Single Parameter Equations Research Articles

Prediction Model of the Sound Speed of Seafloor Sediments on the Continental Shelf of the East China Sea Based on Empirical Equations

Based on the data of the acoustic and physical properties of seafloor sediments obtained on the continental shelf area of the East China Sea (ECS), prediction equations of the sediment sound speed based on single and dual parameters were established, and the correlation of the sound speed with physical parameters was discussed. The results show that the sediment sound speed (c) is strongly correlated with water content (w), density (ρ), void ratio (e), mean grain size (Mz) and median grain size (Md), and the coefficient of determination R2 of the empirical regression equation is generally greater than 0.80, while the empirical regression equation coefficient of determination R2 of the compression coefficient (a) and compression modulus (E) are slightly lower, with 0.79 and 0.73, respectively. The coefficients of determination of the dual parameter regression equations between sediment sound speed with physical property parameters are generally higher than those of the single parameter equations, which are all higher than 0.90 indicating better prediction performance. The sensitivity of the physical parameters to the sound speed was analyzed, and the result shows that the sequence of sensitivity from high to low influence on sediment sound speed is void ratio, density, compressibility coefficient, median grain size and mean grain size. The prediction equations established in this study are a good extension and supplement to marine geoacoustic models and is of great significance for obtaining the acoustic properties of the seafloor sediments on the shelf of the East China Sea.

Magnetic field tuning of mechanical properties of ultrasoft PDMS-based magnetorheological elastomers for biological applications

We report tuning of the moduli and surface roughness of magnetorheological elastomers (MREs) by varying applied magnetic field. Ultrasoft MREs are fabricated using a physiologically relevant commercial polymer, SylgardTM 527, and carbonyl iron powder (CIP). We found that the shear storage modulus, Young’s modulus, and root-mean-square surface roughness are increased by ∼41×, ∼11×, and ∼11×, respectively, when subjected to a magnetic field strength of 95.5 kA m−1. Single fit parameter equations are presented that capture the tunability of the moduli and surface roughness as a function of CIP volume fraction and magnetic field strength. These magnetic field-induced changes in the mechanical moduli and surface roughness of MREs are key parameters for biological applications.

Estimation of Liveweight from Body Measurements through Best Fitted Regression Model in Dezhou Donkey Breed

Dezhou donkey is an excellent local hide, meat and milk breed in Shandong Province. To accelerate the speed of breeding, reproduction and conversation, correlation and multiple regression analysis between body weight (BW) and body size of Dezhou donkey rearing under intensive farms was made by SAS 9.4 software (Statistical Analysis for Windows). A total of 162 donkeys of both gender of age 2 ~ 10 years old were used to investigate the relationships between BW and body dimensional traits (cm) including height of withers, body length; thoracic depth, thoracic girth (TG), thoracic width (TW), circumference of cannon bone (CB), height of rump, rump length (RL) and rump width (RW). The results showed that BW and body measurements have positive and great correlations with R2 value ranged from 0.58 to 0.88 (P <0.01). The R2 values from the single-parameter equations showed that the TG was highly related to BW (0.72, P < 0.01). The stepwise regression equations were applied to obtain the best prediction equations, and the results indicated that the prediction accuracy for BW was improved with the inclusion of more body measurement variables. The “best fit” models were: BW (kg) = 1.88 × TG + 1.27 × BL + 2.55 × TW + 4.61 × CB + 2.18 × RW + 1.78 × RL - 422.8 (R2 = 0.906, P < .01). The predicted BW from the present equations showed the nearest value to the real BW (R2 > 0.94, P < .01). In addition, the equations derived to predict the BW of donkeys in Britain, Morocco were less satisfactory for use with the present Dezhou donkey breed because they overestimated or underestimated the BW due to the different donkey breed.

