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It is important to consider nonlinear effects when designing controllers to maximise generated energy in wave energy converters (WECs). Due to the substantial extra computation and complexity added when considering nonlinearities in the controller calculations, quantifying the extent of nonlinearity in WECs’ behaviour is crucial to avoid designing overcomplicated control strategies. This paper suggests two nonlinearity measures to quantify the nonlinearity degree of wave-to-wire (W2W) models in steady-state, using the best linear approximation identified through a minimisation problem as a benchmark. The first measure, referred to as the original nonlinearity measure, evaluates the nonlinear effects of the wave-absorber hydrodynamic interaction. The second measure, referred to as the power nonlinearity measure, quantifies the nonlinear effects in power take-off (PTO) systems, considering the quadratic response of the power signal. The degree of nonlinearity of two WEC models, a partially-nonlinear hydrodynamic model with an ideal PTO model and a complete nonlinear W2W model, is evaluated using monochromatic and polychromatic waves over a wide range of wave periods and heights, covering the whole operational space of a WEC.

This study evaluated the level and length of time of vitamin A supplementation and its effects on carcass and cuts yield, meat quality, and myopathies in 42-day-old broilers. A total of 1,920 birds were divided into six groups, and each group received a different level of vitamin A: 0; 6,000; 16,000; 26,000; 36,000 and 46,000 IU/ kg. From day 1 to 21, the treatments were distributed among 16 replicates with 20 birds. From the 22nd day on, 8 repetitions remained with the initial treatment and the others received diets with no vitamin A supplementation. Twelve birds were slaughtered per treatment to evaluate carcass and cuts yield, shear force, cooking loss, water holding capacity and the presence of substances reactive to thiobarbituric acid. The remaining birds were slaughtered and evaluated in loco for Wooden Breast (WB) and White Striping (WS). Wings weight was affected by vitamin A levels. The duration of the vitamin A supplementation process had effects on the weight of breast, legs with a dorsal portion, and meat color in the yellow intensity (b*). Incidence of WB had higher scores in birds supplemented until 42 days of age. WS showed a quadratic response and a lower response with supplementation of 29,700 IU/ kg. Even for WS, a higher occurrence of the normal score was found in birds supplemented until 21 days of age. Minimal quadratic responses were obtained for normal, moderate and severe scores, in supplementations of 29,301; 29,959 and 29,827 IU/ kg, respectively. WB had lower occurrence rates in birds supplemented until 21 days of age. Consequently, the severe score was more frequent when supplementation was provided until 42 days of age. The level of vitamin A and the length of time during which this supplementation was provided had influence on cuts yield, meat color and the incidence of WB and WS of the 42-day-old birds.

The excited-state absorption in a set of fluorene oligomers are simulated based on the LR-TDDFT and QR-TDDFT calculations. It is shown that the results obtained from LR-TDDFT are in good agreement with the data of QR-TDDFT and the experimental results. The advantage of the LR-TDDFT over QR-TDDFT method is that the computational cost is scaling as only N 4 . In addition, it is noticed that the influences of the used exchange correlation functional in LR-TDDFT and QR-TDDFT for the simulations of ESA also show similar effects. Accordingly, LR-TDDFT can be used as an alternative to QR-TDDFT for studying the ESA of conjugated polymers.

Heat treated EN24 steel is turned with uncoated tungsten carbide inserts in dry cutting environment following Taguchi L16 design of experiments (DOE); and influence of machining process parameters on the surface roughness characteristics (i.e. Ra and Rz) is investigated. The multiple responses are optimized simultaneously using Taguchi based grey relational analysis. Analysis of Variance (ANOVA) for grey relational grade reveals that cutting speed is the most significant parameter followed by feed; and the influence of depth of cut is insignificant. Quadratic response surface models are generated for both the responses; and their adequacy is verified.

Published literature elucidating dietary valine (Val) requirements for female broilers is limited and lacks data for the finisher phase. Three experiments (Exp) were conducted to determine the Val requirement for Cobb MX × 500 females during the grower (Exp 1; 14–28 days), finisher (Exp 2; 28–42 days), and withdraw periods (Exp 3; 42–56 days). Two additional Exp were conducted to determine the Val requirement for Cobb MV × 500 male (Exp 4) and female (Exp 5) broilers from 14–35 days. Corn-soybean meal diets were fed in the experimental period of all Exp to create Val dose response titration diets. Dietary titration levels of digestible Val to digestible Lys (Val/Lys) ratios were: 64–82 in Exp 1; 65–83 in Exp 2 and 3; and 57–92 in Exp 4 and 5. Body weight (BW) gain, feed intake, and feed conversion ratio were determined for each experimental period. At the conclusion of Exp 2 through 5, broilers were processed to determine carcass traits. Requirements were determined using regression analysis, considering the requirement to be 95 % of the quadratic response. No significant linear or quadratic responses were determined for Exp 1 through 3. In Exp 4 and 5, significant responses were observed for feed conversion ratio, but not processing yields. The lack of responsiveness in Exp 1 through 3 are likely due to an inadequate reduction in dietary Val to observe female quadratic responses. Valine requirements were determined to be 78 and 77 Val/Lys for males and females, respectively, based on feed conversion responses.

