Sojourn Times in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">PH</Emphasis>/1 Processor Sharing Queue

We give in this paper an algorithm to compute the sojourn time distribution in the processor sharing, single server queue with Poisson arrivals and phase type distributed service times. In a first step, we establish the differential system governing the conditional sojourn times probability distributions in this queue, given the number of customers in the different phases of the PH distribution at the arrival instant of a customer. This differential system is then solved by using a uniformization procedure and an exponential of matrix. The proposed algorithm precisely consists of computing this exponential with a controlled accuracy. This algorithm is then used in practical cases to investigate the impact of the variability of service times on sojourn times and the validity of the so-called reduced service rate (RSR) approximation, when service times in the different phases are highly dissymmetrical. For two-stage PH distributions, we give conjectures on the limiting behavior in terms of an M/M/1 PS queue and provide numerical illustrative examples.This revised version was published online in June 2005 with corrected coverdate     

Long-range DNA charge transport

The stack of base pairs within double helical DNA has been shown to mediate charge transport reactions. Charge transport through DNA can result in chemistry at a distance, yielding oxidative DNA damage at a site remote from the bound oxidant. Since DNA charge transport chemistry depends on coupling within the stacked base pair array, this chemistry is remarkably sensitive to sequence-dependent DNA structure and dynamics. Here, we discuss different features of DNA charge transport chemistry, including applications as well as possible biological consequences and opportunities.     

Lower semicontinuity for approximate social Nash equilibria

We introduce a suitable concept of approximate social Nash equilibrium and we determine sufficient conditions of minimal character which guarantee, for a parametric social Nash equilibrium problem, the lower semicontinuity of the set-valued function defined by these approximate solutions. Received: December 2001     

FLAVIN SENSITIZED PHOTOOXIDATION OF (POLY)AMINO ACIDS: FATE OF THE PHOTOSUBSTRATE

Abstract— With respect to literature data, which seemed to be contradictory, we examined the fate of ethylenediaminetetraacetate (EDTA) and nitrilotriacetate (NTA) in flavin-sensitized photooxidation reactions by quantitation of all possible products, i.e. CO₂ by acidimetric titration, CH₂O by colometry and glyoxylate enzymatically; N-methyl groups were quantified by ₁H-NMR. Nitrilotriacetate yields 100% oxidative photodecarboxylation with CH₂O formation, while EDTA behaves quite differently, yielding quantitative amounts of CO₂ and glyoxylate, but no CH₂O. The electron balance in this reaction is found to be maintained by co-formation of one equivalent >N-CH₃. From these data it is concluded that the photooxidation of the structural element >NCH₂C0₂ containing a tertiary nitrogen atom, occurs by electron transfer, followed by decarboxylation. The neutral radical that is formed is reductant and will give off an electron equivalent to yield the easily hydrolysed structural element >N⁺= CH₂. With EDTA, containing the fragment –O₂CCH₂ >NCH₂CH₂N< CH₂CO₂–, the electron transfer towards flavin is strongly favoured by stabilisation of a cisoid mesomeric radical cation (₀₂cch₂ >₊ NCH₂CH₂N_CH2CO2 o₂cch₂ >NCH₂CH₂N_+CH2CO2), which, after loss of CO₂ undergoes internal 1,6-hydrogen shift to yield the more stable radical: _CH2>CH₂CH₂N CH₂CO₂CH₂lt NCH₂CH₂N_HCO2. The latter radical will easily be oxidized to the iminium ion >N_*= CH-C0_2-. which in turn hydrolyses to glyoxylate. Chelation of EDTA by metal cations prevents the 1,6-hydrogen shift, and leads to the product pattern obtained in the NTA photoreaction.     

Mössbauer analysis of Brazilian Oxisols

Three sets of Brazilian Oxisols have been analysed by Mössbauer spectroscopy at 290, 80 and 4.2 K. In most cases two resolved magnetic hyperfine patterns associated with aluminous goethite and hematite are resolved; their ratio is related to soil colour. Samples from a 3 m soil profile show that both oxides become decreasingly aluminium substituted and/or better crystallized with depth. Goethite from surface or deep layers is readily differentiated by its hyperfine parameters. As there is no significant alternate source of iron, the results suggest that both hematite and goethite undergo continuous neoformation throughout the profile in response to the changing pedogenic environment.     

The Manne-Chao-Wilson algorithm for computing competitive equilibria: A modified version and its implementation

We present a modification of the Manne-Chao-Wilson algorithm for computing competitive equilibria and discuss some of its convergence properties. Numerical experiments involving models with up to 100 price responsive agents are provided.This research has been partially supported by the Belgian Department for Science Policy. We are indebted to Alan Manne for helpful comments; all errors and shortcomings are ours.     

Preclinical Assessment of Hypocrellin B and Hypocrellin B Derivatives as Sensitizers for Photodynamic Therapy of Cancer: Progress Update

Abstract— Hypocrellins are perylenequinone pigments with substantial absorption in the red spectral region and high singlet oxygen yield. They are available in pure monomelic form and may be derivatized to optimize properties of red light absorption, tissue biodistribution and toxicity. In vitro screening of synthetic derivatives of the naturally occurring compound, hypocrellin B (HB), for optimal properties of cyto-(dark) toxicity and phototoxicity resulted in selection of three compounds for preclinical evaluation: HBEA-R1 (ethanolaminated HB), HBBA-R2 (butylaminated HB) and HBDP-R1 [2-( N,N -dimethylami-no)-propylamine-HB]. Extinction coefficients at 630 nm (φ₆₃₀) are 6230, 6190 and 4800, respectively; and ¹O₂ quantum yields, φ, 0.60, 0.32 and 0.42. Intracellular uptake is essentially complete within 2 h (HBEA-R1, HBBA-R2) and 20 h (HBDP-R1). Greatest uptake is associated with lysosomes and Golgi. The HBEA-R1 and HBBA-R2 elicit phototoxicity in vitro primarily via the type II mechanism, with some type I activity under stringently hypoxic conditions. Transcutaneous phototherapy with HBEA-R1 permanently ablates EMToVEd tumors growing in the flanks of Balb/c mice, with minimal cutaneous effects. The HBBA-R2 does not elicit mutagenic activity in strains TA98 and TA100 of Salmonella typhi-murium. Further development of selected hypocrellin derivatives as photosensitizers for photodynamic therapy is warranted.