Reformulation of general relativity as a gauge theory

The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials B_μ are introduced and corresponding fields F_μν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of B_μ are generalized spin coefficients, and linear combinations of F_μν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.     

A Whiteheadian approach to Bell's correlations

Certain properties of the Bell-type correlations and, in particular, the impossibility of using them to transmit signals faster than light, are investigated from the point of view of the conceptual structure of quantum mechanics and of Whitehead's process philosophy. The collapses of quantum states are shown to correspond to perspectives of different frames of reference on a Whiteheadian process of self-creation of actual entities. The analysis suggests a fundamental limitation on the capacity to describe the propagation of influences among the results of measurements at space-like separation. It is further shown that, if Whitehead's framework is modified in a specific way, it accounts very well for the apparent existence of superluminal influences, and for the impossibility of using them for superluminal communication.This work was supported in part by a grant from the Colgate Research Council.     

A note on the Stokes resistance tensors of multiparticle systems in shear fields

The Stokes resistance tensors (material tensors) of a multiparticle system subjected to a general shear flow depends on the spatial configuration of the particles, their shape, size and location of some arbitrarily fixed set of points locked to the particles by which their linear velocities are traced. The objective of this work is the determination of some symmetry properties of the material tensors and the transformation laws which govern them under translation of the set of points fixed to the particles.     

Capillary electrophoretic separation of sugars in fruit juices using on-line mid infrared Fourier transform detection

Fourier Transform infrared spectroscopy has been coupled to on-line capillary electrophoresis (CE) for the separation and detection of natural sugars in orange fruit juices. The CE separation electrolyte comprised 50 mM sodium carbonate buffer adjusted to pH 12.3 with NaOH. Galactose was selected as an internal standard. To ensure tight connections between the custom-made IR-transparent flow cell (optical path length was 15 [micro sign]m) and the fused silica capillaries, commercially available O-rings were used. The scanner of the spectrometer was operated at a HeNe laser modulation frequency of 320 kHz, recording interferograms in a double-sided, forward-backward mode with 8 cm(-1) spectral resolution. For each spectrum 64 interferograms (512 for the background) were co-added and a Blackman-Harris 3-term apodization function was performed. A low-pass filter at 1828 cm(-1) was inserted in the IR beam to increase the light throughput in the spectral region of interest (1800 cm(-1)-900 cm(-1)). Using these features a new spectrum could be obtained every two seconds. Sucrose, glucose and fructose were structurally identified and quantified in orange juice samples. The limits of detection (3S/N) for all analytes were in the low millimolar range (0.7-1.9 mM) or, in absolute amounts, the low nanogram range (1.5-3.2 ng). The resolution ranged between 1.14 to 3.15 and the RSD of the proposed method was 1.8-4.4%.     

Kinetics and mechanism of acrylonitrile polymerization by p-toluenesulfinic acid. III. Initiation through disproportionation

A mechanism for radical formation from aromatic sulfinic acids through the disproportionation reaction is suggested. It is postulated that two parallel steps, one a bimolecular reaction and the other involving a trimer of sulfinic acid, yield sulfenyl sulfonate. This labile compound decomposes into free radicals or reacts with another molecule of sulfinic acid producing thiol sulfonate and sulfonic acid. This mechanism explains the variety and unusually high orders encountered in polymerization initiated by sulfinic acid initiators. The proposed kinetic scheme is in agreement with the proton dependence found for both the initiation as well as the disproportionation reactions.     

