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The Brunswik lens model typically represents a judge's accuracy using parameters derived from linear regression. This is not optimal if the judgment or the ecological criterion is dichotomous. Alternative approaches, modeling dichotomies using logistic regression, or linearizing judgments with confidence ratings, have not been compared with the same data. Four techniques for deriving lens model equation parameters were compared: (i) linear and (ii) logistic regression applied to dichotomous patient outcomes and judgments; (iii) linear regression with confidence-adjusted judgments but dichotomous patient outcomes; and (iv) a hybrid with a linear model of the confidence-adjusted judgments and a logistic model of the patient outcomes. Judgment accuracy (ra) was slightly higher with confidence adjustment of the categorical judgments. The logistic lens model accounted for a higher proportion of ra than the linear lens model; the confident-linear and hybrid lens models were intermediate. For up to a quarter of participants, different methods identified different cues as most important. Display condition differences in achievement ra and in lens model components are similar with all lens model methods. Each of the three alternative lens model equation methods improves on the linear lens model equation's decomposition of the accuracy of dichotomous judgments. Confidence adjustment improves achievement although it requires additional work from the subjects. The logistic lens model equation explains the highest proportion of achievement, but with a small stimulus set, it is more vulnerable to cue intercorrelations than either the linear or the confident linear lens model equation. Copyright © 2016 John Wiley & Sons, Ltd.

The coseismic surface uplift of the Longmen Shan (LMS) created an instantaneous topographic load over the western margin of the Sichuan Basin, where surface subsidence, decreasing eastward, has been measured using several methods, such as GPS, SAR and levelling. Using an elastic flexural model, we aim to interpret the coseismic surface uplift and subsidence, and constrain the effective lithospheric elastic thickness (Te) of the Sichuan Basin. Using different effective elastic thickness values for the Sichuan Basin, a series of subsidence curves were computed by the elastic flexure model equation for a broken elastic plate. The curves, produced by models using an effective elastic thickness of 30–40 km, provided the best fit to the general pattern of observed coseismic subsidence of the Sichuan Basin. However, the calculated subsidence (∼40–70 cm) at the front of the LMS is evidently lower than the observed values (∼100 cm), suggesting that the effective elastic thickness therein should be lower. These results indicate that the lithospheric strength may decrease westward from the Sichuan Basin to the LMS.

The migration model of contaminants from inks on paper packaging to food is developed based on the penetration of ink in paper and Fick's diffusion. The printed paper is divided as ink layer and paper layer. The mass transfer coefficient hm and partition coefficient KF,P in the interface between paper and food are considered in the model. The model equation is solved, and the migration expression is obtained by using the method of separation of variables. The fitting method is used between the model and the migration experimental data to obtain the diffusion coefficients and mass transfer coefficients for dibutyl phthalate (DBP) and acetyl tributyl citrate (ATBC). It is found that there exist linear relationships between ln(DP) and 1/T, and also between ln(hm) and 1/T for DBP and ATBC. The migrations of DBP in the paper sample 2402 at different temperatures and of ATBC in the paper sample 2401 at 50°C are predicted by using the model, and a good agreement is obtained between the model predictions and the migration experimental data. Copyright © 2014 John Wiley & Sons, Ltd.

Succinylation of corn starch was carried out through a dry process by using response surface methodology with four variables and five levels. A multi-linear regression method was chosen to fit the relationship between the response variable (y, the degree of substitution (DS)) and the four regressors (xi), i.e. concentration of sodium bicarbonate (x1), moisture content of reaction system (x2), reaction temperature (x3) and time (x4). A second-order model equation was obtained and then examined through experiments. The model adequacy was satisfactory as the coefficient of determination (R2) was 0.9103. The predicted optimal value for the DS was 0.150. The actual experimental results showed that DS and reaction efficiency (RE) were 0.151 and 93.25%, respectively. FTIR, XRD, and SEM were used to characterize the obtained succinate starches.

Inthispaper,weconsidertheproblemfordistributedoptimalcontrolofthegeneralizedGinzburg–Landumodelequation in population. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved, and the optimality system is established. Copyright © 2013 John Wiley & Sons, Ltd.

Farhad Gharagheizi, Poorandokht Ilani-Kashkouli, and Mehdi SattariThermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus,King George V Avenue, Durban 4041, South AfricaAmir H. MohammadiMINES ParisTech, CEP/TEP, Centre E´nerge´tique et Proce´de´s, 35 Rue Saint Honore´, 77305 Fontainebleau, FranceThermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus,King George V Avenue, Durban 4041, South AfricaDeresh RamjugernathThermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus,King George V Avenue, Durban 4041, South AfricaDominique RichonTechnical University of Denmark, Center for Energy Resources Engineering (CERE), Dept. of Chemical andBiochemical Engineering, DK-2800 Kgs. Lyngby, DenmarkThermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus,King George V Avenue, Durban 4041, South AfricaDOI 10.1002/aic.13938Published online November 9, 2012 in Wiley Online Library (wileyonlinelibrary.com).In this communication, a general model for representation/presentation of the liquid thermal conductivity of chemicalcompounds (mostly organic) at 1 atm pressure for temperatures below normal boiling point and at saturation pressure fortemperatures above the normal boiling point is developed using the Gene Expression Programming algorithm.Approximately 19,000 liquid thermal conductivity data at different temperatures related to 1636 chemical compoundscollected from the DIPPR 801 database are used to obtain the model as well as to assess its predictive capability. Theparameters of the model comprise temperature, acentric factor, critical pressure, normal boiling temperature, andmolecular weight. Nearly 80% of the data set (15,221 data) is randomly assigned to develop the model equation, 10% of thedata set (1902 data) is used to validate the model, and the remaining data (1902 data) were implemented to evaluate itspredictive power. The average absolute relative deviation of the model results from the DIPPR 801 data is less than 9%. Interms of simplicity and wide range of applicability, this empirical model shows acceptable accuracy.

