Lower bounds for boundary roughness for droplets in Bernoulli percolation

We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l², for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l^1/3(logl)^–2/3. This complements the upper bound of order l^1/3(logl)^–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions. The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43     

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

Characteristics of high energy interactions I. High energy gamma-ray spectra near the top of the atmosphere

An emulsion chamber was used to study the characteristics of high energy nuclear interactions from the production spectra ofγ-rays. The emulsion chamber, which comprised of two parts, namely the detector and the graphite producer unit, was exposed to cosmic rays for about 7 hr at an atmospheric depth of 10 g cm⁻² at Hyderabad (geomagnetic latitude 7·6°N). 720 electromagnetic cascades due toγ-rays were recorded in the detector. These cascades were classified into three groups; (a)γ-rays from nuclear interactions in the detector (b)γ-rays from nuclear interactions in the producer unit and (c)γ-rays of atmospheric origin. The energies of the cascades were determined using photometric method. The spectra ofγ-rays from groups (a) and (c) were determined and compared with similar spectra obtained at greater atmospheric depths. The spectra were found to obey a power law. The spectrum ofγ-rays of atmospheric origin was found to steepen at high energies,E _r>2200 GeV.     

Lithium-7 NMR Study of Several Li+-Crown Ether Complexes in Binary Acetone-Nitrobenzene Mixtures

⁷Li NMR measurements were employed to monitor the stoichiometry andstability of Li⁺ ion complexes with 12-crown-4 (12C4), 15-crown-5 (15C5), benzo-15-crown-5 (B15C5) l8-crown-6 (18C6), dicyclohexano-18-crown-6 (DC18C6) and dibenzo-18-crown-6 (DB18C6) in binary acetone-nitrobenzene mixtures of varying composition. In all cases studied, the variation of ⁷Li chemical shift with the crown/Li⁺ mole ratio indicated the formation of 1:1 complexes. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. In all solvent mixtures used, the stabilities of the resulting 1:1 complexes varied in the order15C5 > B15C5 > DC18C6 > 18C6 > 12C4 >DB18C6. It was found that,in the case of all complexes, an increase in the percentage of acetone in thesolvent mixtures significantly decreased the stability of the complexes.     

The stability of the acetic acid dimer in microhydrated environments and in aqueous solution

The thermodynamic stability of the acetic acid dimer conformers in microhydrated environments and in aqueous solution was studied by means of molecular dynamics simulations using the density functional based tight binding (DFTB) method. To confirm the reliability of this method for the system studied, density functional theory (DFT) and second order M?ller-Plesset perturbation theory (MP2) calculations were performed for comparison. Classical optimized potentials for liquid simulations (OPLS) force field dynamics was used as well. One focus of this work was laid on the study of the capabilities of water molecules to break the hydrogen bonds of the acetic acid dimer. The barrier for insertion of one water molecule into the most stable cyclic dimer is found to lie between 3.25 and 4.8 kcal mol(-1) for the quantum mechanical methods, but only at 1.2 kcal mol(-1) for OPLS. Starting from different acetic acid dimer structures optimized in gas phase, DFTB dynamics simulations give a different picture of the stability in the microhydrated environment (4 to 12 water molecules) as compared to aqueous solution. In the former case all conformers are converted to the hydrated cyclic dimer, which remains stable over the entire simulation time of 1 ns. These results demonstrate that the considered microhydrated environment is not sufficient to dissociate the acetic acid dimer. In aqueous solution, however, the DFTB dynamics shows dissociation of all dimer structures (or processes leading thereto) starting after about 50 ps, demonstrating the capability of the water environment to break up the relatively strong hydrogen bridges. The OPLS dynamics in the aqueous environment shows--in contrast to the DFTB results--immediate dissociation, but a similar long-term behavior.     

Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

Journal of Optimization Theory and Applications - In this paper, we study robust necessary optimality conditions for a nondifferentiable complex fractional programming with uncertain data. A robust...     

