Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.     

Synthetic strategies and functional reactivity of versatile thiophene synthons

Abstract

Thiophenes are a highly important group of heterocycles and have been of great interest to researchers due to their various reactivities. Many synthetic strategies are used to generate functionalized thiophene derivatives. Several reactions are described, depending on the reactivity of the substituents attached to the thiophene nucleus toward different nucleophiles to yield the versatile thiophene products. Many diverse applications have been utilized for thiophenes from medicinal chemistry to material science.     

Electrooxidative C–H thiocyanation of hetarenes: voltammetric assessment of thiocyanogen reactivity

1. Download : Download high-res image (92KB)
2. Download : Download full-size image

     

Intrinsic infrared absorption for carbon–fluorine bonding in fluorinated nanodiamond

1. Download : Download high-res image (155KB)
2. Download : Download full-size image

     

Exploring high pressure structural transformations,electronic properties and superconducting properties of MH2 (M = Nb,Ta)

The high-pressure structures and properties of MH₂ (M = Nb, Ta) are explored through an ab initio evolutionary algorithm for crystal structure prediction and first-principles calculations. It is found that NbH₂ undergoes a phase transition from a cubic Fm$\overline{3}$m structure with regular NbH₈ cubes to an orthorhombic Pnma structure with fascinating distorted NbH₉ tetrakaidecahedrons at 48.8 GPa, while the phase transition pressure of TaH₂ from a hexagonal P6₃mc phase with slightly distorted TaH₇ decahedron to an orthorhombic Pnma phase with attractive distorted TaH₉ tetrakaidecahedrons is about 90.0 GPa. Besides, the calculated electronic band structure and density of states demonstrate that all of these structures are metallic. The Poisson’s ratio, electron localization function, and Bader charge analysis suggest that these phases possess dominant ionic bonding character with the effective charges transferring from the metal atom to H. From our electron–phonon calculations, the calculated superconducting critical temperature T_c of the Pnma-NbH₂ is 6.903 K at 50 GPa. Finally, via the quasi-harmonic approximation method, the phase diagrams at pressure up to 300 GPa and temperature up to 1000 K of MH₂ (M = Nb, Ta) are established, where the transition pressure of Fm$\overline{3}$m-NbH₂ → Pnma-NbH₂ and P6₃mc-TaH₂ → Pnma-TaH₂ were found to decrease with increasing temperature.     

Bacterial response to eukaryotic cells. Analysis of differentially expressed proteins using nano liquid chromatography-electrospray ionization tandem mass spectrometry

Host-bacteria interactions have mostly been investigated with regard to the host response or to activities of pathogenic bacteria. In contrast, we aim to identify reactions of non-pathogenic bacteria that result from their contact with host cells of the gastrointestinal tract. In a proteomic approach, the response of non-pathogenic human Escherichia coli bacteria on gut epithelial cells (rat IEC-6) was investigated in an in vitro co-culture model. For this purpose, a sensitive analytical procedure was developed based on the identification of two-dimensional polyacrylamide gel electrophoresis separated proteins by online nanoLC-electrospray ionization MS/MS using a quadrupole time-of-flight tandem mass spectrometer for accurate mass determination. We demonstrate here the efficiency of this technique by the identification of a total of 43 differentially expressed proteins, out of which 25 were up-regulated and 18 were down-regulated. They represent a wide range of molecular weight and different metabolic and physiological functions.     

Preparation of a sulfonated fused-silica capillary and its application in capillary electrophoresis and electrochromatography

