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The article studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers, the problem is reduced to solving a nonlinear integro-differential equation for the film thickness deviation from the undisturbed level. The nature of branching of wave modes of the unperturbed flow with a flat interface has been investigated. The steady-state traveling solutions with wave numbers that are far enough from the neutral ones, have been numerically found. Using methods of stability theory, the analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that, similarly to the case of the falling film, this model equation has solutions in the form of solitons-humps.

The periodic table of chemistry contains all synthetic and naturally occurring elements. The elements are arranged in seven horizontal periods from left to right with increasing atomic number. The periodic table is divided into two groups: metals and nonmetals, within elements moving from left to right, the elements get less metallic, culminating in nonmetals on the far right side of the table. Further, the elements are also arranged in eight vertical columns or groups for those with similar physical and chemical properties. A model equation has been developed based on the 8-group and the 7-periods from which trends of elements has been calculated. Among the trends in the periodic table that were calculated are ionization energy, atomic size and effective nuclear charge. It has been discovered that the calculated theoretical values from the model equation rhyme well with the actual values for each element with few exceptions.

The aim of this work was to model, optimize, and compare fluoride removal by LaFeO3-NPs using the RSM (Response Surface Methodology), ANN (Artificial Neural Network), and GA (Genetic Algorithm) techniques.The input variables considered were pH, time, temperature, LaFeO3-NPs dose, and fluoride. The CCD (central composite design) plan was exercised for the analysis of RSM, and ANN to determine their capabilities of prediction of the response. Their performances were evaluated using the regression coefficient (R2), RMSE, SEP, and the AAD. Also, RSM and GA were used to maximize the response and their optimum conditions evaluated. Both RSM (R2 = 0.9970, AAD = 0.00001, RMSE = 0.0037, SEP = 0.0042) and ANN (R2 = 0.9919, AAD = 0.00044, RMSE = 0.0066, SEP = 0.0074) gave high degree of accuracy. The model equation obtained for the process through RSM was adequate. The GA and RSM gave very close values for the optimization of the fluoride reduction process; RSM gave optimum fluoride removal of 96.35% (at pH 8.6, time = 75.03 min, temperature = 34.9 °C, dose = 0.225 g, and concentration = 23.68 mg L−1) while the GA gave 96.30% (at pH 10, time = 120.39 min, temperature = 28.41 °C, dose = 1.030 g, and concentration = 16.31 mg L−1). But from the confirmation experiments, RSM and GA data gave 96.52% and 96.63%, respectively. RSM, ANN, and GA were capable of modeling and optimizing the elimination of fluoride using LaFeO3-NPs.

We explore the implications of the generalized uncertainty principle (GUP) on the nuclear equation of state (EoS) and on the structure of neutron stars. Two approaches of GUP are used: the quadratic GUP approach, satisfying minimal length and the linear GUP approach, satisfying both minimal length and maximal momentum. The resulting invariant phase space volumes from these GUP approaches are applied to the [Formula: see text]-[Formula: see text] or Walecka model, serving as a starting point for neutron matter in the relativistic mean field theory. We find that linear GUP increases the range of energy densities corresponding to instabilities in the [Formula: see text]-[Formula: see text] EoS, while quadratic GUP decreases it. A stable EoS was constructed from the GUP-modified EoS via Maxwell construction, and this was fed into the Tolman–Oppenheimer–Volkoff equations and the mass–radius relation of neutron stars was obtained. We observe linear GUP to decrease both the maximum mass and limiting radius of the neutron star, while shifting the whole mass–radius relation to the low-radius regime. Meanwhile, quadratic GUP increases the maximum mass and limiting radius, and the mass-radius relation is shifted to the high-radius regime. The effects that are observed for both GUP modifications in the EoS and mass–radius relations get more prominent as we increase the values of the still unknown GUP parameters.

The purpose of this study is to verify the mediating effect of self - management on the relationship between fencing player "s Fighting Spirit and sport concentration. For this purpose, belonging to college and unemployment team 177 fencing athletes were selected as subjects. The collected data were analyzed using SPSS 21 and AMOS 18 programs, and Exploratory factor analysis, Confirmatory Factor Analysis, reliability analysis, frequency analysis, correlation analysis, and structural model equation were performed. All significance levels in this study were .05 Respectively. The results: First, there was a statistically significant positive correlation between Fighting Spirit and self - management, sports concentration. Second, self - management a mediating role in the relationship between the Fighting Spirit and sports concentration.

