G-matrix Method Research Articles

On a batch matching system with impatient servers and boundedly rational customers

In this paper we consider a batch matching system with impatient servers and boundedly rational customers, which is essentially a double-ended batch service system. Each server is responsible for a batch of customers and serves them instantaneously. Especially, we assume that the servers have the characteristic of ”impatience”, which will lead to incomplete batch processing of each service. To derive the stationary distribution of system states, we combine two methods (called probability generating function method and G-matrix method), and some main performance measures are captured. In addition, we assume the customers are boundedly rational, that is, they are unable to estimate their sojourn times and utilities accurately. To deal, a logit model is employed to model this characteristic of the customers, and by which, we obtain the customers’ equilibrium joining fraction which is compared with the equilibrium joining probability of fully rational customers afterwards. Depending on whether the service is visible or invisible, we conduct some numerical analyses to show main parameters’ impact on equilibrium fraction, along with some intuitive explanations. Finally, to make the system viable economically, a function of service provider’s utility is developed and several numerical plots are presented to study the impact of several main parameters on the utility. Through the PSO (Particle Swarm Optimization) algorithm, we numerically obtain the maximum utility point within a certain range of multiple parameters.

Array Factor Forming for Image Reconstruction of One-Dimensional Nonuniform Aperture Synthesis Radiometers

Nonuniform aperture synthesis radiometers (NASRs) have the advantage of flexibility in practical applications. However, the main limitation of NASRs for Earth observation is the poor reconstruction quality. In this letter, the array factor of 1-D NASR is analyzed. Array factor forming (AFF) is introduced to improve the reconstruction quality of 1-D NASRs. The limitations of the AFF on array configurations are given. The NASR that meets the given limitations is called the optimizable NASR (ONASR). The numerical results and experimental results demonstrate that the AFF is able to improve the reconstruction quality of 1-D ONASRs. To assess the performance of the AFF thoroughly, the comparisons are made against the linear interpolation and the regularized G-matrix method. Meanwhile, the comparisons between the AFF-based 1-D ONASRs and the 1-D uniform ASRs are also made. The comparison results demonstrate that the AFF can obtain better reconstruction quality than the linear interpolation and the regularized G-matrix method. Additionally, the comparison results also demonstrate that the reconstruction quality of AFF-based 1-D ONASRs can approach that of 1-D uniform ASRs.

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

ABSTRACTWe 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.

Correlations in microscopic optical model for nucleon elastic scattering off doubly closed-shell nuclei

The random phase approximation (RPA) long-range correlations are known to play a significant role in understanding the depletion of single particle-hole states observed in ($e,{e}^{'}$) and ($e,{e}^{'}p$) measurements. Here the RPA theory, implemented using the D1S force is considered for the specific purpose of building correlated ground states and related one-body density matrix elements. These may be implemented and tested in a fully microscopic optical model for NA scattering off doubly closed-shell nuclei. A method is presented to correct for the correlations overcounting inherent to the RPA formalism. One-body density matrix elements in the uncorrelated (i.e., Hartree-Fock) and correlated (i.e., RPA) ground states are then challenged in proton scattering studies based on the Melbourne microscopic optical model to highlight the role played by the RPA correlations. Agreement between the parameter free scattering predictions and measurements is good for incident proton energies ranging from 200 MeV down to approximately 60 MeV and becomes gradually worse in the lower energy range. Those features point unambiguously to the relevance of the g-matrix method to build microscopic optical model potentials at medium energies, and emphasize the need to include nucleon-phonon coupling, that is, a second-order component of the Feshbach type in the potential at lower energies. Illustrations are given for proton scattering observables measured up to 201 MeV for the $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ target nuclei.

Low-momentum nucleon–nucleon interaction and shell-model calculations

We discuss the use of the low-momentum nucleon–nucleon (NN) interaction Vlow-k in the derivation of the shell-model effective interaction and emphasize its practical value as an alternative to the Brueckner G-matrix method. We present some selected results of our current study of exotic nuclei around closed shells, which have been obtained starting from the CD-Bonn potential. We also show some results of calculations performed with different phase-shift equivalent NN potentials, and discuss the effect of changes in the cutoff. momentum which defines the Vlow-k potential.

