On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

Synthesis, X-ray crystal structure and catalytic activity of the manganese(II) complex [Mn(bdoa)(H2O)3](bdoaH2 =benzene-1,2-dioxyacetic acid)

Benzene-1,2-dioxyacetic acid (bdoaH2) reacts with Mn(CH3CO2)2·4H2O in an ethanol-water mixture to give the manganese(II) complex [Mn(bdoa)(H2O)3]. The X-ray crystal structure of the complex shows the metal to be pseudo seven-coordinate. The quadridentate bdoa2− dicar☐ylate ligand forms an essentially planar girdle around the metal, being strongly bondedtransoid by a car☐ylate oxygen atom from each of the two car☐ylate moieties (mean MnO 2.199A˚) and also weakly chelated by the two internal ether oxygen atoms (mean MnO 2.413A˚). The coordination sphere about the manganese is completed by three water molecules (mean MnO 2.146A˚) lying in a meridional plane orthogonal to that of the bdoa2− ligand. Magnetic, conductivity and voltammetry data for the complex are given, and its use as a catalyst for the disproportionisation of H2O2 is described.

Boundary value problems for the N-wave interaction equations

We consider boundary value problems for the N-wave interaction equations in one and two space dimensions, posed for x [greater-or-equal, slanted] 0 and x,y [greater-or-equal, slanted] 0, respectively. Following the recent work of Fokas, we develop an inverse scattering formalism to solve these problems by considering the simultaneous spectral analysis of the two ordinary differential equations in the associated Lax pair. The solution of the boundary value problems is obtained through the solution of a local Riemann–Hilbert problem in the one-dimensional case, and a nonlocal Riemann–Hilbert problem in the two-dimensional case.

Hepatozoon griseisciuri in grey squirrels (Sciurus carolinensis): changes of blood leucocyte numbers resulting from infection

Numbers of leucocytes in squirrels with gametocytes of Hepatozoon in their blood (infected) were compared with animals without gametocytes (uninfected). Typical values for leucocytes/mm(3) blood in uninfected squirrels were: leucocytes 5-7 x 10(3), granulocytes 3-4 x 10(3), lymphocytes 2-0 x 10(3) and monocytes 0-3 x 10(3) cells. Infection caused an increase in monocytes, lymphocytes and granulocytes, and there was a significant positive association between parasitaemia level and numbers of both total leucocytes and monocytes. Infected animals had more uninfected monocytes/mm(3) blood than did uninfected animals. The proportions of monocytes were more variable over time in infected animals, but no shift between infected and uninfected status was detected. Transfer of serum from infected squirrels to mice resulted in elevated counts of total blood leucocytes, monocytes and granulocytes, but not of lymphocytes, as compared with controls. Serum from squirrels with high parasitaemias had a more marked effect than serum from squirrels with low parasitaemias. Results indicate an infection - related monocytosis, possibly controlled by cytokines, that increases the number of cells available for invasion by gametocytes, thus enhancing the chances of parasite transmission.

A comparison of the reactivity of germylene and dimethylgermylene with some methylgermanes. Direct kinetic and quantum chemical studies

Time-resolved studies of germylene, GeH2, and dimethygermylene, GeMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to try to obtain rate coefficients for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas-phase. GeH2 + Me2GeH2 was studied over the pressure range 1-100 Torr with SF6 as bath gas and at five temperatures in the range 296-553 K. Only slight pressure dependences were found (at 386, 447 and 553 K). RRKM modelling was carried out to fit these pressure dependences. The high pressure rate coefficients gave the Arrhenius parameters: log(A/cm(3) molecule(-1)s(-1)) = -10.99 +/- 0.07 and E-a = -(7.35 +/- 0.48) kJ mol(-1). No reaction could be found between GeMe2 + Me2GeH2 at any temperature up to 549 K, and upper limits of ca. 10(-14) cm(3) molecule(-1)s(-1) were set for the rate coefficients. A rate coefficient of (1.33 +/- 0.04) x 10(-11)cm(3) molecule(-1)s(-1) was also obtained for GeH2 + MeGeH3 at 296 K. No reaction was found between GeMe2 and MeGeH3. Rate coefficient comparisons showed, inter alia, that in the substrate germane Me-for-H substitution increased the magnitudes of rate coefficients significantly, while in the germylene Me-for-H substitution decreased the magnitudes of rate coefficients by at least four orders of magnitude. Quantum chemical calculations (G2(MP2,SVP)// B3LYP level) supported these findings and showed that the lack of reactivity of GeMe2 is caused by a positive energy barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper.