Linear profiling of horses has been used in the Czech Republic for 20 years but without preceding genetic evaluation (predictions of breeding values). The main objective of this study was to estimate genetic parameters of linear profiling of the population of sport horses in the Czech Republic. A linear profiling database was obtained for the period 1997–2015 and it comprised 12 455 horses in total and 25 traits were evaluated. The model equation included fixed effects of gender, horse age, place, classifier*year and individual. Genetic parameters were computed by a single-trait BLUP-AM analysis. The range for heritability coefficients were between 0.05 and 0.31 for linear type traits and between 0.43 and 0.67 for measured traits. Genetic correlations were computed by a two-trait analysis between the evaluated traits and they were in the range of 0.0–0.93. The estimated genetic parameters suggest that a selection programme can be based on the genetic evaluation of linear profiling, which will lead to an improvement in conformation traits according to the defined breeding objectives.

The upwards flow of particles in an Upflow Bubbling Fluidized Bed (UBFB) is studied experimentally and modelled from pressure drop considerations and energy loss equations. For Geldart group A powders tested, the upward solid flux, G s , in the tube can be expressed in terms of the applied superficial gas velocity, the free fall (terminal) velocity of the particles during their hindered settling, KU t , the pressure exerted at the base of the conveyor tube, and the tube length. The model expression $${{\boldsymbol{G}}}_{{\boldsymbol{s}}}=\frac{{\boldsymbol{\Delta }}{\boldsymbol{P}}}{({U}_{{\boldsymbol{g}}}-{\boldsymbol{K}}{{\boldsymbol{U}}}_{{\boldsymbol{t}}}){\boldsymbol{+}}\frac{{{\boldsymbol{K}}}^{{\boldsymbol{2}}}{\boldsymbol{g}}{\boldsymbol{L}}}{({{\boldsymbol{U}}}_{{\boldsymbol{g}}}-{\boldsymbol{K}}{{\boldsymbol{U}}}_{{\boldsymbol{t}}})}}$$ G s = Δ P ( U g − K U t ) + K 2 g L ( U g − K U t ) can be used for design purposes, with K, the correction factor for hindered settling of the particles, approximately equal to 0.1 at high G s -values, but a function of the solids fraction in the upward conveying. The energy efficiency of the system increases with increasing U and Gs. The model equation was tentatively applied to predict the effects of particle size, tube length and operation in Circulating Fluidized Bed mode. It is demonstrated that the UBFB is an efficient and flexible way of transporting particles upwards, with limited particle attrition or tube erosion due to the low gas velocity applied.

Spectroscopic methods are employed to determine the experimental solubility of 3,4,5-trimethoxybenzoic acid dissolved in propylene carbonate, in 19 alcohol, in 4 alkyl ether, in 5 alkyl alkanoate and in 4 alkoxyalcohol solvents at 298.2 K. 3,4,5-Trimethoxybenzoic acid is believed to exist predominantly in monomeric form in each of the 34 organic solvents studied. The measured solubilities in 29 of the organic solvents are used to calculate the Abraham model solute descriptors for the monomeric form of 3,4,5-trimethoxybenzoic acid. Solubilities in the remaining five solvents could not be used in the solute descriptor computations because Abraham model equation coefficients are not available for these solvents. The derived solute descriptors back-calculated the observed solubility data to within 0.10 log units.

EDXRF analysis is typically carried out under vacuum to reach the optimum performance, particularly for low Z elements. However, when analyzing PM10 loaded filters, the application of vacuum is responsible for the mass loss of volatile components preventing further analysis on the same sample. Alternatives include EDXRF analysis in helium (He) or air medium. The standardless EDXRF analysis using He and air analytical medium was evaluated against analysis under vacuum. The spectral peak intensities and quantification results of EDXRF using He and air medium were compared to the ones using vacuum. The intensities were found to be almost identical except for Cl, Mo and Ba. The quantification results were similar with a few exceptions. In addition to standardless analysis, the external calibration using standards analyzed by ICP-MS was also tested. The measurement uncertainty of standardless EDXRF analysis using He and air medium was estimated by a pre-established model equation and by a field study. The model equation was confirmed by the field study for many elements, except for Ca, Mg, Ni and Cr. The data quality objective (DQO) of the European Directive for Air Quality was met for Pb by the standardless EDXRF analysis using He and air medium, and for As by the external calibration. For Ni and Cd, none of the quantification methods could meet the DQO, most likely due to low loadings of those elements on the studied PM10 samples. It was demonstrated that analyzing air filters by the standardless EDXRF analysis using He and air medium is a valid alternative to vacuum.