Tryptophan (Trp) is involved in regulation of animal behaviour, since it originates serotonin and melatonin, especially in low crude protein diets, and Trp metabolism requires B6 vitamin (B6) as enzymatic cofactor. The objective of this study was to feed low protein diets with different levels of standardized ileal digestible (SID) Trp and B6 for barrows and gilts (70–100 kg) and to measure day-night behaviour, performance and carcass traits. In experiment 1 (Exp. 1) sixty four barrows (initial BW = 70.77 ± 2.07 kg) were used, and in experiment 2 (Exp. 2) sixty four gilts (initial BW = 70.52 ± 2.95 kg) were used. In both experiments a 2 × 4 factorial arrangement of treatments was used: two B6 levels (1 and 5 mg kg −1 ) and four levels of SID Trp (Exp. 1: 0.130, 0.155, 0.180, 0.205%; and Exp. 2: 0.140, 0.167, 0.194, 0.221%). Day-night behaviour was recorded at the end of weeks 1, 2 and 3 (days 7, 14 and 21) during 24 h. Scan-sampling was used to determine time-budget behaviour. Growth performance and carcass traits were measured at the end of the experimental period, when animals reached about 100 kg BW (in average 26 days). In Exp. 1 (barrows), stationary behaviour in daytime period (from 6:00 h to 18:00 h) increased quadratically ( P = 0.005) as Trp content in diets increased from 0.130 to 0.165%, but it decreased until 0.205% of SID Trp. Interacting behaviour in night-time period (from 18:00 h to 6:00 h) was affected by B6 ( P = 0.031). Sleeping behaviour decreased linearly ( P = 0.003) as Trp content in diets increased from 0.130 to 0.205% and feeding behaviour showed quadratic response ( P = 0.008) to SID Trp (0.161%). In Exp. 2 (gilts) sleeping behaviour in daytime period decreased quadratically ( P = 0.001) as SID Trp content in diets increased from 0.140 to 0.179%, but it decreased until 0.221% of SID Trp. Feeding behaviour was affected by the interaction Trp × B6 ( P = 0.030) as supplementary B6 (5 mg kg −1 ) decreased visits to feeder up to 0.194% Trp content. Sleeping behaviour in night-time period was affected by the interaction Trp × B6 ( P = 0.030) once supplementary B6 (5 mg kg −1 ) markedly decreased time spent sleeping when compared to basal B6 (1 mg kg −1 ) as Trp levels increased in diets. Feeding behaviour responded quadratically ( P = 0.001) to Trp (0.173%). In both experiments performance variables and carcass traits were not different ( P > 0.05) neither for Trp nor B6. SID Trp levels from 0.130 to 0.205% (barrows) and 0.140 to 0.221% (gilts) even as B6 content (1 or 5 mg kg −1 ) in diets had no consistent effects on behaviour and did not alter performance of pigs.

SUMMARY Using apparent ileal digestible (AID) amino acids (AA) for feed formulation is considered preferable to formulating diets based on a total AA basis. However, data on AID tryptophan (Trp) requirements of broiler chicks are scarce. This study was conducted to determine the AID Trp requirements for broiler chicks from 22 to 42 d of age. A total of 1,008 (504 male and 504 female) 22-day-old broilers (Cobb 500) were randomly allocated within sex to 7 treatments (8 replicates with 9 birds per cage). The birds were fed diets based on corn, soybean meal, cotton seed meal, and corn gluten meal, which were supplemented with 0, 0.018, 0.036, 0.054, 0.072, 0.09, or 0.108% crystalline L-Trp (basal diet contained 0.144% Trp) in order to supply 0.144, 0.162, 0.1180, 0.1198, 0.216, 0.234, or 0.252% designed total Trp. Performance, meat quality, and fat deposition were evaluated at the end of the 21 d trial. The AID of AA was measured using the indicator method. There were no significant differences in the AID of AA between male and female broilers. The performance of female broilers was not affected by Trp level. However, weight gain and feed intake of male broilers showed a quadratic response to Trp levels (P

Response surface methodology was applied to estimate the effects of two independent variables, microwave power and pre-treatment time, of linseed on the cold-pressed linseed oil parameters associated with health and sensory characteristics. Microwave-treated oils had lower amounts of secondary oxidation products (AnV = 0.97–1.47) and antioxidant activity (DPPH = 209.9–315.1 μmol TE/100 g) than those of untreated oil (AnV = 1.37 and DPPH = 353.0 μmol TE/100 g). However, these oils were a richer source of oleic acid and had a higher sensory scores for odour and flavour. The optimal conditions were predicted and the quadratic response surfaces were drawn from the mathematical models in order to ensure the best quality of linseed oils. The pre-treatment of linseed using microwave radiation is a promising technology that can improve the chemical and sensory properties of cold-pressed linseed oils.

