Theoretical study of group 11 metal–silonyl complexes: M–SiO and M–(SiO)2 (M = Cu, Ag, or Au)

 The spectroscopic properties of M–SiO and M–(SiO)₂ (1–1 and 1–2 complexes with M = Cu, Ag, or Au) have been theoretically studied. It has been shown that both M–SiO and M–(SiO)₂ compounds in their ground state are bent with a metal–Si bonded structure. The calculated M(ns) spin density agrees well with the electron spin resonance experimental data. From a topological analysis, it has been shown that a rather large charge transfer occurs from the metal towards the SiO moiety, and that the M–Si bond energy correlates with the electron density located at the M–Si bond path (bond critical point). Received: 6 July 2000 / Accepted: 11 October 2000 / Published online: 19 January 2001     

Intramolecular proton transfers in stereoisomeric gas-phase ions and the kinetic nature of the protonation process upon chemical ionization

The isobutane chemical ionization (CI) mass spectra of cis- and trans-1-butyl-3- and -4-dimethylaminocyclohexanols and of their methyl ethers exhibit abundant [MH - H(2)O](+) and [MH - MeOH](+) ions respectively. On the other hand, only the MH(+) ions of the cis-isomers exhibit significant [MH - H(2)O](+) and [MH - MeOH](+) ions under collision-induced dissociation (CID) conditions. The non-occurrence of water and methanol elimination in the CID spectra of the trans-isomers indicates retention of the external proton at the dimethylamino group in the MH(+) ions that survive after leaving the ion source and the first quadrupole of the triple-stage quadrupole ion separating system, and the trans-orientation of the two basic sites does not allow proton transfer from the dimethylamino group to the hydroxyl or methoxyl. Such transfer is allowed in the cis-amino alcohols and amino ethers via internal hydrogen-bonded (proton-bridged) structures, resulting in the elimination of water and methanol from the surviving MH(+) ions of these particular stereoisomers upon CID. The abundant [MH - ROH](+) ions in the isobutane-CI mass spectra of the trans-isomers indicates protonation at both basic sites, affording two isomeric MH(+) ions in each case, one protonated at the dimethylamino group and the other at the less basic oxygen function. These results show that the isobutane-CI protonation of the amino ethers and amino alcohols is a kinetically controlled process, occurring competitively at both basic sites of the molecules, despite the large difference between their proton affinities ( approximately 25 and approximately 35 kcal mol(-1); 1 kcal = 4.184 kJ). Copyright 1999 John Wiley & Sons, Ltd.     

Dielectronic recombination rate coefficients of Ni-like barium and tungsten

Ab initio calculations of the total dielectronic recombination (DR) rate coefficient of Ni-like barium () and tungsten () in the ground state have been performed using the HULLAC atomic code package. Resonant and nonresonant stabilizing radiative transitions are included. Collisional transitions following electron capture are neglected. The present level-by-level calculations include the DR contributions of all of the levels (over 17000) in the Cu-like inner-shell excited configurations 3d ⁹ 4ln'l' (), 3p ⁵ 3d ¹⁰ 4ln'l' (), and 3s3p ⁶ 3d ¹⁰ 4ln'l' (). For both ions, the configuration complexes with a hole in the 3p inner shell contribute almost 10% to the total DR rate coefficient, while the complexes with a hole in the 3s inner shell contribute about 1%. The converging contributions of the 3d ⁹ 4ln'l' (n' > 9) configurations are evaluated by applying the complex-by-complex extrapolation method and are found to comprise up to about 20% of the total DR rate coefficients throughout a wide electron temperature range. The total DR rate coefficients are fitted to an easy-to-use analytic expression which reproduces the original data with an accuracy of about 2% or better in a very wide temperature range. Received: 1 February 1999     

Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime

We consider a controlled queueing system of the $G/M/n/B+GI$ G / M / n / B + G I type, with many servers and impatient customers. The queue-capacity $B$ B is the control process. Customers who arrive at a full queue are blocked and customers who wait too long in the queue abandon. We study the tradeoff between blocking and abandonment, with cost accumulated over a random, finite time-horizon, which yields a queueing control problem (QCP). In the many-server quality and efficiency-driven (QED) regime, we formulate and solve a diffusion control problem (DCP) that is associated with our QCP. The DCP solution is then used to construct asymptotically optimal controls (of the threshold type) for QCP. A natural motivation for our QCP is telephone call centers, hence the QED regime is natural as well. QCP then captures the tradeoff between busy signals and customer abandonment, and our solution specifies an asymptotically optimal number of trunk-lines.     

