Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source

Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou, 2006 Christoforou , C. ( 2006 ). Hyperbolic systems of balance laws via vanishing viscosity . J. Diff. Eq. 221 ( 2 ): 470 – 541 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup 𝒫 generated by the vanishing viscosity limit in the general case which includes also nonconservative systems. Furthermore, we prove uniqueness of solutions by means of local integral estimates and show that every “viscosity solution” can be constructed as a limit of vanishing viscosity approximations.     

Numerical investigations of supercavitation around blunt bodies of submarine shape

Cavitation occurs when liquid is subjected to rapid changes of pressure. If the local pressure is lower than the liquid saturation pressure, the liquid changes its phase into vapor. A fast moving solid body underwater will reduce the local pressure around the body. Under certain conditions, the local pressure can be lower than the water saturation pressure, accordingly causing cavitation. If the velocity of the moving body increases further, a supercavitation will occur. In this paper, the cavitation and supercavitation were studied by the SST k–ω turbulence model combined with a finite-rate mass transfer modeling under the mixture assumption. The validations of these models were performed through comparisons between numerical simulations and experiments. After the validations, the supercavitation generated by a high speed moving body, which can be described as a large bubble, was studied. The studies were on several blunt bodies, such as a submarine hull shape, a submarine hull shape with appendages and a full submarine shape with sail and appendages. It was found that the naked submarine hull is difficult to have the supercavitation covering the whole body. The sail and appendages can help supercavitation occurs earlier. Furthermore the effects of the supercavitation on the submarine and generation mechanism of the supercavitation is discussed based on the simulations.     

Preparative isolation of pseudolaric acids A and B,and their glucosides from the root bark of Pseudolarix kaempferi using high‐speed counter‐current chromatography

In order to provide the chemical markers for the quality control of herbal medicines, four diterpenoids, pseudolaric acids A and B (PAA and PAB), and their glucosides were isolated from the methanol extract of the Chinese herb Pseudolarix kaempferi using high‐speed counter‐current chromatography (HSCCC). The diphase solvent system was n‐hexane/EtOAc/MeOH/H₂O which was used at two ratios (5:5:5:5 and 1:9:4:6 by volume) in the separation of pseudolaric acids and their glycosides, respectively. As a result, PAA (14 mg), PAB (129 mg), PAA‐O‐β‐D ‐glucopyranoside (8 mg, PAAG), and PAB‐O‐β‐D ‐glucopyranoside (42 mg, PABG) were obtained from 0.5 g of the crude extract. Their purities were determined to be above 97% by HPLC analysis. Their chemical structures were confirmed by ¹H and ¹³C NMR analysis or HPLC comparison with the reference compounds.     

Preparative isolation and purification of atractylon and atractylenolide III from the Chinese medicinal plant atractylodes macrocephala by high-speed counter-current chromatography

The medicinal plant Atractylodes macrocephala (Baizhu in Chinese) has been widely used in traditional Chinese medicine for energy and stomach complaints, treatment of dyspepsia and anorexia, anti-inflammation, anticancer and for increasing assimilation. A high-speed counter-current chromatography (HSCCC) method was developed for the preparative separation and purification of two main bioactive components, namely, atractylon and atractylenolide III from A. macrocephala by using light petroleum (60-90 degrees C)-ethyl acetate-ethanol-water (4:1:4:1 v/v) as the two-phase solvent system in dual-mode elution. Compared with the separation using the normal-mode elution, the dual-mode HSCCC can be achieved with shorter elution time. Atractylenolide III (32.1 mg) at 99.0% purity and 319.6 mg atractylon at 97.8% purity could be obtained from 1000 mg crude sample in a single run. The recoveries of atractylenolide III and atractylon were 95.4 and 92.6%, respectively.     

