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A novel image analysis method was developed to determine the volume expansion ratio of cooked rice, and study the kinetics of the volume expansion ratio changes of rice as a function of the cooking time. The correlation between volume expansion ratio and various physicochemical factors has been studied to elucidate the key factors affecting the changes in cooked rice volume. The results demonstrated that the image analysis method is capable of both visually and quantitatively analyzing the volume expansion properties of rice throughout the cooking process. This method revealed that five models can effectively simulate (with a correlation coefficient R2 > 0.95) the changes in the volume expansion ratio for Koshihikari and Thai Jasmine rice as a function of cooking time. These models consider cooking time as a variable. Consequently, a linear equation based solely on cooking time was derived, which can predict the volume expansion ratio of rice during the cooking process. The correlation analysis suggested that the apparent amylose content, protein content and grain length had significantly (P < 0.05) negative correlation with the volume expansion ratio; while starch content and grain width had significantly (P < 0.05) positive correlation with the volume expansion ratio; the pasting properties parameters had different relationships with the volume expansion ratio of cooked rice. [ABSTRACT FROM AUTHOR]

The paper is devoted to the investigation of some classes of first-order integro-differential equation with singular kernel and its conjugate equation. The kernel of non-conjugate equation has singularity at the point , and the kernel of conjugate equation has singularity at the point . First, two conjugate classes of functions are introduced and then in these classes of functions the model equations are investigated. Further in three cases, in depending of the roots of the characteristic equation, the solution of studied equations were found in an explicit form. It is shown that the general solution of investigated equations contains some number of arbitrary constants. Also, there were found the case when the model equations has only unique solutions. Also in this work we studied the non-model equation. When the roots of the corresponding characteristic equation are real and different the solution of the non-model equation were found through the resolvent of corresponding Volterra-type integral equation. [ABSTRACT FROM AUTHOR]

To evaluate the concentration of natural radionuclides and to carry out geophysical interpretation of part of Igarra area, Southern Nigeria, an integrated geophysical approach was adopted involving radiometric, gravity, and magnetic methods. The RS-230 Super-Spec spectrometer, G-512 Lacoste and Romberg gravimeter, and the GSM-19v7.0 Overhauser instrument were used for the radiometric, gravity, and magnetic data acquisitions, respectively, along a specified traverse within the area. The datasets were processed using Oasis Montaj, Grav-Master, and Ms-Excel software. Gravity results show that the mean free air and Bouguer anomalies in the area are − 67.42 and − 84.22 mGal, while magnetic survey indicates that the mean corrected magnetic field intensity in this area is 32218.49 nT. Radiometric survey results show that the mean radioactivity concentrations of thorium ( 232 Th ) , uranium ( 238 U ), and potassium ( 40 K ) are 31.81 Bq/kg, 26.48 Bq/kg, and 167.33 Bq/kg, respectively. Further analysis also revealed that the mean radioactivity equivalent of the area is 84.86 Bq/kg; absorbed dose rate is 72.74nGy/h, while the mean external hazard index is 0.30. A novel model equation for estimating absorbed dose rate from radioactivity equivalent was also obtained and validated. The gravity and magnetic survey results indicate the presence of low-density and high magnetic basement rocks underlying this area, while radiometric results reveal that radiations in this area did not exceed acceptable standards of 370 Bq/kg for radioactivity equivalent, 84 nGy/h for absorbed dose rate, and unity which corresponds to 370 Bq/kg for external hazard index as recommended by the United Nations Scientific Committee on the Effects of Atomic Radiation and the International Atomic Energy Agency. [ABSTRACT FROM AUTHOR]

The paper presents the prediction of bearing capacity equation of E-shaped footing subjected to a vertical concentric load and resting on layered sand using machine learning techniques and the data used in the analysis has been extracted from finite element modelling of the same footing. The input variables used in the developed neural network model were the bearing capacity of square footing, thickness ratio, friction angle ratio and the output were the bearing capacity of E-shaped footing on layered sand. Multiple layer perceptron (MLP) and multiple linear regression (MLR) prediction models were used for the determination of error metrics and the ultimate bearing capacity of E-shaped footing resting on layered sand. Finally, for the ANN model development, a model equation was developed with the assistance of weights and biases, based on the MLP and MLR model using open-source WEKA and Anaconda software respectively. Sensitivity analysis has been performed on the data sets which correlates the various input variables with the output variable of both the models. The coefficient of determination (R2) comes out to be 0.99 and 0.98 for the MLP and MLR models respectively indicating that both the models were able to predict the bearing capacity for the E shaped footing with acceptable accuracy. [ABSTRACT FROM AUTHOR]

