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This paper proposes a novel approach to include stochastic variation in the framework of a macroscopic traffic model. Simultaneously, the effects of insufficient data quality and consequent inaccurate identification are investigated. The traffic density distribution over time and space provides a deeper understanding of the evolution of jams, which in turn is vital for the development of traffic network control algorithms. Model parameters are estimated using both Eulerian and Lagrangian sensing. Instead of using deterministic model parameters directly, this work proposes to use stochastic model parameters. Therefore, in addition to the estimated mean of model parameters, a corresponding covariance matrix is estimated as well. The utilized traffic model supports arbitrary Fundamental Diagrams defined by (a combination of) model parameters. Using an analytic approach to define the resulting variation in the Fundamental Diagram is generally impossible, due to the nonlinear combination of random variables in the parameterization of the Fundamental Diagram. A general approach to deal with complex combinations of random variables in the definition of Fundamental Diagrams and, consequently, in the traffic model, is proposed. The core idea is to utilize Monte Carlo Simulation to create a discretized lookup table for the density-speed relationship. Thereby computational effort is significantly reduced, while preserving the ability of the traffic model to reflect variation in the driving behavior. The proposed approach is validated via simulation with state-of-the-art software and Monte Carlo Simulations. [ABSTRACT FROM AUTHOR]

In the method of variation of parameters, a sufficient condition is often imposed in order to obtain a particular solution for a higher order linear nonhomogeneous differential equation. We show that this condition arises naturally by converting the higher order equation to a system of first order linear differential equations and searching for a particular solution for the system. [ABSTRACT FROM AUTHOR]

The usual process for solving a nonhomogeneous system of linear differential equations is to find the general complementary homogeneous solution first and then construct a particular solution from it. When can we flip the script on this process and compute a particular solution first? This paper argues this is possible when the nonhomogeneous forcing function is analytic. It presents two different series expansions for this particular particular solution using power series methods, and reveals a surprising connection to the more familiar variation of parameters formula. [ABSTRACT FROM AUTHOR]

AbstractBackground: Relations among psychological variables are assumed to be complex and to vary over time. Personalized networks can model multivariate complex interactions. The development of time-varying networks allows to model the variation of parameters over time. Objectives: We aimed to determine the value of time-varying networks for clinical practice. Methods: We applied time-varying mixed graphical models (TV-MGM) and time-varying vector autoregressive models (TV-VAR) to intensive longitudinal data of nine participants with depressive symptoms (n = 6) or anxiety (n = 3). Results: Most of the participants showed temporal changes in network topology within the assessment period of 30 days. Time-varying networks of participants with small, medium, and large time variability in edge parameters clearly show the different temporal evolvements of dynamic interactions between variables. The case example indicates clinical utility but also limitations to the application of time-varying networks in clinical practice. Conclusion: Time-varying network models provide a data-driven and exploratory approach that could complement current diagnostic standards by reflecting interacting, often mutually reinforcing processes of mental health problems and by accounting for variation over time. They can be used to generate hypotheses for further confirmatory and clinical testing. [ABSTRACT FROM AUTHOR]

Measurement error, which occurs when some variables of interest cannot be observed exactly. It often leads to invalid conclusions and lamentable implications if ignored. Therefore, the aim of the present work is to investigate ways to handle them when the observations on both the study and auxiliary variables are spoiled with measurement errors. A general class of estimators for the estimation of population mean in presence of correlated measurement errors on study and auxiliary variables has been considered. The variations in the properties of the estimators under the influence of measurement errors has been discussed in detail. The considered class of estimators is compared with the recently proposed family of exponential-type estimators. Simulation studies are carried out to show the impact on the behavior of estimators due to variation in parameters of the measurement error model. [ABSTRACT FROM AUTHOR]

In this paper, we establish a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used. We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters. Numerical simulations are also provided to illustrate the occurrence of periodic phenomena. [ABSTRACT FROM AUTHOR]

