A stratification of the moduli space of pointed non-singular curves

We consider the moduli space of pointed non-singular curves of genus g whose Weierstrass gap sequence has the largest gap \(\ell _g\) equal to \(2g-3\). We stratify the moduli space by the sequence of osculating divisors associated to a canonically embedded curve. A monomial basis for the space of higher orders regular differentials on the curves in each stratum is constructed. Numerical conditions are given on the semigroup imposing that one of the strata is empty. Several examples are presented.     

New Imatinib Derivatives with Antiproliferative Activity against A549 and K562 Cancer Cells

Tyrosine kinase enzymes are among the primary molecular targets for the treatment of some human neoplasms, such as those in lung cancer and chronic myeloid leukemia. Mutations in the enzyme domain can cause resistance and new inhibitors capable of circumventing these mutations are highly desired. The objective of this work was to synthesize and evaluate the antiproliferative ability of ten new analogs that contain isatins and the phenylamino-pyrimidine pyridine (PAPP) skeleton, the main pharmacophore group of imatinib. The 1,2,3-triazole core was used as a spacer in the derivatives through a click chemistry reaction and gave good yields. All the analogs were tested against A549 and K562 cells, lung cancer and chronic myeloid leukemia (CML) cell lines, respectively. In A549 cells, the 3,3-difluorinated compound (3a), the 5-chloro-3,3-difluorinated compound (3c) and the 5-bromo-3,3-difluorinated compound (3d) showed IC₅₀ values of 7.2, 6.4, and 7.3 μM, respectively, and were all more potent than imatinib (IC₅₀ of 65.4 μM). In K562 cells, the 3,3-difluoro-5-methylated compound (3b) decreased cell viability to 57.5% and, at 10 µM, showed an IC₅₀ value of 35.8 μM (imatinib, IC₅₀ = 0.08 μM). The results suggest that 3a, 3c, and 3d can be used as prototypes for the development of more potent and selective derivatives against lung cancer.     

Dressed coordinates: The path-integral approach

The recently introduced dressed coordinates are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the sum rules established in a previous work.     

Amorphous IZO TTFTs with saturation mobilities exceeding 100 cm2/Vs

In this paper we demonstrate the use of amorphous binary In₂O₃–ZnO oxides simultaneously as active channel layer and as source/drain regions in transparent thin film transistor (TTFT), processed at room temperature by rf sputtering. The TTFTs operate in the enhancement mode and their performances are thickness dependent. The best TTFTs exhibit saturation mobilities higher than 10² cm²/Vs, threshold voltages lower than 6 V, gate voltage swing of 0.8 V/dec and an on/off current ratio of 10⁷. This mobility is at least two orders of magnitude higher than that of conventional amorphous silicon TFTs and comparable to or even better than other polycrystalline semiconductors. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photoelimination of HF by hexafluoroacetylacetone: A tandem laser study

Tandem chemical laser techniques have been used to detect HF formed through photoelimination from 1,1,1,5,5,5-hexafluoroacetylacetone, HFAA. Information about the HF vibrational population ratios is deduced: N₂/N₁ < 0.37 and N₁/N₀ < 0.45. This work supports the deduction by Bassett and Whittle that photodecomposition of the enol form of HFAA results mainly in HF elimination and ring closure to a dihydrofuranone, a new type of reaction.     

Busemann functions and equilibrium measures in last passage percolation models

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or time-invariant) measures for the related (multi-class) interacting fluid system. As we shall see, in the classical Hammersley model, where each point has weight one, this approach brings a new and rather geometrical solution of the longest increasing subsequence problem, as well as a central limit theorem for the Busemann function.     

Determination of total mercury in nuts at ultratrace level

Total mercury, at μg kg⁻¹ level, was determined in different types of nuts (cashew nut, Brazil nuts, almond, pistachio, peanut, walnut) using a direct mercury analyser after previous sample defatting and by cold vapour atomic fluorescence spectrometry. There is not enough sensitivity in the second approach to determine Hg in previously digested samples due to the strong matrix effect. Mercury levels in 25 edible nut samples from Brazil and Spain were found in the range from 0.6 to 2.7 μg kg⁻¹ by using the pyrolysis of sample after the extraction of the nut fat. The accuracy of the proposed method was confirmed by analysing certified reference materials of Coal Fly Ash-NIST SRM 1633b, Fucus-IAEA 140 and three unpolished Rice Flour NIES-10. The observed results were in good agreement with the certified values. The recoveries of different amounts of mercury added to nut samples ranged from 94 to 101%. RSD values corresponding to three measurements varied between 2.0 and 14% and the limit of detection and quantification of the method were 0.08 and 0.3 μg kg⁻¹, respectively.     

Attractiveness of Brownian queues in tandem

Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in distribution to a Brownian motion as n goes to infinity. In particular this implies that the Brownian motion is an attractive invariant measure for the Brownian queueing operator. Our proof exploits the relationship between Brownian queues in tandem and the last-passage Brownian percolation model, developing a coupling technique in the second setting. The result is also interpreted in the related context of Brownian particles acting under one-sided reflection.

     

Equivalence of Many-Gluon Green’s Functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock Statistical Quantum Field Theories

We prove the equivalence of many-gluon Green’s functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 3, pp. 368–374, June, 2005.