A note on regular Ramsey graphs

We prove that there is an absolute constant C>0 so that for every natural n there exists a triangle‐free regular graph with no independent set of size at least \({{C}}\sqrt{{{n}}\log{{n}}}\). © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 244–249, 2010     

Fractionation and characterization of starch granules using field-flow fractionation (FFF) and differential scanning calorimetry (DSC)

Starch is one of the main carbohydrates in food; it is formed by two polysaccharides: amylose and amylopectin. The granule size of starch varies with different botanical origins and ranges from less than 1 μm to more than 100 μm. Some physicochemical and functional properties vary with the size of the granule, which makes it of great interest to find an efficient and accurate size-based separation method. In this study, the full-feed depletion mode of split-flow thin cell fractionation (FFD-SF) was employed for a size-based fractionation of two types of starch granules (corn and potato) on a large scale. The fractionation efficiency (FE) of fraction-a for corn and potato granules was 98.4 and 99.4%, respectively. The FFD-SF fractions were analyzed using optical microscopy (OM) and gravitational field-flow fractionation (GrFFF). The respective size distribution results were in close agreement for the corn starch fractions, while they were slightly different for the potato starch fractions. The thermal properties of FFD-SF fractions were analyzed, and the results for the potato starch showed that the peak temperature of gelatinization (T_p) slightly decreases as the size of the granules increases. Additionally, the enthalpy of gelatinization (ΔH) increases when the granule size increases and shows negative correlation with the gelatinization range (ΔT).

     

Dense Free Sets

Let κ = 2 ^ω , and assume \(f:\mathbb {R}\rightarrow \mathcal {P}(\mathbb {R})\) satisfies the intersection properties C(ω,κ) and C(κ,ω). We prove that if \(\mathfrak {r}<\text {cf}(\kappa )\) then there exists a dense free set for f.     

Selective bromination of perylene diimides under mild conditions

A novel method for the bromination of perylene diimides, PDI (1), under mild conditions is reported. Variation of the reaction conditions allows mono- and dibromination of PDIs to afford 2 and 3 (these can be separated through standard procedures) or exclusive dibromination to afford 3. Pure 1,7 regioisomers are obtained through repetitive crystallization. The structure of 1,7-3b was elucidated by a single-crystal X-ray analysis. The facility of the bromination reaction, which decreases in the order 1a > 1b > 1c, depends on PDI aggregation propensities. Monobrominated PDIs were utilized for the syntheses of novel unsymmetrical piperidinyl (4a and 4b) and trimethylsilylethynyl derivatives (5a and 5b). Computational studies (DFT) on imide substituent rotation in PDIs reveal that in the case of bulky groups there is a restricted rotation leading to isomers, in agreement with our experimental results. An aromatic core twist in PDIs bearing one and two bromine substituents was also investigated by DFT.     

Thermal response in crystalline Ibeta cellulose: a molecular dynamics study

The influence of temperature on structure and properties of the cellulose Ibeta crystal was studied by molecular dynamics simulations with the GROMOS 45a4 force-field. At 300 K, the modeled crystal agreed reasonably with several sets of experimental data, including crystal density, corresponding packing and crystal unit cell dimensions, chain conformation parameters, hydrogen bonds, Young's modulus, and thermal expansion coefficient at room temperature. At high-temperature (500 K), the cellulose chains remained in sheets, despite differences in the fine details compared to the room-temperature structure. The density decreased while the a and b cell parameters expanded by 7.4% and 6%, respectively, and the c parameter (chain axis) slightly contracted by 0.5%. Cell angles alpha and beta divided into two populations. The hydroxymethyl groups mainly adopted the gt orientation, and the hydrogen-bonding pattern thereby changed. One intrachain hydrogen bond, O2'H2'...O6, disappeared and consequently the Young's modulus decreased by 25%. A transition pathway between the low- and high-temperature structures has been proposed, with an initial step being an increased intersheet separation, which allowed every second cellulose chain to rotate around its helix axis by about 30 degrees . Second, all hydroxymethyl groups changed their orientations, from tg to gg (rotated chains) and from tg to gt (non-rotated chains). When temperature was further increased, the rotated chains returned to their original orientation and their hydroxymethyl groups again changed their conformation, from gg to gt. A transition temperature of about 450 K was suggested; however, the transition seems to be more gradual than sudden. The simulated data on temperature-induced changes in crystal unit cell dimensions and the hydrogen-bonding pattern also compared well with experimental results.