International audience; The study presented here consisted of the calculation of cross relationships between growth performance parameters, body growth composition, and feed characteristics, using data from an experiment reported in 2 previous publications. In the previous experiment, 30 pelleted diets were given to broiler chickens (8/diet) (21 to 35 d) for in vivo measurement and prediction of AMEn and net energy (NE) values of diets, using 3 trials with 10 diets/trial. In the course of NE determination, individual values for growth, feed intake, and deposition of lipid and protein were measured. Average energy deposited as lipid and protein represented 25.4 and 19.1% AME intake, respectively. Using a multiple regression predicting AME intake, the partial efficiencies of AME for energy deposition as lipid and protein were calculated to be 91.6 and 67.3%, respectively, and the daily amount of AME required for maintenance was evaluated at 0.683 MJ/kg BW0.7. The mean diet NE/AMEn ratios were predicted by an equation combining the lipid content of body growth (positive coefficient) and the apparent digestible protein (ADP) to AMEn ratio (ADP/AMEn), with a quadratic expression for the latter variable. This quadratic response expressed a positive asymptotic relationship, with a plateau for ADP/AMEn values above 1.45 [%/(MJ/kg)]. The equations predicting growth always included either the dietary percentage of water-insoluble cell wall or the AMEn value. The other major parameters predicting growth were either the lipid content of body growth or the CP/AMEn ratio. In many cases, quadratic responses were observed in growth prediction equations. Regressions predicting feed efficiency showed only linear responses. Feed efficiency was predicted precisely by multiple linear regressions based only on AMEn and a dietary protein parameter. According to these regressions, 1% CP was equivalent to 0.247 MJ/kg AMEn in terms of feed efficiency. The most efficient regression predicting the individual lipid content of body growth combined the protein efficiency value (negative coefficient), the CP/AMEn ratio (negative coefficient), AMEn (positive coefficient), and the feather content of body growth (positive coefficient).

Spiral concentrator and spiral plant modelling of chromite bearing ore is investigated in this paper. Spiral product stream responses (grade and recovery) were modelled according to variations in feed conditions (grade, density, flow rate) and primary splitter settings. The two modelling approaches constituted a quadratic response surface and an extension (to accommodate feed conditions) on the original Holland-Batt (1990) spline model. Additional validation of the extended Holland-Batt model behaviour was performed via regression on a second data set, based on hematite separation using spiral concentrators (Sadeghi, 2015). The quadratic model showed higher performance values on the training set; however, the extended Holland-Batt model showed better performance on the test data. Finally, both models were compared in terms of spiral concentrator plant modelling ability (based on an industrial spiral concentration plant). Quadratic response surface models were unable to produce acceptable grade-recovery curve simulations. The extended Holland-Batt model proved to be the superior spiral plant simulation model due to its ability to produce valid grade-recovery curves. The extended Holland-Batt spline-based model shows promise as an improvement over RSM for spiral modelling (and spiral plant simulation). The extended Holland-Batt model can provide the same screening, characterization and optimization functionality of RSM models for single-spiral experimental modelling, with the added benefit of simple extension to spiral plant simulation.

Different ways to extract properties of excited states from time-dependent density functional theory (TD-DFT) calculations are compared toab initioresults obtained with the Equation of Motion Coupled Clusterapproach. The recently proposeda posterioriTamm Dancoff approximation (ATDA) predicts the perma-nent dipole moments to be underestimated by 25% on average, close to the results of the relaxed densityTD-DFT formalism, quadratic response formalism, and numerical energy derivatives, while the unrelaxeddensity approximation results are less accurate (40% overestimate). We also propose a correction for TD-DFT excitation energies, which are known to be problematic for charge transfer states. The static DFTenergies evaluated on the relaxed densities of the excited states are found to be more accurate thanTD-DFT excitation energies (RMSD is 0.7 eV vs. 1.1 eV, while maximum deviation is 1.0 eV vs. 2.0 eV). This validates ATDA for description of nonlinear optical properties of donor acceptor mole-cules, exempli“ed by para-nitroaniline, and extends this method to improve the excitation energypredictions. 2013 Elsevier B.V. All rights reserved.

A long-term selection experiment for high (HWS) and low (LWS) BW at 8 wk of age (BW8) was conducted in White Plymouth Rock chickens. Over 54 generations of selection, responses to bidirectional selection were profound. Increase in BW8 in line HWS was linear, and there was a significant quadratic response in line LWS for BW at both 4 and 8 wk of age. Although there is no indication that line HWS has come close to approaching a selection limit in more than 50 generations, selection limits occurred in line LWS chickens at generation 48 for females and generation 50 for males. Evidence also exists that one or more beneficial mutations have occurred in line HWS, aiding in progressive increases in BW8 over generations. Analyses of ratios of BW at 4 wk of age with those at 8 wk of age (ratio 4/8) revealed that LWS females grew proportionately faster through 4 wk of age than LWS males or HWS chickens. Comparisons of the selected lines with contemporary lines in which selection had been relaxed (discontinued) indicated that, in line HWS, the relaxed lines generally regressed toward original (preselection) values, suggesting that the linear response to single-trait selection was at least partially due to continued genetic variance. In LWS chickens, a series of plateaus in selection response occurred, but relaxed contemporary lines still regressed toward preselection values for BW8. In spite of the length of this selection experiment (54 generations), genetic variance and beneficial mutations have allowed continued, linear response to selection for increased BW8. Response to selection for decreased BW8 has been tempered by physiological barriers that have decreased survival of young chicks or the ability of females to reproduce. These findings are discussed in a historical perspective.

We apply a non-linear flow response formalism to the recently measured event plane correlations. We find that the observed event plane correlations can be understood as an average of the linear and quadratic response.

