An exact, closed-form solution for equilibrium of trveling, sagged, elastic cables under uniformly distributed loading

IntroctionThquilibrium of sagged, elastic cable s under its own weight loading is needed in tiledesign of cable structures. In 1851 RO'htsLll first investigated a uniform, inextensible suspendedchain hanging freely under its own weight. Ro.th[Zj considered a model of a heterogeneouschain hanging in the form of a cycloid, and application of this model to the uniform chainreduced to the Rohrs model when the sag ratio is small. However, the chain was modeled asinextensible. Pugsley['] develope…     

A Convenient Route to 5,6-Diphenyl-5,6-dihydro-uracils

Diphenylcyclopropenone(1) reacts with a variety of thiopseudoureas to eventually afford dihydrouracils     

An efficient approach for the isolation, identification and evaluation of antimicrobial plant components on an analytical scale, demonstrated by the example of Radix imperatoriae

Using Radix imperatoriae (the root of masterwort) as an example, we describe an efficient approach for the isolation, identification and evaluation of bioactive plant components on an analytical scale. The extraction of Radix imperatoriae with ethyl acetate was enhanced by the application of ultrasound oscillations. This rhizome extract was applied to three pathogenic bacteria (Bacillus cereus, Escherichia coli, and Staphylococcus aureus) to determine its antimicrobial activity. Disk diffusion was utilized to determine susceptibility. The extract components were separated using a series of chromatography approaches (semi-preparative RP-HPLC, or RP-HPLC on an analytical scale), followed by testing. All fractions were analyzed by LC-UV-ESI-MS and 600 MHz microcoil ¹H NMR spectroscopy. Among other findings, in the fraction with the highest antibacterial activity we were able to identify oxypeucedanin and oxypeucedanin hydrate. Subsequent analysis revealed that only oxypeucedanin hydrate had antibacterial activity, whereas oxypeucedanin itself was inactive at the concentrations applied. Furthermore, oxypeucedanin hydrate appears to be largely, or exclusively, a by-product of sample preparation, since it is either not synthesized by the plant as a second metabolite or is produced by it in only very small quantities.     

Optimal transportation on non-compact manifolds

In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type d ^r , r > 1, where d is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.     

Criteria for the appearance of recirculating and non-stationary regimes behind a cylinder in a viscoplastic fluid

The appearance of a recirculation zone and the formation of non-stationary vortices behind a cylinder in the unconfined flow of a Herschel–Bulkley fluid have been studied by numerical simulation. The Herschel–Bulkley constitutive equation was regularised by using the Papanastasiou model. Special attention was paid to determining the numerical parameters and comparing them to existing results. The influence of the Oldroyd number and power-law index on flow morphology and, in particular, on the unyielded zones was studied over a wide spectrum (0 ≤ Od ≤ 10) and (0.3 ≤ n ≤ 1.8). It was seen that the greater the Oldroyd number, the greater the critical Reynolds numbers and Strouhal number for the two flow regimes. The influence of the power-law index is more complex.