Surprisingly slow reaction of dimethylsilylene with dimethylgermane: time-resolved kinetic studies and related quantum chemical calculations

Time-resolved studies of silylene, SiH2, and dimethylsilylene, SiMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to obtain rate constants for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas phase. SiMe2 + Me2GeH2 was studied at five temperatures in the range 299-555 K. Problems of substrate UV absorption at 193 nm at temperatures above 400 K meant that only three temperatures could be used reliably for rate constant measurement. These rate constants gave the Arrhenius parameters log(A/cm(3) molecule(-1) s(-1)) = -13.25 +/- 0.16 and E-a = -(5.01 +/- 1.01) kJ mol(-1). Only room temperature studies of SiH2 were carried out. These gave values of (4.05 +/- 0.06) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + Me2GeH2 at 295 K) and also (4.41 +/- 0.07) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + MeGeH3 at 296 K). Rate constant comparisons show the surprising result that SiMe2 reacts 12.5 times slower with Me2GeH2 than with Me2SiH2. Quantum chemical calculations (G2(MP2,SVP)//B3LYP level) of the model Si-H and Ge-H insertion processes of SiMe2 with SiH4/MeSiH3 and GeH4/MeGeH3 support these findings and show that the lower reactivity of SiMe2 with Ge-H bonds is caused by a higher secondary barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper. Other, related, comparisons of silylene reactivity are also presented.

Control of framework stoichiometry in MeGaPO laumontites using 1-methylimidazole as structure-directing agent

A series of heterometal substituted gallium phosphates, (N2C4H7)(0.5+x)[Me0.5+xGa2.5-x(PO4)(3)] (Me = Mn, Fe, Co and Zn, x approximate to 0.25), has been synthesised under solvothermal conditions at 433 K in ethylene glycol using I-methylimidazole as a templating agent and their structures determined at 150 K using single-crystal X-ray diffraction. The compounds are isostructural, crystallising in the monoclinic space group C 2/c, with lattice parameters ca. 15 x 13 x 15 angstrom and beta = 112 degrees, and adopt the laumontite framework type (LAU). The incorporation of 1-methylimidazole cations into the one-dimensional pore systems of these materials is about three quarters the uptake value obtained previously for the less-bulky amine cations of imidazole and pyridine in other MeGaPO laumontites, which have the formula (TH)[MeGa2(PO4)(3)] (Me = Mn, Fe, Co and Zn; T = C5H5N and C3N2H4). The size, shape and charge of the amine clearly influence both the metal-phosphate framework stoichiometry (i.e. Me2+:Ga3+ ratio) and the framework charge. (C) 2007 Elsevier Inc. All rights reserved.

Higher oxides of chlorine: absorption cross-sections of Cl2O6 and Cl2O4, the decomposition of Cl2O6, and the reactions of OClO with O and O-3

The absorption cross-sections of Cl2O6 and Cl2O4 have been obtained using a fast flow reactor with a diode array spectrometer (DAS) detection system. The absorption cross-sections at the wavelengths of maximum absorption (lambda(max)) determined in this study are those of Cl2O6: (1.47 +/- 0.15) x 10(-17) cm(2) molecule(-1), at lambda(max) = 276 nm and T = 298 K; and Cl2O4: (9.0 +/- 2.0) x 10(-19) cm(2) molecule(-1), at lambda(max) = 234 nm and T = 298 K. Errors quoted are two standard deviations together with estimates of the systematic error. The shapes of the absorption spectra were obtained over the wavelength range 200-450 nm for Cl2O6 and 200-350 nm for Cl2O4, and were normalized to the absolute cross-sections obtained at lambda(max) for each oxide, and are presented at 1 nm intervals. These data are discussed in relation to previous measurements. The reaction of O with OCIO has been investigated with the objective of observing transient spectroscopic absorptions. A transient absorption was seen, and the possibility is explored of identifying the species with the elusive sym-ClO3 or ClO4, both of which have been characterized in matrices, but not in the gas-phase. The photolysis of OCIO was also re-examined, with emphasis being placed on the products of reaction. UV absorptions attributable to one of the isomers of the ClO dimer, chloryl chloride (ClClO2) were observed; some Cl2O4 was also found at long photolysis times, when much of the ClClO2 had itself been photolysed. We suggest that reports of Cl2O6 formation in previous studies could be a consequence of a mistaken identification. At low temperatures, the photolysis of OCIO leads to the formation of Cl2O3 as a result of the addition of the ClO primary product to OCIO. ClClO2 also appears to be one product of the reaction between O-3 and OCIO, especially when the reaction occurs under explosive conditions. We studied the kinetics of the non-explosive process using a stopped-flow technique, and suggest a value for the room-temperature rate coefficient of (4.6 +/- 0.9) x 10(-19) cm(3) molecule(-1) s(-1) (limit quoted is 2sigma random errors). The photochemical and thermal decomposition of Cl2O6 is described in this paper. For photolysis at k = 254 nm, the removal of Cl2O6 is not accompanied by the build up of any other strong absorber. The implications of the results are either that the photolysis of Cl2O6 produces Cl-2 directly, or that the initial photofragments are converted rapidly to Cl-2. In the thermal decomposition of Cl2O6, Cl2O4 was shown to be a product of reaction, although not necessarily the major one. The kinetics of decomposition were investigated using the stopped-flow technique. At relatively high [OCIO] present in the system, the decay kinetics obeyed a first-order law, with a limiting first-order rate coefficient of 0.002 s(-1). (C) 2004 Elsevier B.V. All rights reserved.

