Flow/sequential injection determination of gaseous ammonia with a glass diffusion denuder

A new combination of a flow/sequential injection method for the analysis of ammonia has been developed. Gaseous ammonia is selectively absorbed in a phosphoric acid coated glass tube and determined with Berthelot reagents by flow injection. The combination of the gas diffusion denuder sampler with flow injection makes this method very sensitive and selective. The limit of detection of 0.15 mug NH(3).     

An apparatus for the determination of volatile analytes by stopped-flow injection analysis using an integrated fiber optic detector

A new method for the analysis of volatile analytes using a stopped-flow injection system originating from either a gas or liquid phase has been developed. It uses an integrated fiber optic detector which also serves as a reactor. This system combines the advantages of gas diffusion and stopped-flow, making the overall assay very sensitive. Both gas streams and aqueous solutions containing ammonia were analyzed. The limits of detection are 40 ppb for gas phase analysis and 1.0 ppm for aqueous phase analysis.     

An indexed set of density bounds on lattice packings

It has long been known that the admissibility of a lattice with respect to a symmetric convex bodyB is equivalent to being a packing lattice for 1/2B. This fact is the basis of the interplay between the classical theory of the arithmetic minima of positive definite quadratic forms, on the one hand, and the dense lattice packing of spheres inR ⁿ , on the other.We give an indexed set of bounds _L (B) a _j , where 0 j n/2, on the lattice packing density ofB. The casej=0 reduces to the aforementioned long-known fact, andj=1 was proved by Elkies, Odlyzko, and Rush, and was used to obtain record high packing densities for various superballs. The new cases make possible the use of smaller primes in the construction of these dense packings.Supported by National Science Foundation grant DMS-9103233.     

Electron-cluster interactions

Beam depletion spectroscopy has been used to measure absolute total inelastic electron-sodium cluster collision cross sections in the energy range fromE0.1 toE6 eV. The investigation focused on the closed shell clusters Na₈, Na₂₀, and Na₄₀. The measured cross sections show an increase for the lowest collision energies where electron attachment is the primary scattering channel. The electron attachment cross section can be understood in terms of Langevin scattering, connecting this measurement with the polarizability of the cluster. For energies above the dissociation energy the measured electron-cluster cross section is energy independent, thus defining an electron-cluster interaction range. This interaction range increases with the cluster size.     

Common supports as fixed points

A family S of sets in R ^d is sundered if for each way of choosing a point from rd+1 members of S, the chosen points form the vertex-set of an (r–1)-simplex. Bisztriczky proved that for each sundered family S of d convex bodies in R ^d , and for each partition (S , S ), of S, there are exactly two hyperplanes each of which supports all the members of S and separates the members of S from the members of S . This note provides an alternate proof by obtaining each of the desired supports as (in effect) a fixed point of a continuous self-mapping of the cartesian product of the bodies.     

Second-order epi-derivatives of integral functionals

Epi-derivatives have many applications in optimization as approached through nonsmooth analysis. In particular, second-order epi-derivatives can be used to obtain optimality conditions and carry out sensitivity analysis. Therefore the existence of second-order epi-derivatives for various classes of functions is a topic of considerable interest. A broad class of composite functions on ⁿ called fully amenable functions (which include general penalty functions composed withC ² mappings, possibly under a constraint qualification) are now known to be twice epi-differentiable. Integral functionals appear widely in problems in infinite-dimensional optimization, yet to date, only integral functionals defined by convex integrands have been shown to be twice epi-differentiable, provided that the integrands are twice epi-differentiable. Here it is shown that integral functionals are twice epi-differentiable even without convexity, provided only that their defining integrands are twice epi-differentiable and satisfy a uniform lower boundedness condition. In particular, integral functionals defined by fully amenable integrands are twice epi-differentiable under mild conditions on the behavior of the integrands.This work was supported in part by the National Science Foundation under grant DMS-9200303.     

A global Newton method II: Analytic centers

This paper modifies the convergence conditions of a back-tracking global Newton method announced in Goldstein (1991), making them sharper and easier to apply. A new version of the Kantorovich inequalities is presented that is simple to state and prove. An application is made to the centering problem for polytopes. Based on an idea of Ye (1989), an algorithm is given for the feasibility problem of linear inequalities.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.     

Synthesis of Highly Porous Organic/Inorganic Hybrids by Ambient Pressure Sol-Gel Processing

This paper reports the synthesis of highly porous organic/inorganic hybrids by a two-step acid-base catalyzed sol-gel process and ambient pressure drying. In the method organic and inorganic precursors are copolymerized so as to incorporate organic ligands into the solid network. The two-step acid-base catalyzed process was used to prevent phase segregation during the hydrolysis and co-condensation of organic and inorganic precursors. The organic ligands incorporated into the solid gel network modify the surface chemistry. Thus, the wetting angle is significantly increased so that the collapse of the gel network is greatly reduced upon the removal of pore fluid during drying. Organic/inorganic hybrids with BET surface areas above 1250 m2/g, porosities above 75% and pore sizes of 8 nm have been synthesized.     

Carbon-13 nuclear magnetic resonance studies of coumarin and related compounds

Fourier-transform ¹³C NMR spectra of nine coumarinoid compounds of medicinal interest are reported. All of the carbon resonances are assigned with the aid of various spectral techniques and stable isotopic labeling. The substituent effects on the chemical shifts in several systems are also discussed.     

Are 1,5-disubstituted semibullvalenes that have C2v equilibrium geometries necessarily bishomoaromatic?

Unrestricted density functional theory (UB3LYP), CASSCF, and CASPT2 calculations have been employed to compute the relative energies of the C(s) and C(2v) geometries of several 1,5-disubstituted semibullvalenes. Substitution at these positions with R = F, -CH(2)-, or -O- affords semibullvalenes that are predicted to have C(2v) equilibrium geometries. Calculated singlet-triplet energy splittings and the energies of isodesmic reactions are used to assess the amount of bishomoaromatic character at these geometries. The results of these calculations show that employing strain to destabilize the C(s) geometries of semibullvalenes can lead to a significant decrease in the amount of bishomoaromatic stabilization of the C(2v) geometries, due to reduced through-space interaction between the two allyl groups. However, the C(2v) equilibrium geometries of the 1,5-disubstituted semibullvalenes with R = F and -RR- = -O- do benefit from stabilizing through-bond interactions between the two allyl groups. These interactions involve mixing of the bisallyl HOMO with the low-lying C-F or C-O sigma orbital combinations of the same symmetry. In contrast, for -RR- = -CH(2)-, through-bond interactions destabilize the bisallyl HOMO and are predicted to make the ground state of this semibullvalene a triplet.