Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion

Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently. In this work, we focus on the problem of expressing with a closed formula multivariate monotone cumulants in terms of free and Boolean cumulants. In the process, we introduce various constructions and statistics on non-crossing partitions. Our approach is based on a pre-Lie algebra structure on cumulant functionals. Relations among cumulants are described in terms of the pre-Lie Magnus expansion combined with results on the continuous Baker–Campbell–Hausdorff formula due to A. Murua.

     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.     

Measurement of the decay amplitudes of B0 --> J/psiK*0 and B(s)(0) --> J/psistraight phi decays

An angular analysis of B0-->J/psiK(*0) and B(0)(s)-->J/psistraight phi has been used to determine the decay amplitudes with parity-even longitudinal ( A0) and transverse ( A( parallel)) polarization and parity-odd transverse ( A( perpendicular)) polarization. The measurements are based on 190 B0 and 40 B(0)(s) candidates obtained from 89 pb(-1) of &pmacr;p collisions at the Fermilab Tevatron. The longitudinal decay amplitude dominates with |A0|(2) = 0.59+/-0. 06+/-0.01 for B0 and |A0|(2) = 0.61+/-0.14+/-0.02 for B(0)(s) decays. The parity-odd amplitude is found to be small with |A( perpendicular)|(2) = 0.13(+0.12)(-0.09)+/-0.06 for B0 and |A( perpendicular)|(2) = 0.23+/-0.19+/-0.04 for B(0)(s) decays.     

Search for new particles decaying to t&tmacr; in p&pmacr; collisions at radicals = 1.8 TeV

We use 106 pb (-1) of data collected with the Collider Detector at Fermilab to search for narrow-width, vector particles decaying to a top and an antitop quark. Model independent upper limits on the cross section for narrow, vector resonances decaying to t&tmacr; are presented. At the 95% confidence level, we exclude the existence of a leptophobic Z' boson in a model of top-color-assisted technicolor with mass M(Z')<480 GeV/c(2) for natural width gamma = 0.012M(Z'), and M(Z')<780 GeV/c(2) for gamma = 0.04M(Z').     

Search for second and third generation leptoquarks including production via technicolor interactions in p&pmacr; collisions at radicals = 1.8 TeV

We report the results of a search for second and third generation leptoquarks using 88 pb(-1) of data recorded by the Collider Detector at Fermilab. Color triplet technipions, which play the role of scalar leptoquarks, are investigated due to their potential production in decays of strongly coupled color octet technirhos. Events with a signature of two heavy flavor jets and missing energy may indicate the decay of a second (third) generation leptoquark to a charm (bottom) quark and a neutrino. As the data are found to be consistent with standard model expectations, mass limits are determined.     

Synthesis of (+/-)-madindolines and chemical models. Studies of chemical reactivity

[reaction: see text] The madindolines are believed to inhibit cytokine signaling through the gp130 receptor. Model compounds of madindolines were synthesized and tested for thiol reactivity. The heterocyclic moiety of madindoline was shown to form thiol adducts via the Savige-Fontana reaction. The enedione moiety was found to be unreactive toward simple thiols unless the quaternary center was removed. Using the powerful Moore reaction, we have synthesized (+/-)-madindoline A and B in 11 steps.     

Determination of the size of the representative volume element for random quasi-brittle composites

A representative volume element (RVE) is related to the domain size of a microstructure providing a “good” statistical representation of typical material properties. The size of an RVE for the class of quasi-brittle random heterogeneous materials under dynamic loading is one of the major questions to be answered in this paper. A new statistical strategy is thus proposed for the RVE size determination. The microstructure illustrating the methodology of the RVE size determination is a metal matrix composite with randomly distributed aligned brittle inclusions: the hydrided Zircaloy constituting nuclear claddings. For a given volume fraction of inclusions, the periodic RVE size is found in the case of overall elastic properties and of overall fracture energy. In the latter case, the term “representative” is discussed since the fracture tends to localize. A correlation factor between the “elastic” RVE and the “fracture” RVE is discussed.     

Synthesis and in vitro inhibition properties of siRNA conjugates carrying glucose and galactose with different presentations

Oligoribonucleotide conjugates and the corresponding siRNA duplexes against tumor necrosis factor carrying one, two, or four glucose and galactose residues at the 5′-end have been prepared using phosphoramidite chemistry. Carbohydrate-modified siRNA duplexes have similar inhibitory properties than unmodified RNA duplexes in HeLa cells transfected with oligofectamine. When HeLa cells were treated with siRNA carrying one, two, or four glucose residues without oligofectamine, no inhibition was observed. The inhibitory properties of siRNA carrying galactose residues without transfecting agent were tested on HuH-7 cells that have abundant asialoglycoprotein receptors. In these cells siRNA carrying galactose residues have slight anti-TNF inhibitory properties (25% in the best case) that are eliminated if the receptors are blocked with a competitor. These results demonstrate receptor-mediated uptake of siRNA carrying galactose residues, although the efficacy of the process is not enough for efficient RNA interference experiments.     

Synthesis and characterization of magnetic diphase ZnFe(2)O(4) /γ-Fe(2)O(3) electrospun fibers

Magnetic nanofibers of ZnFe₂O₄/γ-Fe₂O₃ composite were synthesized by electrospinning from a sol-gel solution containing a molar ratio (Fe/Zn) of 3. The effects of the calcination temperature on phase composition, particle size and magnetic properties have been investigated. Zinc ferrite fibers were obtained by calcinating the electrospun fibers in air from 300 to 800 °C and characterized by thermogravimetric analyses, Fourier transformed infrared spectroscopy, X-ray photoemission spectroscopy, X-ray diffraction, vibration sample magnetometry and magnetic force microscopy. The resulting fibers, with diameters ranging from 90 to 150 nm, were ferrimagnetic with high saturation magnetization as compared to bulk. An increase in the calcination temperature resulted in an increase in particle size and saturation magnetization. The observed increase in saturation magnetization was most likely due to the formation and growth of ZnFe₂O₄/γ-Fe₂O₃ diphase crystals. The highest saturation magnetization (45 emu/g) was obtained for fibers calcined at 800 °C.