55.8 K. This single lanthanide ion polyoxometalate is the inorganic analogue of the bis(phthalocyaninato)lanthanide SMMs, both exhibiting very similar ligand field symmetries around the lanthanide ion (idealized D4d). It is chemically stable and offers new avenues for organization and processing of single-molecule magnets. Furthermore, it can be made free from nuclear spins and opens the possibility to be used for studies of decoherence on unimolecular qubits.     

Airy Equation for the Topological String Partition Function in a Scaling Limit

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.     

Recent Advances in Nanomaterial‐Modified Pencil Graphite Electrodes for Electroanalysis

Pencil graphite electrodes (PGEs) have several advantages over other carbon‐based or commercial metal electrodes, including widespread availability, very low cost, and ease of modification. To make the best use of PGEs in electroanalysis, significant recent advances in the development of different nanomaterial‐PGEs have been observed. The literature published up to mid‐2015 is summarized in the present review, with a focus on the various methodologies used to readily modify graphite pencil electrodes using nanomaterials. This review also touches on the surface characterization of these electrodes and their potential applications in a variety of electrochemical detection applications. The review outlines the scope for further research in this area and discusses the importance of surface modifications of conventional PGE electrodes using nanomaterials or a combination of nanomaterials and electroactive polymers.     

Ailanthus altissima (Miller) Swingle fruit - new acyl β-sitosteryl glucoside and in vitro pharmacological evaluation

β-Sitosterol-3-O-(6?-O-13?-octadecenoyl)-β-D-glucoside (1), a new acyl β-sitosteryl glucoside, along with three known compounds β-sitosterol-3-O-β-D-glucoside (2), β-sitosterol (3) and methyl gallate (4) have been isolated from the ethyl acetate soluble fraction of methanolic extract of Ailanthus altissima fruits. Their structures were elucidated through spectroscopic data including 2D NMR, ESI-MS, methanolysis and oxidative cleavage of double bond. Antibacterial, antifungal, cytotoxic, phytotoxic and insecticidal activities were evaluated of compound 1, crude extract and its fractions so far for the first time. Pharmacological activities results showed that n-butanol fraction was good active against Pseudomonas aeruginosa and Salmonella typhi bacteria, and moderate active against Microsporum canis fungus. Crude extract, n-butanol and aqueous fractions showed good cytotoxicity. Moreover, compound 1, extract and all fractions showed notable phytotoxicity at higher concentrations, whereas all inactive against assayed insects.     

Variation of student numerical and figural reasoning approaches by pattern generalization type,strategy use and grade level

This paper explored variation of student numerical and figural reasoning approaches across different pattern generalization types and across grade level. An instrument was designed for this purpose. The instrument was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. Analysis of data showed that the numerical reasoning approach seems to be more dominant than the figural reasoning approach for the near and far pattern generalization types but not for the immediate generalization type. The findings showed that for the recursive strategy, the numerical reasoning approach seems to be more dominant than the figural reasoning approach for each of the three pattern generalization types. However, the figural reasoning approach seems to be more dominant than the numerical reasoning approach for the functional strategy, for each generalization type. The findings also showed that the numerical reasoning was more dominant than the figural reasoning in lower grade levels (grades 4 and 5) for each generalization type. In contrast, the figural reasoning became more dominant than the numerical reasoning in the upper grade levels (grades 10 and 11).     

A new 14-membered cyclopeptide alkaloid from Zizyphus oxyphylla

One new 14-membered frangulanine-type cyclopeptide alkaloid, oxyphyl line-A (1) has been isolated from the stem bark of Zizyphus oxyphylla together with the known 13-membered cyclopeptide, nummularine R (2). The structure was established on the basis of spectral studies particularly 2D NMR.     

A novel antimicrobial triterpenic acid from the leaves of Ficus benjamina (var. comosa)

The chloroform extract of the leaves of Ficus benjamina (var. comosa) (Moraceae) afforded a new triterpenic acid named as (9,11), (18,19)-disecoolean-12-en-28-oic acid (1) along with β-amyrin (2). Their structures were established on the basis of chemical and physical evidences (IR, ¹H NMR, and MS data). The compound 1 exhibited significant antimicrobial activity against Salmonella typhimurium (MTCC-98), Candida albicans (IAO-109), Staphylococcus aureus (IAO-SA-22), Escherichia coli (K-12) and low activity against Aspergillus niger (lab isolate ICAR) and Aspergillus brassicola.     

Synthesis,Crystal Structure,Ab Initio Studies and Fingerprint Plots of 2-Chloro-1,3-dioxo-2,3-dihydro-1H-inden-2-yl acetate

Abstract  

2-Chloro-1,3-dioxo-2,3-dihydro-1H-inden-2-yl acetate, C₁₁H₇ClO₄ (Fig. 1), has been synthesized and the structure has been solved by IR and X-ray diffraction studies. The crystals are triclinic, space group P [`1] \bar{1} , with a = 7.62060(10) ?, b = 11.5944(2) ?, c = 13.0753(3) ?, α = 97.2820(10)°, β = 101.5740(10)°, γ = 101.7930(10)°, Mr = 238.62, V = 1090.82(3) ?³, Z = 4 and R = 0.0557. In the title compound there are two molecules in the asymmetric unit. The molecules are linked via weak C–H···O hydrogen bonds forming R₄⁴(28) rings. The intermolecular interactions were analysed by means of the fingerprint plots derived from the Hirshfeld surfaces. The fingerprint plots evidenced subtle differences in the intermolecular contacts for the two independent molecules.