Management decision-making in the single period optimum pricing problem

Management of the firm implementing revenue management has many decisions to make regarding the details of the implementation. In this article we examine seven different decisions surrounding the implementation of aggressive ‘revenue management’ pricing in the context of a firm facing a single period stochastic pricing and stocking problem. We demonstrate through use of an example, that some of the decisions have a large financial impact, while other options that require considerable computational work to implement may provide little financial impact.     

Amphiphilic maleic acid-containing alternating copolymers—2. Dilute solution characterization by light scattering,intrinsic viscosity,and PGSE NMR spectroscopy

The dilute solution behavior of several alternating copolymers of maleic acid has been characterized by static and dynamic light scattering, intrinsic viscosity, and pulsed-gradient spin-echo NMR spectroscopy. The copolymer of maleic acid–sodium salt and isobutylene (IBMA-Na, M_w ∼350 kg/mol) dissolves readily in concentrated aqueous salt solutions. Changes in chain dimensions with ionic strength and pH are similar to those of the lesser salt solution-soluble poly(acrylic acid-sodium salt). The hydrophobically modified (with n-butyl, n-hexyl, n-octyl, and phenethyl amines) copolymers of maleic acid–sodium salts and isobutylene (IBMA-NHR-Na) show no sign of large intermolecular aggregation in 0.1 N sodium acetate (NaAc). However, the sizes of the copolymers are relatively small compared to that of the ionized parent copolymer (IBMA-Na, M_w ∼350 kg/mol), suggesting intramolecular aggregation of the alkyl side-chain groups along the polymer backbone. The copolymer modified with the longer chain n-decyl, on the other hand, forms stable large intermolecular aggregates containing 33 chains/aggregate. The copolymers of maleic acid–sodium salt and styrene (SMA-Na) appear to have no signs of aggregation, despite being a hydrophobic polyelectrolyte. The copolymer of maleic acid–sodium salt and di-isobutylene (DIBMA-Na) has a similar salting-out concentration as SMA-Na. The radius of gyration measurements by static light scattering suggest that at least some fraction of the DIBMA-Na chains form large intermolecular aggregates. The copolymers of maleic acid–sodium salt with n-alkenes (n-C_mMA-Na) in 0.1 N NaAc form small intermolecular aggregates (three to five chains/aggregate). In contrast to these static light scattering results, PGSE NMR diffusion measurements for the above aggregated systems indicate only one diffusion coefficient consistent with the motion of single isolated chains. A plausible explanation for this discrepancy is that the population of the aggregates is too small to be sufficiently detected in the PGSE NMR experiment. Furthermore, it is likely that the aggregate has a larger relaxation rate than the nonaggregate, and therefore has a comparatively reduced signal in the PGSE NMR experiment. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3584–3597, 2004     

Photochemistry in ordered physisorbed monolayers of dinitrogen tetroxide

The effects of physisorption and two-dimensional ordering on the photochemistry of N₂O₄ were investigated. Ordered monolayers were prepared by adsorption of NO₂ at 100 K on a water-ice surface. Irradiation with a continuous light source in the wavelength region 300–400 nm or with pulsed laser radiation at 355 nm resulted in exclusive desorption of NO₂. This desorption was induced by electronic absorption directly in the adsorbate via a transition corresponding to the ( )¹B_2u←( )¹A_g transition in N₂O₄, as in the gas phase. However, the subsequent dynamics in the excited state were markedly different from the gas-phase counterpart. Time-of-flight mass spectrometry of NO₂ photodesorbed at 355 nm revealed a most probable fragment translational energy of ca. 17 meV; and the angular distribution of the nascent NO₂ was peaked sharply in a direction around 10° from the normal. It is apparent that, despite the weak interaction with the substrate, significant energy transfer occurs in the ordered physisorbed monolayer to yield nascent NO₂ with very low translational energy and a constrained angle of escape which is consistent with a high degree of adsorbate order and alignment.     

Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.     

Complexity in Complex Analysis

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces.     

Nanocrystalline titanium carbide thin films deposited by reactive magnetron sputtering

We investigated the structure and composition of titanium carbide thin films deposited by the reactive magnetron sputter ion plating process as a function of deposition parameters. The films were sputtered onto unheated glass substrates by means of an unbalanced planar d.c. magnetron equipped with a titanium target using a mixture of argon and methane. The deposition parameters ranged from 0.05 Pa to 2 Pa for total working gas pressurep _T, from 10% to 60% (volume) for relative methane concentration in the working gas mixture, from 45 mm to 85 mm for the substrate-to-target distanced _s-t and from −50V to −800V for the substrate biasU _S. It was found that the crystallinity of the thin films strongly decreases with increasingp _T,d _s-t andU _S. The experiments described show the conditions necessary to obtain sputter-deposited nanocrystalline titanium carbide films. This work has been partially supported by the Grant Agency of the Czech Republic under Grant No. 106/96/K245 and by the Ministry of Education of the Czech Republic under Grant No. VS96 059.     

Torands: Planar polyazamacrocyclic ligands for metal ions

A series of macrocyclic ligands related to hexaaza[18]-annulene form stable complexes with alkali metal and alkaline earth ions. A planar, substituent-solubilized torand, consisting of multiply fused pyridine rings, has been synthesized and has been found to sequester calcium from a dilute source.     

Existence and uniqueness for an equation of mixed type in a rectangle

A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure.