Implications of order reduction for implicit Runge-Kutta methods

Stability analysis of Runge-Kutta (RK) formulas was originally limited to linear ordinary differential equations (ODEs). More recently such analysis has been extended to include the behaviour of solutions to nonlinear problems. This extension led to additional stability requirements for RK methods. Although the class of problems has been widened, the analysis is still restricted to a fixed stepsize. In the case of differential algebraic equations (DAEs), additional order conditions must be satisfied [6] to achieve full classical ODE order and avoid possible order reduction. In this case too, a fixed stepsize analysis is employed. Such analysis may be of only limited use in quantifying the effectiveness of adaptive methods on stiff problems.In this paper we examine the phenomenon of order reduction and its implications on variable-step algorithms. We introduce a global measure of order referred to here as the observed order which is based on the average stepsize over the region of integration. This measure may be better suited to the study of stiff systems, where the stepsize selection algorithm will vary the stepsize considerably over the interval of integration. Observed order gives a better indication of the relationship between accuracy and cost. Using this measure, the observed order reduction will be seen to be less severe than that predicated by fixed stepsize order analysis.Supported by the Information Technology Research Centre of Ontario, and the Natural Science and Engineering Research Council of Canada.     

FUROCOUMARIN-PHOTOSENSITIZEDHYDROXYLATION OF GUANOSINE IN RNA AND DNA

Abstract— Guanosine hydroxylation was used as a marker for assessing photooxidation of DNA and RNA sensitized by monofunctional and bifunctional furocoumarins. DNA or RNA, treated with sensitizer and UVA light, was enzymatically hydrolyzed, dephosphorylated and then analyzed by reversed-phase HPLC with electrochemical detection. Hydroxylated guanosine, i.e. 8-hydroxy-2'-deoxyguanosine (8-OHdG) or 8-hydroxyguanosine (8-OHG), was quantitated. 3-Carbethoxypsoralen (3-CP) was found to be an efficient photosensitizer for oxidation of guanosine in DNA, resulting in conversion of up to 0.4% of guanosine residues to 8-OHdG. In contrast, dramatically lower levels of guanosine hydroxylation were observed in 3-CP-photosensitized RNA. Psoralen was found to be a more efficient photosensitizer than angelicin in both DNA and RNA. Additional studies of oxidation of 3-CP-photosensitized DNA indicated that double-stranded DNA is 10 times more susceptible to photooxidation than single-stranded DNA, implicating 3-CP binding to DNA as an important mechanistic step in photooxidation of guanosine. The effects of D₂O and degassing with argon on photooxidation of guanosine in DNA sensitized by 3-CP were inconsistent with a mechanism involving ¹O₂. In addition, chelation of adventitious metal ions present in preparations of DNA photosensitized by 3-CP had no effect on hydroxylation of guanosine.     

Indirect neutron absorptiometry

A preliminary account is given of the use of the neutron absorption of suitable elements (such as gadolinium) for the determination of non-absorbing elements (such as fluorine) by measuring the absorption of a dissolved precipitate (in the case quoted, gadolinium fluoride). This indirect determination by neutron absorption gives reproducible results rapidly and non-destructibly. The applications of the method are being studied.     

EDTA and mixed-ligand complexes of tetravalent and trivalent plutonium

EDTA forms stable complexes with plutonium that are integral to nuclear material processing, radionuclide decontamination, and the potentially enhanced transport of environmental contamination. To characterize the aqueous Pu(4+/3+)EDTA species formed under the wide range of conditions of these processes, potentiometry, spectrophotometry, and cyclic voltammetry were used to measure solution equilibria. The results reveal new EDTA and mixed-ligand complexes and provide more accurate stability constants for previously identified species. In acidic solution (pH < 4) and at 1:1 ligand to metal ratio, PuY (where Y4- is the tetra-anion of EDTA) is the predominant species, with an overall formation constant of log beta110 = 26.44. At higher pH, the hydrolysis species, PuY(OH)- and PuY(OH)(2)2-, form with the corresponding overall stability constants log beta(11 - 1) = 21.95 and log beta(11 - 2) = 15.29. The redox potential of the complex PuY at pH = 2.3 was determined to be E(1/2) = 342 mV. The correlation between redox potential, pH, and the protonation state of PuY- was derived to estimate the redox potential of the Pu(4+/3+)Y complex as a function of pH. Under conditions of neutral pH and excess EDTA relative to Pu4+, PuY(2)4- forms with an overall formation constant of log beta120 = 35.39. In the presence of ancillary ligands, mixed-ligand complexes form, as exemplified by the citrate and carbonate complexes PuY(citrate)3- (log beta1101 = 33.45) and PuY(carbonate)2- (log beta1101 = 35.51). Cyclic voltammetry shows irreversible electrochemical behavior for these coordinatively saturated Pu4+ complexes: The reduction wave is shifted approximately -400 mV from the reduction wave of the complex PuY, while the oxidation wave is invariant.     

Synthesis and thermolysis of alkyl- and phenylamido diphenylgallium, [Ph(2)GaN(H)R](2). isolation and structural characterization of (PhGaNMe)(7) and (PhGaNPh)(4)

Alkyl- and phenylamido diphenylgallium compounds, [Ph(2)GaN(H)R](2) (R = Me, 1; Et, 2; (n)Pr, 3; (i)Bu, 4; Ph, 5), were prepared from the reactions of Ph(3)Ga with the corresponding primary amines and aniline at elevated temperatures and were characterized by elemental analysis, mass spectroscopy, and (1)H NMR and IR spectroscopy. These dimeric compounds contained bridging amido groups and exhibited both trans and cis isomers in solution. Thermolysis of compounds 1 and 5 was carried out either without solvent or in dodecane solutions, and two clusters, (PhGaNMe)(7) 6 and (PhGaNPh)(4) 7, were isolated in 24% and 55% yields and characterized. The structure of 6 consisted of a heptameric Ga(7)N(7) core constructed with Ga(2)N(2) and Ga(3)N(3) rings, and the structure of 7 possessed a Ga(4)N(4) cubane core.     

EFFICIENCY OF REPAIR OF PYRIMIDINE DIMERS AND PSORALEN MONOADDUCTS IN NORMAL AND XERODERMA PIGMENTOSUM HUMAN CELLS

Abstract —Repair of DNA damage produced by ultraviolet light or 5-methylisopsoralen in normal and xeroderma pigmentosum human cells involves many similar steps. Aphidicolin and cytosine arabinoside block repair of both kinds of damage with similar efficiency, indicating that DNA polymerase a has a major role in repair for these lesions. In xeroderma pigmentosum cells of various complementation groups, the relative efficiency of excision repair for both ultraviolet- and 5-methylisopsoralen-induced damage was group A < C < D, indicating a close resemblance between both kinds of lesions in relation to the repair deficiencies in these groups. At high doses, the maximum rate of repair of damage by ultraviolet light was about twice that for methylisopsoralen damage, possibly because ultraviolet-induced damage forms a substrate that is more readily recognized and excised than that of the psoralen adducts. Differences in the structural distortions to DNA caused by these kinds of damage could be detected using single strand specific nucleases which excised dimers but not 5-MIP adducts from double strand DNA.     

Isocyanate formation in the catalytic reaction of CO + NO on Pd(111): an in situ infrared spectroscopic study at elevated pressures

The catalytic CO + NO reaction to form CO2, N2, and N2O has been studied on a Pd(111) surface at pressures up to 240 mbar using in situ polarization modulation infrared reflection absorption spectroscopy (PM-IRAS). At 240 mbar, for a pressure ratio of PCO:PNO = 3:2 and under reaction conditions, besides adsorbed CO, the formation of isocyanate (-NCO) was observed. Once produced at 500-625 K, the isocyanate species was stable within the entire temperature range studied (300-625 K). On the other hand, its formation required a total CO + NO pressure of at least 0.6 mbar, illustrating the importance of in situ infrared experiments under high-pressure conditions. The significance of the isocyanate formation for the CO + NO reaction on Pd(111) is discussed.     

Uniform exhaustivity and Banach lattices

Summary The measure theoretic notion of strong boundedness is extended to the setting of a real -complete Banach lattice X; the lattice theoretic concept which corresponds to strong boundedness is termed exhaustivity. Uniformly exhaustive subsets of X are studied, and various characterizations are presented. One of these characterizations involves the order continuity of the norm on X. The exhaustive elements of certain classical lattices are cataloged. Applications are given to spaces of measures.     

Determination of chloro-s-triazines including didealkylatrazine using solid-phase extraction coupled with gas chromatography-mass spectrometry

Chloro-s-triazines are a class of compounds comprising atrazine, simazine, propazine, cyanazine and their chlorinated metabolites. The US Environmental Protection Agency (EPA) has determined that selected chloro-s-triazines--atrazine, simazine, propazine, deethylatrazine, deisopropylatrazine, and didealkylatrazine--have a common mode of toxicity related to endocrine disruption. In this paper, a dual-resin solid-phase extraction (SPE) gas chromatography-mass spectrometry (GC-MS) method is reported that provides for each of these chloro-s-triazines including the polar metabolite, didealkylatrazine. The method utilizes deuterated internal standards for quantitation and terbuthylazine as a recovery standard. The limit-of-detection was 0.01 microg/L for simazine, deethylatrazine, deisopropylatrazine and didealkylatrazine, and 0.02 microg/L for atrazine and propazine in surface water. Mean recoveries for 0.5 and 3.0 microg/L spikes for atrazine, simazine, propazine, deethylatrazine, deisopropylatrazine and didealkylatrazine were 94, 104, 103, 110, 108 and 102%, respectively, in surface water. The method was also validated by matrix spikes into fourteen different raw and treated natural surface waters. This method is useful for monitoring "total chloro-s-triazines" in both raw and treated drinking waters.