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.     

XPS and resistive studies on thin films of a copper(II)‐based coordination polymer deposited on functionalized interdigital electrodes

A symmetrical 2‐thiopyrimidine based molecule with an expanded π‐electron system is synthesized and used to form a self‐assembled monolayer (SAM) on gold surfaces. Utilizing chemical vapor deposition a monolayer of (3‐mercaptopropyl)triethoxysilane is formed on silicon dioxide substrates. Both of these SAM coated substrates are characterized by X‐ray photoelectron spectroscopy and the growth of a coordination polymer built up from 5,5′‐(ethyne‐1,2‐diyl)bis(2‐hydroxyacetophenone) and copper(II) on dual SAM coated transducers is studied. After the deposition procedure on interdigital electrodes the electrical properties of the polymer are investigated performing resistive measurements. A significant change of the resistance, which depends on the surrounding atmosphere, proves the sensing behavior of the synthesized coordination polymer. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 335–344     

Tris(triphenylphosphine)rhodium cyano and triphenylcyanoborate complexes: Structures and a DFT study

The structures of [Rh(CN)(PPh₃)₃](EtOH) (1), [Rh(NCBPh₃)(PPh₃)₃] (2), and [Rh(CNBPh₃)(PPh₃)₃] (3) are reported together with a density functional theory (DFT) study of the model compounds [Rh(NCBH₃)(PH₃)₃] and [Rh(CNBH₃)(PH₃)₃]. Compound 1 crystallizes in space group Pc with a = 10.4798(15) Å, b = 12.5410(18) Å, c = 19.974(3) Å and = 112.215(6)°; compound 2 crystallizes in space group with a = 12.929(2) Å, b = 14.362(2) Å, c = 17.575(3) Å and = 92.544(3)°, = 90.214(3)°, = 113.831(3)°; compound 3 crystallizes in space group with a = 12.915(2), b = 14.296(2), c = 17.664(3) Å and = 92.469(3)°, = 90.088(3)°, = 113.768(3)°. All three complexes show slight tetrahedral distortion from ideal square planar geometry (largest for 1). Differences in the reactivity and stability of 2 and 3 are interpreted according to the results of a density functional theory study.     

A new synthesis of lysophosphatidylcholines and related derivatives. Use of p-toluenesulfonate for hydroxyl group protection

A new stereoselective synthesis of lysophosphatidylcholines is reported. The synthesis is based upon (1) the use of 3-p-toluenesulfonyl-sn-glycerol to provide the stereocenter for construction of the optically active lysophospholipid molecule, (2) tetrahydropyranylation of the secondary alcohol function to achieve orthogonal protection of the sn-2- and sn-3-glycerol positions, and (3) elaboration of the phosphodiester headgroup using a 2-chloro-1,3,2-dioxaphospholane/trimethylamine sequence. In the course of developing the synthesis it has been discovered that methoxyacetate displacement of the sn-3-p-toluenesulfonate yields a reactive methoxyacetyl ester, which in turn can be selectively cleaved with methanol/tert-butylamine, while the ester group at the sn-1-position remains unaffected. The sequence has been shown to be suitable for preparation of spectroscopically labeled lysophosphatidylcholines. One of these compounds was readily converted to a double-labeled mixed-chain phosphatidylcholine applicable for real-time fluorescence resonance energy transfer (FRET) assay of lipolytic enzymes. In addition, the work led to new synthetic strategies based on chemoselective manipulation of the tosyl group in the presence of other base-labile groups such as FMOC derivatives that are often used for the protection of amino and hydroxyl groups in syntheses.     

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     

Degradation and stabilization of polycyanoacrylates

Polycyanoacrylates were found to be inherently unstable. Even in the absence of a deliberately added strong base, their molecular weights decreased drastically on standing in solution in accord with observations by Ryan and McCann (Makromol Chem Rapid Commun 1996, 17, 217). The initial high molecular weight polymer disappeared over the course of a few hours in solution and was replaced by a much lower molecular weight material. For polymers made by anionic polymerization, the entire sample degraded, but for polymers made by free-radical polymerization, only a portion of the sample was affected. This behavior was consistent with the mechanism proposed by Ryan and McCann, in which the polymer chains are in dynamic equilibrium with their monomers and the polymer degrades from its chain terminus. Surprisingly, the degradation in molecular weight even occurred slowly in the solid state. The degradation was inhibited by acids and could be prevented by free-radical copolymerization with small amounts of more stable monomers. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4570–4581, 1999