Soft-core hyperon-nucleon potentials

A new Nijmegen soft-core OBE potential model is presented for the low-energy $\mathrm{YN}$ interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. The potentials are generated by the exchange of nonets of pseudoscalar, vector, and scalar mesons. As is standard in the Nijmegen soft-core models, we also include the $J=0$ contributions from the tensor ${f}_{2}{,f}_{2}^{\ensuremath{'}}{,a}_{2},$ and pomeron Regge trajectories, and use Gaussian form factors to guarantee that the potentials have a soft behavior near the origin. An important innovation with respect to the original soft-core potential is the assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices in accordance with broken $\mathrm{SU}{(3)}_{F},$ which serves to connect the $\mathrm{NN}$ and the $\mathrm{YN}$ channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the ${}^{3}{P}_{0}$ model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. Charge-symmetry breaking in the $\ensuremath{\Lambda}p$ and $\ensuremath{\Lambda}n$ channels is included as well. We present six hyperon-nucleon potentials which describe the available $\mathrm{YN}$ cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\ensuremath{\Sigma}N$ and $\ensuremath{\Lambda}N$ channels. In all cases, we obtained ${\ensuremath{\chi}}^{2}{/N}_{\mathrm{data}}\ensuremath{\approx}0.55$ for 35 $\mathrm{YN}$ data. In particular, we were able to fit the precise experimental datum ${r}_{R}=0.468\ifmmode\pm\else\textpm\fi{}0.010$ for the inelastic capture ratio at rest. For the scalar-meson mixing angle we obtained values ${\ensuremath{\theta}}_{S}=37\ifmmode^\circ\else\textdegree\fi{}--40\ifmmode^\circ\else\textdegree\fi{},$ which points to almost ideal mixing angles for the scalar $q\overline{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\ensuremath{\Lambda}$ hypernuclei.

Vibrational spectra and force field studies of [PtCl3(CO)]− anion labelled with 13C16O, 12C18O, and radioactive 14C16O

Detailed infrared and Raman studies are reported for [PtCl3(12C16O)]−, [PtCl3(13C16O)]−, [PtCl3(12C18O)]−, and [PtCl3(14C16O)]− together with assignments. Bands observed for the 14C16O species at 2005, 483, 507, and 466 cm−1 are assigned to CO and PtC stretching, PtCO in-plane and out-of-plane linear bending modes, respectively. Force constants have been calculated using a modified valence force field, with constrained off-diagonal force constants based on [PtCl4]2− and [PtX3(CO)]− (X = Br, I). The effective G-matrix method (EGM) has been used for approximate calculation of CO and PtC stretching force constants for some other square-planar platinum–carbonyl complexes. The results are discussed with the assistance of stretching force constants for some of the simpler complexes. Key words: vibrational spectra, force constant calculation, 13C, 14C, and 18O labelled [PtCl3(CO)]−.

Relativistic transport theory for hadronic matter

We derive coupled equations of motion for the density matrices for nucleons, Δ resonances, and π mesons, as well as for the pion-baryon interaction vertex function for the description of nuclear reactions at intermediate energies. We start from an effective hadronic Lagrangian density with minimal coupling between baryons and mesons. By truncating at the level of three-body correlations and using the G-matrix method to solve the equations of motion for the two-body correlation functions, a closed equation of motion for the one-body density matrices is obtained. A subsequent Wigner transformation then leads to a tractable set of relativistic transport equations for interacting nucleons, deltas, and pions.

Normal co-ordinate analysis and force constants for the thionyl halides

Using W ilson's F- and G-matrix method and data in the literature, force constants have been calculated for the three thionyl halides F 2SO, Cl 2SO and Br 2SO. A valence force field with six independent constants was used. The stretching constants for the SO bonds follow closely the “SO stretching frequencies” and both vary as would be expected qualitatively assuming that increased electronegativity of the halogen atoms favors greater pπ- dπ SO bonding.