IR spectrum and radiative forcing of CF4 revisited

Carbon tetrafluoride (CF4) is included as a greenhouse gas within the Kyoto Protocol. There are significant discrepancies in the reported integrated infrared (IR) absorption cross section of CF4 leading to uncertainty in its contribution to climate change. To reduce this uncertainty, the IR spectrum of CF4 was measured in two different laboratories, in 0 933 hPa of air diluent at 296 +/- 2K over the wavelength range 600-3700 cm(-1) using spectral resolutions of 0.03 or 0.50 cm(-1). There was no discernable effect of diluent gas pressure or spectral resolution on the integrated IR absorption, and a value of the integrated absorption cross section of (1.90 +/- 0.17) x 10(-16) cm(2) molecule(-1) cm(-1) was derived. The radiative efficiency (radiative forcing per ppbv) and GWP (relative to CO2) of CF4 were calculated to be 0.102 W m(-2) ppbv(-1) and 7200 (100 year time horizon). The GWP for CF4 calculated herein is approximately 30% greater than that given by the Intergovernmental Panel on Climate Change (IPCC) [ 2002] partly due to what we believe to be an erroneously low value for the IR absorption strength of CF4 assumed in the calculations adopted by the IPCC. The radiative efficiency of CF4 is predicted to decrease by up to 40% as the CF4 forcing starts to saturate and overlapping absorption by CH4, H2O, and N2O in the atmosphere increases over the period 1750-2100. The radiative forcing attributable to increased CF4 levels in the atmosphere from 1750 to 2000 is estimated to be 0.004 W m(-2) and is predicted to be up to 0.033 W m(-2) from 2000 to 2100, dependent on the scenario.

Oxidation of oleic acid at the air-water interface and its potential effects on cloud critical supersaturations

The oxidation of organic films on cloud condensation nuclei has the potential to affect climate and precipitation events. In this work we present a study of the oxidation of a monolayer of deuterated oleic acid (cis-9-octadecenoic acid) at the air-water interface by ozone to determine if oxidation removes the organic film or replaces it with a product film. A range of different aqueous sub-phases were studied. The surface excess of deuterated material was followed by neutron reflection whilst the surface pressure was followed using a Wilhelmy plate. The neutron reflection data reveal that approximately half the organic material remains at the air-water interface following the oxidation of oleic acid by ozone, thus cleavage of the double bond by ozone creates one surface active species and one species that partitions to the bulk (or gas) phase. The most probable products, produced with a yield of similar to(87 +/- 14)%, are nonanoic acid, which remains at the interface, and azelaic acid (nonanedioic acid), which dissolves into the bulk solution. We also report a surface bimolecular rate constant for the reaction between ozone and oleic acid of (7.3 +/- 0.9) x 10(-11) cm(2) molecule s(-1). The rate constant and product yield are not affected by the solution sub-phase. An uptake coefficient of ozone on the oleic acid monolayer of similar to 4 x 10(-6) is estimated from our results. A simple Kohler analysis demonstrates that the oxidation of oleic acid by ozone on an atmospheric aerosol will lower the critical supersaturation needed for cloud droplet formation. We calculate an atmospheric chemical lifetime of oleic acid of 1.3 hours, significantly longer than laboratory studies on pure oleic acid particles suggest, but more consistent with field studies reporting oleic acid present in aged atmospheric aerosol.

