Oscillation of nonlinear vector differential equations

Summary Oscillation criteria are obtained for vector partial differential equations of the type Δv+b(x, v)v=0, x∈G, v∈E^m, where G is an exterior domain in E_n, and b is a continuous nonnegative valued function in G × E^m. A solution v: G→E^m is called h-oscillatory in G whenever the scalar product [v(x), h] (|h|=1) has zeros x in G with |x| arbitrarily large. It is shown that the spherical mean of [v(x), h] over a hypersphere of radius r in Eⁿ satisfies a nonlinear ordinary differential inequality. As a consequence, the main theorems give sufficient conditions on b(x, t), depending upon the dimension n, for all solutions v to be h-oscillatory in G. Entrata in Redazione il 26 giugno 1975.     

A Stochastic Model for Bidding

Competitive bidding situations involve considering a multiplicity of factors. Organizations must be able to weigh the relative probability of potential projects based on resource usage, project duration and competitor actions to decide which of many possible bids to submit. A bidding strategy designed to maximize expected long run return is crucial, since an organization can usually submit only one bid per project.This paper presents a family of stochastic dynamic programming models considering different bidding situations. Several projects, each with several potential bids, are available for each situation. The objective is to determine what bidding strategy will maximize expected returns. Models are developed for two principle bidding situations: sequential, where projects are bid individually; and simultaneous, where several projects are bid at one time. Next, the effects of over- or under-commitment of resources are incorporated into the models. Finally, changes in project timing and the resultant effects on bidding strategy are included.A numerical example traces the changes in bidding strategy which occur as the models are expanded. The general formulation of bidding problems is also discussed, including changing the bid success probabilities due to competitor actions, the possibility of crashing projects and alternate methods of performing projects.     

A unified Monte Carlo treatment of the transport of electromagnetic energy, electrons, and phonons in absorbing and scattering media

The scalar Boltzmann transport equation (BTE) is often applicable to radiative energy transfer, electron-beam propagation, as well as thermal conduction by electrons and phonons provided that the characteristic length of the system is much larger than the wavelength of energy carriers and that certain interference phenomena and the polarization nature of carriers are ignored. It is generally difficult to solve the BTE analytically unless a series of assumptions are introduced for the particle distribution function and scattering terms. Yet, the BTE can be solved using statistical approaches such as Monte Carlo (MC) methods without simplifying the underlying physics significantly. Derivations of the MC methods are relatively straightforward and their implementation can be achieved with little effort; they are also quite powerful in accounting for complicated physical situations and geometries. MC simulations in radiative transfer, electron-beam propagation, and thermal conduction by electrons and phonons have similar simulation procedures; however, there are important differences in implementing the algorithms and scattering properties between these simulations. The objective of this review article is to present these simulation procedures in detail and to show that it is possible to adapt an existing MC computer code, for instance, in radiative transfer, to account for physics in electron-beam transport or phonon (or electronic thermal) conduction by sorting out the differences and implementing the correct corresponding steps. Several simulation results are presented and some of the difficulties associated with different applications are explained.     

Functional derivative for the distribution function of a Λ-nucleon pair in nuclear matter

An exact expression for the functional derivative of the distribution function of a -nucleon pair in nuclear matter is derived. An approximate expression is also derived by means of the Kirkwood superposition approximation. The latter expression is subsequently used to obtain the Euler equation for the correlation functionf(r1) of a -nucleon pair in nuclear matter.     

Determination of Fenofibric Acid in Human Plasma by LC–MS/MS and LC–UV

A sensitive, high-throughput and economic liquid chromatographic method for determination of fenofibric acid in human plasma was developed and validated by ultraviolet detection and tandem mass spectrometry, then applied in pharmacokinetic study to investigate Lipanthyl™ 200 mg MC bioavailability under food and fasting conditions. Fenofibric acid with 2-chloro fenofibric acid-d6 (internal standard) was extracted from 100 µL of human plasma by acetonitrile in a single extraction step. 25 and 2 µL from supernatant were injected onto ACE column, 50 mm, 5 micron with 4.6 mm inner diameter for LC–UV and 2.1 mm for LC–MS/MS, and both systems were eluted isocratically by water:methanol:formic acid (35:65:0.1, v/v/v), with a constant flow rate of 1 mL min⁻¹. The established calibration curve was linear between 0.05–20 µg mL⁻¹, and the within- and between-day precisions were all below 13 % in both LC–MS/MS and LC–UV systems during validation, and accuracies ranged between 91 and 112 %. Twenty-eight healthy adult subjects participated in this clinical study, and the pharmacokinetic parameters including coefficient of variation were calculated and discussed. A dramatic decrease in C _max and AUC0-72 (3.63- and 1.85-fold, respectively) were observed for Lipanthyl™ MC under fasting conditions with more variable inter subject measurements comparing to the fed state.

