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Quadratic Equation (quadratic + equation)
Selected AbstractsModelling the photosensitization-based inactivation of Bacillus cereusJOURNAL OF APPLIED MICROBIOLOGY, Issue 3 2009Y. Le Marc Abstract Aims:, To study and to develop a model for the photo-destruction of the foodborne pathogen Bacillus cereus, initially treated with a precursor of endogenous photosensitizers (5-aminolevulinic acid, ALA). Materials and methods:, The cells were incubated in the presence of ALA (3 or 7·5 mmol l,1) for incubation times ranging from 2 to 60 min, inoculated onto the surface of LB Agar plates and submitted to light irradiation. The Weibull model was used to describe the survival curves of B. cereus. Quadratic equations were used to describe the effects of ALA concentration and incubation time on the Weibull model parameters. Results:, ALA-based photosensitization proved to be an effective tool for inactivation of B. cereus. The decrease in viable counts observed after 20 min of irradiation, ranged from 4 to 6 log CFU g,1. Conclusions:, The developed model proved to be a parsimonious and robust solution to describe the observed data. Significance and Impact of the Study:, The study demonstrates the effectiveness of photosensitization on B. cereus on agar plates. The model developed may be useful to optimize inactivation treatments by photosensitization. [source] Kinetics of Bis(p -nitrophenyl)phosphate (BNPP) Hydrolysis Reactions with Trivalent Lanthanide Complexes of N -Hydroxyethyl(ethylenediamine)- N,N,,N, -triacetate (HEDTA),EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 8 2009C. Allen Chang Abstract Kinetic studies of hydrolysis reactions of BNPP [sodium bis(p -nitrophenyl)phosphate] with trivalent lanthanide (Ln3+) complexes of HEDTA [HEDTA = N -hydroxyethyl(ethylenediamine)- N,N,,N, -triacetate] were performed at pH 6.96,11.34 and 25 °C by a spectrophotometric method and by HPLC analysis. The reaction rates increase with increasing atomic number of lanthanide and solution pH from PrHEDTA to EuHEDTA and then decrease for heavier LnHEDTA complexes. Plots of pseudo-first-order rate constants (kobs) vs. pH could be fitted to the equation kobs = kLnL(OH)[LnL]T/{1,+,exp[,2.303(pH,,,pKh)]}, where kLnL(OH) is the rate constant for the reaction of LnHEDTA(OH), with BNPP, Kh is the hydrolysis constant of LnHEDTA, and [LnL]T is the total concentration of LnHEDTA. The pKh values obtained by the kinetic method are in the range 8.2,10.3 and are similar to those measured by potentiometric methods. At [LnL]T = 10,70 mM and pH 10.5, most of the observed pseudo-first-order rate constants could be fitted to a simple saturation kinetic model, kobs = k1K[LnHEDTA(OH),]/{1 + K[LnHEDTA(OH),]}, where K is the equilibrium constant for the formation for LnHEDTA(OH),BNPP and is in the range 2,147 M,1. The k1 values are in the range 1.12,×,10,5,2.71,×,10,3 s,1. The kobs data for TbHEDTA and HoHEDTA were fitted to a quadratic equation. It was observed that the dinuclear species are more reactive. ESI mass spectrometry confirmed that the reaction between BNPP and EuHEDTA is a simple hydrolysis but not a transesterification, presumably because the three inner-sphere coordinated water molecules are far away from the coordinated hydroxyethyl group. Hydrolysis is likely to occur by proton transfer from one inner-sphere coordinated water molecule to the deprotonated ethyl oxide group followed by nucleophilic attack of the resulting hydroxide ion on the bonded BNPP anion.(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009) [source] Evaluation of practical diets containing different protein levels on gonad development of female redclaw crayfish Cherax quadricarinatusAQUACULTURE NUTRITION, Issue 4 2009H. RODRÍGUEZ-GONZÁLEZ Abstract The effect of five experimental diets with different crude protein content (220, 270, 330, 390 and 450 g kg,1) on gonad development of female Cherax quadricarinatus was tested under laboratory conditions. After 70 days, a significant linear relationship indicated that higher concentrations of protein and carbohydrates in the hepatopancreas were produced as the dietary crude protein increased (P < 0.05). There were significant responses of the gonadosomatic index, hepatosomatic