An experiment was conducted to determine dietary energy (ME) and CP requirements of quail chicks using response surface methodology. A total of 40 floor pens of 20 birds each were assigned to 9 diets of central composite design (CCD) containing 5 levels of ME (2,809 to 3,091 kcal/kg) and CP (19 to 24.8% of diet) from 7 to 14 d of age. The experimental results of CCD were fitted with quadratic response models, and ridge analysis was used to compute the optimal response for BW gain (BWG) and feed conversion ratio (FCR). Regression analysis showed that the linear effect of independent variables was significant on bird responses. The quadratic and cross-product effects did not have significant effects on performance. Dietary levels of CP linearly affected BWG and FCR, but the effect of dietary ME was not significant. The ridge maximum analysis on BWG and minimum analysis on FCR models revealed that the maximum BWG may be achieved with 2,950 kcal of ME/kg and 25% CP; and minimum FCR may be obtained with 2,878 kcal of ME/kg and 24.4% CP. The results of this study showed that response surface analysis with the CCD platform was successfully used to optimize dietary requirements of Japanese quail and this methodology could be used for other nutrients.

A radial basis function neural network (RBF) and genetic algorithm (GA) were applied to improve the efficiency of the oxidative decolourization of the recalcitrant dye Reactive Black 5 (RB 5) by a technical laccase (Trametes spp.) and the natural mediator acetosyringone (ACS). The decolourization of RB 5 in aqueous solution was studied with a 34 factorial design including different levels of laccase (2, 100, 200 U L−1), acetosyringone (5, 50, 100 μM), pH value (3, 4.5, 6) and incubation time (10, 20, 30 min). The generated RBF network was mathematically evaluated by several statistical indices and revealed better results than a classical quadratic response surface (RS) model. The experimental data showed that within 10 min of incubation time a complete decolourization (>90%) was achieved by using the highest amount of laccase (200 U L−1) and acetosyringone (100 μM) at pH 6. By applying the RBF-GA methodology, the efficiency of the laccase-mediated decolourization was improved by minimising the required amount of laccase and acetosyringone by 25% and 21.7% respectively. Complete decolourization (>90%) was obtained within 10 min at the GA-optimised process conditions of laccase (150 U L−1) and acetosyringone (78.3 μM) at pH 5.67. These results illustrate that the RBF-GA methodology could be a powerful technique during scale-up studies.

Experimental results of a study on the wavelength dependence and the dynamic range of the quadratic response of commercial grade light emitting diodes (LEDs) are reported over a broad spectral range of 680 nm to 1080 nm using ~ 100 fs duration laser pulses from cw mode locked laser oscillator. A large dynamic range of the quadratic response has been demonstrated in a reverse biased LED. The observed dynamic range compares well with that obtained using a biased photomultiplier tube with large internal gain.

The consumption of EPA and DHA has been associated with reduced risk for cardiovascular disease morbidity and mortality. Mean intakes of EPA and DHA in the United States and elsewhere are below levels recommended by health authorities. The main non-marine source of dietary (n-3) fatty acids (α-linolenic acid) is poorly converted to EPA in humans. Stearidonic acid (SDA) is a non-marine fatty acid that appears to be more readily converted to EPA in humans. Results from previous studies suggested that SDA, relative to EPA, increases RBC EPA, with reported efficiencies ranging from ~16 to 30%. A recently published, randomized, single-blind, controlled, parallel group study in healthy men and women characterized the relationships between intakes of SDA and EPA and EPA enrichment of RBC membranes over a 12-wk period. %EPA in RBC membranes was greater after EPA (0.44, 1.3, or 2.7 g/d, respectively) and SDA (1.3, 2.6, or 5.2 g/d, respectively) consumption compared to a safflower control (all P < 0.02). Based on quadratic response surface models, for EPA intakes of 0.25, 0.50, and 0.89 g/d, SDA intakes of 0.61, 1.89, and 5.32 g/d, respectively, would be required to produce equivalent values for RBC %EPA, translating to relative efficiencies of 41.0, 26.5, and 16.7%. Thus, dietary SDA over a range of intakes increases RBC %EPA, with declining relative efficiency as SDA intake increases.

In fish, a quadratic relationship between feed intake and feed efficiency is observed most-often, with optimal nutrient retention occurring at moderate levels of feed restriction. Determining how mechanisms controlling nutrient utilization are affected by feed intake, with a particular emphasis on those that impact protein turnover, will enable a better understanding of the metabolic processes that contribute to variations in nutrient retention. In the present study, rainbow trout were fed for 10 weeks at different levels of satiation and indices of growth, nutrient retention, and protein degradation were determined. As-fed and dry-weight feed efficiency, specific growth rate, and protein, lipid, and energy retention displayed a positive quadratic response to feeding level (P