Nano- $g$ accelerometers are widely used in space exploration and measurement of the earth’s gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this article, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison to the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultralow frequency. [ABSTRACT FROM AUTHOR]

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This paper carried out simulations of a channel flow experiment and a case study of granular avalanche flow using two kinds of methods, depth-integrated continuum method and discrete element method. In the simulation of the channel flow experiment, we presented a method for calculating normal force and bending moment of the rigid wall based on the depth-integrated continuum method. Although the peak value of the normal force and bending moment cannot be obtained using the depth-integrated continuum method, the residual value can be obtained rapidly and accurately. Then, Frank landslide in Canada was simulated using the two methods. Calculation results of the extent and duration of the granular avalanche were in good agreement with actual situation, which validated the correctness and effectiveness of the two methods. The velocity process, energy process, and risk zoning of the granular avalanche were obtained. Calculation results showed that the maximum average velocity of the granular avalanche was about 68 m/s at 20 s. The computational efficiency of the depth-integrated continuum method was better than that of the discrete element method, while the energy process of the granular avalanche could be better traced using the discrete element method. Detailed comparison and discussion were carried out in the simulations of the experiment and the case study which can provide a scientific reference and basis for the simulation of the granular avalanche flow. [ABSTRACT FROM AUTHOR]

We consider a problem of factoring the scattering matrix for Schrödinger equation on the real axis. We find the elementary factorization blocks in both the finite and infinite cases and establish a relation to the matrix conjugation problem. We indicate a general scheme for constructing a large class of scattering matrices admitting a quasirational factorization. [ABSTRACT FROM AUTHOR]

We consider the nonlinear Boltzmann equation in the framework of the Shakhov model for the classical problem of gas flow in a plane layer. The problem reduces to a system of nonlinear integral equations. The nonlinearity of the studied system can be partially simplified by passing to a new argument depending on the solution of the problem itself. We prove the existence theorem for a unique solution of the linear system and the existence theorem for a positive solution of the nonlinear Urysohn equation. We determine the temperature jumps on the lower and upper walls in the linear and nonlinear cases, and it turns out that the difference between them is rather small. [ABSTRACT FROM AUTHOR]

A stable high-order Runge-Kutta discontinuous Galerkin (RKDG) scheme that strictly preserves positivity of the solution is designed to solve the Boltzmann kinetic equation with model collision integrals. Stability is kept by accuracy of velocity discretization, conservative calculation of the discrete collision relaxation term, and a limiter. By keeping the time step smaller than the local mean collision time and forcing positivity values of velocity distribution functions on certain points, the limiter can preserve positivity of solutions to the cell average velocity distribution functions. Verification is performed with a normal shock wave at a Mach number 2.05, a hypersonic flow about a two-dimensional (2D) cylinder at Mach numbers 6.0 and 12.0, and an unsteady shock tube flow. The results show that, the scheme is stable and accurate to capture shock structures in steady and unsteady hypersonic rarefied gaseous flows. Compared with two widely used limiters, the current limiter has the advantage of easy implementation and ability of minimizing the influence of accuracy of the original RKDG method. [ABSTRACT FROM AUTHOR]

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave regimes of the film freely flowing down a vertical surface. The first case describes a ferromagnetic fluid film affected by the magnetic field, and the second case touches upon a dielectric fluid film affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces have a great impact on the flow. [ABSTRACT FROM AUTHOR]

The article reports on research which was conducted to evaluate a model of determining instantaneous values of velocity and average acceleration in 100 meter sprinters. Researchers tested the model with several professional sprinters. They found that it was able to effectively and accurately measure velocity and average acceleration.

