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.     

Simultaneous densitometric determination of artemisinin, artemisinic acid and arteannuin-B in Artemisia annua using reversed-phase thin layer chromatography

A rapid and simple RP-TLC method for simultaneous quantification of pharmacologically important sesquiterpene artemisinin (AM) together with its precursors arteannuin-B (AB) and artemisinic acid (AA) in the inflorescence part of Artemisia annua plant has been developed. The RP-TLC of sesquiterpenes was performed on RP-18 F254 S thin-layer chromatographic plates by developing in mobile phase, containing 0.2% TFA in water/ACN (35:65, v/v). The densitometric determination of AM, AB and AA was carried out after derivatization with anisaldehyde reagent at 426 nm in absorption-reflectance mode.     

Chromatographic separation and determination of Zr in bauxites and aluminum alloys

Summary A simple thin-layer chromatographic method for the complete separation of Zr from aluminum is described. The optimum solvent composition is evaluated by means of the simplex method of optimization. Quantitative determination and regression analysis is carried out.     

Separation of fuels,heavy fractions,and crude oils into compound classes: A review

Practically all the conventional chromatographic techniques are used in the characterization of the highly complex mixtures of organic compounds occurring in fuels, heavy fractions, and crude oils. This paper surveys the techniques employed for class determination, preparative fractionation of the main classes, and determination of subgroups after class fractionation.     

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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Thin-layer adsorption chromatography with mixed mobile phases. 4. Extension of Ościk's equation to heterogeneous adsorbents

In this paper the equation for thin-layer adsorption chromatography with multicomponent mobile phases, proposed by O?cik in 1965 is extended to energetically heterogeneous solid surfaces. Other forms of this equation, more convenient in practical applications, are presented. Model calculations are made for TLC with binary mobile phases according to the modified form of O?cik's equation. Finally, this equation is compared with that of Snyder.