Transition-metal dichalcogenides have been investigated using Raman spectroscopy both being off-resonance and in resonance. The first-order Raman spectra of MoS 2 , MoSe 2 , WS 2 and WSe 2 single crystal synthesized by vapor transport technique have been studied as a function of hydrostatic pressure (0-20 GPa) and temperature (80-300 K). Isobaric and isothermal mode-Grüneisen parameters have been determined from the temperature and pressure-dependent Raman spectra. The pressure dependence of the chalcogen-chalcogen and metal-chalcogen force constant has been obtained using a central force model. Separation of the temperature dependence of Raman mode wavenumbers into quasi-harmonic and purely anharmonic contributions using measured high-pressure Raman data allows us to extract the changes in the phonon wavenumbers arising exclusively due to anharmonic interactions.

Given a morphism T from a Banach algebra B to a commutative Banach algebra A, a multiplication is defined on the Cartesian product space A × B perturbing the coordinatewise product resulting in a new Banach algebra A × T B. The Arens regularity as well as amenability (together with its various avatars) of A × T B are shown to be stable with respect to T .2010 Mathematics subject classification: primary 46H05; secondary 46J05.

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Stability criteria for second-order dynamical systems with time lag are presented here in a simple chart form. The results cover negative as well as positive values of the parameters. These stability charts for second-order difference-differential equations are likely to serve the same purpose as the Strutt-Ince chart does for the Mathieu equation.