Rational Abandonment from Tele-Queues: Nonlinear Waiting Costs with Heterogeneous Preferences

We consider the modelling of abandonment from a queueing system by impatient customers. Within the proposed model, customers act rationally to maximise a utility function that weights service utility against expected waiting cost. Customers are heterogeneous, in the sense that their utility function parameters may vary across the customer population. The queue is assumed invisible to waiting customers, who do not obtain any information regarding their standing in the queue during their waiting period. Such circumstances apply, for example, in telephone centers or other remote service facilities, to which we refer as tele-queues. We analyse this decision model within a multi-server queue with impatient customers, and seek to characterise the Nash equilibria of this system. These equilibria may be viewed as stable operating points of the system, and determine the customer abandonment profile along with other system-wide performance measures. We provide conditions for the existence and uniqueness of the equilibrium, and suggest procedures for its computation. We also suggest a notion of an equilibrium based on sub-optimal decisions, the myopic equilibrium, which enjoys favourable analytical properties. Some concrete examples are provided to illustrate the modelling approach and analysis. The present paper supplements previous ones which were restricted to linear waiting costs or homogeneous customer population.     

Reflection at a complex potential barrier in the semiclassical theory of scattering

The reflection of spherical waves at a complex potential barrier is discussed in the semiclassical approximation. We study the complex WKB method and the Uniform Approximation in the special case of weakly absorptive barriers, typical of surface transparent optical potentials used in heavy-ion reactions. It is found that the complex WKB results lead to a very accuratecross- section despite their inaccuracy in the most importantphase shifts. Thereby, the amazing stamina of the WKB has been confirmed once more. One of us (Y.A.) spent the summer of 1976 at the Max-Planck Institute at Heidelberg where the present work has been done. He would like to thank J. Hüfner and H. Weidenmüller for the hospitality extended to him.     

Designing a call center with an IVR (Interactive Voice Response)

A call center is a service operation that caters to customer needs via the telephone. Call centers typically consist of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents. In this paper we study a Markovian model for a call center with an IVR. We calculate operational performance measures, such as the probability for a busy signal and the average wait time for an agent. Exact calculations of these measures are cumbersome and they lack insight. We thus approximate the measures in an asymptotic regime known as QED (Quality and Efficiency Driven) or the Halfin–Whitt regime, which accommodates moderate to large call centers. The approximations are both insightful and easy to apply (for up to 1000’s of agents). They yield, as special cases, known and novel approximations for the M/M/N/N (Erlang-B), M/M/S (Erlang-C) and M/M/S/N queue.     

Semiclassical analysis of edge state energies in the integer quantum Hall effect

Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separately, this problem is equivalent to that of a one dimensional harmonic oscillator centered at x = x_c and an infinite wall at x = 0, and appears in numerous physical contexts. The eigenvalues E_n(x_c) for a given quantum number n are solutions of the equation S(E,x_c)=π[n+ γ(E,x_c)] where S is the WKB action and 0 < γ < 1 encodes all the information on the connection procedure at the turning points. A careful implication of the WKB connection formulae results in an excellent approximation to the exact energy eigenvalues. The dependence of γ[E_n(x_c),x_c] ≡γ_n(x_c) on x_c is analyzed between its two extreme values as x_c ↦-∞ far inside the sample and as x_c ↦∞ far outside the sample. The edge-state energiesE_n(x_c) obey an almost exact scaling law of the form and the scaling function f(y) is explicitly elucidated.