Preparative purification of five bioactive components from Agrimonia pilosa Ledeb by high-speed counter-current chromatography

High-speed counter-current chromatography (HSCCC) coupled with ultraviolet (UV) detection or evaporative light-scattering detection was successfully applied for preparative separation of five bioactive compounds from Agrimonia pilosa Ledeb. In preliminary process, D101 macroporous resin was used to separate the crude extract of the plant and four fractions (20, 40, 50, and 60% aqueous ethanol elutions) were produced. Then, these fractions were directly subjected to HSCCC purification. Five chemicals including taxifolin-3-glucoside (6.4 mg), quercetin-3-rhamnoside (13.0 mg), tiliroside (14.7 mg), agrimonolide (21.4 mg), and tormentic acid (29.8 mg) with the purities of 94.24, 95.37, 97.42, 95.29, and 96.34% were separated from each 200 mg prepared fraction. The purities were analyzed by high-performance liquid chromatography, and the chemical structures of the products were identified by UV detection, mass spectrometry, nuclear magnetic resonance, and the standards. This paper used a simple method to separate five bioactive compounds from A. pilosa Ledeb, and it could provide a new idea for the purification of bioactive compounds from other medicinal plants.     

Preparative mass‐spectrometry profiling of minor concentrated metabolites in Salicornia gaudichaudiana Moq by high‐speed countercurrent chromatography and off‐line electrospray mass‐spectrometry injection

Salicornia species have just been introduced to the European market as a vegetable named ‘samphire’, ‘green asparagus’, or ‘sea asparagus’. Due to its increasing attention, and associated value, minor compounds of Salicornia gaudichaudiana Moq were investigated. The use of countercurrent chromatography and mass spectrometry enabled the search for known, as well as potentially novel natural products. Their identification was achieved based on molecular weights and mass‐spectrometric fragmentation data. Low detection limits enabled the visualization of all compounds with their identification in almost real time close to the preparative countercurrent chromatography experiment. A list of known natural products from Salicornia genus guided the identification process of compounds occurring in Salicornia gaudichaudiana Moq by tandem mass spectrometry fragment comparison. The natural product classes were divided into four groups: chlorogenic acid derivatives; flavonoid derivatives; pentacyclic triterpenoid saponins; and other compounds.     

A practicable strategy for enrichment and separation of four minor flavonoids including two isomers from barley seedlings by macroporous resin column chromatography,medium‐pressure LC,and high‐speed countercurrent chromatography

Separation of minor compounds especially with similar polarities and structures from complex samples is a challenging work. In the present study, an efficient method was successfully established by macroporous resin column chromatography, medium‐pressure liquid chromatography, and high‐speed countercurrent chromatography for separation of four minor flavonoids from barley seedlings. Macroporous resin column chromatography and medium‐pressure liquid chromatography were used for enrichment of these four flavonoids. High‐pressure liquid chromatography analysis showed the total content of these four flavonoids increased from 2.2% in the crude extract to 95.3% in the medium‐pressure liquid chromatography fraction. It was indicated that the combination of macroporous resin column chromatography and medium‐pressure liquid chromatography could be a practicable strategy for enrichment of minor compounds from complex sample. Then, high‐speed countercurrent chromatography was employed for separation of these four flavonoids using ethyl acetate/n‐butanol/water (0.1% glacial acetic acid) (4:1:5, v/v/v) as solvent system. As a result, four flavonoids including two isomers with purities higher than 98% were obtained. Interestingly, two flavonoids existing in one high‐pressure liquid chromatography peak were also successfully separated. All these indicated high‐speed countercurrent chromatography had great potential for separation of compounds with similar structures and polarities. This study provides a reference for efficient enrichment and separation of minor compounds from complex sample.     

Continuous separation of maslinic and oleanolic acids from olive pulp by high‐speed countercurrent chromatography with elution‐extrusion mode

In this work, a continuous high‐speed countercurrent chromatography method has been developed on the basis of elution‐extrusion mode and this method was successfully applied to the separation of maslinic and oleanolic acid from the extract of olive pulp. In the process of ‘elution’, the sample solution was continuously loaded into the column and the maslinic acid was steadily eluted out in this step while highly retained oleanlic acid always stayed in the column. In the process of ‘extrusion’, the oleanlic acid was pushed out of the column with the stationary phase. In this way, we achieved a large sample loading. A total of 120 mL sample solution (about 89.55% of the column volume) which contains 600 mg olive pulp extract was pumped in the apparatus by a constant‐flow pump and the maslinic and oleanolic acids were largely separated within 120 min. Both of these two compounds presented high yields and high purities (271.6 mg for maslinic acid with 86.7% and 83.9 mg oleanolic acids with 83.4%).