Complete rest or grazing deferment is a general recommendation to encourage vegetative recovery following fire in the western United States. However, effects of grazing deferments on animal performance have not been determined. Prescribed fires were individually applied to nine separate, 1.5-ha pastures each year (2006 and 2007) for a total of 18 pastures. Grazing was deferred until spring (16 May), early summer (19 June), or late summer (1 August) the growing season after fire. At the end of each deferment, a 70-d (2007) or 41-d (2008) grazing period was initiated. Stocking rates were consistent between treatments within year, but were adjusted between years to achieve the targeted residual biomass of approximately 300 kg · ha −1 . Diet quality was assessed approximately every 15 d throughout each grazing period (three pastures · period −1 ) via collection of rumen extrusa throughout the 2-yr study. Ewe body weight was measured on and off-test for each grazing period. Diet extrusa samples for in vitro organic matter disappearance was less ( P = 0.03) for late summer than early summer grazing periods and equal to the spring period (62.9, 64.6, and 61.0 ± 0.90%, respectively for spring, early summer, and late summer grazing periods). In vitro neutral detergent fiber disappearance decreased ( P = 0.01) by 10.6 percentage units from early grazing to late grazing period in 2007, whereas no differences were observed in 2008. Ewe average daily gain did not differ between spring and early summer grazing periods and were greater ( P = 0.03) than the negligible body weight gains of the late summer grazing period. Total gain was 10.9 kg · ha −1 greater in 2008, and a quadratic response was measured for grazing period in 2007. Results indicate that deferment until early summer may be preferable so that stocking rates can be more accurately determined and animal performance is not diminished.

A newly developed rotating brush biofilm reactor was used for DCP, COD and toxicity removal from 2,4-dichlorophenol (DCP) containing synthetic wastewater at different feed COD, TCP concentrations and A/Q (biofilm surface area/feed flow rate) ratios. A Box-Wilson statistical experiment design was used by considering the feed DCP (50-500 mg l(-1)), COD (2000-6000 mg l(-1)) and A/Q ratio (73-293 m(2) d m(-3)) as the independent variables while percent DCP, COD, and toxicity removals were the objective functions. The experimental data were correlated by a quadratic response function and the coefficients were determined by regression analysis. Percent DCP, COD and toxicity removals calculated from the response functions were in good agreement with the experimental data. DCP, COD and toxicity removals increased with increasing A/Q ratio and decreasing feed DCP concentrations. The optimum A/Q ratio resulting in the highest COD (90%), DCP (100%) and toxicity (100%) removals with the highest feed COD (6000 mg l(-1)) and DCP (500 mg l(-1)) contents was nearly 210 m(2) d m(-3). (c) 2007 Elsevier Ltd. All rights reserved.

An experiment was conducted with 180 weaned red deer stags to determine the effects of diets varying in the ratio of concentrate:dried pelleted roughage (concentrate:roughage ratio) on growth performance and carcass traits in venison production. The animals were raised outdoors in nine denuded deer parks. Sixty animals (20 per park) were assigned, according to a completely randomized design, to one of three experimental diets with the following roughage:concentrate ratios: 75:25, 50:50 and 25:75. Results of a 140-day performance study revealed that live weight gain (LWG) was positively and linearly (P 0.05) on the content of C18:2 or the ratio of C18:2 to 18:3. When compared to the 75:25 ratio, the 50:50 roughage:concentrate diet resulted in a decrease in the content of conjugated linoleic (CLA) in carcass fat. A further increase in the proportion of concentrate caused an increase in carcass CLA, resulting in a significant (P < 0.01) quadratic response. This research indicates that a high level of grain feeding is an effective nutritional strategy to enhance growth performance of red deer. The negative impact of grain feeding on carcass fat was offset by desirable changes in the content of MUFA and CLA.

A model for prediction of bacterial spore inactivation was developed. The influence of temperature, pH and NaCl on the heat resistance of Bacillus stearothermophilus spores was described using low-complexity, black box models based on artificial neural networks. Literature data were used to build and train the neural network, and new experimental data were used to evaluate it. The neural network models gave better predictions than the classical quadratic response surface model in all the experiments tried. When the neural networks were evaluated using new experimental data, also good predictions were obtained, providing fail-safe predictions of D values in all cases. The weights and biases values of neurons of the neural network that gave the best results are presented, so the reader can use the model for their own purposes. The use of this non-linear modelling technique makes it possible to describe more accurately interacting effects of environmental factors when compared with classical predictive microbial models.

The purification of crude octacosanol extract from transesterified rice bran wax was carried out by molecular distillation (MD). A central composite rotate design (CCRD) was used in order to optimize the experimental parameters: distilling temperature and vacuum degree. Through the response surface methodology (RSM), the optimal MD conditions were determined and the quadratic response surfaces were drawn from the mathematical models. The results suggest that the distillng temperature and vacuum degree significantly affected both octacosanol content and yield of purified products, while the interaction of distilling temperature and vacuum degree was not significant in the two models. The optimum conditions of the purification of crude octacosanol extract were: distilling temperature 176.1 °C and vacuum degree 1.29 Torr. Optimal values predicted by RSM for the octacosanol content and yield of purified product were 25.93% and 51.09%, respectively. Close agreement between experimental and predicted values was obtained.

The frequency-dependent first dipole hyperpolarizabilities and their geometric derivatives have been calculated for HF, HCl, CO and LiF, using the quadratic response coupled cluster singles and doubles (CCSD) method and quadratic response density functional theory. Results obtained by means of different functionals have been compared with CCSD numbers, and, whenever possible, with experiment. Additionally, convergence of hyperpolarizabilities and their geometric derivatives in a hierarchy of correlation-consistent basis sets has been studied.

