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.

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

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.

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.

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.

Robust Estimation of Parameters in Nonlinear Ordinary Differential Equation Models

Ordinary differential equation(ODE) models are widely used to model dynamic processes in many scientific fields.Parameter estimation is usually a challenging problem,especially in nonlinear ODE models.The most popular method,nonlinear least square estimation,is shown to be strongly sensitive to outliers.In this paper,robust estimation of parameters using M-estimators is proposed,and their asymptotic properties are obtained under some regular conditions.The authors also provide a method to adjust Huber parameter automatically according to the observations.Moreover,a method is presented to estimate the initial values of parameters and state variables.The efficiency and robustness are well balanced in Huber estimators,which is demonstrated via numerical simulations and chlorides data analysis.

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.

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.

Soil Wetting Patterns and Water Distribution as Affected by Irrigation for Uncropped Ridges and Furrows

The ridge-furrow tillage combined with furrow irrigation is being more widely applied and has been shown to be effective in the Loess Plateau of China. Accurate characterization of water infiltration behavior under ridge-furrow irrigation could provide guidelines and criteria for future irrigation system design and operation. Our objective was to investigate soil water behavior during ponding infiltration in a cross-sectional ridge-furrow configuration. Soil water movement within three different soil textures was tested by tracking the spatial and temporal soil water content(SWC) variations in a soil chamber. The two-dimensional transient flow initially transferred rapidly, but gradually decreased with elapsed infiltration time, approaching a stable flow after 90 min. A technical parameter equation incorporating the Philip equation was developed using the water balance method to accurately predict total applied water volume(TAWV). The wetting patterns moved outward in an elliptical shape. The wetted lateral and downward distances fitted using equations accounted for capillary and gravitational driving forces in variably wetted soil media. Increasing initial SWC resulted in an increase in wetted soil volume, which can also be caused by decreasing bulk density in a homogeneous soil. Higher water level produced greater wetted lateral distance and more irrigation uniformity. The wetted lateral distance was almost identical to the wetted depth in silty clay loam soil; hence ridge-furrow irrigation should be implemented in such finer-textured soils. The wetted soil volume differed markedly among different soil textures(hydraulic properties), demonstrating that these properties can largely determine soil water spreading patterns and distribution.

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.

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.