Synthesis yields of organic reactions are one of the most important factors in ranking synthesis routes created by synthesis route design systems such as Transform-Oriented Synthesis Planning and Knowledge base-Oriented Synthesis Planning. If it is possible to predict the yields of synthesis reactions before starting experiments, one can easily determine an order of synthesis routes for experimental works. In the present study, the reaction profiles of the Curtius rearrangement with different substituents were calculated to generate an equation predicting experimental yields of this reaction. Reactions followed by the formation of isocyanates were also analyzed to consider the relationship between reaction times and experimental yields. A partial least squares (PLS) regression was used to correlate the experimental yields with the calculated activation energies, Ea(calc), together with experimental conditions such as dielectric constants of solvents, reaction times, and reaction temperatures as explanatory variables. Although the PLS regression using all the data gave very poor results, we succeeded in making a model equation with R2 = 0.887 using a modified data set. However, there is a conflict between the predictability and the interpretability on the reaction time. This discrepancy mainly comes from unnecessarily long reaction times in the experiments for azides with calculated Ea values of less than 33 kcal mol–1. To construct a good model equation for the experimental yields of the Curtius reaction, we have to use data sets obtained from within 90 min of the reaction for the PLS regression. Copyright © 2011 John Wiley & Sons, Ltd.

Pumpkin is a very appreciated vegetable for both unique sensory characteristics and significant content of substances with healthy effects. Very few “pumpkin-processed foods” with adequate shelf life are available on the market because of poor knowledge relative to its behavior during industrial processes. The possibility to reduce water activity (Aw) and pH of pumpkin samples by osmotic treatment in complex (quaternary) solution was studied by response-surface methodology (RSM). The reduction of pH and Aw until values recognized as safe for spore germination of Clostridium botulinum and Clostridium perfringens was respectively obtained without significant color degradation. Moreover, the modulation of the independent variables, carried out by using the best-fit equation, was aimed at prestabilizing pumpkin creams. PRACTICAL APPLICATIONS The poor knowledge concerning the behavior of pumpkins during industrial processing reduces their uses to produce a variety of “pumpkin food” with adequate shelf life. In this article, the possibility of applying an osmotic treatment in a complex (quaternary) solution in order to simultaneously obtain a reduction in water activity (Aw) and pH was presented. In addition, the utilization of model equation allows the simulation of osmotic dehydration, giving information on the process conditions usable to reach Aw and pH values recognized as risk threshold for spore germination of Clostridium botulinum and Clostridium perfringens.

The aim of this work was to optimize the acceptability of a natural passion fruit beverage using different levels of passion fruit pulp and sucrose, and to determine the equi-sweet concentrations of aspartame, sucralose, and a blend of 80% aspartame + 20% acesulfame-K for the optimized formula. A 22 central composite design was used to optimize the acceptability of the sucrose-sweetened beverage, which was accessed using a 9-point structured hedonic scale. Acceptability data were fitted to a second-order model equation provided in the design. The selected pulp content and sucrose concentration were, respectively, 2.5°Brix and 10%. Measurements of sweetness equivalence were accomplished using two types of sensory methods: magnitude estimation and difference-from-control tests. The concentrations of aspartame, sucralose and a blend of 80% aspartame + 20% acesulfame-K found as equi-sweet to 10% sucrose in the studied passion fruit beverage were, respectively, 0.043, 0.016 and 0.026%. PRACTICAL APPLICATIONS This article deals with formulating a new passion fruit juice beverage with different sweetener systems. The research makes a very important contribution to the literature on sensory science used on product development by demonstrating the necessity to study the substitution of sucrose by high-intensity sweeteners every time a formulation is changed or a new product is developed.

In order to determine the interference caused by chloride ions in Chemical Oxygen Demand (COD) measurements, synthetically prepared samples with various COD and chloride concentrations were analyzed. In addition, statistical analyses of the results were performed to calculate the real COD caused by the presence of organic substances in chlorinated wastewaters. The results of regression analyses showed good correlation between chloride concentrations and COD levels. A mathematical model is proposed on the basis of the statistical analyses. To calculate the real COD value of a wastewater sample, firstly, the chloride and interfered (or apparent) COD concentrations should be measured and then interference due to the chloride is calculated using the model equation proposed in this study. The real COD value was found by subtracting the COD due to chloride from the apparent COD. The reliability of the proposed model was also validated on real domestic wastewater samples, which were mixed with real seawater in various volumetric ratios to generate a range of salinity concentrations. These real saline samples gave good estimates of real COD with the results indicating that the proposed model can be used with acceptable confidence.

