On a zero-crossing probability

Let {X(t), 0E{exp (–sX(t))}=exp (–t(s)), where (s)=(1–(s)), is the intensity of the Poisson process, and (s) is the Laplace transform of the distribution of nonnegative jumps. Consider the zero-crossing probability =P{X(t)–t=0 for some t,0<t<}. We show that =() where is the largest nonnegative root of the equation (s)=s. It is conjectured that this result holds more generally for any stochastic process with stationary independent increments and with sample paths that are nondecreasing step functions vanishing at 0.     

Clustering and mechanics in dense depletion and thermal gels

We report on the microstructure and mechanical properties (elastic modulus) of concentrated depletion and thermal gels of octadecyl-coated silica particles for different values of the strength of interaction--polymer concentration for depletion gels and temperature for thermal gels. The depletion gels are composed of dense clusters and voids, while the thermal gels are devoid of clusters. Shear breaks up clusters in depletion gels while it induces clustering in the thermal gels. In both of these gels, the microstructure recovers to the presheared state upon cessation of shear. The recovery of the elastic modulus mimics the microstructure in the sense that the elastic modulus recovers to the presheared sheared state after shearing is stopped. Calculations of the gel boundary by modeling the interactions with an effective one-component square-well model reveals that suspensions with similar ranges of attraction gel at the same volume fraction at a fixed strength of attraction. Calculations of the elastic modulus using the na?ve mode coupling theory for depletion gels are in good agreement with experimental measurements provided clustering is taken into account and have the same magnitude as the elastic moduli of thermal gels with similar strengths of attraction. These calculations, in addition to the experimental observations reinforce the point that the microscopic parameter determining the elastic modulus of dense gels and its recovery is the localization length which is only a fraction of the particle diameter and not the structure on the length scale of the particle diameter and larger.     

Air-liquid interfaces of aqueous solutions containing ammonium and sulfate: spectroscopic and molecular dynamics studies

Investigations of the air-liquid interface of aqueous salt solutions containing ammonium (NH(4)(+)) and sulfate (SO(4)(2-)) ions were carried out using molecular dynamics simulations and vibrational sum frequency generation spectroscopy. The molecular dynamics simulations show that the predominant effect of SO(4)(2-) ions, which are strongly repelled from the surface, is to increase the thickness of the interfacial region. The vibrational spectra reported are in the O-H stretching region of liquid water. Isotropic Raman and ATR-FTIR (attenuated total reflection Fourier transform infrared) spectroscopies were used to study the effect of ammonium and sulfate ions on the bulk structure of water, whereas surface sum frequency generation spectroscopy was used to study the effect of these ions on the interfacial structure of water. Analysis of the interfacial and bulk vibrational spectra reveal that aqueous solutions containing SO(4)(2-) perturb the interfacial water structure differently than the bulk and, consistent with the molecular dynamics simulations, reveal an increase in the thickness of the interfacial region.     

Photooxidation of cedrelone, a tetranortriterpenoid from Toona ciliata

Cedrelone, a tetranortriterpenoid on photolysis by UV light yields a true photooxidation product 3 [14 beta,15beta,22beta,23beta-diepoxy-6-hydroxy-1,5, 20(22)-meliatriene-2,7,21-trione] whose structure is well established by NMR studies and confirmed by X-ray crystallography, along with product 4 [14 beta,15beta-epoxy-6,23-dihydroxy-1,5,20(22)-meliatriene-2,7, 21-trione]. Addition of rose bengal increases the rate of photooxidation whereas DABCO decreases rate of photolysis proving the involvement of singlet oxygen in the photooxygenation. Both the photoproducts exhibited antifeedant activity.     

Microwave-assisted ketone-ketone rearrangement: an improved synthesis of 3-(4-alkoxyphenyl)-3- methylbutan-2-ones

[reaction: see text] A novel procedure for the preparation of 3-(4-alkoxyphenyl)-3-methylbutan-2-one in excellent yield is described via polymer-supported AlCl3-catalyzed rearrangement of 1-(4-ethoxyphenyl)-2,2-dimehtylpropan-1-one, followed by O-alkylation under microwave irradiation condition.     

Azadirachtol,a tetranortriterpenoid from neem kernels

The title compound, di­methyl (?)‐(2aR,3R,4R,4aS,5R,7aS,8R,10S,10aR)‐3,8,10‐tri­hydroxy‐4‐[(2R,6R)‐2‐hydroxy‐11‐methyl‐5,7,10‐trioxatetra­cyclo­[6.3.1.0^2,60^9,11]­dodec‐3‐en‐9‐yl]‐4‐methyl­per­hydro­isobenzo­furano­[5,4,3a‐cd]­isobenzofuran‐5,10a‐di­acetate, C₂₈H₃₆O₁₃, which exhibits higher antifeedant activity than azadirachtin‐A, a known potent antifeedant, was isolated from neem kernels. The asymmetric unit of the structure contains two independent mol­ecules, which differ in the conformations of their functional groups and also in the conformations of some of the rings. The relative orientation between the decalin and furan­yl moieties is similar to that observed in the majority of azadirachtin structures, but is different from that in azadirachtin‐A. The two symmetry‐independent mol­ecules are linked into dimeric units by intermolecular O—H?O hydrogen bonds.     

Studies on the La2−xSrxNiO4 (0 ⩽ x ⩽ 1) system

A new series of solid solutions of composition La_2?xSr_xNiO₄ (0 ? x ? 1) in which the oxidation state of nickel varies from +2 at x = 0 to +3 at x = 1 has been prepared. All the members of the system crystallize in the tetragonal K₂NiF₄ structure. The tetragonality ratio $\text{c}\text{a}$ shows a maximum at x = 0.5 which is interpreted as arising from a weak cooperative Jahn-Teller distortion due to octahedral site low-spin Ni³⁺ ions. The variation of electrical properties in the system is attributed to changes in electronic configuration of Ni³⁺.     

Flourimetric and prototropic studies on the inclusion complexation of 2-amino and 4-aminodiphenyl ethers with β-cyclodextrin: Unusual behavior of 4-aminodiphenyl ether

The fluorescence characteristics of diphenyl ether (DPE), 2-aminodiphenyl ether (2ADPE) and 4-aminodiphenyl ether (4ADPE) and prototropic behavior of 2ADPE and 4ADPE on inclusion complexation with β-cyclodextrin have been investigated. DPE forms 1:1 complex whereas 2ADPE and 4ADPE form 1:2 complex with β-CDx. The fluorimetric and prototropic behaviors of 4ADPE in β-CDx are different from those in aqueous solution. The dual fluorescence of 4ADPE in β-CDx is found to be due to twisted intramolecular charge transfer (TICT) character induced by inclusion complexation. The two equilibria viz. monocation↔monocation solvent exciplex↔neutral reported for 4ADPE in aqueous solution are not observed in presence of β-CDx. The ground and excited state pK_a values for monocation-neutral equilibrium of 2ADPE and 4ADPE have been reported.     

Error analysis of variable degree mixed methods for elliptic problems via hybridization

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new variable degree Raviart-Thomas method, but also new error estimates for the classical uniform degree method with less stringent regularity requirements than previously known estimates. The error analysis is achieved by using a variational characterization of the Lagrange multipliers wherein the other unknowns do not appear. This approach can be applied to other hybridized mixed methods as well.