Solvent, structural, quantum chemical study and antioxidative activity of symmetrical 1-methyl-2,6-bis[2-(substituted phenyl)ethenyl]pyridinium iodides

15 symmetric 1-methyl-2,6-bis[2-(substituted phenyl)ethenyl]pyridinium iodides were synthesized in this work. Their structures were characterized using IR, 1H and 13C NMR, and UV–Vis spectroscopy. DFT calculations indicated that s-trans/s-trans conformation prevail in all compounds. The effects of specific and non-specific solvent–solute interactions on the UV–Vis absorption maxima shifts were evaluated using linear solvation-free energy relationships (LSER), i.e., Kamlet–Taft and Catalan models. A linear free energy relationship (LFER) in the form of single substituent parameter equations (SSP) was used to postulate quantitative structure–property relations of substituent effect on NMR data. TD-DFT results showed dependence of electronic transition on the substituent effects. The push–pull character of these compounds was analyzed by differences in 13C chemical shift of the ethylenic double bond in 2- and 6-positions of cross-conjugated with pyridinum central ring. Also, the quotient of the occupations for the bonding π and anti-bonding π* orbitals of this bond was considered. Good correlations of the selected parameter between double bond lengths with π*/π and 13C chemical shift differences of the bridging group proved them to be adequate descriptor of push–pull character. Synthesized compounds were screened for the antioxidant activity, using 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) radical methods, and results demonstrated moderate antioxidant potential.

Single-Parameter Thin-Layer Drying Equations for Long-Grain Rice

Abstract. The use of multiple parameters in thin-layer drying equations makes it difficult to compare and quantify the impact of drying air temperature, relative humidity, and other factors on the drying characteristics of an agricultural crop. In this study, two single-parameter equations are proposed to quantify thin-layer drying characteristics of contemporary long-grain rice cultivars grown in the Mid-South U.S. Drying runs were first performed to obtain drying curves for cultivar ‘Roy J’ under 18 air conditions; several drying equations were evaluated for their fit to each drying curve. The proposed single-parameter equations (modified Page equation and infinite-series diffusion equation) described the experimental drying data very accurately; the root mean square errors in moisture ratio obtained for the modified Page and infinite-series diffusion equations varied in the ranges of 0.2 to 1.4 and 0.3 to 1.5 percentage points, respectively. The dependence of drying air temperature and relative humidity on drying parameters of the modified Page and infinite-series diffusion equations was described by second-order polynomial regression equations. The impact of harvest moisture content on the drying characteristics of rice was observed to be negligible. The validity of the developed single-parameter equations was also evaluated for five other long-grain rice cultivars; for these cultivars, the maximum errors in the moisture ratio prediction using the modified Page and infinite-series diffusion equations were 2.9 and 3.4 percentage points, respectively. This study provides thin-layer drying data for contemporary rice cultivars in the Mid-South U.S. The resulting thin-layer drying equations are expected to improve the accuracy of deep-bed drying models. While the proposed single-parameter equations were tested only for long-grain rice, the methodology presented in this research could be used to develop similar single-parameter thin-layer drying equations for short-grain and medium-grain rice, as well as other agricultural crops. As such, these equations could be readily used in quantifying the impacts of air and rice variables on drying rates. Keywords: Mathematical modeling, Rice, Thin-layer drying.

Accurate eGFR reporting for children without anthropometric data

IntroductionReporting estimated glomerular filtration rate (eGFR) instead of serum concentrations is advised in current guidelines. Most creatinine-based eGFR equations for children require height, a parameter not readily available to laboratories. Combining height-dependent creatinine- and cystatin C-based eGFR improves performance. Recently, a height-independent creatinine-based eGFR equation has been developed. AimTo compare the combination of height-independent creatinine- and cystatin C-based equations with a combination of equations using anthropometric data. MethodsRetrospective analysis of 408 pediatric inulin clearance studies with simultaneous height, creatinine, cystatin C and urea measurements. eGFR calculation using the recalibrated Schwartzcrea (height-dependent), FASage (height-independent) and the Schwartzcys equation. The means (Schwartzcrea+Schwartzcys)/2 and (FASage+Schwartzcys)/2 were compared with the CKiD3 equation incorporating cystatin C, creatinine, urea, height and gender in terms of %prediction error and accuracy. ResultsAll three single parameter equations performed similarly (P30 accuracy around 80%). (FASage+Schwartzcys)/2 (P30 89.2%) and (Schwartzcrea+Schwartzcys)/2 (P30 89.0%), performed comparably to CKiD3 (P30 90.0%). If the difference between the creatinine- and the cystatine C based eGFR was <40%, P30 accuracy of the mean exceeded 90%. ConclusionCombining the height-independent FASage and SchwartzCys equations substantially improves accuracy and performs comparably to height-dependent equations. This allows laboratories to directly report eGFR in children.