Oxidation of biogenic and water-soluble compounds in aqueous and organic aerosol droplets by ozone: a kinetic and product analysis approach using laser Raman tweezers

The results of an experimental study into the oxidative degradation of proxies for atmospheric aerosol are presented. We demonstrate that the laser Raman tweezers method can be used successfully to obtain uptake coeffcients for gaseous oxidants on individual aqueous and organic droplets, whilst the size and composition of the droplets is simultaneously followed. A laser tweezers system was used to trap individual droplets containing an unsaturated organic compound in either an aqueous or organic ( alkane) solvent. The droplet was exposed to gas- phase ozone and the reaction kinetics and products followed using Raman spectroscopy. The reactions of three different organic compounds with ozone were studied: fumarate anions, benzoate anions and alpha pinene. The fumarate and benzoate anions in aqueous solution were used to represent components of humic- like substances, HULIS; a alpha- pinene in an alkane solvent was studied as a proxy for biogenic aerosol. The kinetic analysis shows that for these systems the diffusive transport and mass accommodation of ozone is relatively fast, and that liquid- phase di. ffusion and reaction are the rate determining steps. Uptake coe. ffcients, g, were found to be ( 1.1 +/- 0.7) x 10(-5), ( 1.5 +/- 0.7) x 10 (-5) and ( 3.0 - 7.5) x 10 (-3) for the reactions of ozone with the fumarate, benzoate and a- pinene containing droplets, respectively. Liquid- phase bimolecular rate coe. cients for reactions of dissolved ozone molecules with fumarate, benzoate and a- pinene were also obtained: k(fumarate) = ( 2.7 +/- 2) x 10 (5), k(benzoate) = ( 3.5 +/- 3) x 10 (5) and k(alpha-pinene) = ( 1-3) x 10(7) dm(3) mol (-1) s (- 1). The droplet size was found to remain stable over the course of the oxidation process for the HULIS- proxies and for the oxidation of a- pinene in pentadecane. The study of the alpha- pinene/ ozone system is the first using organic seed particles to show that the hygroscopicity of the particle does not increase dramatically over the course of the oxidation. No products were detected by Raman spectroscopy for the reaction of benzoate ions with ozone. One product peak, consistent with aqueous carbonate anions, was observed when following the oxidation of fumarate ions by ozone. Product peaks observed in the reaction of ozone with alpha- pinene suggest the formation of new species containing carbonyl groups.

Macrocyclic amines as structure-directing agents for the synthesis of three-dimensional antimony-sulfide frameworks

A new family of antimony sulfides, incorporating the macrocyclic tetramine 1,4,8,11-tetraazacyclotetradecane ( cyclam), has been prepared by a hydrothermal method. [C10N4H26][Sb4S7] (1), [Ni(C10N4H24)][Sb4S7] (2), and [Co(C10N4H24)](x)[C10N4H26](1-x)[Sb4S7] (0.08 <= x <= 0.74) (3) have been characterized by single-crystal X-ray diffraction, elemental analysis, thermogravimetry, and analytical electron microscopy. All three materials possess the same novel three-dimensional Sb4S72- framework, constructed from layers of parallel arrays of Sb4S84- chains stacked at 90 to one another. In 1, doubly protonated macrocyclic cations reside in the channel structure of the antimonysulfide framework. In 2 and 3, the cyclam acts as a ligand, chelating the divalent transition- metal cation. Analytical and X-ray diffraction data indicate that the level of metal incorporation in 2 is effectively complete, whereas in 3, both metalated and nonmetalated forms of the macrocycle coexist within the structure.

Evaluation of milk urea nitrogen as a diagnostic of protein feeding

An evaluation of milk urea nitrogen (MUN) as a diagnostic of protein feeding in dairy cows was performed using mean treatment data (n = 306) from 50 production trials conducted in Finland (n = 48) and Sweden (n = 2). Data were used to assess the effects of diet composition and certain animal characteristics on MUN and to derive relationships between MUN and the efficiency of N utilization for milk production and urinary N excretion. Relationships were developed using regression analysis based on either models of fixed factors or using mixed models that account for between-experiment variations. Dietary crude protein (CP) content was the best single predictor of MUN and accounted for proportionately 0.778 of total variance [ MUN (mg/dL) = -14.2 + 0.17 x dietary CP content (g/kg dry matter)]. The proportion of variation explained by this relationship increased to 0.952 when a mixed model including the random effects of study was used, but both the intercept and slope remained unchanged. Use of rumen degradable CP concentration in excess of predicted requirements, or the ratio of dietary CP to metabolizable energy as single predictors, did not explain more of the variation in MUN (R-2 = 0.767 or 0.778, respectively) than dietary CP content. Inclusion of other dietary factors with dietary CP content in bivariate models resulted in only marginally better predictions of MUN (R-2 = 0.785 to 0.804). Closer relationships existed between MUN and dietary factors when nutrients (CP to metabolizable energy) were expressed as concentrations in the diet, rather than absolute intakes. Furthermore, both MUN and MUN secretion (g/d) provided more accurate predictions of urinary N excretion (R-2 = 0.787 and 0.835, respectively) than measurements of the efficiency of N utilization for milk production (R-2 = 0.769). It is concluded that dietary CP content is the most important nutritional factor influencing MUN, and that measurements of MUN can be utilized as a diagnostic of protein feeding in the dairy cow and used to predict urinary N excretion.

