ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

An Efficient Accurate Direct Solution of Poisson's Equation for Computation of Meteorological Parameters

Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.

THE SOLVABILITY OF THE INITIAL-BOUNDARY PROBLEM FOR EQUATIONS IN COMBUSTION DYNAMICS WITH LARGY PARAMETER

In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.

CONSTITUTIVE EQUATION OF A NEW AVIATION LUBRICATING OIL

The traction of a new aviation lubricating oil was measured on a self-made test rig. The calculating formulae of the rheological parameters of the oil such as Erying stress, limiting shear stress and shear elastic modulus were obtained under the condition of the high shear strain rate in elastohydrodynamic lubrication（EHL）. The constitutive equation of this oil was determined and verified by test. The results of experiments show that the behavior of the new aviation lubricating oil behaves as visco-elastic fluid and the theoretical value agrees fairly well with the measured data, which implies that the constitutive equation of this oil is correct and feasible.

A New Equation for Solute Retention in Liquid Chromatography

In consideration of the adsorption of solvent,diluent and solute molecules on the surface of a stationary phase,a new equation for solute retention in liquid chromatography is presented. This equation includes three parameters: the displacement equilibrium constant( K _ sd ) between the solvent and diluent molecules on the surface of the stationary phase,the total number( N ) of the solvent and diluent molecules released from the stationary phase after one solute molecule being adsorbed,and the parameter( I ) related to the thermodynamic equilibrium constant for the solute adsorption on the stationary phase. Over the whole concentration range of the solvent in the mobile phase,the experimental retention data can be well described by this equation,parameters K _ sd ,N and I can be obtained by the regression analysis of the experimental retention data,and consequently the number of the solvent and the diluent molecules displaced by one solute molecule from the stationary phase can also be derived at different solvent concentrations in the mobile phase.

Artificial Sun synchronous frozen orbit control scheme design based on J_2 perturbation

Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.

THEORETICAL PREDICTION OF THE KINETICS CURVES OFPEARLITIC TRANSFORMATION IN HYPO-PROEUTECTOID STRUCTURAL STEELS

Supposing carbon contents of ferrite phases in pearlite precipitating from austenite in multicomponent steel at temperature T and in Fe-C ystem at T' are the same the pearlite formation temperature diference, can be calculated from the FeX phase diagrams and the equilibrium temperature Al. Using Tp and Fe-C binary thermodynamic model, the driving forces for phase transformation from austenite to pearlite in multicomponent steels have been successfully calculated. Through the combination of simplified Zener and Hillert's model for pearlite growth with Johnson-Mehl equation, using data from known TTT diagrams, the interfacial energy parameter and activation energy for pearlite formation can be determined and expressed as functions of chemical composition in steels by regression analysis. The calculated starting curves of pearlitic transformation in some commercial steels agree well with the experimental data.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Exploring traffic safety climate with driving condition and driving behaviour:a random parameter structural equation model approach

This study aimed to explore traffic safety climate by quantifying driving conditions and driving behaviour.To achieve the objective,the random parameter structural equation model was proposed so that driver action and driving condition can address the safety climate by integrating crash features,vehicle profiles,roadway conditions and environment conditions.The geo-localized crash open data of Las Vegas metropolitan area were collected from 2014 to 2016,including 27 arterials with 16827 injury samples.By quantifying the driving conditions and driving actions,the random parameter structural equation model was built up with measurement variables and latent variables.Results revealed that the random parameter structural equation model can address traffic safety climate quantitatively,while driving conditions and driving actions were quantified and reflected by vehicles,road environment and crash features correspondingly.The findings provide potential insights for practitioners and policy makers to improve the driving environment and traffic safety culture.