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

We introduce delay dynamics to an ordinary differential equation model of tumour growth based upon von Bertalanffy's growth model, a model which has received little attention in comparison to other models, such as Gompertz, Greenspan and logistic models. Using existing, previously published data sets we show that our delay model can perform better than delay models based on a Gompertz, Greenspan or logistic formulation. We look for replication of the oscillatory behaviour in the data, as well as a low error value (via a Least-Squares approach) when comparing. We provide the necessary analysis to show that a unique, continuous, solution exists for our model equation and consider the qualitative behaviour of a solution near a point of equilibrium.

The adsorption behaviour of safranine O and malachite green oxalate dyes on activated carbon as a function of temperature for a fixed initial concentration was investigated at T = (303, 313 and 323) K and p = 0.1 MPa through adsorption isotherms and their thermodynamic parameters ΔGo, ΔHo and ΔSo. The isotherms were correlated with a new model based on the principle of phase equilibrium. The new model equation comprising of 4 adjustable parameters correlates the isotherms as a function of temperature, sorbate melting temperature. The overall deviation between the experimental and the correlated results was less than 6.85% in averaged absolute relative deviation (AARD).

This work reports on the prediction of the liquid-vapor densities as well as the rectilinear diameter of argon in the vicinity of the critical region. A previously formulated equation of state (EOS) [A. Rizi, A. Abbaci, J. Mol. Liq. 171, 64 (2012)] based on the Landau-Ginzburg crossover formalism for argon is used for this purpose. We thus present a comparison of the crossover model equation of argon with the experimental phase equilibrium data and describe the singularity of the rectilinear diameter very close to the critical point. The obtained results show that percent deviations between the experimental data and the calculated rectilinear diameter from the crossover model do not exceed 0.05%.

The dimensions of good corporate governance can certainly affect the condition of the company, including LQ 45 Company. The LQ 45index is the value of the market capitalization of 45most liquid stocks and has a large capitalization value which is theliquidationindicator. LQ 45 index uses 45 selected stocks based on stock trade liquidity and adjusted every six months (every early February and August). LQ 45 index only consists of 45 selected stocks of various selection criteria, so it will be consisting of stocks with high liquidity and market capitalization. Thus, it is understandable that companies included in LQ45 areones with a good performance. However, theinfluence of good corporate governance implementation is not yet known through the demographic organization and characteristics of the board toward the company performance. Therefore, it is necessary to conduct further research related to good corporate governance in LQ 45 companies in the aspect of organization demography and the board’scharacteristics. This research was conducted to determine the relationship between organization demography and the characteristics of the board of directors toward the accounting performance (ROA and ROE) in LQ 45. Statistical analysis in this study is conducted by multiple linear regressions. The regression equation in this study is formulated into a model equation, as in the hypotheses and research framework model. In this study, 2 testing of multiple regression analysis were conducted. The regression equation for the first test is as follows. The results showed that: (1) there is a significant effect of organization demographyto the characteristics of the board, (2) there is a significant influence of the characteristics of the board on the performance of accounting, (3) there is no significant influence of the age of the organization to the characteristics of the board, (4 ) there is a significant positive influence of the size of the organization on the characteristics of the board, (5) there is no significant influence of the length of time the organization is listed on the Stock Exchange (BEI)to the characteristics of the board, (6) there is a significant positive influenceof the size of the board to the accountingperformance, (7) There is no significant influence of the CEO duality to the accountingperformance, (8) there is no significant influence of the independence of the CEO on the accountingperformance, (9) there is no significant influence of gender on the accounting performance. Key word: organization demography, the characteristics of the board of direction, accounting performance.

Objections against utilizing the peak fitting method in computing the kinetics parameters of thermoluminescence (TL) glow-peaks were discussed previously in the literature. These objections came through testing the accuracy of the peak fitting by applying on simulated peaks. The results showed that in some cases the simulated peaks may have unusual geometrical properties and do not reflect the real properties of TL peaks. Thereby, estimating the accuracy of the peak fitting by applying on such peaks would be misleading. Two main reasons may lead to unrealistic simulated peaks; the improper selection of the simulation inputs, and performing the TL simulation process via the heating stage only. It has been proved that considering the irradiation and the relaxation stages in the simulation process is crucial. However, there are other cases in which the analytical methods were not able to reveal the real values of the simulated peaks. These cases were successfully resolved using analytical expressions derived from the one trap-one recombination (OTOR) level model and the non-interactive multiple trap system (NMTS) model. A general conclusion can be drawn that the accuracy of the peak fitting method is critically dependent on the TL analytical expressions utilized in this method. The failure of this method in estimating the TL kinetic parameters should be attributed to the TL model equation utilized in fitting process.

