A higher order finite element method with modified graded mesh for singularly perturbed two-parameter problems

This paper presents a modified graded mesh for singularly perturbed two-parameter problems. The mesh is generated recursively using Newton's algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on higher order polynomials of degree p≥1. We prove parameter uniform convergence of optimal order in ε-weighted energy norm. A test example is taken to compare the proposed graded mesh with others found in the literature.     

Chiral bis-Acetal Porphyrazines as Near-infrared Optical Agents for Detection and Treatment of Cancer

We report the preparation of chiral oxygen atom-appended porphyrazines (pzs) as biomedical optical agents that absorb and emit in the near-IR wavelength range. These pzs take the form M[pz(A_4-nB_n)], where “A” and “B” represent moieties appended to the pz’s pyrrole entities, A = (2R,3R) 2,3-dimethyl-2,3-dimethoxy-1,4-diox-2-ene, B = β,β′-di-isopropoxybenzo, M is the incorporated metal ion (M = H₂, Zn), and n = 0, 1, 2 (-cis/-trans) and 3 ( Scheme 1 ). When dissolved in polar media, H₂[pz(trans-A₂B₂)] 5a does not fluoresce and has a negligible quantum yield for singlet oxygen generation (Ф_Δ = 0.074 ± 0.001, methanol), as measured by the photo-oxidation of DMA. However, when sequestered in the nonpolar environment of a liposome, it displays strong NIR emission (λ _max = 705 nm, Ф _f = 0.087) and an extremely high singlet oxygen quantum yield (Ф_Δ→1). Of this series, H₂[pz(trans-A₂B₂)] 5a is attractive as a potential optical probe, showing strongly fluorescent uptake by cells in culture, while 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide measurements of cell viability show no evidence of dark toxicity. This agent does show significant photoinduced toxicity suggesting that pzs such as 5a have promise as “theranostic” optical agents that can be visualized with fluorescence imaging while acting as a sensitizer for photodynamic therapy.

Figure Scheme 1. Open in figure viewer PowerPoint Synthesis of Porphyrazines 3a – 7a , 3b – 7b .     

Loss formulas and their application to optimization for cellularnetworks

We develop a performance model of a cell in a wireless communication network where the effect of handoff arrival and the use of guard channels is included. Past recursive formulas for the loss probabilities of new calls and handoff calls are developed. Monotonicity properties of the loss probabilities are proven. Algorithms to determine the optimal number of guard channels and the optimal number of channels are given. Finally, a fixed-point iteration scheme is developed in order to determine the handoff arrival rate into a cell. The uniqueness of the fixed point is shown     

Magnetic properties of the mixed spinel NiAlxCrxFe2-2xO4

The crystal structure and magnetic properties of the Al and Cr cosubstituted disordered spinel series NiAl_xCr_xFe_2-2xO₄ are investigated by means of Xray diffraction, magnetization, a.c. susceptibility and Mössbauer effect measurements. The lattice constants are determined and the applicability of Vegard's law has been tested. The variation of the saturation magnetic moment per formula unit measured at 77 K and 300 K with Al–Cr content is satisfactorily explained on the basis of Neel's collinear spin ordering model for =0.1–0.5. The Mössbauer spectra at 300 K have been fitted with two sextets in the ferrimagnetic state corresponding to Fe³⁺ at tetrahedral (A) and octahedral (B) sites for 0.5. Mössbauer results confirm a collinear ferrimagnetic structure for =0.1–0.5. The Curie temperature obtained from a.c. susceptibility decreases nearly linear with increase of Al–Cr concentration from =0.1 to 0.5.     

Synthesis and characterization of 5-substituted 1,3-diazacyclohexane derivatives

Three synthetic routes to 5-substituted 1,3-diazacyclohexane derivatives 1 are reported. The first method involves treatment of 1, 3-diaminopropan-2-ol 2 with paraformaldehyde to yield 5-hydroxy-1, 3-diazacyclohexane 3. A second method is based on the condensation of 2-bromo-2-nitro-1,3-propanediol with tert-butylamine and formaldehyde to yield 1,3-di-tert-butyl-5-bromo-5-nitro-1, 3-diazacyclohexane 22. The third method relies on the cycloalkylation of methylenebisacetamide with 3-chloro-2-chloromethyl-2-propene to provide 5-exomethylene-1, 3-diacetyl-1,3-diazacyclohexane 28. Functional group manipulations of 3, 22, and 28 provide a number of novel 1,3-diazacyclohexanes functionalized at the 5-position.     

Local Structure Analysis of Strontium Sorption to Hydrous Manganese Oxide

To develop mechanistic models of contaminant distribution processes, we conducted an X-ray absorption fine structure analysis of strontium sorption to hydrous manganese oxide (HMO). Sr K-edge measurements were performed at 298, 220, and 77 K, and at sample loadings from 10(-4) to 10(-2) mol Sr/g HMO. Results from fitting the first shell in the sorbed samples indicate that strontium is surrounded by 10-12 oxygen atoms at an average distance of 2.58 ?. This coordination environment is consistent with the strontium atom remaining hydrated upon sorption to the oxide, where in water hydrated strontium has approximately 9 atoms of oxygen at 2.62 ?. Furthermore, the temperature dependence of the strontium-oxygen bond also suggests physical adsorption due to the large contribution of the dynamic component of the Debye Waller factor. Although second-shell data are consistent with either 3 manganese atoms at 4.12 ? or 6 strontium atoms at 3.88 ?, both the near-edge and fine structure data for the manganese K-edge indicate that the local coordination environment of the manganese ion remains intact as a function of time or strontium sorption. Furthermore, the local structure of amorphous manganese oxide is highly ordered. Copyright 2000 Academic Press.