The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.     

Electronic control of stereoselectivity. 20. Crystal and molecular structure of the ferrocene derived from tricyclo[5.2.1.02,6]Deca-2,5,8-triene

Reaction of the isodicyclopentadienide anion and its dehydro congener with Fe(II) leads to a stereochemically homogeneous ferrocene derivative in each instance. Through chemical correlation and X-ray analysis, above-plane complexation is established for both halves within the two sandwich compounds.     

The 4051-Angstroms band of C3 (A 1Piu-X 1Sigmag +, 000-000): perturbed low-J lines and lifetime measurements

Rotational analyses have been carried out at high resolution for the 000-000 and 000-100 bands of the A (1)Pi(u)-X (1)Sigma(g) (+) transition of supersonic jet-cooled C(3). Two different spectra have been recorded for each band, using time gatings of 20-150 and 800-2300 ns. At the shorter time delay the spectra show only the lines observed by many previous workers. At the longer time delay many extra lines appear, some of which have been observed previously by [McCall et al.Chem. Phys. Lett. 374, 583 (2003)] in cavity ring-down spectra of jet-cooled C(3). Detailed analysis of these extra lines shows that at least two long-lived states perturb the A (1)Pi(u), 000 state. One of these appears to be a (3)Sigma(u) (-) vibronic state, which may possibly be a high vibrational level of the b (3)Pi(g) state, and the other appears to be a P = 1 state with a low rotational constant B. Our spectra also confirm the reassignment by McCall et al. of the R(0) line of the 000-000 band, which is consistent with the spectra recorded towards a number of stars that indicate the presence of C(3) in the interstellar medium. Fluorescence lifetimes have been measured for a number of upper-state rotational levels. The rotational levels of the A (1)Pi(u) state have lifetimes in the range of 230-190 ns, decreasing slightly with J; the levels of the perturbing states have much longer lifetimes, with some of them showing biexponential decays. An improved value has been obtained for the nu(1) vibrational frequency of the ground state, nu(1) = 1224.4933 +/- 0.0029 cm(-1).     

A discrete method of optimal control based upon the cell state space concept

A discrete method of optimal control is proposed in this paper. The continuum state space of a system is discretized into a cell state space, and the cost function is discretized in a similar manner. Assuming intervalwise constant controls and using a finite set of admissible control levels (u) and a finite set of admissible time intervals (), the motion of the system under all possible interval controls (u, ) can then be expressed in terms of a family of cell-to-cell mappings. The proposed method extracts the optimal control results from these mappings by a systematic search, culminating in the construction of a discrete optimal control table.The possibility of expressing the optimal control results in the form of a control table seems to give this method a means to make systems real-time controllable.Dedicated to G. LeitmannThe material is based upon work supported by the National Science Foundation under Grant No. MEA-82-17471. The author is also indebted to Professor G. Leitmann for his many helpful comments.