The Uehling-Uhlenbeck (U-U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U-U model equation. DSMC analysis based on the U-U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U-U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green-Kubo expression and the shock layer of a dilute Bose gas around a cylinder.

Relationships between the purity, pH, hydrophobicity (logKow) of the carbon substrate, and the critical micelle concentration (CMC) of rhamnolipid type biosurfactants (RL) were investigated using a quantitative structure-property relationship (QSPR) approach and are presented here for the first time. Measured and literature CMC values of 97 RLs, representing biosurfactants at different stages of purification, were considered. An arbitrary scale for RLs purity was proposed and used in the modelling. A modified evolutionary algorithm was used to create clusters of equations to optimally describe the relationship between CMC and logKow, pH and purity (the optimal equation had an R2 of 0.8366). It was found that hydrophobicity of the carbon substrate used for the biosynthesis of the RL had the most significant influence on the final CMC of the RL. Purity of the RLs was also found to have a significant impact, where generally the less pure the RL the higher the CMC. These results were in accordance with our experimental data. Therefore, our model equation may be used for controlling the biosynthesis of biosurfactants with properties targeted for specific applications.

The main aim of this tutorial is to apprise readers about parameter extraction and bias-point calculation using Enz–Krummenacher–Vittoz compact metal oxide semiconductor (MOS) model equation. The model equation has been applied to an NMOS (N-channel metal oxide semiconductor) transistor case present on the P-substrate and P-well. Two cases are considered to show parameters extraction and bias-point calculation for a modified/unmodified value of the transistor threshold voltage. After presenting equation simplification for the two cases, different parameter extraction methods are discussed. Then a common drain configuration biased by a resistance is simulated to match by hand-calculated results.

A novel method was introduced based on a type of profiling elastic press roller to solve the problem that soil compaction pressure is difficult to monitor in real time. The pressure real-time values were acquired through the measurement of the profiling elastic press roller’s eccentricity. In order to evaluate the relationship between the profiling elastic press roller’s eccentricity and the pressure, the study was conducted in an indoor soil bin, in July 2015. Three experimental treatments with soil volumetric moisture content 14.9%, 22.7% and 29.7%, were used in clay soils. The relationship between the profiling elastic press roller’s eccentricity and soil cone index, and the relationship between the static pressure and soil cone index, were investigated. With the equivalent relationship of the cone index, the data was curve fitted and the model equation was established between eccentricity and pressure, in the topsoil layer in which the depth is 0–0.1 m. The correlation coefficient values (R 2 ) of the model equation all reached 0.99 at three experimental treatments, indicating the high degree of correlation. In order to evaluate the pressure measurement method, the validation experiments were conducted. The relationship was compared between the cone index predicted from the press roller measurements and the cone index measured from the manual measurements. The results showed that the dots of scatter diagram are all concentrated around the 1:1 ratio line, with high R 2 values, at three volumetric moisture contents. These experiments indicate that the predictions were very consistent with the manual measurements, indicating the pressure measurement method based on the profiling elastic press roller can be used into real-time pressure monitoring.

The Reynolds averaged Navier-Stokes equation and the turbulence model equation which modified by buoyancy and the species transport equation are used to numerically calculate leakage and diffusion of combustible gas under the influence of obstacle in limited space in order to obtain the influence of obstacle on leakage and diffusion and furthermore get the concentration distribution of different positions of leakage holes. The results show that the obstacle can block diffusion of combustible gas and different positions have different concentration flied. When the leakage hole is at opposite side with outlet, the higher the position of leakage hole, the bigger the burst area. The bigger the height of obstacle, the bigger the burst area of finite space. The simulation results are contribute to safety design of indoor gas pipelines and can supply reference for preventing explosion accidents of indoor combustible gas.

In this paper, we consider a Markovian multi-server queuing system with balking and catastrophes. The probability generating function technique along with the Bessel function properites is used to obtain a transient solution to the queuing model. The transient probabilities for the number of customers in the system are obtained explicitly. The expressions for the time-dependent expected number of customers in the system are also obtained. Finally, applications of the model are also discussed.

We consider a model equation from [ 14 ] that captures important properties of the water wave equation. We give a new proof of the fact that wave packet solutions of this equation are approximated by the nonlinear Schrodinger equation. This proof both simplifies and strengthens the results of [ 14 ] so that the approximation holds for the full interval of existence of the approximate NLS solution rather than just a subinterval. Furthermore, the proof avoids the problems associated with inverting the normal form transform in [ 14 ] by working with a modified energy functional motivated by [ 1 ] and [ 8 ].