Taper functions and merchantable timber for temperate forests of northern Mexico

Taper functions are required in modern forest management in estimation of the end forest products, to be classified for their life time in the environment. Based on a sample of 1640 trees of 10 species measured in volume, biomass and taper project on Mexico’s northern temperate, mixed, uneven-aged coniferous forests, 12 stem profile taper functions were fitted in order to select the equation that provides better diameter estimates at commercial tree height. Although several equations fitted better specific tree species, the Newnham (1990) equation consistently yielded better diameter estimates at any length of the stem for all studied species. The confidence intervals on the Newnham (1990) equation parameters showed that each species has an unique stem profile and, therefore, single parameter equations are reported. Because of lack of analytical integration, the recommended taper equation (when numerically integrated) provided compatible, unbiased total bole volume when contrasted to conventional timber volume assessments. Data for 637 circular, 1/10 ha, plots from temperate forests of Central Durango, Mexico estimated a mean of 135 m3 ha-1, of which 18, 59, 30, and 17 m3 ha-1 could be classified as poles, sawn wood, plywood and secondary forest products, respectively. This information can be used for the planning of the forest industry to optimize forest products derived from timber harvesting, as well as for estimating other environmental components.

Improved parameter estimation by noise compensation in the time-scale domain

It was shown recently that parameter estimation can be performed directly in the time-scale domain by isolating regions wherein the prediction error can be attributed to the error of individual dynamic model parameters [1]. Based on these single-parameter equations of the prediction error, individual model parameters error can be estimated for iterative parameter estimation. An added benefit of this parameter estimation method, besides its unique convergence characteristics, is the added capacity for direct noise compensation in the time-scale domain. This paper explores this benefit by introducing a noise compensation method that estimates the distortion by noise of the prediction error in the time-scale domain and incorporates that as a confidence factor to bias the estimation of individual parameters error. This method is shown to improve the precision of the estimated parameters when the confidence factors accurately represent the noise distortion of the prediction error.

A single parameter representation of hygroscopic growth and cloud condensation nucleus activity – Part 2: Including solubility

Abstract. The ability of a particle to serve as a cloud condensation nucleus in the atmosphere is determined by its size, hygroscopicity and its solubility in water. Usually size and hygroscopicity alone are sufficient to predict CCN activity. Single parameter representations for hygroscopicity have been shown to successfully model complex, multicomponent particles types. Under the assumption of either complete solubility, or complete insolubility of a component, it is not necessary to explicitly include that component's solubility into the single parameter framework. This is not the case if sparingly soluble materials are present. In this work we explicitly account for solubility by modifying the single parameter equations. We demonstrate that sensitivity to the actual value of solubility emerges only in the regime of 2×10−1–5×10−4, where the solubility values are expressed as volume of solute per unit volume of water present in a saturated solution. Compounds that do not fall inside this sparingly soluble envelope can be adequately modeled assuming they are either infinitely soluble in water or completely insoluble.

Single-Parameter and Two-Parameter Rheological Equations of State for Nondilute Emulsions

The existing viscosity−concentration equations for concentrated emulsions of nearly spherical noncolloidal droplets are first reviewed. The equations of emulsion relative viscosity ηr vs volume fraction of dispersed-phase φ existing in the literature are characterized as single-parameter equations because viscosity ratio (ratio of dispersed-phase viscosity to continuous-phase viscosity) is the only parameter in the equations. The equations are evaluated in light of a large body of experimental data for concentrated emulsions, covering a broad range of viscosity ratios. The existing equations generally give good predictions of relative viscosity only at low values of φ (φ < 0.2). Several new equations are proposed and evaluated with experimental data. The proposed ηr vs φ equations are characterized as two-parameter equations because they contain two parameters, namely, the viscosity ratio and φm, the maximum packing volume fraction of droplets. The proposed equations generally show good agreement with the experimental data.

