Montecrinanes A–C: Triterpenes with an Unprecedented Rearranged Tetracyclic Skeleton from Celastrus vulcanicola. Insights into Triterpenoid Biosynthesis Based on DFT Calculations

Three new triterpenoids with an unprecedented 6/6/6/6‐fused tetracyclic carbon skeleton, montecrinanes A–C ( 1 – 3 ), were isolated from the root bark of Celastrus vulcanicola, along with known D:B‐friedobaccharanes ( 4 – 6 ), and lupane‐type triterpenes ( 7 – 12 ). The stereostructures of the new metabolites were elucidated based on spectroscopic (1D and 2D NMR) and spectrometric (HR‐EIMS and HR‐ESIMS) techniques. Their absolute configurations were determined by both NMR spectroscopy, with (R)‐(?)‐α‐methoxyphenylacetic acid as a chiral derivatizing agent, and biogenetic considerations. Biogenetic pathways for montecrinane and D:B‐friedobaccharane skeletons were proposed and studied by DFT methods. The theoretical results support the energetic feasibility of the putative biogenetic pathways, in which the 1,2‐methyl shift from the secondary baccharenyl cation represents a novel and key reaction step for a new montecrinane skeleton.     

An analytical method for the determination of stress and strain concentrations in textile-reinforced GF/PP composites with elliptical cutout and a finite outer boundary and its numerical verification

Stress concentrations in the vicinity of cutouts can often be regarded to be the limiting factor for a whole structure. As a further development of prior research at the Institute of Lightweight Engineering and Polymer Technology, an analytical method for the determination of the whole stress-strain fields in the vicinity of holes in multilayered textile-reinforced composites has been developed, which takes into consideration the influences of a finite outer boundary of the specimen. The analytical method is based on the classical laminate theory and the use of complex-valued potential functions. To account for the shape of the specimen, the method of conformal mappings is applied for the inner boundary, while a combination of boundary collocation and least squares method is used for the outer boundary. The method allows a layer-by-layer analysis of stress concentrations. For the verification of the developed calculation model, extensive experimental and numerical finite-element (FE) studies have been carried out on multilayered GF/PP plates with different laminate layups, notches, and specimen dimensions. The comparison of the experimentally or numerically determined results with the analytically calculated ones shows a very good correlation, of which the numerical studies are presented here for the first time. In a second step, the applicable boundary conditions on the outer boundary have been extended in such a way that varying stress and moment resultants can be applied, so that the calculation method can be used as an analytical sub-model in combination with FE techniques.     

Wide binaries as a critical test of classical gravity

Modified gravity scenarios where a change of regime appears at acceleration scales a<a ₀ have been proposed. Since for 1M _⊙ systems the acceleration drops below a ₀ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 10⁴ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a ₀ acceleration regime. Our results are suggestive of a breakdown of Kepler’s third law beyond a≈a ₀ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.     

Optimisation of sensor positions in random linear arrays based on statistical relations between geometry and performance

Due to the widespread use of acoustic arrays, optimisation techniques for array design, focused on improving array performance, have been widely published. This paper exploits the statistical relation between different measures of sidelobe levels and the spacing of elements in random linear arrays made up of a small number of sensors. This paper defines the methodology to obtain maximum probability functions, associating array geometry and performance. These maximum probability functions allow a pre-selection of those array geometries that are more likely to be associated to specified sidelobe level values. This pre-selection results in a significantly reduced computational burden.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Simultaneous Determination of Barbital and Thiobarbituric Acid by Derivative Spectrophotometry

A new method for the simultaneous determination of barbital and thiobarbituric acid by derivative spectrophotometry is proposed. The method allows the resolution of mixtures of the two components over the concentration ranges 0.37–4.70 μg/ml (barbital) and 0.40–4.50 μg/ml (thiobarbituric acid) provided the ratio between their concentrations does not exceed 5:1. It was applied to the determination of the two compounds in synthetic samples and blood serum.     

Entropy for Symbolic Dynamics with Overlapping Alphabets

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces and show that it is equal to a limit of entropies of standard (non-overlapping) shifts when the underlying shift is of finite type. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.