Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

Euler–Bernoulli arbitrary discontinuous beams acted upon by static loads are addressed. Based on appropriate Green’s functions here derived in a closed form, the response variables are obtained: (a) for stepped beams with internal springs, as closed-form functions of the beam discontinuity parameters, without enforcing neither internal nor boundary conditions; (b) for stepped beams with internal springs and along-axis supports, as closed-form functions of the unknown reactions of the along-axis supports only, to be computed by enforcing pertinent conditions. A remarkable reduction in computational effort is achieved, in this manner, compared to competing methods in the literature.     

Synthesis and NMR Spectroscopic Study of a New Bis(aminophosphonate) with Terminal Furyl Groups

1,3-Bis[ N -methyl(diethoxyphosphonyl)-1-(2-furyl)]diaminobenzene has been synthesized through the addition of diethyl phosphite to the Schiff base N , N '-difurfurylidene- m -phenylenediamine. The compound has been characterized by elemental analysis, TLC, IR, and 1 H, 13 C, and 31 P NMR spectra. The NMR studies show that the reaction product is a mixture of two diastereomers ( meso and racemic forms). The 31 P NMR data revealed 61% content for the predominant and 39% for the minor form.     

Conformationally Rigid Hosts Containing Phosphonic Units

We present here a new class of cleft-like receptor molecules containing two or four phosphonates anions, tailored for multipoint binding of their substrates. Depending on the accessibility of the cleft, these hosts are water soluble and selective for short or long f , y -diammonium compounds. Due to their inherent chirality, we found that only those host-guest combinations which allow a three-point-interaction were effective.     

Synthesis ofN,N′-ditosyl-8, 19-dimethoxy-2,5-diaza-[6.1]-naphthyl-cyclophane: crystal and molecular structure of its 1∶1 chloroform solvate

Journal of Inclusion Phenomena and Macrocyclic Chemistry - The title compound, C41H40N2O6S2, has been synthesised in good yield and was found to form a 1∶1 inclusion compound with CHCl3 and...     

How does the substrate affect the Raman and excited state spectra of a carbon nanotube?

We study the optical properties of a single, semiconducting single-walled carbon nanotube (CNT) that is partially suspended across a trench and partially supported by a SiO₂-substrate. By tuning the laser excitation energy across the E ₃₃ excitonic resonance of the suspended CNT segment, the scattering intensities of the principal Raman transitions, the radial breathing mode (RBM), the D mode and the G mode show strong resonance enhancement of up to three orders of magnitude. In the supported part of the CNT, despite a loss of Raman scattering intensity of up to two orders of magnitude, we recover the E ₃₃ excitonic resonance suffering a substrate-induced red shift of 50 meV. The peak intensity ratio between G band and D band is highly sensitive to the presence of the substrate and varies by one order of magnitude, demonstrating the much higher defect density in the supported CNT segments. By comparing the E ₃₃ resonance spectra measured by Raman excitation spectroscopy and photoluminescence (PL) excitation spectroscopy in the suspended CNT segment, we observe that the peak energy in the PL excitation spectrum is red-shifted by 40 meV. This shift is associated with the energy difference between the localized exciton dominating the PL excitation spectrum and the free exciton giving rise to the Raman excitation spectrum. High-resolution Raman spectra reveal substrate-induced symmetry breaking, as evidenced by the appearance of additional peaks in the strongly broadened Raman G band. Laser-induced line shifts of RBM and G band measured on the suspended CNT segment are both linear as a function of the laser excitation power. Stokes/anti-Stokes measurements, however, reveal an increase of the G phonon population while the RBM phonon population is rather independent of the laser excitation power.     