An electro-rheological (ER) fluid showing trembling shear behavior was fabricated with chitosan particles that had benzene, amine and azo-pendent side groups. This modified-chitosan dispersed suspension showed four regions in a plot of shear stress against shear rate at high electric field. We analyzed this specific behavior with our suggested model. The model was developed with the spring-damper model. Our suggested model equation treated the wide range of shear rate and specific behaviors of shear stress in ER fluids. In this study, we successfully obtained various ER fluids showing different behaviors just by changing the side functional groups of the particles in the ER fluids. All of the curves of the shear stress plotted against shear rate were fitted well by our spring-damper model.

The dependence of the pitting potential (E-p) of aluminum on chloride concentration, pH and the temperature of the solution was studied by the potentiodynamic method according to a statistical experimental design. The parameters of the statistical E-p model offered on the basis of Box-Wilson experimental design method were evaluated with the use of the experimental data. Comparison of the predicted values from the model with the observed values showed that the model is a good fit. From the model equation the most noble E-p value of -420 mV was obtained when Cl- ion concentration, temperature and pH of the solution were 57 ppm, 22 degrees C, and 8.3 respectively. Box-Wilson experimental design technique was proved to be applicable in modelling E-p of aluminum.

Summary A new model equation for drawing up water sorption isotherms, applicable over a wide range of water activity, has been suggested from which safe moisture levels for dehydrated food storage may be easily calculated.

Summary A study was made on the theoretical prediction of water activity (aW) in multicomponent aqueous solutions of strong electrolytes, in the range of aW of most interest for intermediate moisture foods (IMF). A simplified model proposed by Ross (1975) is tested against a rigorous model equation developed on the basis of recent statistical theories of electrolytes. As a result of this study a new simple and very accurate model equation is proposed for predicting aW in aqueous solutions of mixed strong electrolytes in the aW range of most interest to IMF.

In batch cooling crystallization, the supersaturation courses, obtained at different operating conditions, directly influence the crystallization kinetics. Therefore, the product sizes obtained strongly depend on the operating conditions. In order to control the supersaturation level during batch processes, a cooling model was introduced which included the seeding conditions, cooling rate, batch time, and crystallization kinetics. The cooling profiles, which maintain the different constant levels of supersaturation, were, therefore, predicted by numerically solving the model equation. Furthermore, the mean product sizes, obtained with the different specified cooling profiles, were simulated using the mass balance and the moment transformation of the population balance. Based on the simulation results, the relationship between the operating conditions, the supersaturation level, and product size was established. Hence, a strategy to select the appropriate operating conditions, in order to meet the required mean product size, was demonstrated. The results highlight that, by using the developed strategy, the batch cooling crystallization can be operated at optimal conditions, e.g., short batch time, slow cooling rate, or low seed loading. A potassium dihydrogen phosphate (KDP) system was selected for the case study.

Phytoplankton response to nutrients was examined with a 26-yr database from the Delaware Estuary. Biomassnormalized primary production did not increase linearly with increasing nutrient concentrations and instead showed saturation at comparatively low nutrient concentrations and decreased at high concentrations. To separate the effects of light availability and temperature on primary production from those of other environmental variables, we developed an empirical model of areal primary production. The model equation was obtained for the entire dataset and the effect of the residual variables was expressed as correction factors of observed primary production to the model estimates. The model accounted for 67% of variability of observed primary production overall, indicating that production of the estuary was mainly controlled by light availability and temperature. In contrast, a similar model applied to a Chesapeake Bay database had shown a poorer fit, indicating consistent light limitation in the Delaware Estuary and varying strengths of light and nutrient limitation in the Chesapeake Bay. The relationships between nutrients and correction factors for the Delaware Estuary showed that the model underestimates primary production at low and mid nutrient concentrations and overestimates it at high concentrations. The model fit and correction factors for five regions of the estuary indicate a high-nutrient, low-growth situation in the Delaware Estuary because of varying influences of light limitation, proportions of nutrients, and probably toxic contaminants in areas with large anthropogenic inputs—including high nutrients.

A series of blend films with different ratio of poly(4-vinylpyridine) (PVP) to lignin were subjected to dynamic DSC and TGA measurement under nitrogen atmosphere at various heating rates. DSC curves showed that the glass transition temperatures of these blends decreased with the increase of lignin content. TGA studies indicated that the lignin content produced obvious effect on the thermal stability of these blends. The kinetic model function of the thermal decomposition of these blends obeyed the Avrami-Erofeev model equation, g(α) = [-ln(1-α)]1/m. The degradation kinetic parameters were also obtained. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1875–1879, 2005

Relationships between effective mobility (m(eff)), calculated charge (Z(c)), and molecular weight (MW) are semi-empirically derived for pharmaceuticals using pressure-assisted capillary electrophoresis (PACE). We determined the m(eff) at 12 different pH points (2.0-11.4) of 66 pharmaceutical-like compounds ranging in MW from 79 to 825 g/mol. Plots of the observed m(eff) values versus Z(c)/MW(x ) (where x is a fractional coefficient) gave linear relationships. For anions, it was found that the best correlation (R(2) = 0.9666) exists when the fractional coefficient is equal to 0.4920, resulting in the equation m(eff) = 0.1853 (Z(c)/MW (0.4920)). For cations, the best linear relationship (R(2) = 0.9861) gave the equation m(eff) = 0.3888 (Z(c)/MW (0.6330)). The m(eff), Z(c)/MW(x) relationships were then applied to: (i) developing a technique for selecting an appropriate pH to achieve optimal separation of pharmaceuticals and (ii) determining the maximum charge of a molecule in the pH range of determination of negative log of the dissociation constants (pK(a)) by PACE, thus enabling the correct choice of model equation to be automated without structure analysis.