index, biochemical composition of the gonad (protein, lipids, carbohydrates and energy) and frequency of secondary vitellogenic oocytes to dietary protein level, as indicated by significant fits of the quadratic equation to the observed experimental data. The optimal response of the criteria parameters corresponded to levels of crude protein in the range 284,355 g kg,1. Overall, 330 g kg,1 crude protein with a protein : energy ratio of 15.6 mg kJ,1 was considered the most adequate concentration of dietary protein for gonad development and biochemical composition in female redclaw crayfish. [source] AN APPROXIMATION FOR THE OPTIMAL LINEAR INCOME TAX RATEAUSTRALIAN ECONOMIC PAPERS, Issue 3 2009JOHN CREEDY This paper derives a convenient method of calculating an approximation to the optimal tax rate in a linear income tax structure. Individuals are assumed to have Cobb-Douglas preferences and the wage rate distribution is lognormal. First, the optimal tax rate is shown, for a general form of social welfare function, to be the smallest root of a quadratic equation involving a welfare-weighted average wage rate. Second, an approximation to this average is derived for an isoelastic social welfare function. This average depends on the degree of inequality aversion of the welfare function and the coefficient on consumption in individuals' utility functions. Calculations show that the method performs well in comparison with standard simulation methods of computing the optimal tax rate. [source] Plasma concentrations of haloperidol are related to CYP2D6 genotype at low, but not high doses of haloperidol in Korean schizophrenic patientsBRITISH JOURNAL OF CLINICAL PHARMACOLOGY, Issue 3 2001Hyung-Keun Roh Aims, This study was carried out to evaluate the influence of CYP2D6 genotype on the steady state plasma concentrations of haloperidol and reduced haloperidol in Korean schizophrenic patients. Methods, One hundred and twenty Korean schizophrenic patients treated with various, clinically determined, doses of haloperidol (range 3,60, median 20 mg day,1) during monotherapy were recruited. CYP2D6 genotypes were determined by analysis of the CYP2D6*10 allele using allele-specific PCR and the CYP2D6*5 allele by long-PCR. Steady state plasma concentrations of haloperidol and reduced haloperidol were analysed by h.p.l.c. Results, Twenty-three (19.2%), 60 (50.0%), 1 (0.8%), 33 (27.5%) and 3 patients (2.5%) possessed the CYP2D6 genotypes *1/*1, *1/*10, *1/*5, *10/*10 and *10/*5, respectively. The allele frequencies of CYP2D6*1, *10 and *5 were 44.6%, 53.8% and 1.7%, respectively. Significant relationships between dose and plasma concentrations of haloperidol (linear; r2 = 0.60, P < 0.0001) and reduced haloperidol (quadratic equation; r2 = 0.67) were observed. Overall, the concentrations normalized for dose (C/D) of haloperidol were significantly different between the CYP2D6*1/*1, *1/*10 and*10/*10 genotype groups (one-way anova; P = 0.028). No significant differences between the genotype groups were found with respect to the C/D of reduced haloperidol (P = 0.755). However, in patients with daily doses less than 20 mg, significant differences in the C/D of haloperidol (P = 0.003), but not of reduced haloperidol, were found between the three major genotype groups. In patients with doses higher than 20 mg, no differences were found between the genotype groups for either haloperidol or reduced haloperidol. 68 patients (57%) used benztropine, an antimuscarinic agent. All four patients with a *5 allele (one together with *1 and three with *10) were found to use benztropine. The patients homozygous for the *1 allele seemed to need less benztropine than the patients with one or two mutated alleles (Fisher's exact test; P = 0.036). Conclusions, The dose-corrected steady state plasma concentrations of haloperidol, but not of reduced haloperidol, were significantly different between the CYP2D6*1/*1, *1/*10 and *10/*10 genotype groups when doses lower than 20 mg haloperidol were given. No differences were found at higher doses. These results suggest the involvement of CYP2D6 in the metabolism of haloperidol at low doses of haloperidol (< 20 mg daily), while another enzyme, probably CYP3A4, contributes at higher doses. [source] Generation and forward displacement