Two experiments were conducted to evaluate the Met requirement of Hy-Line W36 laying hens. In experiment 1 the temperature decreased to 26.7°C at night and reached 29.4°C during the day. In experiment 2 the temperature reached 29.4°C during the day and was not allowed to go below 28.6°C at night. Tunnel ventilation with no evaporative cooling was used in both houses. The Met requirement for egg production was obtained with 260.2 ± 4.0 and 239.4 ± 8.0 mg/d for 47.17 and 37.86 g egg content, for hens in experiments 1 and 2, respectively. There was a quadratic response for increased Met in both experiments. Maximum energy consumption was 271 and 225 kcal/d for hens in experiments 1 and 2, respectively. It is suggested that the lack of energy consumption was the cause of the low EP in experiment 2. The Met content greater than 0.30% in the diet in experiment 2 resulted in a decrease of 2.4% in egg production, 0.3 g in egg weight, and 1.6 g in egg content. This finding indicated that methionine was not the factor limiting performance.

Two experiments (Exp.) were conducted to determine the growth response of White Pekin ducks to inclusion of microbial phytase in finisher diet. In Exp. 1, 1-d-old male ducks (240 total) were reared in litter-floor pens and fed regular starter diet until 3 wk of age. At 3 wk of age, ducks were randomly divided into six groups of 10 ducks each and each group was fed one of four diets. Three finisher diets containing 16% CP and 0.18% available phosphorus (AP) without supplemental P were formulated with microbial phytase (Natuphos) added at 0, 750, or 1,500 phytase units/kg of diet. The fourth diet was a control finisher diet that was supplemented with dicalcium phosphate (DCP) to supply dietary AP of 0.41%. Group BW and feed intake were measured weekly to assess growth response. At 6 wk of age, leg bones (tibia, femur, metatarsus) from five randomly selected ducks were removed and analyzed for bone characteristics. In Exp. 2, a total of 120 ducks reared as in Exp. 1 were randomly divided into six groups of five ducks each and fed one of four diets. A basal finisher diet was formulated to contain 16% CP and 0.18% AP. Monosodium phosphate was added to the basal diet to give dietary AP levels of 0.18, 0.27, and 0.36%. The fourth diet was the basal diet supplemented with microbial phytase (750 phytase units/kg of diet). Ducks were fed these diets from 3 to 6 wk of age. At the end of the study, ducks were bled by cardiac puncture and blood plasma was analyzed for P concentration. Leg bones from all ducks were removed and analyzed for bone characteristics as in Exp. 1. Feed intake increased linearly with increased level of dietary phytase, whereas the weight gain response was quadratic only during the last week of Exp. 1. In Exp. 2, there was a quadratic response for weight gain due to dietary AP. Weight gain due to phytase (750 units) was not different from ducks fed diets at 0 or 0.18% AP. Plasma P concentration increased linearly as dietary AP increased. Plasma P levels of ducks fed phytase were similar to those of ducks fed 0.18% AP but lower than in ducks fed 0.27% AP. Estimates of AP resulting from the addition of 750 units of phytase to basal diet were 0.05 and 0.07% based on plasma P concentration and weight gain, respectively. Using regression analysis, the AP due to phytase effect in the diet was estimated to range from 0.06 to 0.08%. Results suggest that phytase can be used in finisher diets similar to the one used in this study for ducks from 3 to 6 wk of age to improve growth performance and leg bone development similar to ducks fed diets supplemented with P from inorganic sources.

The energy widths of the states of protons and antiprotons moving at arbitrary velocities in a homogeneous electron gas are evaluated within a quadratic response theory and the random-phase approximation (RPA). It is found that at low and intermediate velocities the Z13 correction causes a considerable reduction in the energy width of the states of antiprotons, though it is found to be less important than in the evaluation of both the stopping power and the energy-loss straggling.

Coherent double-plasmon mean free paths of swift electrons passing through an electron gas are studied, following a many-body perturbation-theoretic analysis. Both linear and quadratic response functions are evaluated in the full random-phase-approximation, and theoretical predictions for this second-order process are given as a function of the projectile velocity. The validity of previously studied analytical estimations is discussed, and comparison with experiments is made.

Multi-configuration quadratic response calculations with complete account of the spin-orbit coupling operator are performed to study the singlet-triplet absorption and emission spectra of the short ...

The stages involved in developing a predictive model are illustrated using data describing the effects of temperature (3–20°C), NaCl concentration (0.5–4.5% w/v) and pH (4.6–7.0) on the aerobic growth of Aeromonas hydrophila (cocktail of 6 strains). Optical density measurements using micro-titre plates were used as an initial screen, to determine the appropriate sampling times for viable counts to be made and to determine the approximate boundaries for growth. Growth curves were generated from viable counts and fitted using a modified Gompertz equation. Quadratic response surface equations were fitted to the log of lag and generation times, in response to the variables of temperature, NaCl and pH (in terms of hydrogen ion concentration). The effects of various combinations of these controlling factors are described. Comparisons between predicted growth rates and lag times from our response surface equations and other models for growth of a A. hydrophila, developed with viable count data and optical density measurements, are made, together with comparisons with data from the literature on the growth of this bacterium in foods.

Quadratic response function theory for self-consistent field and multiconfiguration self-consistent field wavefunctions have been used to calculate the Verdet constants for the nitrogen and acetylene molecules. The correlation contribution is oppositely directed in these two molecules and is important in obtaining close agreement with experimental results.