SUMMARY: Pharmacokinetic studies were performed in 10 stable kidney transplantation patients who received microemulsion formulation (Neoral®) of cyclosporine A (CsA) twice daily. No agents having pharmacokinetic effects on CsA had been used in these patients. The values of various basic pharmacokinetic parameters were similar to those reported in Western literature. The complete area under the blood concentration–time curve (AUC) of CsA for the duration of 12 h (12-h AUC) was determined using the linear trapezoidal rule from seven concentrations at 0, 1, 2, 4, 6, 8, and 12 h after CsA administration. The mean values of 12-h AUC were 4603.63 ± 344.61 ng h/mL. CsA concentrations at 2 h after dosing (not the trough levels) showed the best correlation with the complete AUC (r2 = 0.9322). The abbreviated AUC of CsA was calculated either by stepwise multiple linear regression analysis or by the linear trapezoidal rule from a few sampling time points. Using stepwise multiple linear regression analysis, which was used in calculating abbreviated AUC in all previous studies, the model equation that had the highest correlation and the lowest prediction error with the complete AUC was derived by using CsA concentrations at 2 and 8 h after dosing (12-h AUC = 4.262C2 + 8.390C8− 669.417; r2 = 0.9808, absolute prediction error = 3.97 ± 0.96). Two model equations derived using the linear trapezoidal rule provided the best correlation with the complete AUC: (1) The two time points selected model equation 12-h AUC = 4C2 + 5C8; r2 = 0.9780, absolute prediction error = 6.41 ± 1.22). (2) The three time points selected model equation 12-h AUC = 4C0 + 3C2 + 5C6; r2 = 0.9475, absolute prediction error = 5.00 ± 1.41). When different pharmacokinetic data sets were applied to the model equations derived using regression analysis, the values of coefficients and the constant of the regression equation had changed from the initial equation. Thus, new model equations will emerge every time the new data are applied. In contrast, the values of coefficients in the model equation calculated using trapezoidal rule were unaltered when tested by the new pharmacokinetic data set. Thus, the abbreviated AUC derived using the linear trapezoidal rule would be simpler than and superior to that obtained using stepwise multiple linear regression analysis in prediction of the complete AUC.

In this first article of a series a new method is introduced that enables the accurate determination of the power consumption in a shaking flask. The method is based on torque measurements in the drive and appropriate compensation of the friction losses. The results for unbaffled shaking flasks at low viscosities are presented after varying shaking frequency, flask size, filling volume, shaking diameter, and surface quality (hydrophilic and hydrophobic) of the inner flask walls. The order of magnitude of the values of power consumption in shaking flasks is equal to, or even higher than, the values typical for agitated tank bioreactors. A physically based model equation for shaking flasks is derived that introduces a modified power number and a resulting constant as the only fitting parameter. With this equation, the measured results are correlated with sufficient accuracy. For the first time, comprehensive data for the power consumption in unbaffled shaking flasks at low viscosity is available, giving a detailed picture of the influences of the different variables. © 2000 John Wiley & Sons, Inc. Biotechnol Bioeng 68: 589–593, 2000.

Considered is the feed-forward control design for an elastic heavy rope that is model by a quasilinear partial differential equation of hyperbolic type. The problem is solved by means of a flatness-based approach that involves the solution of a Cauchy problem associated with the model equation. Simulation results are given to illustrate the results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytical modeling and computer-aided solution of the model equation have been done to characterize the impedance properties of the resonant-cap circuit in terms of cavity parameters and frequency. The results of the modeling are in good qualitative agreement with the previous experimental observations, and can also provide a better physical insight regarding the important characteristics of the cap circuit and optimum performance of the cap-type IMPATT sources. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 400–403, 1997.

A film diffusional effect on the apparent kinetic parameters in packed-bed reactors containing the enzyme immobilized on the surface of a nonporous support was investigated. A comparison of the plug-flow reactor model equation, expressed analytically in terms of the apparent kinetic parameters, with experimental data showed that the conventional linearized plot based on the reactor model equation was essentially nonlinear. Simulations for the apparent kinetic parameters were made using the intrinsic kinetic parameters and volumetric mass-transfer coefficient previously determined from experimental data. Consequently, the apparent kinetic parameters were found to decrease monotonically with the increase of liquid flow rate. On the other hand, with the increase of reactor-inlet substrate concentration, these constants first increased, passed through a maximum, and finally decreased toward their respective intrinsic values. © 1997 SCI.