The article considers the joint flow of a liquid film entrained by turbulent gas. Since liquid velocity is small in comparison with gas velocity, the problem is reduced to the calculation of pressure and shear stresses produced by the gas flowing over a wavy wall with small amplitude. Further, these data are used at the boundary conditions, when the flow of a liquid film is considered separately. As a result, we obtain a new system of equations for modeling the dynamics of long-wave perturbations on the surface of a viscous liquid film entrained by turbulent gas at microgravity. At small Reynolds numbers typical to the condition of microgravity, it was proved that this system is reduced to one evolution equation for the film thickness. Some numerical solutions of this equation have been received in this work. [ABSTRACT FROM AUTHOR]

This paper deals with the development of a simple mathematical model for experimental validation of the performance of a small evaporative cooling system in a tropical climate. It also presents the coefficient of convective heat transfer of wide range of temperatures based on existing model. Extensive experiments have been performed during January to February 2013 for a small evaporative cooling system designed for storage of fruits and vegetables. The model considered the thermal properties of the material of the cooling pad and assumed that the cooling pad is a plain porous wall bounded by two convective air at different temperature at the two surfaces. The predicted and experimental value of various cooling efficiency at different range of inlet temperature has been determined. In addition the values of the coefficient of convective heat transfer for a wide range of temperatures is also presented. [ABSTRACT FROM AUTHOR]

The flows of viscous liquid film over the outer surface of a vertical cylinder are examined. Investigation of wave regimes in the case of low flow rates and large cylinder radii is reduced to the analysis of solutions to a nonlinear evolution equation for the film thickness. There are countable numbers of steady-state traveling solution families in the considered model. In turn, most of them are unstable to 2D and 3D perturbations. Thus, evolution of initial perturbations in different ranges of parameter values differs significantly. Some typical scenarios of perturbation development are presented in this work. Initial perturbations with some symmetries, kept in the process of evolution, are of a particular interest. In these cases, solutions are drawn up to the steady-state traveling solutions with similar symmetry. [ABSTRACT FROM AUTHOR]

In this paper we prove the global in time well-posedness of the following non-local diffusion equation with α ∈ (0, 2/3): The initial condition u 0 is positive, radial, and non-increasing with u 0 ∈ L 1 ∩ L 2+δ(ℝ3) for some small δ > 0. There is no size restriction on u 0. This model problem appears of interest due to its structural similarity with Landau's equation from plasma physics, and moreover its radically different behavior from the semi-linear Heat equation: u t = ▵ u + αu 2. [ABSTRACT FROM AUTHOR]

Evolution of disturbances on the surface of liquid film falling free over a vertical plane is considered. In the case of low Reynolds numbers, the problem is reduced to investigation of a single equation describing evolution of film thickness disturbances. With the use of information about the structure of the family of steady-state traveling solutions to this equation, the typical scenarios of evolution for periodic disturbances were identified. [ABSTRACT FROM AUTHOR]

A new system of equations for modeling the dynamics of long-wave perturbations on the surface of a viscous liquid film flowing down a vertical plane was investigated. It is shown that the system obtained agrees with a known system derived by the variable changing method but unlikely has a conservative form that is perfect for designing of numerical efficient conservative difference schemes. The system is reduced to a single conservative equation for the function analogous to the hydrodynamic stream function with the appropriate boundary conditions. For the case of moderate Reynolds number it is noted that the equation with boundary conditions coincide with the well known Shkadov's model under the assumption of self-similar profile of longitudinal velocity. At small Reynolds numbers typical to the condition of microgravity it was proved that the system is reduces to one evolution equation for the film thickness. [ABSTRACT FROM AUTHOR]

In this paper, the functional equivalence problem for processes, which is an important constituent of process optimization, is considered in object-oriented environments. Two basic cases are investigated: when the turn of operations execution is not essential for some objects while it is essential for the rest of them. In the first case, those objects are named commutative. Environments with both commutative and non-commutative objects are named partially commutative. It is shown, that the equivalence problem of processes in partially commutative environments that contain two or more commutative objects with more than one operation is unsolvable. The largest class of partially commutative environments is outlined where the equivalence problem is solvable (decidable). It is shown, that if there is only one object with two or more operations among commutative objects then the equivalence problem is solvable. [ABSTRACT FROM AUTHOR]