In this paper, the set-membership state and parameter estimation problems are considered for linear time-varying systems. The noises in the system are unknown but bounded and the variation of parameters is considered as a bounded expansion. The entire estimator is an interactive estimation of parameters and states. In parameter estimation, the exact set of parameter estimates may be non-convex because of the uncertain states. A polytopic linear parameter varying (LPV) enclosure of the system regression expression is constructed as a convex relaxation. The result of parameter estimation is a set to include the true parameter of the model. Meanwhile, in the state estimation, a similar LPV enclosure of the state-space model is also used to bound the state matrix uncertainties. This LPV enclosure in the state estimation is narrowed by the parameter estimation, and then the set of state estimates is computed to include the true state. The constrained zonotope (CZ) is used to describe sets of interest and the necessary set operations are expanded to LPV mapping. Because of the highly adjustable accuracy of CZ, the proposed algorithm can make a better trade-off between computational accuracy and efficiency. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The two-dimensional problem of wave generation by a time-harmonic pressure distribution on the surface in a finite-depth ocean is studied in this article. Here, it is considered that the ocean has a flexible base, which is modelled as a thin elastic plate and is governed by the Euler–Bernoulli beam equation. The effect of surface tension at the free surface is also taken into account. Within the framework of the linearised theory of water waves, the initial boundary value problem is solved using the Laplace–Fourier transform technique and the integral form of the free surface elevation is obtained. The method of stationary phase is used to evaluate the asymptotic solutions of the free surface elevation for large time and distance. Different forms of the surface elevation have been demonstrated graphically for variation of parameters in a number of figures, and appropriate conclusions are drawn. Moreover, the dispersion relation associated with the wave motion is also derived and analysed using contour plots to understand the characteristics of the roots. Further, the phase and group velocities of the wave motion have also been investigated in this study for both shallow and deep water. [ABSTRACT FROM AUTHOR]

Cross-flow in packed bed reactors (PBRs) was often encountered in industries. However, the effect of inlet and outlet nozzle position on the droplet diameter was little considered. In this study, the effect of inlet and outlet nozzle angles of the gas on the spray disintegration was assessed by changing the angle (i.e., 0°, 30°, 45°, and 60°). A 3D computational fluid dynamic (CFD) model was involved to understand the influence of cross-flow of a single and two-phase gas–liquid flow in PBR. An Eulerian–Lagrangian approach (E-L) was used for solving the flow pattern and the spray disintegration. The RNG k-ε model was employed to simulate the turbulent flow. First, an indirect validation of the cross-flow packed bed was proposed based on a single phase. Second, the variation in parameters such as superficial liquid and gas velocity, mass flow rate, and gas angle orientation were investigated and graphically represented. A new correlation of Sauter mean diameter was developed using particle swarm optimization (PSO) with respect to gas angle orientation. This correlation was done for 64 cases and validated with existing correlations in the literature, giving an MAPE of ±12% and indicating a good agreement with the data. [ABSTRACT FROM AUTHOR]

The problem of complete controllability is addressed for a class of switched time-varying impulsive systems under multiple input delays. Several controllability criteria are obtained with the aid of algebraic and geometric tools. Firstly, the explicit expression of solution on every impulsive interval for such systems is derived by mathematical induction and variation of parameters. Then, complete controllability is investigated for the underlying system based on the solution established. Specifically, the new necessary or/and sufficient algebraic controllability conditions are obtained without assuming that all impulse-dependent matrices are non-singular. In addition, the geometric criteria with regard to the constant matrices are further discussed when the considered system reduces to a time-invariant case. Finally, numerical examples are worked out to demonstrate the controllability tests derived in this paper. It is shown that the existence of the delayed term will potentially affect the controllability of the studied system. In contrast to the existing literatures, the criteria derived in this paper removing some constrained assumptions have less conservatism and can be used to verify the controllability of a more general linear hybrid system. [ABSTRACT FROM AUTHOR]

For fluidized bed drying, the heat and mass transfer process can be modeled by using the volumetric heat transfer coefficient between the drying gas and the particulate matter. Part 1 of this series offered a heat and mass transfer model developed for calculating the particles and drying gas conditions in a fluidized bed dryer. In this part, an algorithm was developed based on this model. The variation of parameters along the height of the dryer and versus drying time can be calculated. The results of the simulation have been validated by using experimental data from a pilot plant fluidized bed dryer with agricultural seeds. We found that the method of determining the logarithmic temperature difference greatly influences the values of the drying parameters and thus the drying time and the height of the desorption zone. [ABSTRACT FROM AUTHOR]