Effects of pickling conditions including salt concentration, pickling temperature, blanching time and CaCl₂ concentration on texture change kinetics of bamboo shoots were investigated during pickling process. The results showed that salt concentration, pickling temperature, blanching time and CaCl₂ concentration can affect the hardness of pickled bamboo shoots significantly. The hardness changes of bamboo shoots during pickling conform to the first‐order kinetic model. According to the improved first‐order kinetic classical equation, a modified kinetic model for the texture changes of bamboo shoots during pickling was established. All samples were suitably fitted with the kinetic model (R² > 0.9836), indicating that texture changes of bamboo shoots under different pickling conditions can be described and predicted by the established model equation. These research results can provide references for texture quality control of pickled bamboo shoots and other vegetables. PRACTICAL APPLICATIONS: Texture is an important evaluation factor of pickled vegetables and a key determinant of consumers' satisfaction to products. Effect of pickling conditions on vegetable texture during pickling is significant to control texture quality. In this study, texture changes of bamboo shoots under different pickling conditions were described and predicted through a modified kinetic model of hardness changes. Research results could provide references for texture quality control of pickled bamboo shoots and other vegetables, as well as improvement of pickling technique.

Die Gultigkeit einer vor kurzem vorgeschlagenen Modellgleichung fur die voraussage des Elastizitatsmoduls von Verbundwerkstoffen wird anhand der experimentellen Ergebnisse aus der Literatur nachgepruft. Dem eingefuhrten Modell liegt eine bestimmte Art der Verbundwerkstoffstruktur zu grunde, namlich diejenige mit spharoidalen einlagerungen. Somit werden nur Verbundwerkstoffe mit eingelagerten Partikeln betrachtet, wobei als Matrixwerk-stoffe Keramik, Glas und Polymer dienen. Der Vergleich theorie-Experiment zeigte eine gute quantitative Ubereinstimmung, insbesondere wenn die Einlagerungsform und orientierung die eigentlichen Gefugeparameter, die in dieser gleichung vorkommen genau bekannt waren. Diese Parameter konnen aus realen gefugestrukturellen Daten, ohne jegliches „fitting”, uber eine quantitative Gefugeanalyse sowie Stereologie bestimmt werden. Dank dieser Tatsache kann die vorgeschlagene Gleichung einen wesentlichen Betrag fur die praktische Anwendung leisten. Experimental Verification of a New Enquation for the Youngs Modulus of Composite Materials A recently proposed model equation for the prediction of Youngs modulus of elasticity of composite materials has been compared with extensive experimental data from the literature. As the derivation of the equation assumes a definite matrix-type microstructure with spheroidal inclusions, only composites containing particulate inclusions of different geometries were considered, including data on ceramic, glass and polymer matrix composites. A quantitative good agreement between theory and experiment was found, specially when the inclusion shape and orientation, being the microstructural parameters entering in the equation, were accurately known. The microstructural parameters involved in the equation can be obtained from real microstructural data via quantitative microstructural analysis and sterology, no fitting is involved. This fact makes the proposed equation substantial also for practical applications.

Several zero-order models for estimating gross N mineralization rate (M) using 15 N have been proposed. In a comparison of the Ms estimated with some experimentally determined values, different models sometimes gave substantially different results. Although the Ms are estimated by using changes in NH 4 -N (NH 4 - 14 N + NH 4 - 15 N) and NH 4 - 15 N, a comprehensive comparison based on model equations is lacking. I compared four zero-order models to clarify the extent of the difference in estimated Ms between models under different conditions of changes in NH 4 -N and NH 4 - 15 N. The ratio of M by one model equation to M by another is expressed by R = (AT 2 /AT 1 ) and r = (AL 2 /AL 1 ), where AT is NH 4 -N, AL is NH 4 - 15 N, and the subscripts 1 and 2 denote the initial and final values, respectively. Ranges of R and r are R > 0 and 0 r. The farther r is from 1, the more different the estimated Ms are. Estimation of M must be done with caution when r ≤ 0.2 since model differences increase uncertainties in estimates.

Calculation of the gas phase acidity of some hydrocarbons and nitrohydrocarbons is studied using direct (quantum mechanical) methods as well as a model equation, derived with the aid of correlation analysis, relating empirical values to computational molecular parameters. Agreement between directly calculated and empirical values is improved by correlation equations. The correlation analysis model is statistically significant and physically reasonable; gas phase acidity increases with acidity modelling parameters and decreases with basicity modelling parameters.