In the present paper, two new methods, sol-gel and chemical bonding methods, were proposed for preparation of sulfonated fused-silica capillaries. In the sol-gel method, a fused-silica capillary was coated with the sol solution obtained by hydrolysis of 3-mercaptopropyltrimethoxysilane (MPTS) and tetramethoxysilane, and followed by age; while in the chemical bonding method, a capillary was chemically bonded directly with MPTS. Then, both the resulting capillaries were oxidized with an aqueous solution of hydrogen peroxide solution (H2O2) (30%, m/m) to obtain the sulfonated capillaries. The electroosmotic flow (EOF) for the sulfonated capillaries was found to remain almost constant within the studied pH range, and greater than that of the uncoated capillary. However, the coating efficiency of the capillary prepared by chemical bonding method was higher than that by sol-gel method, by comparing their magnitude of the EOF, the degree of disguise of the silanol and reproducibility of preparation procedure. The effects of the electrolyte's concentration and the content of methanol (MeOH) on the EOF were also studied. Especially, the study of the apparent pH (pH*) on the EOF in a water-MeOH system was reported. Finally, capillary electrophoretic separation of seven organic acids was achieved within 6.5 min under optimal condition using the chemically bonded sulfonated capillary. Moreover, separation of four alkaloids on the sulfonated capillary was compared with that on uncoated capillary in different conditions. Ion-exchange mechanism was found to play a key role for separation of these four basic analytes on the sulfonated capillary.     

Astragalus membranaceus ultrafine powder alleviates hyperuricemia by regulating the gut microbiome and reversing bile acid and adrenal hormone biosynthesis dysregulation

Ethnopharmacological relevanceMetabolic syndrome is closely related to the intestinal microbiota and disturbances in the host metabolome. Hyperuricemia (HUA), a manifestation of metabolic syndrome, can induce various cardiovascular diseases and gout, seriously affecting a patient’s quality of life. Astragalus membranaceus has a long history as a commonly used traditional Chinese medicine to treat kidney disease in China and East Asia.Materials and methodsWe compared the therapeutic effect of benzbromarone and two different doses Astragalus membranaceus ultrafine powder (AMUP) in rats with HUA. Ultra-performance liquid chromatography-mass spectrometer was used to analyze the AMUP metabolism in the plasma, urine, and feces. Further, 16S ribosome RNA sequencing and feces metabolomic were performed to capture the variation of the gut microbiota and metabolites changes before and after drug administration.ResultsAMUP had a notable impact on reducing blood uric acid levels while protecting the liver and kidney. Drug metabolism analysis demonstrated that effective constituent flavonoids are distributed in the blood, whereas saponins remain in the intestine. Gut microbiota analysis showed that low-dose AMUP ameliorated HUA-induced gut dysbiosis by reducing the abundance of harmful bacteria and increasing that of some beneficial bacteria with anti-inflammatory properties, such as Clostridia, Lachnospiraceae, and Muribaculaceae. In addition, HUA-induced changes in metabolite contents in bile acid and adrenal hormone biosynthesis pathways were restored after treatment with AMUP.ConclusionLow-dose AMUP exerts remarkable therapeutic effects on HUA by regulating the gut microbiome and mediating gut metabolism pathways associated with uric acid excretion.     

Dimethyl carbonate as a novel methylating reagent for fatty acids in analytical pyrolysis

Dimethyl carbonate (DMC) was investigated as a mild, harmless and odorless reagent for pyrolytic methylation of fatty acids. Soybean oil was selected as test material for its high content of (poly)unsaturated fatty acids. Pyrolyses were performed at 500, 700 and 900 degrees C by means of a heated platinum filament pyrolyser on-line and off-line to the GC-MS apparatus. Methyl esters of palmitic, linoleic, oleic and stearic acid were formed as prominent products from off-line pyrolysis of soybean oil in the presence of DMC and zeolite 13X. Fatty acid methyl esters (FAMEs) were not observed at important levels in the absence of zeolite, while on-line Py-GC-MS experiments resulted principally in the formation of free fatty acids and hydrocarbons. The FAME profiles obtained from the DMC/zeolite off-line pyrolysis were compared to those resulting from tetramethylammonium hydroxide (TMAH) thermochemolysis and BF3-methanol procedure. The observed differences between pyrolysis and methanolysis methods were principally attributed to the thermal degradation of unsaturated fatty acids. The effectiveness of the DMC/zeolite pyrolytic methylation was further demonstrated by the analysis of tripalmitine and soybean seeds.