Optimality and Greed in Dynamic Allocation

In dynamic allocation items arrive and depart randomly and while present are stored in a limited facility; the job of an allocation algorithm is to decide whether and where to store an arriving item, while trying to minimize the cost incurred by rejections. Ordinarily, to prove the value of such an algorithm, one must either assume a specific arrival distribution (e.g., Poisson-λ), or try to obtain bounds relative to an adversary (as in competitive analysis).We present here a novel method of proving precise optimality for certain kinds of dynamic allocation algorithms, without assuming a specific arrival distribution. We do need to assume memoryless departure for at least some item types, and most importantly, we must assume conditions are such that it is not right to reject arrivals unnecessarily.The method is applied to two simple call assignment problems which arose, in quite different circumstances, at Lucent Technologies. In both cases the method was successful in showing that the intuitively best assignment algorithm really does minimize expected cost under fairly general, and essentially necessary, assumptions.     

Size determination of metallic iron particles by temperature dependent Mössbauer and ferromagnetic resonance studies

The thermal decomposition products of NaX·Fe(CO)₅ after various steps of heat treatment, in vacuum as well as under gas atmosphere (Ar, H₂), have been investigated by temperature-dependent Mössbauer and ferromagnetic resonance measurements. The measured spectra of both techniques consistently are analyzed using superparamagnetic relaxation behavior of magnetic particles. From this analysis information concerning composition and size of magnetic iron particles is derived.     

TE- and TM-polarization-resolved spectroscopy on quantum wells under normal incidence

We present TE- and TM-polarization-resolved photocurrent measurements on quantum well pin diodes under normal incidence. Usually, optical experiments performed in such a geometry yield information only about transitions involving in-plane (p_x and p_y) components of the hole wave functions because of the in-plane (TE) polarization of the light. Information on transitions sensitive to the p_z components can be obtained by focussing a radially polarized laser beam through a microscope objective with high numerical aperture (NA=0.9). With our setup, the electrical field vector at the focal tail has a significant component along the optical axis (TM-polarization!) which enables excitation of transitions sensitive to p_z components also. Additionally, the existence of a degenerate (azimuthally polarized) optical mode enables switching these p_z components on and off easily.Experimental evidence of these features has been achieved by exploiting the selection rules for e–hh and e–lh transitions in a quantum well structure. We present a comparison of our recorded spectra with theoretical predictions obtained from simple geometric optics assumptions. For our quantum wells the polarization effects are small because our measurement averages the intensity distribution of the whole focal plane. We plan to extend our measurements to polarization resolved single quantum dot spectroscopy. By restricting the detection region to the spatial extent of a single dot, one can exploit the almost pure TM-polarization on the optical axis for obtaining high contrast between heavy- and light-hole exciton absorption.     

Interaction of atomic hydrogen with metal surfaces

Received: 23 March 1998/Accepted: 21 August 1998     

Relaxation as seen by nuclei: Comparison between conventional Mössbauer spectra and nuclear resonant scattering of synchrotron radiation

The mechanism of spin‐lattice relaxation has been investigated in the “picket‐fence” porphyrin [Fe(CH₃COO)(TP_pivP)]^-, a high‐spin iron(II) complex with unusual large quadrupole splitting of 4.25 mm s^-1, by conventional Mössbauer spectroscopy as well as by nuclear resonant forward scattering (NFS). Superparamagnetism with a blocking temperature of about 8 K is observable by both methods in the spectra of bacterioferritin from S. olivaceus. From these two examples general conclusions about the merits of both methods can be drawn.     

Strict Kinetic Treatment of the Electron Response to Spatial Field Disturbances in Nonequilibrium Plasmas

In generalization of former approaches for the simplified solution of the inhomogeneous electron Boltzmann equation a higher order solution technique has been developed. This technique is based on a multi-term expansion of the electron velocity distribution function and allows a strict study of the electron kinetics in plasmas acted upon by space-dependent electric fields. This solution technique is used to investigate the response of the plasma electrons to spatially limited disturbances of the electric field in weakly ionized plasmas of helium and mercury. By solving the kinetic equation with increasing order of the multi-term expansion the convergent solution of the kinetic problem and thus the strict spatial behaviour of the velocity distribution and of significant macroscopic properties of the electrons has been determined and analysed. Furthermore, the impact of higher order terms of the expansion has been revealed and the falsification of the velocity distribution and of related macroscopic properties has been evaluated when instead of the multi-term solution the simpler two-term solution of the kinetic equation is used.     

A critical exponent in a degenerate parabolic equation

We consider positive solutions of the Cauchy problem in $\mathbb{R\,}^n$ for the equation $$u_t=u^p\,\Delta u+u^q,\quad p\geq1,\; q\geq 1$$\nopagenumbers\end and show that concerning global solvability, the number q = p + 1 appears as a critical growth exponent. Copyright © 2002 John Wiley & Sons, Ltd.     

Extremal cover times for random walks on trees

Let C_ν(T) denote the “cover time” of the tree T from the vertex v, that is, the expected number of steps before a random walk starting at v hits every vertex of T. Asymptotic lower bounds for C_ν(T) (for T a tree on n vertices) have been obtained recently by Kahn, Linial, Nisan and Saks, and by Devroye and Sbihi; here, we obtain the exact lower bound (approximately 2n In n) by showing that C_ν(T) is minimized when T is a star and v is one of its leaves. In addition, we show that the time to cover all vertices and then return to the starting point is minimized by a star (beginning at the center) and maximized by a path (beginning at one of the ends).