A non-local two-dimensional foundation model

Classical foundation models such as the Pasternak and the Reissner models have been recently reformulated within the framework of non-local mechanics, by using the gradient theory of elasticity. To contribute to the research effort in this field, this paper presents a two-dimensional foundation model built by using a mechanically based non-local elasticity theory, recently proposed by the authors. The foundation is thought of as an ensemble of soil column elements resting on an elastic base. It is assumed that each column element is acted upon by a local Winkler-like reaction force exerted by the elastic base, by contact shear forces and volume forces due, respectively, to adjacent and non-adjacent column elements. As in the Pasternak model, the contact shear forces involve the second-order derivative of the column element displacement. The volume forces are non-local forces assumed to depend (1) on the relative displacement between the interacting column elements through power-law distance-decaying attenuation functions and (2) on the product between the volumes of the interacting column elements. As a result, the equilibrium equations are fractional differential equations, for which a numerical solution can be readily found based on the finite difference method. Solutions are built for different foundation shapes and loading conditions.     

High-performance liquid chromatography/atmospheric pressure chemical ionization tandem mass spectrometry determination of cholesterol uptake by Caco-2 cells

A simple, sensitive and selective liquid chromatography/atmospheric pressure chemical ionization tandem mass spectrometric method (LC/APCI-MS/MS) was developed and applied to quantitative determination of uptake of cholesterol by Caco-2 human intestine cells. Caco-2 cells were cultured in medium containing cholesterol-3,4-13C2 and phytosterols from nutritional supplements after in vitro digestion. Cellular cholesterol (cholesterol-3,4-13C2) and endogenous cholesterol were extracted using methanol/chloroform (1:2, v/v) and directly analyzed using LC/APCI-MS/MS with selected reaction monitoring (SRM), using cholesterol-2,2,3,4,4,6-d6 as an internal standard. Detection and quantification limits were 2.2 and 7.2 pmol, respectively. This method provides an effective tool for rapid determination of cholesterol uptake by cells with increased selectivity and sensitivity in comparison to previously reported LC/APCI-MS analysis using selected ion monitoring (SIM).     

Comparison of four extraction/methylation analytical methods to measure fatty acid composition by gas chromatography in meat

Four different extraction-derivatization methods commonly used for fatty acid analysis in meat (in situ or one-step method, saponification method, classic method and a combination of classic extraction and saponification derivatization) were tested. The in situ method had low recovery and variation. The saponification method showed the best balance between recovery, precision, repeatability and reproducibility. The classic method had high recovery and acceptable variation values, except for the polyunsaturated fatty acids, showing higher variation than the former methods. The combination of extraction and methylation steps had great recovery values, but the precision, repeatability and reproducibility were not acceptable. Therefore the saponification method would be more convenient for polyunsaturated fatty acid analysis, whereas the in situ method would be an alternative for fast analysis. However the classic method would be the method of choice for the determination of the different lipid classes.     

Synthesis,characterization, NMR study and clathration ability of N,N′,N″,N″′-tetratosyl-8,11,21,24-tetramethyl-2,5,14,17,-tetraaza-[6.6]-paracyclophane

The title macrocycle 1 was synthesised in good yield (66%) by a one-pot condensation process from 2,3-bis(chloromethyl)-p-xylene andN,N-ditosylethylendiamine. The macrocycle was found to undergo isomerization processes at elevated temperature on the NMR time scale (G = 87.8 kJ mol^–1) and acts as a suitable host only for toluene. The FAB-MS spectra of1 is rich, and full of interesting and very diagnostic fragmentation pathways.     

The use of SSA fractionation to detect changes in the molecular structure of model ethylene-butene copolymers modified by peroxide crosslinking

Four model ethylene-butene copolymers of different molecular weights modified with various concentrations of peroxide were analyzed by a DSC based successive self annealing method. The original copolymers had the same intra and intermolecular homogeneous branching distribution along the linear chains with approximately 2.4% mol of ethyl branches. The copolymers with average molecular weights of 29,000, 45,000, 81,000 and 125,000 g/mol were modified with different amounts of 2,5-dimethyl-2,5-di(tert-butyl peroxy)-hexane (DBPH) as a crosslinking initiator. The molecular changes induced by the reaction with the peroxide affect the semicrystalline structure of the material. Variations in the crystal thickness distributions of the material as a consequence of the modification are related to the peroxide induced free radical reactions.