Solid scintillation proximity membranes: I: Characterization of polysulfone-inorganic fluor morphologies precipitated from NMP solutions

Solid scintillation proximity membranes were prepared by coagulation of polysulfone polymer solutions containing cerium-activated yttrium silicate particles (CAYS) as a fluor. Membranes were formed by three different solidification processes: precipitation of the polymer-rich phase after liquid–liquid phase separation, vitrification via solvent evaporation, or rapid polymer collapse due to fast exchange between solvent in the solution and nonsolvent in the coagulation bath. The results indicate that when the coagulation process includes the liquid–liquid phase separation due to nucleation of the polymer-lean phase, the inorganic fluor particles are expressed out of the polymer-rich phase and separated from the polymer matrix. On the contrary, solidification by the vitrification of the polymer solution through solvent evaporation results in the inorganic fluors being surrounded by the polymer matrix, much like the dispersed state in the solution. In contrast, rapid collapse of the polymer also induces entrapment of the fluor in the polymer structure. However, fluor impregnation in the polymer matrix is distinguished from that in the vitrified membrane in that the impregnation is due to localized impingement of the fluor on the polymer structure rather than envelopment by polymer molecules.     

Necessary conditions for constrained optimization problems with semicontinuous and continuous data

We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.

     

Job selection and sequencing on a single machine in a random environment

We examine a single machine scheduling problem with random processing times and deadline. Given a set of independent jobs having specified initiation costs and terminal revenues, the objective is to select a subset of the jobs and sequence the selected jobs such that the expected profit is maximized. The job selection aspect considered by us marks a clear departure from the pure sequencing focus found in the traditional scheduling literature. In this paper, we assume an exponentially distributed deadline and do not allow preemption. Even under these conditions, the selection and sequencing problem remains quite difficult (unlike its pure sequencing counterpart); we in fact conjecture that the problem is NP-hard. However, we show that the problem can be efficiently solved as long as the cost parameter is agreeable or an approximate solution is acceptable. To this end, we describe several solution properties, present dynamic programming algorithms (one of which exhibits a pseudo-polynomial time worst-case complexity), and propose a fully-polynomial time approximation scheme. In addition, we study a number of special cases which can be solved in polynomial time. Finally, we summarize our work and discuss an extension where the jobs are precedence related.     

Stochastic programming for nurse assignment

We present a brief overview of four phases of nurse planning. For the last phase, which assigns nurses to patients, a stochastic integer programming model is developed. A Benders’ decomposition approach is proposed to solve this problem, and a greedy algorithm is employed to solve the recourse subproblem. To improve the efficiency of the algorithm, we introduce sets of valid inequalities to strengthen a relaxed master problem. Computational results are provided based upon data from Baylor Regional Medical Center in Grapevine, Texas. Finally, areas of future research are discussed.     

Enriques Surfaces, Analytic Discriminants, and Borcherds's Φ Function

In [Bor 96], Borcherds constructed a non-vanishing weight 4 modular form Φ on the moduli space of marked, polarized Enriques surface of degree 2 by considering the twisted denominator function of the fake monster Lie algebra associated to an automorphism of order 2 of the Leech lattice fixing an 8-dimensional subspace. In [JT 94] and [JT 96], we defined and studied a meromorphic (multi-valued) modular form of weight 2, which we call the K3 analytic discriminant, on the moduli space of marked, polarized, K3 surfaces of degree 2d; in certain cases, including when , where p _k are distinct primes, our meromorphic form is actually a holomorphic form. Our construction involves a determinant of the Laplacian on a polarized K3 surface with respect to the Calabi-Yau metric together with the L ² norm of the image of the period map with respect to a properly scaled holomorphic two form. Since the universal cover of any Enriques surface is a K3 surface, we can restrict the K3 analytic discriminant to the moduli space of degree 2 Enriques surfaces. The main result of this paper is the observation that the square of our degree 2 analytic discriminant, viewed as a function on the moduli space of degree 2 Enriques surfaces, is equal to the Borcherd's Φ function, up to a universal multiplicative constant. This result generalizes known results in the study of generalized Kac-Moody algebras and elliptic curves, and suggests further connections with higher dimensional Calabi-Yau varieties, specifically those which can be realized as complete intersections in some, possibly weighted, projective space. Received: 24 July 1995 / Accepted: 21 March 1997     

Rook Theory—IV. Orthogonal Sequences of Rook Polynomials

We explain combinatorially the occurrence of certain classical sequences of orthogonal polynomials as sequences of rook polynomials, and we give some new examples related to general stairstep boards.     

The Synthesis and Chemistry of 9-Chlorobicyclo[6.1.0]Non-1(9)-Ene

9-Chlorobicyclo[6.1.0]non-l(9)-ene ( 4 ), a 2-chlorinated 1,3-fused cyclopropene, is synthesized and isolated from the dehalogenation of the l-bromo-9,9-dichlorobicyclo[6.1.0]nonane, itself derived from cyclooctene. Compound 4 undergoes ring opening reaction to generate cyclooctenyl chlorocarbene ( 9 ) which reacts with water via conjugate addition and ipso-addition to give ( E )-2-(chloromethylene)cyclooctanol ( 7 ) and cyclooctene-l-carboxaldehyde ( 8 ), respectively. The conjugate addition of 9 with water is more favorable than the ipso-addition by 3:1. Compound 4 , which is stable at ?25 °C for weeks without any decomposition, reacts with oxygen to produce 2-chlorocyclonon-2-enone ( 12 ) via the ring-opening reaction adduct, vinyl alkylcarbene 10 .     

Sorbed iron species on polyurethane foams

Four polyurethane foams were loaded from solutions of ferrous and ferric sulphates and potassium hexacyanoferrate(II) and (III). Evidence was found for more than one type of active site. The rank order of spectral areas for the loaded foams is different for the anion and cation species and both are different to that for the dicyanoaurate anion.