The 'dissection' of energy expenditure of cycling into the metabolic equivalent of the different forms of mechanical work done, inaugurated 30 years ago by di Prampero and collaborators, has been much debated in the last few decades. The mechanical internal work, particularly, which is currently associated to the movement of the lower limbs, has been approached, estimated and discussed in several different ways and there is no agreed consensus on its role in cycling. This paper, through re-processing previously published data of oxygen consumption during pedalling at different frequency, external load and limb mass, proposes a model equation and a multiple non-linear regression as the method to assess the internal work of cycling. With that tool a very consistent metabolic equivalent of the internal work is obtained. However, a software simulation of pedalling limbs showed, as suggested in the literature, that the link with the chain ring allows the system to passively revolve forever, after an initial push. This result challenges the very existence of the 'kinematic internal work' of cycling. We conclude and suggest that the 'viscous internal work', an often neglected and almost unmeasurable portion of the internal work that could be proportional to the 'kinematic' form, is responsible for the extra metabolic expenditure as measured when the pedalling frequency of cycling increases. [ABSTRACT FROM AUTHOR]

The technology that has been developed for real-time analysis of the lightning-caused forest fire risks is discussed. Comparative estimates of the number and areas of such fires are obtained for Russia's regions. The zone of localization of lightning-caused fires is identified through the use of the GIS capabilities. [ABSTRACT FROM AUTHOR]

Waves on the surface of a thin film of a viscous dielectric fluid flowing down the inner surface of one plate of a plane capacitor with alternating voltage applied is considered. It is shown that the volume forces acting from the inhomogeneous electric field are negligibly small in the case of long waves, and the influence of the electric field reduces to the influence of additional pressure onto the film surface. A model equation for determining the deviation of the film thickness from the undisturbed value is derived in the long-wave approximation. Some numerical solutions of this equation are given. [ABSTRACT FROM AUTHOR]

Type B carboxylesterases (acetylcholinesterases, neuropathy target esterase, serine peptidases), catalyse the hydrolysis of carboxyl-ester substrates by formation of a covalent acyl-enzyme intermediate and subsequent cleavage and release of the acyl group. Organophosphorus compounds, carbamates, and others exert their mechanism of neurotoxicity by permanent covalent organophosphorylation or carbamylation at the catalytic site of carboxylesterases. Classical kinetic studies converted the exponential kinetic equation to a logarithmic equation for graphic analysis. This process, however, does not allow analysing complex situations. In this paper, kinetic model equations are reviewed and strategies developed for the following cases: (a) single enzyme, with classical linear equation; (b) multi-enzymatic system—discriminating several inhibitor-sensitive and inhibitor-resistant components; (c) ‘ongoing inhibition’—high sensitive enzymes can be significantly inhibited during the substrate reaction time, the model equations need a correction; (d) spontaneous reactivation (de-phosphorylation)—one or several components can be simultaneously inhibited and spontaneously reactivated; (e) spontaneous reactivation from starting time with the enzyme being partly or totally inhibited; (f) aging—single enzyme can be inhibited, spontaneously reactivated and dealkylating reaction (‘aging’) simultaneously occurs; and (g) aging and spontaneous reactivation from starting time with the enzyme being partly or totally inhibited. Analysis of data using the suggested equations allows the deduction of inhibition kinetic constants and the proportions of each of the enzymatic components. Strategies for practical application of the models and for obtaining consistent kinetic parameters, using multi-steps approaches or 3D fitting, are presented. [ABSTRACT FROM AUTHOR]

Using model equations of the form Δ u + u σ = 0 as an example, in both linear ( σ = 1) and nonlinear ( σ > 1) cases, we present some direct methods of proof of the blow-up of positive solutions in semi-infinite plane domains. We consider semi-infinite strips, both straight and exponentially decreasing, with homogeneous Neumann condition on the upper and lower boundaries. [ABSTRACT FROM AUTHOR]

The paper examines the impact of development activities on water pollution in Malaysia. Hence, the main objective of this paper is not just to examine the trends of development-induced water pollution around the region of the country but to know where the problems are and the policy measures taken by the government. It evaluates the probable causative relationship between problems introduced due to technology employed in water pollution control and governmental policy measures. It examines the relationship between development indicators as sources of pollution and polluted rivers over a period of 12 years. The findings of the paper have shown that despite the policy enforcement actions against the identified sources of water pollution, all the three development indicators (chosen based on those identified sources) still accounted for high percentage of river pollution in Malaysia. The findings of the paper were used to identify the central fact of the location of the problem. Some crucial conclusions of where the problems likely to be, as reflected in the findings, are: (a) the issue of interactive-effects between pollutants that many policy-makers are not aware of. This is when policy measures concentrate only on one source of water pollution; (b) the enforcement strength and/or effectiveness of policy measures themselves; (c) financial constraints to invest in appropriate technology especially sewerage systems for controlling human source of water pollution in the country; as well as those confronting small polluting industries (d) finally, lack of cooperation between government and private business firms to comply with regulatory policies for water pollution control. [ABSTRACT FROM AUTHOR]

