Vinylogous anionic processes in the formation and interconversion of tetracyclic ring systems

Tandem oxy-Cope and transannular vinylogous aldol reactions and/or vinylogous retro-aldol, conjugate addition, and transannular vinylogous aldol reactions transformed some tricyclic vinyl enones into fused tetracycles under basic conditions. Mesylates derived from similar tetracyclic products underwent efficient skeletal reorganization via transannular ring-opening but then different modes of transannular ring-closure upon treatment with tert-butoxide.     

Compressed liquid densities and excess molar volumes for (CO2 + 1-pentanol) binary system at temperatures from 313 to 363 K and pressures up to 25 MPa

Measurements of compressed liquid densities for 1-pentanol and for {CO₂ (1) + 1-pentanol (2)} system were carried out at temperatures from 313 K to 363 K and pressures up to 25 MPa. Densities were measured for binary mixtures at 10 different compositions, x₁ = 0.0816, 0.1347, 0.3624, 0.4651, 0.6054, 0.7274, 0.8067, 0.8573, 0.9216, and 0.9757. A vibrating tube densimeter was used to perform density measurements using two reference calibration fluids. The uncertainty is estimated to be better than ±0.2 kg · m^?3 for the experimental density measurements. For each mixture and for 1-pentanol, the experimental densities were correlated using an explicit volume equation of six parameters and an 11-parameter equation of state (EoS). Excess molar volumes were determined for the (CO₂ + 1-pentanol) system using 1-pentanol densities calculated from the 11-parameter EoS and CO₂ densities calculated from a multiparameter reference EoS.     

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brézis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73–97.] Brézis and Friedman prove that certain nonlinear parabolic equations, with the δ-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186–196.] Colombeau and Langlais prove that these equations have a unique solution even if the δ-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais’ result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371–399.].     

Interactions of germanium atoms with silica surfaces

GeH₄ is thermally cracked over a hot filament depositing 0.7-15 ML Ge onto 2-7 nm SiO₂/Si(1 0 0) at substrate temperatures of 300-970 K. Ge bonding changes are analyzed during annealing with X-ray photoelectron spectroscopy. Ge, GeH_x, GeO, and GeO₂ desorption is monitored through temperature programmed desorption in the temperature range 300-1000 K. Low temperature desorption features are attributed to GeO and GeH₄. No GeO₂ desorption is observed, but GeO₂ decomposition to Ge through high temperature pathways is seen above 750 K. Germanium oxidization results from Ge etching of the oxide substrate. With these results, explanations for the failure of conventional chemical vapor deposition to produce Ge nanocrystals on SiO₂ surfaces are proposed.     

Some aspects of groups acting on finite posets

Let P be a finite poset and G a group of automorphisms of P. The action of G on P can be used to define various linear representations of G, and we investigate how these representations are related to one another and to the structure of P. Several examples are analyzed in detail, viz., the symmetric group $\text{G}$_n acting on a boolean algebra, GL_n(q) acting on subspaces of an n-dimensional vector space over GF(q), the hyperoctahedral group B_n acting on the lattice of faces of a cross-polytope, and $\text{G}$_n acting on the lattice Π_n of partitions of an n-set. Several results of a general nature are also proved. These include a duality theorem related to Alexander duality, a special property of geometric lattices, the behavior of barycentric subdivision, and a method for showing that certain sequences are unimodal. In particular, we give what seems to be the simplest proof to date that the q-binomial coefficient $\text{k+l}\text{k}$ has unimodal coefficients.     

Characterization of leukemic and normal white blood cells by Curie-point pyrolysis—mass spectrometry: I. Numerical evaluation of the results of a pilot study

A preliminary study was undertaken to determine the usefulness of Curie-point pyrolysis—mass spectrometry followed by computer analysis for character diseased white blood cells. White blood cells from normal, infected, polyeyrhemic and leukemic persons were pyrolyzed in front of the electron impact ion source of a quadrupole mass spectrometer on 510°C and 355°C Curie-point filaments. Visual inspection and computer assisted pattern analysis using the ARTHUR program revealed marked differences in the spectra among the different diagnostic categories. The 510°C pyrolysis—mass spectra from leukemic patients were found to have increased intensity at mass peaks related to RNA and DNA as well as decreased intensity at mass peaks related to choline containing phospholipids when compared to controls. The spectra from the polyeyrhemic patient and the two infected patients were found to have intermediate intensities for these two characteristic series. Pyrolysis at 355°C was found to enhance the differences seen in the 510°C pyrolysis spectra. Though the number of patients is too small to allow rigorous statistical analysis of the observed differences, numerical analysis of the spectra appears to hint at the possibility of using Curie-point pyrolysis—mass spectrometry as a diagnostic tool in discriminating different types of leukemias. An investigation with many more samples is needed to confirm these preliminary findings.     

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144:13–29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144:13–29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green’s theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.     

On an anti‐Ramsey problem of Burr,Erdős,Graham, and T. Sós

Given a graph L, in this article we investigate the anti‐Ramsey number χ_S(n,e,L), defined to be the minimum number of colors needed to edge‐color some graph G(n,e) with n vertices and e edges so that in every copy of L in G all edges have different colors. We call such a copy of L totally multicolored (TMC). In 7 among many other interesting results and problems, Burr, Erd?s, Graham, and T. Sós asked the following question: Let L be a connected bipartite graph which is not a star. Is it true then that In this article, we prove a slightly weaker statement, namely we show that the statement is true if L is a connected bipartite graph, which is not a complete bipartite graph. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 147–156, 2006