The analysis of the M/M/1 queue with two vacation policies (M/M/1/SWV+MV)

We consider an M/M/1 queue with two vacation policies which comprise single working vacation and multiple vacations, denoted by M/M/1/SMV+MV. Using two methods (called R-matrix method and G-matrix method), we obtain the stationary distribution of queue length (including the customer being in service) and make further analysis on the stationary numbers of customers in the working vacation and vacation period, respectively. The stochastic decomposition results of stationary queue length and the sojourn time of a customer are also derived. Meanwhile, we show that a simple and direct method of decomposition developed in Liu et al. [Stochastic decompositions in the M/M/1 queue with working vacations, Oper. Res. Lett. 35 (2007), pp. 595–600] is also applicable to our model. Furthermore, busy period is analysed by the limiting theorem of alternative renewal process. Finally, some boundary properties and numerical analysis on performance measures are presented.     

On the complex formation of CdCl2 with 1-furoylthioureas: Preconcentration and voltammetric behavior of Cd(II) at carbon paste electrodes modified with 3-monosubstituted and 3,3-disubstituted derivatives

Two series of 1-furoylthioureas were used as modifiers of carbon paste electrodes (CPE). The preconcentration of Cd(II) at CPE modified with these 3-monosubstituted and 3,3-disubstituted 1-furoylthioureas and its subsequent voltammetric determination was studied with Cd(II) test solution. The preconcentration of cadmium at the surface of the modified CPE varied with the steric and electronic nature of the present CS neighboring groups. This is in accord with the changes observed in the Raman spectra of the ligands after complexation with CdCl₂, and with the chemical yields of the complexes obtained.     

On multi-soliton solutions for the (2+1)-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide

In this work, we construct multi-soliton solutions of the $(2+1)$-dimensional breaking soliton equation with variable coefficients by using the generalized unified method. We employ this method to obtain double- and triple-soliton solutions. Furthermore, we study the nonlinear interactions between these solutions in a graded-index waveguide. The physical insight and the movement role of the waves are discussed and analyzed graphically for different choices of the arbitrary functions in the obtained solutions. The interactions between the solitons are elastic whether the coefficients of the equation are constants or variables.