Viscous holographic f(Q)cosmology with some versions of holographic dark energy with generalized cut-offs

The work reported in this paper demonstrates the cosmology of f(Q)gravity and the reconstruction of various associated parameters with different versions of holographic dark energy with generalized cut-offs,where Q=6 H^(2).The Universe is considered to be filled with viscous fluid characterized by a viscous pressureΠ=-3 Hξ,whereξ=ξ0+ξ1 H+ξ2(˙H+H^(2)and H is the Hubble parameter.Considering the power law form of expansion,we have derived the expression of f(Q)under a non-viscous holographic framework and it is then extended to viscous cosmological settings with extended generalized holographic Ricci dark energy.The forms of f(Q)for both the cases are found to be monotonically increasing functions of Q.In the viscous holographic framework,f(Q)is reconstructed as a function of cosmic time t and is found to stay at a positive level with Nojiri-Odintsov cut-off.In these cosmological settings,the slow roll parameters are computed and a scope of exit from inflation and quasiexponential expansion are found to be available.Finally,it is observed that warm inflationary expansion can be obtained from this model.

The Role of Technology in the Process of Learning Mathematics

The research was achieved by applying several questionnaires and evaluation tests that have shown the efficacy of using the computer in building active thought and skills in the graphical representation of functions , within a Cartesian reference system xOy. Our research was based on the following hypothesis: if we systematically use, in lessons of algebra and mathematical analysis, the GeoGebra software for drawing the graph of a function, then we shall contribute to building attitudes and competences in using the computer for the graphical representation of functions , within a Cartesian reference system xOy. The purpose of our study is to present a practical computer use model for the students from the Pre- and In-Service Teacher Training Department, “Vasile Alecsandri” University of Bacau, during their pedagogical practice stage of continuous training, aimed at building practical skills in supporting the teaching-learning process with computers. To deal with these issues, we are trying to find the best teaching-learning strategies by using the calculus technique. The research was conducted at the “Stefan cel Mare” National Pedagogical College from Bacau, by assisting 20 lessons of mathematics and 20 lessons of Information and Communication Technology, involving a group of 104 students in the 11th grade. In order to verify the hypothesis, we have established several objectives that orient and guide our activity: knowing the initial level of mathematical training in terms of graphical representation of functions;identifying the frame and reference objectives of the curriculum for mathematical education regarding the graphical representation of functions;designing and conducting a teaching process focused on the use of the computer and the GeoGebra software in learning the graphical representation of functions;final evaluation of the students’ level of training regarding the graphical representation of functions in a plane.

Bianchi type V universe with bulk viscous matter and time varying gravitational and cosmological constants

We consider spatially homogeneous and anisotropic Bianchi type V space- time with a bulk viscous fluid source, and time varying gravitational constant G and cosmological term A. The coefficient of bulk viscosity ζ is assumed to be a simple linear function of the Hubble parameter H （i.e. ζ = ζ0 ＋ ζ1H, where ζ0 and ζ1 are constants）. The Einstein field equations are solved explicitly by using a law of varia- tion for the Hubble parameter, which yields a constant value of the deceleration pa- rameter. Physical and kinematical parameters of the models are discussed. The models are found to be compatible with the results of astronomical observations.

Observational Hubble parameter data constraints on the interactive model of f(T) gravity with particle creation

In this study,we consider an open system from the thermodynamic perspective for an adiabatic FRW universe model in which particle creation occurs within the system.In this case,the modified continuity equation is obtained,and then,we make it correspond to the continuity equation of f(T)gravity.Therefore,we take f(T)gravity with a viscous fluid in the flat-FRW metric,where T is the torsion scalar.We assume the contents of the universe to be dark matter and dark energy and consider an interaction term between them.An interesting point of this study is that we make the modified continuity equation resulting from particle creation equivalent to the matter continuity equation resulting from f(T)gravity.The result of this evaluation establishes a relationship between the number of particles and scale factor.In what follows,we write the corresponding cosmological parameters in terms of the number of particles and also reconstruct the number of particles in terms of the redshift parameter.We then parameterize the Hubble parameter derived from power-law cosmology with 51 data points from the Hubble observational parameter data.Next,we plot the corresponding cosmological parameters for dark energy in terms of the redshift to investigate the accelerated expansion of the universe.In addition,by using the sound speed parameter,we discuss the stability and instability analyses of the present model in different eras of the universe.Finally,we plot the density parameter values for dark energy and dark matter in terms of the redshift parameter.

