Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media

In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially.     

Asymptotic stability of the Degasperis–Procesi antipeakon–peakon profile

The aim of this paper is to prove that the Degasperis–Procesi antipeakon–peakon profile is asymptotically stable for all time. We start by proving the asymptotic stability of a single Degasperis–Procesi peakon and antipeakon with respect to perturbations having a momentum density that is first negative and then positive. Then this result is extended towards a well-ordered trains of antipeakons–peakons under such perturbations. In particular, the asymptotic stability of the antipeakon–peakon profile holds.     

Minimax principles for elliptic mixed hemivariational–variational inequalities

In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems.     

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

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Intrinsic infrared absorption for carbon–fluorine bonding in fluorinated nanodiamond

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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.