The key techniques in a traditional first course in differential equations are linked by reexpressing them in terms of differential operators and change-of-basis ideas, including integrating factors, variation of parameters, and the method of undetermined coefficients. The main tool is to convert linear operators from sums to compositions. [ABSTRACT FROM AUTHOR]

In this paper, we give a new and straightforward method to solve the non-homogeneous second-order linear difference equations with constant coefficients. It is new because it does not require the uniqueness theorem of the solution of the problem of initial values. Neither does it require a fundamental system of solutions, nor the method of variation of parameters. Moreover, we get a unique formula that expresses the general solution independently of the multiplicities of the roots of the characteristic equation. [ABSTRACT FROM PUBLISHER]

In this paper, we generalize a straightforward method to solve the nonhomogeneous second-order linear differential equations with constant coefficients published in a previous paper, for the case of linear differential equations of order n. As in the case of order 2, this new method does not require the uniqueness and existence theorem of the solution of the problem of initial values nor the characterization of the linear independence of solutions by the Wronskian nor the method of variation of parameters. Moreover, we get a unique formula that expresses the general solution independently of the multiplicities of the roots of the characteristic equation. [ABSTRACT FROM AUTHOR]

In this paper, we give a straightforward method to solve non-homogeneous second-order linear differential equations with constant coefficients. The advantage of this method is that it does not require the uniqueness and existence theorem of the solution of the problem of initial values. Neither does it require the characterization of the linear independence of solutions by the Wronskian, nor the unnatural method of variation of parameters. As an additional benefit of this method, we obtain a single formula for the general solution, that is, a formula that expresses the general solution independent of the nature of the roots of the characteristic equation, namely it does not matter if the roots are equal or different real numbers or if they are two conjugated complex numbers. [ABSTRACT FROM PUBLISHER]

If crops were polluted by heavy metals, the spectra will change. Therefore, the variation information of spectral changes has become an important basis for heavy metal pollution monitoring. Based on spectral frequency domain, we studied the spectra of maize leaves. Combined with time-frequency analysis method, we proposed DDCR-Db (Second-order Differential Continuum Removal- Daubechies) method to detect the sensitive spectral ranges of leaves. Furthermore, we proposed VCPs (Variation Characteristic Parameters), and studied correlation between VCPs and heavy metal content of leaves. And compared with CSI (Conventional Spectral Index) to explore the spectral ranges which are particularly sensitive to Cu2+ (Copper ion) and Pb2+ (Lead ion) stress. Finally, combined with the nonlinear time-frequency distribution, we constructed DDCR-Db-CW (Second-order Differential Continuum Removal-Daubechies-Choi-Williams) transform of the spectra transformation method to distinguish copper and lead pollution. The results showed that DDCR-Db can effectively extract weak spectral information of leaves under copper and lead stress. We obtained the spectral ranges which are particularly sensitive to Cu2+ and Pb2+ stress. DDCR-Db-CW transform can distinguish the spectral difference between no heavy metal stress and heavy metal stress, and intuitively distinguish the types of copper and lead stress. [ABSTRACT FROM AUTHOR]

In this paper, we study a differential hemivariational inequality (DHVI, for short) in the framework of reflexive Banach spaces. Our aim is three fold. The first one is to investigate the existence and the uniqueness of mild solution, by applying a general fixed-point principle. The second one is to study its exponential stability, by employing the formula for the variation of parameters and inequality techniques. Finally, the third aim is to illustrate an application of our abstract results in the study of an initial and boundary value problem which describes the contact of an elastic rod with an obstacle. [ABSTRACT FROM AUTHOR]