Cosmic acceleration with bulk viscosity in an anisotropic f(R, Lm) background

In this article,we investigate the observed cosmic acceleration in the framework of a cosmological f(R,Lm)model dominated by bulk viscous matter in an anisotropic background.We consider the locally rotationally symmetric Bianchi type I metric and derive the Friedmann equations that drive the gravitational interactions in f((R,Lm)gravity.Further,we assume the functional form f(R,Lm)=R/2+Lαm,where a is a free model parameter,and then find the exact solutions of field equations corresponding to our viscous matter dominated model.We incorporate the updated H(z)data and the Pantheon data to acquire the best-fit values of parameters of our model by utilizing theχ2 minimization technique along with the Markov Chain Monte Carlo random sampling method.Further,we present the behavior of physical parameters that describe the Universe’s evolution phase,such as density,effective pressure and EoS parameters,skewness parameter,and the statefinder diagnostic parameters.We find that the energy density indicates expected positive behavior,whereas the negative behavior of bulk viscous pressure contributes to the Universe’s expansion.The effective EoS parameter favors the accelerating phase of the Universe’s expansion.Moreover,the skewness parameter shows the anisotropic nature of spacetime during the entire evolution phase of the Universe.Finally,from the statefinder diagnostic test,we found that our cosmological f(R,Lm)model lies in the quintessence region,and it behaves like a de-Sitter universe in the far future.We analyze different energy conditions in order to test the consistency of the obtained solution.We find that all energy conditions except strong energy condition(SEC)show positive behavior,while the violation of SEC favors the recently observed acceleration with the transition from decelerated to an accelerated epoch of the Universe’s expansion in the recent past.

Artificial frozen orbit control scheme based on J_2 perturbation

Since the inclination of frozen orbit with non-rotation of the perigee that occurs due to J2 perturbation must be equal to the critical inclination, this regulation has restricted the application of frozen orbit a lot. In this paper, we propose two control strategies to eliminate the secular growth of the argument of the perigee for orbits that are not at the critical inclination. One control strategy is using transverse continuous low-thrust, and the other is using both the transverse and the radial continuous low-thrusts. Fuel optimization in the second control strategy is addressed to make sure that the fuel consumption is the minimum. Both strategies have no effect on other orbital parameters’ secular motion. It is proved that the strategy with transverse control could save more energy than the one with radial control. Simulations show that the second control strategy could save 54.6% and 86% of energy, respectively, compared with the two methods presented in the references.

Hot Deformation Behavior of a Novel Ni-Cr-Mo-B Ultra-heavy Plate Steel by Hot Compression Test

Hot deformation behavior of a novel Ni-Cr-Mo-B heavy plate steel was studied by hot compression tests,which were conducted on a Gleeble-3800thermo-mechanical simulator corresponding to the temperature range of850-1 150℃ with the strain rates of 0.01-10s-1 and the true strain of 0.8.The results suggest that the majority of flow curves exhibit a typical dynamic recrystallization（DRX）behavior with an apparent single peak stress followed by agradual fall towards a steady-state stress.Important characteristic parameters of flow behavior as critical stress/strain for initiation of DRX and peak and steady-state stress/strain were derived from curves of strain hardening rate versus stress and stress versus strain,respectively.Material constants of the investigated steel were determined based on Arrhenius-type constitutive equation,and then the peak stress was predicted by the equation with the hot deformation activation energy of 379 139J/mol,and the predicted values agree well with the experimental values.Furthermore,the effect of Zener-Hollomon parameter on the characteristic points of flow curves was studied using the power law relation,and the ratio of critical stress and strain to peak stress and strain were found to be 0.91and0.46,respectively.