analysis of two new classes of analytic 6-SPS parallel manipulatorsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2001Xianwen Kong Analytic manipulators are manipulators with a characteristic polynomial of fourth degree or lower. Using the component approach to generate analytic 6-SPS parallel manipulators (PMs), the generation process is reduced to the generation of analytic components for 6-SPS PMs. Two new classes of analytic components for 6-SPS PMs are generated at first. Then, two new classes, IX and X, of analytic 6-SPS PMs are generated. The forward displacement analysis (FDA) of the new analytic 6-SPS PMs is also performed. The FDA of the 6-SPS PMs of class IX is reduced to the solution of one univariate cubic equation and two univariate quadratic equations, in sequence, while that of the 6-SPS PMs of class X is reduced to the solution of three univariate quadratic equations in sequence. Both of the new analytic 6-SPS PMs have at most eight assembly modes. © 2001 John Wiley & Sons, Inc. [source] On a third-order Newton-type method free of bilinear operatorsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2010S. Amat Abstract This paper is devoted to the study of a third-order Newton-type method. The method is free of bilinear operators, which constitutes the main limitation of the classical third-order iterative schemes. First, a global convergence theorem in the real case is presented. Second, a semilocal convergence theorem and some examples are analyzed, including quadratic equations and integral equations. Finally, an approximation using divided differences is proposed and used for the approximation of boundary-value problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Influence of water temperature on spawning induction and larval development of the sea squirt Halocynthia ritteri (Oka, 1906)AQUACULTURE RESEARCH, Issue 5 2009Kyoung Ho Kang Abstract In order to establish a large-scale hatchery technique for the sea squirt Halocynthia ritteri, the influences of water temperature on spawning induction, larval development and survival of H. ritteri were studied under laboratory conditions. The larvae of H. ritteri exhibited high sensitivity to changes in temperature. As temperature increased from 10 to 21 °C, the duration of larval stage was inversely related to temperature and the time to reach attached larvae stage decreased from 42.0 to 59.4 h. The biological minimum temperature for the early development of H. ritteri was estimated to be 0.22 °C. In relation to temperature, quadratic equations showed significant fits to the data of spawning rate, fecundity, fertilization, larval survival and attachment. Optimal temperatures for spawning rate, fecundity, fertilization rate, larval survival rate and attachment rate were estimated to be 14.9, 14.7, 13.2, 14.1 and 14.7 °C respectively. It is concluded that the range of 13,15 °C is optimal for spawning and larval rearing of sea squirts. [source] Fenton and photo-Fenton treatment of distillery effluent and optimization of treatment conditions with response surface methodologyASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2010Mojtaba Hadavifar Abstract Two chemical processes, Fenton and photo-Fenton, were tested separately for the treatment of vinasse, which was generated from an alcohol distillery process. In order to evaluate the processes effectiveness, four independent variables viz. SCOD concentration, initial pH, H2O2 and FeSO4 dosage were applied. Experiments were conducted based on a central composite design (CCD) and analyzed using response surface methodology (RSM). UV radiation for 80 min was applied in each experiment during the photo-Fenton process. Two modified quadratic equations were used for data fitting. The most significant model terms in the processes were found to be the initial chemical oxygen demand (COD) concentration and the initial pH. A higher removal efficiency was achieved in the photo-Fenton process compared to Fenton alone. The efficiency varied from 18 to 97% for the photo-Fenton process, while it was in the range of 5,47% for Fenton process. The R2 value of the models (R2 > 0.97) shows a very high degree of correlation between the parameters. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] | |||||||||||||