This paper addresses the tracking control problem of a single-arm manipulator actuated by Pneumatic Artificial Muscle (PAM) subjected to perturbation in parameters. The super-twisting sliding-mode control (STSMC) has been designed for the PAM system and the stability analysis has been presented to prove the asymptotic convergence of tracking errors. A perturbation observer-based on sliding-mode methodology has been proposed to estimate the uncertainty in system parameters and it is combined with STSMC to establish a robust controller against variation in parameters and to improve the capability of SMC in terms of chattering reduction. The stability analysis based on Lyapunov showed that the estimation error could converge asymptotically and the closed-loop system of an observer-based controlled PAM manipulator is asymptotically stable. Also, to improve the performance of the observer-based controlled system, a modern optimization technique based on Particle Swarming Optimization (PSO) has been suggested and developed for tuning the design parameters of the super-twisting sliding mode-controlled PAM robot based on Sliding-Mode Perturbation Observer (SMPO). The computer simulation based on MATLAB programming format showed the effectiveness of the both proposed observer and controller. [ABSTRACT FROM AUTHOR]

In this article, the fractional-order model, namely HIV-1 infection of CD4+ T-cells combined with the effect of antiviral drug treatment, is investigated. The model includes three unknown factors, (i) the uninfected CD4+ T-cells, (ii) the infected CD4+ T-cells, and (iii) the density of virions in the plasma. The most effective techniques such as the variation-of-parameters method, the variational iteration method, the homotopy perturbation method and the adomian decomposition method are implemented to tackle the mathematical models of Caputo's fractional derivative. Graphical illustration and numerical results are presented to show the validity and accuracy of the obtained results. It is found that the fractional-order model can be easily solved by means of analytical approaches with less computational cost and the HPM technique is slightly better than others. It is also perceived that the fractional-order approximate solutions can get closer to classical approximate solutions when δ → 1. [ABSTRACT FROM AUTHOR]

Frequencies and energies of vibrations for a honeycomb sandwich plate with negative Possion's ratio are investigated. Based on Reddy's third-order shear deformation plate theory, von Karman type nonlinear theory and Hamilton theory, the equations of motion for the plate are obtained, free vibrations and vibrations with the damping and in-plane force of the plate are considered, respectively. The changes of real parts of the eigenvalues with the damping and in-plane forces of the plate are obtained. In order to obtain the analytic solutions of the frequencies and energies of the plate, lateral free vibrations are considered by using the Hamilton energy method, and we compare the results with that of the previous free vibrations. The potential energies and the total energies variation with parameters of the plate are given. The research results from the two methods show that the change trends of the frequencies and energy of the plate are exactly consistent, but the values of natural frequencies and potential energies are lager in lateral vibrations. [ABSTRACT FROM AUTHOR]

In this paper, we analyzed changing of dynamics of redistribution of dopant during the manufacturing of diffusion-junction rectifier in a heterostructure due to radiation processing. In this regard, concentration of charge carriers will also be changed. We also introduce an analytical approach to analyze mass transport with account nonlinearity, space and time variation of parameters of the transport. [ABSTRACT FROM AUTHOR]

This paper proposes a new stability concept called p-exponential input-to-state stability (pISS) for impulsive stochastic delayed partial differential equations (ISDPDEs). By employing the formula for the variation of parameters, the average impulsive interval approach and a new impulsive integral inequality, the sufficient conditions for pISS of ISDPDEs are derived. The issue of impulsive stabilisation to pISS of ISDPDEs is studied. It is unveiled that if the continuous stochastic delay partial differential equations may not be pISS, it can be stabilised by impulsive control. An example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

Study aims to investigate the effects of vermicomposts containing oil processing wastes, dairy manure, municipal open market wastes and straw on the growth, nutrient concentrations and nutrient uptakes of corn plant. For this, there different mixtures were prepared. Vermicomposts were applied with the rates of 0, 5000, 10000, and 20000 kg ha−1 to 2 kg soil containing pots. Study was conducted in growth chamber for 2 months. Vermicompost applications increased plant growth, some plant nutrient concentrations and uptake. Also, vermicomposts showed the variation on parameters depending on their mixtures. Results showed that nutrients taken by the plant increased with the vermicompost until 10000 kg ha−1 dose. Most of the nutrient concentrations such as phosphorus, potassium, calcium, magnesium, iron, and manganese (P, K, Ca, Mg, Fe, and Mn) were not increased in plant tissues, whereas uptake of them by the plant showed a significant increase. In addition, residual soil nutrients increased with the increase in vermicompost levels. [ABSTRACT FROM AUTHOR]

