Dynamical response of fractional-order nonlinear system with combined parametric and forcing excitation

A dynamical analysis of a Mathieu-van der Pol-Duffing nonlinear system with fractional-order derivative under combined parametric and forcing excitation is studied in this paper. The approximate analytical solution is researched for 1/2 sub harmonic resonance coupled with primary parametric resonance based on the improved averaging approach. The steady-state periodic solution including its stability condition is established. The equivalent linear stiffness coefficient (ELDC) and equivalent linear damping coefficient (ELSC) for this nonlinear fractional-order oscillator are defined. Then, the numerical simulations are presented in three typical cases by iterative algorithms. The time history, phase portrait, FFT spectrum and Poincare maps are shown to explain the system response. Some different responses, such as quasi-periodic, multi-periodic and single periodic behaviors are observed and investigated. The results of comparisons between the numerical solutions and the approximate analytical solutions in three typical cases show the correctness of the analytical solutions. The influences of the fractional-order parameters on the system dynamical response are researched based on the ELDC and ELSC. Through analysis, it could be found that the increase of the fractional-order coefficient would result in the rightward and downward movements of the amplitude-frequency curves. The increase of the fractional-order coefficient will also move the bifurcation point rightwards and will make the existing range of steady-state solution larger. It could also be found that the ELSC will become larger and ELDC smaller when the fractional order is closer to zero, so that the decrease of the fractional order would make the response amplitude larger. At last, the detailed conclusions are summarized, which is beneficial to design and control this kind of fractional-order nonlinear system

5-(4-Pyrid­yl)-1,3,4-thia­diazole-2(3H)-thione

The title compound C7H5N3S2, occurs as the thione tautomer in the solid state; the dihedral angle between the pyridine and thia­diazole ring planes is 2.08 (6)°. In the crystal, mol­ecules are linked by N—H⋯N hydrogen bonds, generating C(8) chains propagating in [010]

Study of ‘Fingerprints’ for Green Tea from Different Planting Areas in Eastern China

Green tea is one of the main teas in China, which is unfermented and retains more natural substances of fresh tea leaves. This is the preliminary study of  application of ‘fingerprints’ based on differences in component composition of green tea. Five green teas from different areas in eastern China are  analyzed, which are processed by microwave-assisted solvent (ethanol) extraction method to obtain tea polyphenols, flavonoids, polysaccharides,  pigments (thearubigins, theaflavins, theabrownins). The results show that the component composition of five green teas are varied from each other;  based on these contents varieties, we have constructed a ‘fingerprint’ and applied linear discriminant analysis (LDA) and hierarchical cluster analysis  (HCA) to assist in the identification of these five green teas. This method does not require large, expensive instruments (such as high performance liquid  chromatograph, gas chromatograph, mass spectrometer, etc.), and is easy to use, which provides a new avenue for the identification of tea.&nbsp