In Vitro and In Silico Screening and Characterization of Antimicrobial Napin Bioactive Protein in Brassica juncea and Moringa oleifera

The study aimed to investigate the antibacterial activity of Mustard (Brassica juncea) and Moringa (Moringa oleifera) leaf extracts and coagulant protein for their potential application in water treatment. Bacterial cell aggregation and growth kinetics studies were employed for thirteen bacterial strains with different concentrations of leaf extracts and coagulant protein. Moringa oleifera leaf extract (MOS) and coagulant protein showed cell aggregation against ten bacterial strains, whereas leaf extract alone showed growth inhibition of five bacterial strains for up to 6 h and five bacterial strains for up to 3 h. Brassica juncea leaf extract (BJS) showed growth inhibition for up to 6 h, and three bacterial strains showed inhibition for up to 3 h. The highest inhibition concentration with 2.5 mg/mL was 19 mm, and furthermore, the minimum inhibitory concentration (MIC) (0.5 mg/mL) and MBC (1.5 mg/mL) were determined to have a higher antibacterial effect for <3 KDa peptides. Based on LCMS analysis, napin was identified in both MOS and BJS; furthermore, the mode of action of napin peptide was determined on lipoprotein X complex (LpxC) and four-chained structured binding protein of bacterial type II topoisomerase (4PLB). The docking analysis has exhibited moderate to potent inhibition with a range of dock score −912.9 Kcal/mol. Thus, it possesses antibacterial-coagulant potential bioactive peptides present in the Moringa oleifera purified protein (MOP) and Brassica juncea purified protein (BJP) that could act as an effective antimicrobial agent to replace currently available antibiotics. The result implies that MOP and Brassica juncea purified coagulant (BJP) proteins may perform a wide degree of antibacterial functions against different pathogens.     

Antioxidant Assessment of Prenylated Stilbenoid-Rich Extracts from Elicited Hairy Root Cultures of Three Cultivars of Peanut (Arachis hypogaea)

Peanut produces prenylated stilbenoids upon biotic stress. However, the role of these compounds against oxidative stress have not been thoroughly elucidated. To this end, the antioxidant capacity of extracts enriched in prenylated stilbenoids and derivatives was studied. To produce these extracts, hairy root cultures of peanut cultivars Hull, Tifrunner, and Georgia Green were co-treated with methyl jasmonate, cyclodextrin, hydrogen peroxide, and magnesium chloride and then the stilbenoids were extracted from the culture medium. Among the three cultivars, higher levels of the stilbenoid derivatives arachidin-1 and arachidin-6 were detected in cultivar Tifrunner. Upon reaction with 2,2-diphenyl-1picrylhydrazyl, extracts from cultivar Tifrunner showed the highest antioxidant capacity with an IC₅₀ of 6.004 µg/mL. Furthermore, these extracts had significantly higher antioxidant capacity at 6.25 µg/mL and 3.125 µg/mL when compared to extracts from cultivars Hull and Georgia Green. The stilbenoid-rich extracts from peanut hairy roots show high antioxidant capacity and merit further study as potential nutraceuticals to promote human health.     

Template synthesis and spectroscopic studies of highly conjugated tetraiminetetraamide macrocyclic complexes from 1,2-diphenylethane-1,2-dione dihydrazone

A new class of tetraiminetetraamide macrocyclic (Ph4[20]tetraene, N8O4, and Ph6[20]tetraene, N8O4) complexes have been prepared through the metal ion controlled reaction of 1,2-diphenylethane-1,2-dione dihydrazone (DPEDDH) with succinic acid [ML1X2] or phthalic acid [ML2X2] [M=Mn, Co, Ni, Cu or Zn; X=Cl or NO3]. The structures of the complexes have been elucidated on the basis of i.r, 1H-n.m.r, e.p.r. and electronic spectral data and conductance, as well as magnetic, properties. An octahedral geometry is assigned for all the complexes, involving coordination of the all-imine nitrogens.