Nanoscale zinc antimonides: synthesis and phase stability

Highly crystalline single-phase nanoparticles of the important thermoelectric materials Zn4Sb3 and ZnSb were prepared from solvochemically activated powders of elemental zinc and elemental antimony. Low-temperature reactions with reaction temperatures of 275-300 degrees C were applied using an excess of elemental zinc. The nanoscale thermoelectrics obtained were characterized by X-ray powder diffraction, transmission electron microscopy, and thermal analysis. nc-Zn4Sb3 showed particle sizes of 50-70 nm, whereas particle sizes of 15-20 nm were observed for nc-ZnSb. Calorimetric investigations showed an increased heat capacity, Cp, for nc-Zn4Sb3 with respect to the bulk material which could be reduced to the bulk value by annealing nc-Zn4Sb3 at 190 degrees C. Interestingly, nc-Zn4Sb3 showed exothermic decomposition into zinc-poorer ZnSn at 196 degrees C in an open system, indicating that Zn4Sb3 is metastable in nanocrystalline form at room temperature.     

Influence of perfluorinated carboxylic acids on ion-pair reversed-phase high-performance liquid chromatographic separation of betacyanins and 17-decarboxy-betacyanins

The ability of trifluoroacetic acid, pentafluoropropionic acid and heptafluorobutyric acid to act as ion-pairing agents for betacyanins and 17-decarboxy-betacyanins during HPLC analysis on a Luna C18(2) reversed-phase column is reported. While the perfluorinated carboxylic acids affect the retention of both groups of compounds by changing the pH of the mobile phase, the possibility of ion-pair chromatography for 17-decarboxy-betacyanins was noticed. In order to explain the accessibility of the positive charge for the counter-anion in decarboxy-betacyanins, the mesomeric structures of the polymethine system at low pH (around a value of 1.5), when the carboxylic group in the 2 position is protonated, should be taken into consideration.     

Baryogenesis from the Kobayashi-Maskawa phase

The smallness of quark masses suppresses the CP violation from the Kobayashi-Maskawa phase to a level that is many orders of magnitude below what is required to explain the observed baryon asymmetry. We point out that if, as a result of time variation in the Yukawa couplings, quark masses were large at the time of the electroweak phase transition, then the Kobayashi-Maskawa mechanism could be the source of the asymmetry. The Froggatt-Nielsen mechanism provides a plausible framework where the Yukawa couplings could all be of order 1 at that time, and settle to their present values before nucleo-synthesis. The problems related to a strong first order electroweak phase transition may also be alleviated in this framework. Our scenario reveals a loophole in the commonly held view that the Kobayashi-Maskawa mechanism cannot be the dominant source of CP violation to play a role in baryogenesis.     

Slicing and Dicing the Genome: A Statistical Physics Approach to Population Genetics

The inference of past demographic parameters from current genetic polymorphism is a fundamental problem in population genetics. The standard techniques utilize a reconstruction of the gene-genealogy, a cumbersome process that may be applied only to small numbers of sequences. We present a method that compares the total number of haplotypes (distinct sequences) with the model prediction. By chopping the DNA sequence into pieces we condense the immense information hidden in sequence space into a function for the number of haplotypes versus subsequence size. The details of this curve are robust to statistical fluctuations and are seen to reflect the process parameters. This procedure allows for a clear visualization of the quality of the fit and, crucially, the numerical complexity grows only linearly with the number of sequences. Our procedure is tested against both simulated data as well as empirical mtDNA data from China and provides excellent fits in both cases.     

On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method

Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary ``length' for %E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W. The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.Supported in part by NSF grant DMS-98-03623Supported in part by the Russian Foundation of Basic Research, grant # 00-01-00194, and by NSF grant DMS-98-03623Mathematics Subject Classification (2000):Primary 62E20; Secondary 60E05     

Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

A function f(x) defined on $\text{X}$ = $\text{X}$₁ × $\text{X}$₂ × … × $\text{X}$_n where each $\text{X}$_i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on $\text{X}$, is said to be multivariate totally positive of order 2 (MTP₂). A random vector Z = (Z₁, Z₂,…, Z_n) of n-real components is MTP₂ if its density is MTP₂. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ^?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP₂ properties. The MTP₂ property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP₂ kernels are presented and amplified by a wide variety of applications.