The relative stabilities of the unknown larger closo-borane dianions B(n)()H(n)()(2)(-) (n = 13-17), were evaluated at the B3LYP/6-31G level of density functional theory by comparing the average energies, E/n, and also by the energies using the model equation: B(n)()(-)(1)H(n)()(-)(1)(2)(-) + B(6)H(10) --> B(n)()H(n)()(2)(-) + B(5)H(9) (n = 6-17). Starting with the small closo-borane, B(5)H(5)(2)(-), the sequential addition of BH groups is represented by formal transfer from B(6)H(10) to build up larger and larger clusters. Most of the energies for these sequential steps are exothermic, but not for the B(12)H(12)(2)(-) to B(13)H(13)(2)(-) and the B(14)H(14)(2)(-) to B(15)H(15)(2)(-) stages. The cumulative total energies (DeltaH(add)) of these BH group additions, based on B(5)H(5)(2)(-) as the reference zero, tend to increase with increasing cluster size. DeltaH(add) indicates that the larger unknown closo-boranes B(13)H(13)(2)(-) to B(17)H(17)(2)(-) are more stable than B(9)H(9)(2)(-), B(10)H(10)(2)(-), and B(11)H(11)(2)(-); this agrees with E/n and with Lipscomb's earlier conclusion based on the PRDDO average energies. B(13)H(13)(2)(-), B(14)H(14)(2)(-), and B(15)H(15)(2)(-) are less stable than B(12)H(12)(2)(-), which has the lowest average energy on a per vertex basis among the closo-borane dianions. However, the total DeltaH(add) treatment indicates the larger B(16)H(16)(2)(-) and B(17)H(17)(2)(-) to be favorable relative to B(12)H(12)(2)(-), because of the larger number of vertexes. The formation of B(13)H(13)(2)(-) from B(12)H(12)(2)(-) is especially unfavorable. The further formation of B(14)H(14)(2)(-) and B(15)H(15)(2)(-) via BH transfer also is endothermic. These are not the only thermodynamic difficulties in building up large closo-borane dianions beyond B(12)H(12)(2)(-). The highly exothermic disproportionation of larger and smaller closo-borane dianions, e.g., B(12+)(n)()H(12+)(n)()(2)(-) + B(12)(-)(n)()H(12)(-)(n)()(2)(-) --> 2B(12)H(12)(2)(-) (n = 1-5), also indicate possible synthetic problems in preparing larger closo-boranes with more than 12 vertexes under condition where smaller boranes are present. All the larger closo-B(n)()H(n)()(2)(-) (n = 13-17) cluster exhibit "three-dimensional aromaticity", judging from the computed Nucleus Independent Chemical Shifts (NICS), which range from -30.9 to -36.5 ppm. The trends in NICS values are similar to the variations in the bond length alternations, Deltar. Thus, the qualitative relationships between geometric and magnetic criteria of aromaticity found earlier for the smaller clusters extends to the larger closo-borane dianions, B(n)()H(n)()(2)(-) (n = 13-17).

We study large time asymptotic behavior of solutions to the Cauchy problem for a class of non linear non local equations with dissipation. The asymptotics of solutions for a generalization of the Kolmogorov Petrovsky Piscounov equation, a model equation studied by Whitham, and an equation introduced by Ott, Sudan, and Ostrovsky is found

Basic characteristics of on-line extractive fermentation of organic acids were examined using a general model for the integrated process in order to illustrate the effects of various process parameters and operational modes on system performance. The strong pH dependence of both the fermentation kinetics and the extraction efficiency has been outlined and taken into account by inclusion of a model equation which predicts the pH profile. Simulation results using data from butyric acid fermentations show that our complete model system is adequate to evaluate different operational modes of the process, including simple batch fermentation, batch or fed-batch fermentation with extractive recycle, and continuous fermentation with extractive recycle. In the case where a second undesired acidic byproduct is also produced, our model predictions suggest that on-line extractive fermentation using a suitable solvent results in an effective gross separation of the two acids. On a examine les caracteristiques de base de la fermentation extractive continue d'acides organiques a l'aide d'un modele general pour le procede integre afin de decrire les effets de divers parametres de procedes et modes operationnels sur la performance du systeme. La forte dependance au pH de la cinetique de fermentation et du rendement de l'extraction est decrite puis prise en consideration par l'inclusion d'une equation de modele qui predit le profil de pH. Les resultats de la simulation qui utilisent des donnees de fermentation de l'acide butyrique montrent que notre systeme de modele complet convient pour evaluer les differents modes operationnels du procede, dont la fermentation discontinue simple, la fermentation discontinue ou a alimentation discontinue avec recyclage extractif et la fermentation continue avec recyclage extractif. Dans le cas ou un deuxieme produit acidique non desire est egalement produit, nos predictions de modele suggerent que la fermentation extractive continue utilisant un solvant adequat permet une separation brute efficace des deux acides.

The onset of the confinement transition in the early universe is studied within the Friedmann model. Exploiting a bag model equation of state for the deconfined matter, which is generalized to include also metastable states, the possibility of a mini-inflationary epoch is demonstrated. A criterion of metastability is derived to estimate parameters of this mini-inflation.

This short paper describes the use of Excel spreadsheet Solver facility for deriving estimates in a solute mixing model equation with more than one unknown.

The aim of this study was to perform reliable measurements of the diffusion (D) and perfusion ( D * ) coefficients and perfusion fraction (f) for normal liver using IVIM model. Six volunteers considered to have normal liver underwent DW imaging at 1.5 Tesla. A respiratory triggered diffusion‐weighted single‐shot echo‐planar MRI sequence was performed. The diffusion gradients were applied in the slice select direction and the b values used in the protocol were: 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 650 and 800 s / mm 2 . Diffusion decays for all regions of interest (ROIs) were analyzed using a Levenberg‐Marquardt nonlinear least‐squares fit to the IVIM model equation and the parameters D, f, and D * were obtained. Diffusion coefficients and perfusion fraction maps were calculated on a pixel‐by‐pixel basis as well and color overlaid onto the corresponding anatomical images ( b =0 s / mm 2 ). No significant difference in results was observed between the whole‐liver ROIs and the peripherally located 100 pixel ROIs. To within experimental error, all patients had the same values of D ( 1.041±0.105 mm 2 / s ), D * ( 54.97±14.92 mm 2 / s ), and f (43.11±4.06 %). This shows that there are no gradual variations across the liver, as long as areas that contain large blood vessels are excluded. By increasing both the number and the range of b‐values used in the protocol we were able to get more consistent results than previously reported in the literature. Correct values for D, D * and f for normal liver are critically necessary when evaluating any distribution of patients, normal or abnormal.

