The Forbes 400, the Pareto power-law and efficient markets

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.     

Nonvanishing theorems for L-functions of modular forms and their derivatives

Inventiones mathematicae -     

Analysis of patient self-assessment visual analogue scales

The present paper describes an example of practical analysis of data from an application of visual analogue scales. Potentially useful and simple methods for analysing visual analogue scales are described for effective handling of complex data when the desire is to compare two or more groups of patients. Visual analogue scales were used to assess subjective tolerability in the International Prospective Primary Prevention Study in Hypertension, a large scale clinical trial. The methods are illustrated on the IPPPSH data.     

Triggered single photons and entangled photons from a quantum dot microcavity

Current quantum cryptography systems are limited by the attenuated coherent pulses they use as light sources: a security loophole is opened up by the possibility of multiple-photon pulses. By replacing the source with a single-photon emitter, transmission rates of secure information can be improved. We have investigated the use of single self-assembled InAs/GaAs quantum dots as such single-photon sources, and have seen a tenfold reduction in the multi-photon probability as compared to Poissonian pulses. An extension of our experiment should also allow for the generation of triggered, polarization-entangled photon pairs. The utility of these light sources is currently limited by the low efficiency with which photons are collected. However, by fabricating an optical microcavity containing a single quantum dot, the spontaneous emission rate into a single mode can be enhanced. Using this method, we have seen 78% coupling of single-dot radiation into a single cavity resonance. The enhanced spontaneous decay should also allow for higher photon pulse rates, up to about 3 GHz. Received 8 July 2001 and Received in final form 25 August 2001     

Influence of a single quantum dot state on the characteristics of a microdisk laser

We report a quantum dot microcavity laser with a cw sub-microW lasing threshold, where a significant reduction of the lasing threshold is observed when a single quantum dot (QD) state is aligned with a cavity mode. The quality factor exceeds 15,000 before the system lases. When no QD states are resonant, below threshold the cavity mode initially degrades with increasing pump power, after which saturation occurs and then the cavity mode recovers. We associate the initial cavity mode spoiling with QD state broadening that occurs with increasing pump power.     

Synthesis and pH‐Dependent Spectroscopic Behavior of 2,4,6‐Trisubstituted Pyridine Derivatives

Seven 2,4,6‐trisubstituted pyridine derivatives with N,N‐diethylaniline substituents at the 4‐position were synthesized, and their spectroscopic properties in the absence and presence of acid were studied. The spectral effects of protonation, molar absorptivities, pK_a values, and the structural origins of the observed spectral behavior were ascertained. The pyridine nitrogen was found to be more basic than the diethylamino nitrogen atom. Protonation of the pyridine ring nitrogen is associated with the appearance of a red‐shifted intramolecular charge transfer peak in the UV‐visible spectra. Favorable color indicating properties result from electron‐donating substitution at the 2 and 6 positions of pyridine, which provide a greater absorptivity of the red‐shifted peak associated with protonation of the pyridine nitrogen. These findings will assist in the design and optimization of these compounds for ion‐indicating and pH‐sensing applications.     

The complexity of central series in nilpotent computable groups

The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders.     

Electronic structure of a low-spin heme/Cu peroxide complex: spin-state and spin-topology contributions to reactivity

This study details the electronic structure of the heme–peroxo–copper adduct {[(F8)Fe(DCHIm)]-O2-[Cu(AN)]}+ (LS(AN)) in which O2(2–) bridges the metals in a μ-1,2 or “end-on” configuration. LS(AN) is generated by addition of coordinating base to the parent complex {[(F8)Fe]-O2-[Cu(AN)]}+ (HS(AN)) in which the O2(2–) bridges the metals in an μ-η2:η2 or “side-on” mode. In addition to the structural change of the O2(2–) bridging geometry, coordination of the base changes the spin state of the heme fragment (from S = 5/2 in HS(AN) to S = 1/2 in LS(AN)) that results in an antiferromagnetically coupled diamagnetic ground state in LS(AN). The strong ligand field of the porphyrin modulates the high-spin to low-spin effect on Fe–peroxo bonding relative to nonheme complexes, which is important in the O–O bond cleavage process. On the basis of DFT calculations, the ground state of LS(AN) is dependent on the Fe–O–O–Cu dihedral angle, wherein acute angles (<~150°) yield an antiferromagnetically coupled electronic structure while more obtuse angles yield a ferromagnetic ground state. LS(AN) is diamagnetic and thus has an antiferromagnetically coupled ground state with a calculated Fe–O–O–Cu dihedral angle of 137°. The nature of the bonding in LS(AN) and the frontier molecular orbitals which lead to this magneto-structural correlation provide insight into possible spin topology contributions to O–O bond cleavage by cytochrome c oxidase.