This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the functional and the vector model equations, the structure of the approximating vector model is investigated. The stationary vector process is used to predict the functional process. A bound for the difference between vector and functional best linear predictor is derived. The paper concludes by applying functional ARMA processes for the modeling and prediction of highway traffic data., 30 pages, 9 figures

The efficiency of the developed model for predicting the kinetics of the stabilizer extraction from rigid and plasticized polyvinyl chloride was assessed. The model shows high efficiency in the predicting the kinetics of the stabilizer extraction from rigid polyvinyl chloride. The extraction of the stabilizer from the plasticized polyvinyl chloride proceeds in two stages and the kinetic dependences do not obey the model equation.

We present a novel analytical solution for hydro-acoustic waves in a weakly compressible fluid flow over a slowly varying bottom. Application of a multiple-scale perturbation technique and matched asymptotic analysis leads to a uniform analytical solution of the depth-averaged governing equations in three dimensions. We show that the slow depth variation has a leading-order effect on the evolution of the normal mode amplitude and direction. This dynamics is much richer than the two-dimensional limit analysed in previous studies. For tsunamigenic disturbances, we show that the hydro-acoustic wave field is made up by longshore trapped and offshore propagating components, which were not explicated in previous work. For a plane beach, we find an exact analytical solution of the model equation in terms of integrals of Bessel functions. Our model offers a physical insight into the evolution of hydro-acoustic waves of interest for the design of tsunami early warning systems.

Errors are found in the mathematical correlation based on the combined Jouyban–Acree and Modified Apelblat models for describing the variation in the mole fraction solubility of cefpiramide with temperature and solvent composition for the binary aqueous–ethanol solvent system. The equation coefficients given by Tang and coworkers, when substituted into the model equation, do not yield the authors’ calculated mole fraction solubilities of cefpiramide.

Wave overtopping phenomenon under the strong wind often closes roads along a coast, and also causes a serious salt damage on landward area. The crown height of the seawall is usually determined by the design wave and the depth at the foot of the seawall to satisfy an allowable wave overtopping rate. On the other hand, wind parameters such as velocity and direction are not taken into account. In order to achieve a safety land use on coastal area, it is important to clear the effect of the wind on the wave overtopping phenomenon. Furthermore, wind parameters are desired to be included in seawall design. This study investigates the effect of the wind velocity on individual wave overtopping quantities generated by random waves, and proposes a model equation to estimate the wave overtopping rate under wind blowing conditions. Each volume of water over the seawall tended to increase with the wind velocity. This increasing tendency differed depending on the seawall type and wave conditions. This study confirmed the agreement between proposed model equation and experimental data obtained from the different type of seawall.

This paper introduces the simulation of the MOSFET common-source amplifier circuit, and provides a method to jointly solve the physical model of the device and the external circuit to simulate the transient electro-thermal characteristics of a single device in the actual operation of the circuit. The spectral element time-domain (SETD) method is used to solve the coupling drift-diffusion model equation by using the electronic quasi-fee potential, the hole quasi-Fei potential and the potential as variables. The corresponding current density and electrical strength distributed in the device can be used to couple the heat transfer equation. Furthermore, the Kirchhoff laws should be satisfied when the MOSFET device is inserted in the circuit. The numerical results demonstrate the validity of the proposed method.

The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the equation has slightly different forms. In this article, we investigate a model Boltzmann equation with highly oscillatory media in the small Knudsen number regime, and study the numerical behavior of the Generalized Multi-scale Finite Element Method (GMsFEM) in the fluid regime when high oscillation in the media presents. The Generalized Multi-scale Finite Element Method (GMsFEM) is a general approach to numerically treat equations with multi-scale structures. The method is divided into the offline and online steps. In the offline step, basis functions are prepared from a snapshot space via a well-designed generalized eigenvalue problem (GEP), and these basis functions are then utilized to patch up for a solution through DG formulation in the online step to incorporate specific boundary and source information. We prove the wellposedness of the method on the Boltzmann equation, and show that the GEP formulation provides a set of optimal basis functions that achieve spectral convergence. Such convergence is independent of the oscillation in the media, or the smallness of the Knudsen number, making it one of the few methods that simultaneously achieve numerical homogenization and asymptotic preserving properties across all scales of oscillations and the Knudsen number.