The paper sequently published in five parts deals with the logical interdependence between the technological process of silicon layer doping and the situation of its being empirically governed on the one hand, and its being theoretically explained on the other. The present first part of the paper concerns a brief description of epitaxial CVD silicon layer deposition and layer doping, the main controlling parameters of the latter, and how doping is governed by these parameters. The empirical basis knowledge linking the measuring control values of the process to specific layer properties in the form of control graphs, are transformed to more general empirical control equations of layer doping. Finally, representing the doping process analogous to cybernetic systems, an empirically based and nearly complete model equation is presented. In einer funfteiligen Veroffentlichung wird eine Ubersicht gegeben uber die logische Verknupfung des technologischen Prozesses der Dotierung epitaktischer Siliziumschichten und der empirischen Prozesfuhrung auf der einen und der theoretischen Erklarung des Prozesses auf der anderen Seite. Im ersten Teil der Veroffentlichung werden Schichtabscheidung und Schichtdotierung kurz beschrieben, sowie die Hauptsteuerparameter und ihre Wirkung auf die beeinflusten Schichteigenschaften erlautert. Die empirischen Basiskenntnisse, welche die Steuergrosen und die entsprechenden Schichteigenschaften in Form von Steuerkurven miteinander verknupfen, werden zu empirischen Steuergleichungen des Dotandeneinbaus verallgemeinert. Abschliesend wird aus der Analogiebetrachtung des Schichtdotierungsprozesses zu kybernetischen Systemen eine nahezu vollstandige empirische Modellgleichung gewonnen.

This paper presents a review of important investigations on axial mixing in the continuous phase in rotary disk contactors (RDC) and analyses the various literature data in terms of the flow number (DR N/ue) and a geometry factor Gf. A new model equation has been developed to represent continuous phase axial mixing in the RDC taking into account the factors affecting the recirculation flow within the compartment and the main flow through the compartment in terms of disk-Reynolds number and modified tube-Reynolds number respectively. A satisfactory expression for Gf has been obtained on the basis of the present proposed model and analysis of data of available literature and those of the present work, covering laboratory and industrial size columns of 10 different investigators varying from 3.5 cm to 218 cm dia involving 19 different column geometries. The following forms of generalized correlation for continuous phase axial mixing in RDC have been suggested. On fait, dans le present travail une revue des travaux les plus importants sur le melange axial de la phase continue dans les contacteurs a disques rotatifs (RDC); on presente aussi une analyse de divers resultats publies en fonction du nombre d'ecoulement (DR N/uc) et d'un facteur geometrique Gf. On a etabli un nouveau modele mathematique pour representer le melange axial en phase continue dans les RDC, en tenant compte des facteurs qui affectent l'ecoulement de recirculation dans chaque compartiment et l'ecoulement principal qui le traverse, en fonction respectivement du nombre de Reynolds pour les disques et du nombre modifie de Reynolds pour les tubes. On a obtenu une expression satisfaisante pour Gr, en se basant sur le modele propose, pour analyser les resultats publies, disponibles et ceux du present travail. Ces resultats englobaient les etudes faites par 10 experimentateurs differents, au moyen de colonnes de laboratoire et de colonnes industrielles et dont les diametres variaient entre 3.5 et 218 centimetres; ces colonnes avaient 19 formes geometriques differentes. On propose les types suivants de correlation generalisee pour le melange axial en phase continue dans les contacteurs a disques rotatifs

Phenomenological models of cosmic phase transitions are presented. We consider phase transitions (i) with fixed initial and final states or (ii) in the relaxation time approximation. The Friedmann equations are solved and the entropy production due to the non-equilibnum transition is calculated for a bag model equation of state. Numerical examples are given for the confinement transition, but the formulae presented apply directly to the GUT transition, too. Es werden phanomenologische Modelle fur kosmische Phasenubergange betrachtet. Wir untersuchen Phasenubergange mit festen Anfangs- und End-zustanden sowie die Anwendung der Relaxationszeitapproximation. Die Friedmanngleichungen werden gelost, und die Entropieproduktion vermoge der Nichtgleichgewichts-Phasenubergange wird fur eine Bagmodell-Zustandsgleichung berechnet. Die vorgestellten numerischen Beispiele betreffen zwar den Confinementubergang, der dargestellte Apparat ist jedoch auch direkt auf den GUT-Ubergang anwendbar.