A theoretical and experimental investigation of the quadratic electro-optic effect in KDP is presented. By means of electromagnetic theory an eigenvector approach is employed to account for the quadratic electro-optic effect and also to estimate the contribution of the linear electro-optic effect to the quadratic response of the crystal. A simple method of measuring the coefficient g1212 in uniaxial crystals is described. Its value was found to be nearly two orders of magnitude smaller than the value measured earlier; however, it is comparable with the coefficient g1111 - g1122 reported recently.

We perform multiconfiguration quadratic response theory calculations of vibronically induced symmetry and parity forbidden 1 A 1g − 1 B 2u two-photon transitions of benzene. The following order of vibronic activity is found: ν 14 > ν 15 > ν 18 > ν 19 > ν 17 > ν 16 > ν 20 . The two-photon activity is crucially dependent on the description of the carbon skeletal motion in the ν 14 (b 2u ) mode, which gives a good illustration of the fact that two-photon spectroscopy can be used to derive information on vibronic motions and force fields. It is suggested that the so far unobserved ν 19 mode should appear in a high-resolution experiment. Two-photon polarization ratios are predicted and discussed.

Saw palmetto is a widely distributed shrubby monocot (palm) which occurs in dense stands in the coastal region of the southern USA. Selected areas of an existing stand in peninsular Florida were subjected to harvest intervals of 6, 12, and 24 months, with season of harvest also evaluated. Annual yields were 2–3 Mg ha −1 of foliage (fronds and petioles) dry matter. A quadratic response to harvest interval was obtained with annual foliage regrowth greatest at the 12-month interval. Plant vigour, as indicated by total non-structural carbohydrate (TNC) concentration, and yield per harvest increased linearly with increasing harvest interval. Chemical analyses revealed high extractive content, with 100 mg g −1 ethanol-benzene extract plus 90 mg g −1 ethanol extract. Lignin concentration was also high at 180 mg g −1 . The relatively low biomass yields and high concentrations of extractives and lignin indicate that saw palmetto does not have the desired characteristics for biomass energy conversion. Some potential may exist for specialty uses, such as starter fuel for waste combustion, due to availability and a highly combustible nature produced by the high extractive content.

To determine the influence of free fatty acid (FFA) content on the subsequent nutritive value of fats, the following were studied: tallow (FFA content of 138.4 g/kg) and tallow acid oil (FFA = 952.1 g/kg) in Experiment 1; palm oil (FFA = 57.5 g/kg) and palm acid oil (FFA = 917.5 g/kg) in Experiment 2; and soybean oil (FFA = 14.4 g/kg) and soybean acid oil (FFA = 683.4 g/kg) in Experiment 3. The two fats within each experiment were blended in proportions to give three mixtures of intermediary FFA content. Thus, each experiment investigated five fats by substituting them into a basal diet at the expense of the energy-yielding ingredients at rates of 40, 80, and 120 g/kg. Experimental diets were evaluated for apparent fat availability (AFA) of broiler chicks 1.5 and 7.5 wk of age. Corresponding values for fats were obtained through extrapolation of the linear response, or interpolation of the quadratic response, of AFA of diets. The AME was calculated as the product of fat AFA and gross energy. The degree of saturation had a pronounced effect upon the AME of fats; values decreased in the following order: soybean oil, tallow, and palm oil. Overall AME of fats linearly decreased with increasing FFA content, and the decrease was more pronounced with the younger birds. This rate of reduction appeared to be influenced by degree of saturation of the fat, but only with younger birds. Thus, AME of fats declined from 30.9 to 20.4, 27.7 to 14.8, and 38.5 to 33.1 MJ/kg (1 MJ = .239 Mcal) for young birds in Experiments 1, 2, and 3, respectively. Corresponding data for older birds were from 32.9 to 28.3, 32.3 to 27.5, and 38.5 to 35.1 MJ/kg. Effects of rate of inclusion of fats were minor and, generally, were confined to fats of a higher degree of saturation with greater contents of FFA evaluated with younger birds.

A study was carried out to determine the effect of a fat excipient on the bioavailability of amoxicillin tablets. Three formulations with a fat excipient content of 10, 20, and 30%, respectively, were administered to 15 healthy volunteers according to a Latin-square design. The excretion curves were characterized with the help of two parameters, namely, the quantity of drug excreted between 0-2 and 0-12 hr postadministration, respectively. The effect of the fat excipient content was quantified with the use of polynomials whose corresponding orders were given by the ANOVA. In the case of both parameters, a quadratic response to the fat excipient content was found. At the same time, a dissolution study was carried out using a previously established method. Here, the parameters used to characterize the dissolution curves were the quantities of dissolved drug in 30 and 180 min, respectively. Again, a quadratic response to the fat excipient content was observed in the case of both parameters.