Correlation of ground and excited state dissociation constants oftrans-para- and ortho-substituted cinnamic acids

The ground and excited state dissociation constants oftrans- para- and ortho-substituted cinnamic acids have been determined in 50% (v/v) dioxan-water mixture at 30°C using the Forster cycle. The measured dissociation constants are analysed in the light of single and dual substituent parameter (DSP) equations. Excited state dissociation constants ofp-substituted cinnamic acids correlate well with the exalted substituent constants. The DSP method of analysis shows that resonance effect is predominant relative to inductive effect in the excited state than in the ground state for the para-substituted acids. The single parameter equation gives poor correlation for the ortho-substituted acids. However, the DSP analysis shows fairly good correlation. The inductive effect is predominant relative to the resonance effect in the excited state than in the ground state

A TELLURIUM-125 STUDY OF LITHIUM ALKANE- AND ARENETELLUROLATES

Abstract Lithium alkanetellurolates and lithium arenetellurolates were prepared by reduction of ditellurides with lithium in THF. Tellurium-125 chemical shifts of lithium alkanetellurolates, RTeLi (R = Me, Et, n-Pr, i-Pr, n-Bu, i-Bu, s-Bu and t-Bu) and lithium arenetellurolates, R'-C6H5-TeLi (R' = para-H, Me2N, MeO, Me2CHO, Me, C6H5O, F, C1, Br, Me3Si; R' = meta-MeO, EtO, Me2N, Me, F; R' = ortho-MeO and Me2N) were determined. Chemical shift trends for alkanetellurolates are compared with those previously reported for dialkyl ditellurides, dialkyl tellurides and bis(alkyltelluro)methanes. The 125Te shifts of alkanetellurolates plotted versus 77Se shifts of alkaneselenolates gave an excellent linear correlation. The substituent effects for para- and meta-substituted arenetellurolates are correlated with single- and dual-substituent parameter equations. Single parameter equations gave a poor fit, whereas dual-substituent parameter equations produced good linear correlations. The dual-substituent parameter equation of Taft is slightly better than the two-parameter equation of Swain and Lupton in correlating 125Te shifts of substituted arenetellurolates.

A BOLTZMANN-LIKE MODEL FOR THE SIZE DISTRIBUTION OF BUBBLES OR DROPLETS IN A WELL MIXED DISPERSION

Abstract Results of the named model are derived and shown to compare favorably with other single parameter equations. Also, the distribution is shown to possess the unusual property of stereological in variance.

Law of Deformation of Cured Rubber

Abstract Consideration is made in this article of the uniaxial stress and compression deformation of vulcanized rubber, for which there exists a sufficient amount of accurate experimental data. One of the present authors established a considerable while back that for lattice polymers (vulcanized rubbers) in the coordinates σ (true stress) and ε (deformation) , the equilibrium curves for stress in the range 100 to 200% are expressed by practically straight lines. Furthermore, this behavior was confirmed in a number of our investigations based on more accurate methods of measurement (cf. Reference 2), and also in a number of foreign papers. (Note 1. The stress is regarded in relation to the actual cross-section of the specimen of deformed rubber, the deformation in relation to the initial length of the specimen. Note 2. For comparison of single-parameter formulas with experience the experimental data are presented each time in coordinates such that a straight line corresponded to the formula in these coordinates. For these coordinates we selected the stress σ and the “generalized coordinate” of deformation ε0, which is a different function of the multiple of stress A in the various single-parameter equations.) Within the limits of scatter of the experimental data the equilibrium curves for uniaxial deformation below the limit of proportionality (100–200% with stress and 20–30% for compression) are expressed by the following single-parameter law: