Divergence Criterion for a Class of Random Series Related to the Partial Sums of I.I.D. Random Variables

Journal of Theoretical Probability - Let $$ \{X, X_{n};~n \ge 1 \}$$ be a sequence of independent and identically distributed Banach space valued random variables. This paper is devoted to...     

Liquid chromatographic determination of the plasticizer di(2-ethylhexyl) phthalate (DEHP) in PVC plastics

A fast, simple and reliable method for the analysis of DEHP in PVC products was developed using a one-step Soxhlet extraction prior to HPLC determination. The linear range from 1.25 /g to 250 mg/g of DEHP in PVC was found sufficient to cover the normal concentrations encountered. The reliability of the method was established by comparison with the ASTM method and no potential interferent was identified except a large concentration of DIMP.     

Elliptic Genera of Level N and Elliptic Cohomology

Elliptic genera of level N have been defined by F. Hirzebruch,generalising the earlier notion of elliptic genus due to S.Ochanine. We show that there are corresponding elliptic cohomologytheories which are naturally associated to such genera and thatthese are obtained from the level 1 case by algebraic extensionof the coefficient rings from level 1 to level N modular forms.     

Electronic and vibrational second-order nonlinear optical properties of protein secondary structural motifs

A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.     

PRODEN: A new program for calculating integrated projected populations

Two new computational methods for the evaluation and partitioning of projected, planar, and averaged slab electron densities, implemented in the program PRODEN, are presented. The new algorithms for the projection, demarcation, and integration of electron densities are described and evaluated in terms of speed and numerical accuracy. Integrated Projected Populations are analyzed and some of the advantages and limitations of the methods are discussed.     

Electronic structure of axially ligated rhodium carboxylates: π back-bonding revisited

Fenske-Hall molecular orbital calculations have been applied to a new, structurally isolable analog of the intermediate involved in catalytic rhodium carboxylate carbenoid transformations. Results from the structural characterization of axially ligated rhodium acetate phenylisonitrile complexes have been utilized in approximate molecular orbital calculations. The results from the calculations suggest that a significant degree of π back-bonding exists between the metal and isonitrile fragments which, by analogy, implies that π back-bonding should also exist in the rhodium carbenoid intermediate. Sensitivity of the Fenske-Hall method to the magnitude of π back-donation in these complexes was gauged through calculations involving different phenylisonitrile groups in which the π back-bonding ability was modulated through derivativization. The reliability of the Fenske-Hall method was evaluated through a comparison to a high-level calculation. Received: 13 December 1996 / Accepted: 18 March 1997     

Bislactonization of unsaturated diacids using lead tetraacetate

The reaction of lead tetraacetate with unsaturated carboxylic acids (or salts) to from bislactones (γ or δ) can be controlled to produce efficiently $\text{cis}$ addition of two carboxylic oxygens to the double bond, in consonance with an initial plumbolactonization step followed by S_N2 displacement of lead.     

The first genuine observation of fluorescent mononuclear phthalocyanine aggregates

An initial photophysical study of a tetra-solketal-substituted zinc phthalocyanine is reported; at low temperature this compound exhibits very strong aggregation, and a new red shifted emission peak is observed, lambda max approximately 750 nm, attributed to a fluorescent phthalocyanine dimer.     

Intrinsic and extrinsic factors in anion electron-stimulated desorption: D- from deuterated hydrocarbons condensed on Kr and water ice films

The results of D(-) ion desorption induced by 3-20 eV electrons incident on condensed CD(4), C(2)D(6), C(3)D(8), C(2)D(4), and C(2)D(2) are presented. These compounds were deposited in submonolayer amounts on the surfaces of multilayer solid films of Kr and nonporous and porous amorphous ice. While desorption of the D(-) anions proceeds via well-known processes, i.e., dissociative electron attachment (DEA) and dipolar dissociation, significant perturbations of these processes due to presence of the different film substrates are observed. We have shown that it is possible to distinguish between the character and nature of these perturbations. The presence of the nonporous ice perturbs the D(-) desorption intensity by affecting the intrinsic properties of the intermediate anion states through which dissociation proceeds. On the other hand, the presence of the porous ice introduces extrinsic effects, which can affect electron energy losses prior to their interaction with the hydrocarbon molecule and/or the energies and intensities of the fragment species after dissociation. Simple mechanisms responsible for the observed variations in the intensities of desorbed anionic signals are proposed and discussed. Electron transfer from transient anion states to electron states of the substrate film or nearby hydrocarbon molecules appear as the most efficient mechanism to reduce the magnitude of the DEA process.     

Micelle-encapsulated carbon nanotubes: a route to nanotube composites

We report a general approach toward dispersing single-walled carbon nanotubes (SWNTs) in solvents and polymer materials, by encapsulating SWNTs within cross-linked micelles. Micelles made from polystyrene-block-poly(acrylic acid) (PS-b-PAA), an amphiphilic block copolymer, are first assembled around SWNTs by gradually adding H2O to a suspension of nanotubes in dimethylformamide. The hydrophilic, outer shells of these micelles are then chemically cross-linked with a difunctional linker molecule. Pure encapsulated SWNTs (e-SWNTs) can then be separated from empty cross-linked micelles by consecutive cycles of centrifugation and redispersion. Atomic force and transmission electron microscopies of the resulting nanostructures demonstrate that individual nanotubes (rather than bundles) have been completely encased in polymer shells whose thickness is slightly larger than that of empty micelles. e-SWNTs encapsulated in PS-b-PAA can be permanently redispersed in H2O, in organic solvents, and in both hydrophobic and hydrophilic polymer matrices with minimal sonication. Micelle encapsulation could improve the compositing of SWNTs in a wide variety of polymer materials for structural, electronic, and thermal applications.