Two types of nonthermal plasma processes such as pulsed corona discharge and dielectric barrier discharge were investigated for the decomposition of volatile organic compounds and nitric oxide. The performance equation of the plasma reactor was derived with the assumption that the decomposition rate of the pollutant is directly proportional to the concentration of the pollutant and the discharge power. From this model equation and the experimental decomposition data, the apparent decomposition rate constants of various organic compounds and nitric oxide were determined. Alkene and substituted alkene were found to have much larger decomposition rate constants than aromatics and substituted alkane compounds, which implies that the decomposition of the derivatives of aromatics and alkanes requires more energy. To verify the validity of the model derived, the experimental data in the present study and in the literature were compared with the calculation results, and relatively good agreements were achieved between them [ABSTRACT FROM PUBLISHER]

Based on the urban shantytown renovation project in Hongguang Town, Helan County, Ningxia, in Northwest China, the influence of fly ash and silica fume admixture on the mechanical properties of Self-compacting Concrete (SCC) was tested and analyzed in this work. The experimental tests including compressive strength, splitting strength, triaxial strength and an ultrasonic nondestructive test. Furthermore, the Back Propagation (BP) neural network algorithms were established. The results show that there is an obvious difference between the development law of compressive strength of SCC and that of ordinary concrete. The splitting pressure ratio of SCC is 1/10 to 1/8, while that of ordinary concrete is 1/13 to 1/10. Moreover, the peak strain, peak stress and initial stiffness of SCC increase with the increase of the confining pressure when compressed from three directions. In addition, the ultrasonic amplitude of SCC can reflect the changing laws of its compressive strength. As a conclusion, the addition of fly ash and silica fume increases the splitting pressure ratio of SCC. More importantly, the compressive strength formula for SCC with silica fume and a low content of fly ash is proposed, and the model equation between the amplitude and compressive strength is given. This study provides a reference for the mixture ratio of fly ash and silica fume in the application of SCC. [ABSTRACT FROM AUTHOR]

Establishing a model equation with high accuracy and high computational efficiency is very important for the estimation of battery state of charge (SOC). To ensure better SOC estimation results, most studies have focused on the improvement of the algorithm, while the impact of the model equation which may offset the benefits of advanced algorithms has been overlooked. To address this problem, this paper studies the widely used model equations and presents a new model equation based on a Gaussian function that improves the SOC estimation accuracy and computational efficiency. With the Worldwide harmonized Light Vehicles Test Cycle (WLTC) which is highly dynamic and more realistic than any other driving cycles, the proposed model equation is applied to different filtering algorithms to validate its performance in SOC estimation. The results indicate that the proposed model equation can greatly improve the accuracy of SOC estimation without an increase of computation. In addition, for the traditional polynomial-based model equations, the 6th-order power function polynomial has better performance in SOC estimation than polynomials with other orders. [ABSTRACT FROM AUTHOR]

The concept of limited predictability is reviewed followed by simpleexamples illustrating the sensitivity to small changes in the initial state and/or the forcing of a non-linear system. Limited predictability applies to almost all non-linear systems, and the concept is therefore important to geophysical systems governed by non-linear model equations. The limited predictability determines the upper limit to operational weather forecasts, but it will also be demonstrated that it has an impact on the determination of the effect of changes in the forcing of the system. The general strategy applied by researchers toestimate the atmospheric greenhouse effect is reviewed. It will be demonstrated that the adopted strategy, due to prescribed changes in the forcing of the climate system, is also influenced by limited predictability in the sense that predicted changes are much larger than observed changes in the temperatures at the surface of the Earth. It istherefore very unlikely that the predictions are reliable. The inclusion of the sulfur-aerosol effects are also discussed with the conclusion that although these cooling agents reduce the greenhouse warming, they do not behave as expected in the sulfur-rich and sulfur poor regions. [ABSTRACT FROM AUTHOR]