Inversion of two-dimensional potentials from frequency-resolved spectroscopic data

We report the first successful reconstruction of two-dimensional potential energy surfaces (PES) using the magnitudes and positions of a set of frequency-resolved fluorescence (or absorption) lines. The inversion proceeds by first extracting the phases of the transition-dipole matrix elements, yielding, together with the (ground) PES to (from) which emission (absorption) occurs, a point by point reconstruction of the two-dimensional excited state PES. The inversion procedure is highly accurate even for PES with multiple minima and many missing lines, with typical RMS errors <0.002 cm(-1) in the classically allowed region and <0.018 cm(-1) in the classically forbidden region.     

The isomorphism problem for some universal operator algebras

This paper addresses the isomorphism problem for the universal (non-self-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables, and that this happens if and only if the associated subproduct systems are isomorphic. The proof makes use of the complex analytic structure of the character space, together with some recent results on subproduct systems. Restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry. These commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties. We prove a projective Nullstellensatz connecting closed ideals and their zero sets. Under some technical assumptions, we find that two such algebras are isomorphic as algebras if and only if they are similar, and we obtain a clear geometrical picture of when this happens. This result is obtained with tools from algebraic geometry, reproducing kernel Hilbert spaces, and some new complex-geometric rigidity results of independent interest. The C^?-envelopes of these algebras are also determined. The Banach-algebraic and the algebraic classification results are shown to hold for the wot-closures of these algebras as well.     

Preventive maintenance for inspected systems with additive subexponential shock magnitudes

We examine the long-run average availability and cost rate of a maintained system which deteriorates according to a random-shock process. Shocks arrive according to a Poisson process. The system fails whenever the cumulative damage exceeds a given threshold. The system's failures are not self-announcing, hence, failures must be detected via inspections. The system is inspected at periodic or exponentially distributed intervals. Systems are replaced by preventive maintenance or after failure (corrective maintenance), whichever occurs first. When the distribution function of the shock magnitudes belongs to the class of subexponential distributions, we obtain simple approximations for the availability and the cost rate. Copyright © 2007 John Wiley & Sons, Ltd.     

A discrete-time model of failure and repair

In this paper the authors introduce and study a model of failures and repairs of units with discrete lifetimes. They suppose that a unit has a sequence of tasks to perform and that its lifetime is measured by the number of tasks performed before its final, fatal failure. Upon a failure the unit may be repaired (with some probability) and then it may attempt again to perform the current task. The unit dies when (with some probability) a repair cannot be completed. We derive some stochastic comparisons of pairs of such models. The stochastic comparisons are then applied for obtaining results regarding the inheritance of several aging properties by the repaired unit. Various examples illustrate the applicability of the model. Some variants of the model of this paper can be viewed as discrete analogues of the notion of imperfect repair.     

Maximal solutions of semilinear elliptic equations with locally integrable forcing term

We study the existence of a maximal solution of −Δu+g(u)=f(x) in a domain Ω ∈ ℝ ^N with compact boundary, assuming thatf ∈ (L _loc ¹ (Ω))₊ and thatg is nondecreasing,g(0)≥0 andg satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classicalC _1,2 Wiener criterion, then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition, we discuss the question of uniqueness of large solutions. This research was partially supported by an EC Grant through the RTN Program “Front-Singularities”, HPRN-CT-2002-00274.     

Two dimorphs of 5‐methyl­sulfanyl‐1H‐tetrazole

5‐Methyl­sulfanyl‐1H‐tetrazole, C₂H₄N₄S, crystallizes in dimor­phic forms; the α‐form crystallizes at room temperature in the monoclinic crystal system, space group P2₁/m, and the β‐form crystallizes by sublimation at 423 K in the orthorhombic crystal system, space group Pbcm. In both forms, the mol­ecules occupy crystallographic mirror planes and are connected to one another via N—H⋯N hydrogen bonds, the amino H atoms being disordered. The two forms differ from one another in their packing; there are polar layers in the α‐form and non‐polar layers in the β‐form.     

Uniform estimates for a variational problem with small parameters

Communicated by J. M. Ball     

Rearrangements of (0–1) matrices

Let ℬ(m) be the set of all then-square (0–1) matrices containingm ones andn ²−m zeros, 0<m<n ². The problem of finding the maximum ofs(A ²) over this set, wheres(A ²) is the sum of the entries ofA ²,A ∈ ℬ (m) is considered. This problem is solved in the particular casesm=n ² −k ² andm=k ²,k ²>(n ²/2). This paper forms part of a thesis in partial fulfillment of the requirements for the degree of Doctor of Science at the Technion-Israel Institute of Technology. The author wishes to thank Professor B. Schwarz and Dr. D. London for their help in the preparation of this paper.