The variation of parameters of Si-based MOS-transistors affected by combined infrared and X- ray photons processing were presented. It was found that X-ray irradiated transistor under incoherent infrared radiation is characterized by lowering of radiation sensitivity. As positive charge and its radiation-induced rate of generation in undergate SiO2insulator decreases, we observe a reduction of both ΔUNoand voltage thresholdUthtransistor components. Under pulsed laser processing (λ = 1.06 µm,τ = 10−3s) of the X-rays irradiated transistor the energy density of laser beam corresponding to the minimum threshold voltage was established. It was shown that the combined treatment can be effectively used to control the transistor parameters. The model describing the radiation changes of parameters in Si-SiO2structure was proposed. The effect of Na+, K+and H+ions in undergate insulator on variation of charge state and interface reconstruction under laser irradiation were predicted by proposed model. [ABSTRACT FROM PUBLISHER]

The approximate simulation of storm water run-off over pervious pavement is carried out using both experimental method and numerical simulation. The slope and flow rate changeable flume and uniform porous media are used to approximately simulate the pervious pavement. A 3D computational fluid dynamics – discrete element method is used for numerical simulation of interaction between pervious pavement and fluid. The effects of variation of parameters, including inflow rate, infiltration outflow rate and slope on surface run-off are analysed. The average flow velocity within the surface run-off region and shear velocity increases with the increasing permeability of pervious pavement. The turbulent kinetic energy distribution along depth in the free-flow region is more uniform than empirical relationship for flow over impermeable surfaces. Equations for flow depth and velocity over pervious pavement have been deduced. The results of this study are helpful for the hydraulic design of pervious concrete pavement. [ABSTRACT FROM AUTHOR]

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors. [ABSTRACT FROM PUBLISHER]

A simple and sensitive high-performance liquid chromatographic (HPLC) method was developed to determine the amount of hydrazine in industrial wastewater after derivatization with anthracene-2,3-dicarbaldehyde. The best reaction conditions (a reagent dosage of 200 mg/L, a pH of 11, and reaction for 1 min at room temperature) were established by the variation of parameters. The formed derivative was injected into the HPLC without further extraction or purification procedures. Under the established conditions, the limits of detection and the limits of quantification were 0.02 µg/L and 0.05 µg/L, respectively, and the inter-day relative standard deviation was less than 9% at concentrations of 0.1 and 0.5 µg/L. The calibration curve showed good linearity with r2 = 0.9999. The method was successfully applied to the determination of hydrazine in various kinds of industrial wastewater. [ABSTRACT FROM AUTHOR]

The article focuses on the solution to a mathematical problem on nonhomogeneous differential equations using undetermined coefficients. Topics discussed include variation of parameters being used to solve differential equations, linear algebra, equality of polynomials and substitution being used to prove the solution of the problem, solutions to problems with monomial right hand functions in equations, and solutions to problems with exponential nonhomogeneities.

Recently, Christopher C. Tisdell questions some claims and results that appear in our article [Rivera-Figueroa A, Rivera-Rebolledo JM. A new method to solve the second-order linear difference equations with constant coefficients. Int J Math Educ Sci Technol. 2016;47(4):636–649.] regarding the novelty and simplicity of a method to solve second-order linear difference equations. He argues that our method was not new because the method already appeared in the mathematical literature, neither was simpler than existing ones. After carefully analysing and comparing the references quoted by Tisdell, we confirm that our method differs from that quoted by Tisdell. Moreover, our approach is simpler because it avoids the uniqueness theorem and the method of variation of parameters, in this context, it offers some clear didactic and epistemological advantages. [ABSTRACT FROM AUTHOR]

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring–mass system. We provide a sequence of discovery-based exercises that foster physical and mathematical intuition about polynomial forcing, as we build tools and techniques (including Green's function) to explore the amazing behavior of We encourage the insightful use of a Computer Algebra System, and provide a paired supplemental Maple worksheet. [ABSTRACT FROM AUTHOR]