     

Curcumin Loaded Dendrimers Specifically Reduce Viability of Glioblastoma Cell Lines

Glioblastoma (GB) is a deadly and aggressive cancer of the CNS. Even with extensive resection and chemoradiotherapy, patient survival is still only 15 months. To maintain growth and proliferation, cancer cells require a high oxidative state. Curcumin, a well-known anti-inflammatory antioxidant, is a potential candidate for treatment of GB. To facilitate efficient delivery of therapeutic doses of curcumin into cells, we encapsulated the drug in surface-modified polyamidoamine (PAMAM) dendrimers. We studied the in vitro effectiveness of a traditional PAMAM dendrimer (100% amine surface, G4 NH₂), surface-modified dendrimer (10% amine and 90% hydroxyl-G4 90/10-Cys), and curcumin (Cur)-encapsulated dendrimer (G4 90/10-Cys-Cur) on three species of glioblastoma cell lines: mouse-GL261, rat-F98, and human-U87. Using an MTT assay for cell viability, we found that G4 90/10-Cys-Cur reduced viability of all three glioblastoma cell lines compared to non-cancerous control cells. Under similar conditions, unencapsulated curcumin was not effective, while the non-modified dendrimer (G4 NH₂) caused significant death of both cancerous and normal cells. By harnessing and optimizing the components of PAMAM dendrimers, we are providing a promising new route for delivering cancer therapeutics. Our results with curcumin suggest that antioxidants are good candidates for treating glioblastoma.     

Photophysics of carbazole-containing systems. 1. Dilute solution behavior of poly(N-vinyl carbazole) and N-vinyl carbazole/methyl acrylate copolymers

Steady-state and time-resolved fluorescence techniques have been used to study the photophysical behaviors of poly(N-vinyl carbazole), PNVCz and a series of N-vinyl carbazole-methyl acrylate (NVCz-co-MA) copolymers in dilute solution as a function of both NVCz composition and temperature. A kinetic scheme, intended to describe intramolecular excimer formation across the entire NVCz composition range, is proposed. In low aromatic content copolymers, two monomer species (unquenched and quenched monomer) and two excimer species (the sandwich-like excimer and a higher energy excimer) exist. The contribution from monomer emission to the overall fluorescence decreases with increasing NVCz content through increased excimer formation: this is likely to be consequent upon (1) an increase in the number of excimer forming sites, and (2) increasing efficiency of energy transfer from the excited monomers to the excimer forming sites. In the homopolymer, PNVCz, the only emission that can be observed on a nanosecond timescale is excimeric. This fluorescence appears to originate from three excimer species (the sandwich-like excimer, and two higher energy forms). For the homopolymer, the current observations are consistent with the model proposed by Vandendriessche and De Schryver [Polym. Photochem. 7 , 153 (1986)]. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 963–978, 1997     

The influence of partial emulsification on coalescence suppression and interfacial tension reduction in PP/PET blends

This study examines how the relative role of coalescence suppression and interfacial tension reduction influence the particle size at various levels of in situ compatibilization. The polymers studied are polyethylene terephthalate (PET) as matrix and a polypropylene (PP) as dispersed phase compatibilized by a triblock copolymer of poly(styrene–hydrogenated butadiene–styrene) (SEBS) grafted with maleic anhydride. The interfacial tension was studied by the breaking‐thread method, and it was used along with the morphology to characterize the emulsification efficacy of the copolymers. By modifying the concentration of MA grafted on the SEBS, different levels of emulsification of the blends were obtained. A comparison of 1/99 and 10/90 PP/PET blends compatibilized by SEBS‐g‐MA allows one to distinguish the relative role of interfacial tension and coalescence suppression in diminishing particle size. It is shown that varying degrees of residual coalescence remain, depending on the level of %MA in the copolymer. A detailed study of the 2%MA system below interfacial saturation was carried out to shed further light on the dependence of coalescence suppression on emulsification level and interfacial coverage. After separating out the contribution of interfacial tension on particle size reduction, it is shown that coalescence suppression for this system increases gradually with areal density of modifier at the interface right up to the region of interfacial saturation. Finally, the interfacial and morphological data were used to test the ability of the Lee and Park model to describe coalescence in polymer blends. Reasonable agreement was found between the parameter c₁, describing the coalescence in that model, and the trends related to residual coalescence from this study. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 939–951, 1999