Hypothesizing that experimental variables constituting an exposure situation act independently when in combination, we have reviewed two published data sets dealing with effects of metal mixtures on aquatic animals in order to assess the potential practical significance of factor interactions and their implication to the design of aquatic toxicity tests. Both data sets were re-analyzed using each of the following predictive models: (1) simple-additive, y = a x + b y , where y is an estimated response, a x is the observed response to a concentration of toxicant x when y = 0, and b y is the observed response to a level of toxicant y when x = 0; (2) linear-additive, y = a + b 1 x 1 + b 2 x 2 , in which y is a predicted value, a and b are pooled estimates involving all treatments in the exposure assay; (3) quadratic response, y = a + b 1 x 1 + b 2 x 2 + b 12 x 1 x 2 + b 11 x 1 2 + b 22 x 2 2 , which provides for estimates of interactions and non-linear effects. The relative effectiveness of each model in predicting joint effects of independent test variables was evaluated in terms of calculated mean-square error and goodness-of-fit ( R 2 ) values, as well as by how well predicted treatment effects compared with responses observed by original investigators. Our analyses show that in one case all three models provided similar estimates that closely approximated observed responses, despite the presence of a statistically significant two-factor metal interaction. In comparison, in the second instance, the quadratic response model was the most effective predictor and was appreciably better than the linear-additive model in terms of the calculated parameters. The simple-additive model on the other hand, tended to over-estimate treatment effects, by as much as 80% in some instances, and was least effective of the three models examined. Our re-analyses show that the working hypothesis is rejected, i.e. an assumption of factor independence is not to be accepted a priori . A sequential testing protocol is presented which would permit an evaluation of the existence of factor interactions.

Eighteen Hampshire crossbred wethers (45kg) were used in acompletely randomized experiment (20-day adjustment to basal, 11-day treatment and collection) to test the effects of supplemental boron (B) on fecal and urinary excretion, % digestion (apparent absorption), and % retention of Ca, Mg, K, and P. Supplemental B intakes of 75 (Trt 2) and 200 (Trt 3) mg/d were achieved by adding sodium borate to the corn silage-soybean meal basal ration, Trt 1 (B intake of 30 mg/d). When regressed against day, Ca digestion and retention tended to follow quadratic patterns for all treatments, decreasing until days 5 and 6 for supplemented and control groups, respectively, then increasing through the end of the trial. Significant fit to the quadratic response was observed for Ca digestion (P

An experiment was conducted to examine the effects of prebreeder protein intake on subsequent reproductive performance and to examine body weight, feed consumption, and body composition changes due to aging in Large White turkey breeder hens. One hundred twenty-nine Hybrid Large White turkey breeder hens were fed either 12, 15, or 18% CP diets (2,882 kcal ME/kg) during the prebreeder period from 24 to 32 wk of age. All hens were photostimulated with 15.5 h light/day and fed a standard 16% protein breeder ration from 32 to 55 wk of age. Prebreeder protein intake increased linearly as dietary protein increased. Treatments did not affect body weight, body composition, egg production, feed consumption, fertility, hatch of fertile eggs, or percentages of early or late dead. Body weight increased from 24 to 55 wk in a cubic response to age. Percentage of carcass moisture decreased, whereas percentage of carcass fat increased from 24 to 55 wk in a quadratic response to age. Prebreeder and breeder feed consumption were not significantly affected by treatment or age. This experiment is evidence that a 12% protein prebreeder ration is adequate for subsequent reproductive performance; observed effects of age on body characteristics agree with published data.

Rice and sugarcane are grown in rotation on organic soils in some areas of the Everglades. Both crops have shown positive agronomic responses to pre-plant applications of calcium silicate slag. The magnitude of the response, however, depends on the time at which the material is applied. Data from previous experiments were used to perform an economic analysis. Two timing applications of slag in the three production systems were analyzed: before rice, before cane, and before rice-cane rotation. Results indicate that, under the costs and prices assumed, it is more profitable to apply the slag prior to the rice planting when this crop is grown in rotation with sugarcane. The variables in the profit maximizing equations were translated into general terms to provide agronomists with the means for performing economic analyses of fertilizer responses in production systems involving a rotation. The resulting equations apply to cases where the application is done before the first crop to take advantage of residual effects and for which quadratic response functions are known.

The problem considered is that of estimating the optimum factor combinations in a quantitative multifactor experiment. Under the assumption that the response function is quadratic concave, solutions are obtained for the rectangular experimental region using the criterion of extended D-optimality. Some of the results are developed algebraically and others numerically. A method of deriving optimal designs is also indicated.

The solubilization of uranium from a finely ground ore material was investigated in leaching tests each lasting for about 24 h. Ferric iron, added as Fe 2 (SO 4 ) 3 or produced by prior microbiological oxidation of FeSO 4 , accelerated the rates of uranium leaching, as compared with those obtained with sulfuric acid or acidic ferrous sulfate. Pulp density and initial pH were also test variables. Yields of up to 100% uranium extraction were obtained within 24 h. Quadratic response surfaces were fitted to the experimental leach curves and confidence bands were calculated to assess the significance of the effects of pH, iron concentration, and pulp density on uranium solubilization. The general separation of the confidence bands indicated that each factor had a significant effect.

We derive a general expression for the photocurrent as a quadratic response to an incident photon field. As an application we apply the result to the independent particle model and further reduce the expression using perturbation theory to produce a result similar to Mahan's. The more general formalism can be used to demonstrate the importance of volume and surface effects and inelastic processes in photoemission from solids or liquids.

We derive expressions for the third-order elastic, piezoelectric, and dielectric constants, in terms of the interaction potential, and show that in fluorite structure, equal and opposite dipole moments under homogeneous strain develop. The presence of such latent polarisation is reflected in the dielectric response of the strained crystal.

The quadratic response of an electron gas to an external excitation is given in the self-consistent field framework.