A two-phase model of nuclear matter and quark gluon plasma is presented. Nucleon-nucleon interaction is treated by the mean field theory while the pion-nucleon interaction is taken into account explicitly by using the spectrum of pionic excitations in nuclear matter. Interactions in the quark-gluon plasma are included by first-order corrections to the bag model equation of state. We find large pionic excitations near the constructed phase border line in the fragmentation region. Eine Zweiphasenbeschreibung fur heise und dichte Kernmaterie und Quark-Gluonen-Plasma Ein Zweiphasenmodell fur Kernmaterie und Quark-Gluonen-Plasma wird vorgestellt. Nukleon-Nukleon-Wechselwirkungen werden im Rahmen der mean-field-Theorie behandelt, wahrend die Pion-Nukleon-Wechselwirkungen explizit durch Verwenden des Spektrums von pionischen Anregungen in Kernmaterie berucksichtigt werden. Wechselwirkungen im Quark-Gluonen-Plasma werden durch Korrekturen erster Ordnung zur Bag-Modell-Zustandsgleichung erfast. Wir finden starke pionische Anregungen nahe der konstruierten Phasengrenzlinie in der Fragmentationsregion.

Research was carried out on copolymerization of isoprene with maleic acid monoesters in the presence of free radicals (AIBN). The aim of the study was to observe the effect of the different monoesters obtained with normal alcohols of the aliphatic series: monoethyl maleate, monopropyl maleate, monobutyl maleate, monoheptyl maleate, monolauryl maleate, and monocetyl maleate. On the basis of reactivity ratios determined by the Fineman-Ross method and compared with the Mayo-Lewis method, all the systems studied are typical cases of heterocopolymerization. The parameter r1 is constant for this homologous series with the exception of the low terms. The experimental results agree with the ultimate model equation (with deviation at very high values of [M10]/[M20]), but not with the copolymer composition equation which considers the effect of the penultimate unity (penultimate model). Characterization of the sequential distribution is also presented (considering the effect of the terminal group only), and deviations of the experimental results are also discussed.

In der vorliegenden Arbeit wird die direkte Extraktion von Rapssamen behandelt. Es wurde der Einflus der Miscellenkonzentration im Bereich von 0 bis 60% auf den Extraktionsverlauf untersucht, d. h. auf die Tiefe der Extraktion und auf die Geschwindigkeit, mit der sich der Gleichgewichtszustand einstellt. Die Anwendbarkeit der abgeleiteten Modellgleichung wurde fur den gesamten untersuchten Konzentrationsbereich der Miscella bestatigt. Die Einstellungsgeschwindigkeit des Gleichgewichtszustandes wird mit der Konzentration der Miscella bis um das Funffache niedriger. Betrachtliche Veranderungen des Charakters des Prozesses konnten im hoheren Konzentrationsbereich der Miscella festgestellt werden (Umwandlung des Losungscharakters). Abschliesend wurde ein Algorithmus abgeleitet, der es ermoglicht, die fur die gewunschte Erniedrigung der Olkonzentration im Extraktionsgut erforderliche Anzahl der Extraktionsstufen mathematisch abzuschatzen. Investigations of Extraction of Oil Containing Raw Materials IV: Direct Extraction of Rape Seed In the present work the direct extraction of rape seed is delt. The influence of the miscella concentration in the range from 0–60% on the extraction process was investigated, that means on the degree of the extraction and the speed by which the equilibrium state is achieved. The applicability of the deducted model equation was confirmed for the whole range of concentration of the miscella which has been investigated. The speed of reaching the equilibrium state diminishes with the concentration of the miscella to the fivefold. Considerable changes of the process character were found in higher ranges of concentration of the miscella (change of the solution character). Finally an algorithm was deducted which made possible to tax mathematically the quantity of extraction steps which is necessary for the desired reduction of the oil concentration in the extraction commodities.

A hot-carrier simulator (H2-CAST) is developed using the “effective electron temperature model;” and with this simulator, the LDD structure is analyzed. This simulator is based on a 3-D device simulator, where the carrier motion in the oxide film is also considered. The model equation for the channel hot electron region and the avalanche hot electron region in the NMOS single-drain structure is evaluated. It is found that the model is valid for an analysis of the hot-carrier injection phenomena in both regions. From the analysis of the LDD structure, it is apparent that the injection of the avalanche hot-holes is responsible for the degradation of the device characteristic. This simulator is considered to be an effective tool in designing a device with an effective channel length Leff less than 0.8 μm.

On utilise des methodes d'echelles multiples pour calculer une equation d'evolution non lineaire pour une perturbation d'onde longue dont l'amplitude varie lentement dans l'espace et dans le temps

A mathematical model of the species-area relation is described for a group of limited species. This model is a modification of that proposed earlier (Kobayashi, 1975), being assumed that the limited species are expected to occur in a habitat under consideration. The model equation gives a sigmoid species-log area curve implying that few rare species are found in a group of species. The good agreement between observation and this model is exemplified with the data of plant and arthropod communities. The implication of parameters involved are examined in connection with those of the preceding model, and the underlying ecology of the model is discussed.

A one-dimensional model for the equations of motion of a “simple fluid” according to Noll is proposed. An exterior problem for the model equation is solved by means of a transform method.

A stochastic pure birth process, which describes pore blockage in a filtration process, has been coupled with the Carman-Kozeny equation to simulate the pressure buildup in deep bed filtration. It has been shown that the resultant one parameter model equation fits adequately the experimental data obtained under the straining dominated condition, and that available data obtained under the adhesion dominated condition can also be described by the model.