Scheidegger''s rivers, Takayasu''s aggregates and continued fractions

A discrete model of (1+1)-dimensional aggregation, equivalent to Scheidegger's 1967 river model, is tackled with continued fractions. An exact expression for the power-law distribution of aggregate masses is found.     

The Furstenberg lemma characterizes amenability

We characterize amenability in terms of the existence of equivariant assignments of measures for cocycles into the homeomorphism group of a single compact metric space.

     

REFLECTIVE INFRARED ELLIPSOMETRY OF PLASTIC FILMS

High resolution reflective ellipsometry is used to study freely suspended plastic films. We determine room temperature optical constants in the infrared for a variety of plastics using ellipsometry. The films are typically 6 to 100 μm thick and measurements are performed from near infrared to long wave-IR. The setup includes modeling software to fit the ellipsometric data to a generalized oscillator model. The films studied include acrylics, fluoropolymers, and variations of polyethylene, polystyrene, and polyvinyl chloride (PVC) among others. We are able to determine in-plane and out-of-plane optical constants. Transmission spectra from FTIR measurements are plotted and compared with ellipsometry results.     

Spiders for rank 2 Lie algebras

A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. It is also known as a spherical category, or a strict, monoidal category with a few extra properties, or by several other names. A recently useful point of view, developed by other authors, of the representation theory of sl(2) has been to present it as a spider by generators and relations. That is, one has an algebraic spider, defined by invariants of linear representations, and one identifies it as isomorphic to a combinatorial spider, given by generators and relations. We generalize this approach to the rank 2 simple Lie algebras, namelyA ₂,B ₂, andG ₂. Our combinatorial rank 2 spiders yield bases for invariant spaces which are probably related to Lusztig's canonical bases, and they are useful for computing quantities such as generalized 6j-symbols and quantum link invariants. Their definition originates in definitions of the rank 2 quantum link invariants that were discovered independently by the author and Francois Jaeger.The author was supported by an NSF Postdoctoral Fellowship, grant #DMS-9107908.     

Reserving consecutive layers of inwards excess-of-loss reinsurance

Consider an excess-of-loss reinsurance arranged in a number of layers. A loss reserve is required for each layer. There are two major reasons why the independent application of some conventional loss reserving technique to each layer is inappropriate. First, the experiences in different layers in respect of a particular treaty year will be linked; favourable or adverse experience in one layer is likely to be reflected in favourable or adverse experience in the next. Second, experience data will typically become sparse in the higher layers, rendering analysis in isolation from other layers relatively uninformative. The purpose of the present paper is to analyse the linkages between the loss experiences of different layers, and apply these to obtain linked loss reserves. A numerical example is provided.     

Studies of reactions of o-xylylene-α,α′-dihalides with palladium complexes and the catalytic synthesis of 3-isochromanone

Homogeneous catalysis by palladium complexes with phosphorus(III) ligands of the carbonylation of o-xylylene dihalides in the presence of water to form 3-isochromanone has been studied. Triphenylphosphine was found to provide the most effective catalyst, and by-products and intermediates of systems containing this ligand have been investigated. 2-Indanone is one by-product but is unstable to decomposition under catalytic conditions. Excess PPh₃ is necessary to prolong activity of the catalyst but is also transformed to bis-phosphonium compound [o-C₆H₄(CH₂PPh₃)₂]X₂ (X = Cl or Br); this quaternization has been investigated and the structure of the bromide salt determined by X-ray diffraction. An unstable oxidative addition product of Pd(PPh₃)₄ was detected as a probable intermediate and related to the previously reported but catalytically-inactive complex trans-Pd(o-CH₂C₆H₄CH₂Cl)Cl(PMe₃)₂, which has been structurally characterized by X-ray diffraction in this work.     

Convolution products of nonidentical distributions on a topological semigroup

In this paper we present a number of sufficient conditions on a sequence of probability measuresµ _n on a locally compact (second countable) Hausdorff topological semigroupS that guarantee the weak convergence of the sequence of convolution productsµ _k,n µ _{k + 1} *···*µ _n (k), asn, for allk0.     

Dose Dependencies and Biocompatibility of Renal Clearable Gold Nanoparticles: From Mice to Non‐human Primates

While dose dependencies in pharmacokinetics and clearance are often observed in clinically used small molecules, very few studies have been dedicated to the understandings of potential dose‐dependent in vivo transport of nanomedicines. Here we report that the pharmacokinetics and clearance of renal clearable gold nanoparticles (GS‐AuNPs) are strongly dose‐dependent once injection doses are above 15 mg kg^?1: high dose expedited the renal excretion and shortened the blood retention. As a result, the no‐observed‐adverse‐effect‐level (NOAEL) of GS‐AuNPs was >1000 mg kg^?1 in CD‐1 mice. The efficient renal clearance and high compatibility can be translated to the non‐human primates: no adverse effects were observed within 90 days after intravenous injection of 250 mg kg^?1 GS‐AuNPs. These fundamental understandings of dose effect on the in vivo transport of ultrasmall AuNPs open up a pathway to maximize their biomedical potentials and minimize their toxicity in the future clinical translation.