Gas-phase reactions of NO3 and N2O5 with (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol

The night-time atmospheric chemistry of the biogenic volatile organic compounds (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol, has been studied at room temperature. Rate coefficients for reactions of the nitrate radical (NO3) with these stress-induced plant emissions were measured using the discharge-flow technique. We employed off-axis continuous-wave cavity-enhanced absorption spectroscopy (CEAS) for the detection of NO3, which enabled us to work in excess of the hexenol compounds over NO3. The rate coefficients determined were (2.93 +/- 0.58) x 10(-13) cm(3) molecule(-1) s(-1), (2.67 +/- 0.42) x 10(-13) cm(3) molecule(-1) s(-1), (4.43 +/- 0.91) x 10(-13) cm(3) molecule(-1) s(-1), (1.56 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1), and (1.30 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1) for (Z)-hex-4-en-1-ol, (Z)-hex-3en-1-ol, (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol. The rate coefficient for the reaction of NO3 with (Z)-hex-3-en-1-ol agrees with the single published determination of the rate coefficient using a relative method. The other rate coefficients have not been measured before and are compared to estimated values. Relative-rate studies were also performed, but required modification of the standard technique because N2O5 (used as the source of NO3) itself reacts with the hexenols. We used varying excesses of NO2 to determine simultaneously rate coefficients for reactions of NO3 and N2O5 with (E)-hex-3-en-1-ol of (5.2 +/- 1.8) x 10(-13) cm(3) molecule(-1) s(-1) and (3.1 +/- 2.3) x 10(-18) cm(3) molecule(-1) s(-1). Our new determinations suggest atmospheric lifetimes with respect to NO3-initiated oxidation of roughly 1-4 h for the hexenols, comparable with lifetimes estimated for the atmospheric degradation by OH and shorter lifetimes than for attack by O-3. Recent measurements of [N2O5] suggest that the gas-phase reactions of N2O5 with unsaturated alcohols will not be of importance under usual atmospheric conditions, but they certainly can be in laboratory systems when determining rate coefficients.

Gas-phase rate coefficients for the reactions of nitrate radicals with (Z)-pent-2-ene, (E)-pent-2-ene, (Z)-hex-2-ene, (E)-hex-2-ene, (Z)-hex-3-ene, (E)-hex-3-ene and (E)-3-methylpent-2-ene at room temperature

Rate coefficients for reactions of nitrate radicals (NO3) with (Z)-pent-2-ene, (E)-pent-2-ene, (Z)-hex-2-ene, (E)-hex-2-ene, (Z)-hex-3-ene, (E)-hex-3-ene and (E)-3-methylpent-2-ene were determined to be (6.55 +/- 0.78) x 10(-13) cm(3) molecule(-1) s(-1), (3.78 +/- 0.45) x 10(-13) cm(3) molecule(-1) s(-1), (5.30 +/- 0.73) x 10(-13) cm(3) molecule(-1) s(-1), (3.83 +/- 0.47) x 10(-13) cm(3) molecule(-1) s(-1), (4.37 +/- 0.49) x 10(-13) cm(3) molecule(-1) s(-1), (3.61 +/- 0.40) x 10(-13) cm(3) molecule(-1) s(-1) and (8.9 +/- 1.5) x 10(-12) cm(3) molecule(-1) s(-1), respectively. We performed kinetic experiments at room temperature and atmospheric pressure using a relative-rate technique with GC-FID analysis. The experimental results demonstrate a surprisingly large cis-trans (Z-E) effect, particularly in the case of the pent-2-enes, where the ratio of rate coefficients is ca. 1.7. Rate coefficients are discussed in terms of electronic and steric influences, and our results give some insight into the effects of chain length and position of the double bond on the reaction of NO3 with unsaturated hydrocarbons. Atmospheric lifetimes were calculated with respect to important oxidants in the troposphere for the alkenes studied, and NO3-initiated oxidation is found to be the dominant degradation route for (Z)-pent-2-ene, (Z)-hex-3-ene and (E)-3-methylpent-2-ene.