Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.

Comparative structural and electrochemical properties of mixed P2/O′3-layered sodium nickel manganese oxide prepared by sol-gel and electrospinning methods:Effect of Na-excess content

The effect of Na-excess content in the precursor on the structural and electrochemical performances of sodium nickel manganese oxide(NNMO)prepared by sol-gel and electrospinning methods is investigated in this paper.X-ray diffraction results of the prepared NNMO without adding Na-excess content indicate sodium loss,while the mixed phase of P2/O′3-type layered NNMO presented after adding Na-excess content.Compared with the sol-gel method,the secondary phase of NiO is more suppressed by using the electrospinning method,which is further confirmed by field emission scanning electron microscope images.N_(2) adsorption-desorption isotherms show no remarkably difference in specific surface areas between different preparation methods and Na-excess contents.The analysis of X-ray absorption near edge structure indicates that the oxidation states of Ni and Mn are+2 and+4,respectively.For the electrochemical properties,superior electrochemical performance is observed in the NNMO electrode with a low Na-excess content of 5wt%.The highest specific capacitance is 36.07 F·g^(-1)at0.1 A·g^(-1)in the NNMO electrode prepared by using the sol-gel method.By contrast,the NNMO electrode prepared using the electrospinning method with decreased Na-excess content shows excellent cycling stability of 100%after charge-discharge measurements for 300 cycles.Therefore,controlling the Na excess in the precursor together with the preparation method is important for improving the electrochemical performance of Na-based electrode materials in supercapacitors.

A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.

Experimental study on secondary air mixing along the bed height in a circulating fluidized bed with a multitracer-gas method

A multitracer-gas method was proposed to study the secondary air(SA)mixing along the bed height in a circulating fluidized bed(CFB)using carbon monoxide(CO),oxygen(O_(2)),and carbon dioxide(CO_(2))as tracer gases.Experiments were carried out on a cold CFB test rig with a cross-section of 0.42 m×0.73 m and a height of 5.50 m.The effects of superficial velocity,SA ratio,bed inventory,and particle diameter on the SA mixing were investigated.The results indicate that there are some differences in the measurement results obtained using different tracer gases,wherein the deviation between CO and CO_(2) ranges from 42%to 66%and that between O_(2) and CO_(2) ranges from 45%to 71%in the lower part of the fluidized bed.However,these differences became less pronounced as the bed height increased.Besides,the high solid concentration and fine particle diameter in the CFB may weaken the difference.The measurement results of different tracer gases show the same trends under the variation of operating parameters.Increasing superficial velocity and SA ratio and decreasing particle diameter result in better mixing of the SA.The effect of bed inventory on SA mixing is not monotonic.

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Seasonal variability of the mixed layer depth determined using an improved maximum angle method in the Arctic basins

To investigate the spatiotemporal variations in the mixed layer depth(MLD)in the Arctic basins,a new criterion to determine the MLD,called the improved maximum angle method(IMAM),was developed.A total of 45123 potential density profiles collected using Ice-Tethered Profilers(ITPs)in the Arctic basins during 2005-2021 were used to demonstrate the method’s effectiveness.By comparing the results obtained by the fixed threshold method(FTM),percentage threshold method(PTM),and maximum gradient method(MGM)for profiles in the Canada Basin,Makarov Basin,and Eurasian Basin,we determined that the quality index(1.0 for perfect identification of the MLD)of the IMAM regarding the assessment of the MLD determination method reached 0.94,which is much greater than those of other criteria.Moreover,two types of the density profiles were identified based on the mixed layer development stage.The MLDs of the typical profiles determined using the IMAM were found to have better consistency with the original definition.By utilizing the new mixed layer criterion,the seasonal variations and regional differences in the MLD in the Arctic basins were analyzed.Spatially,the summer and winter MLDs in the Canada Basin were the shallowest(13.55 m in summer,26.76 m in winter)than those in the Makarov(29.51 m in summer,49.08 m in winter)and Eurasian(20.36 m in summer,46.81 m in winter)basins due to the stable stratification in the upper ocean and the subsequent small effects of dynamic and thermodynamic processes(wind-driven stirring and brine rejection)in the Canada Basin.Seasonally,in the three Arctic basins,the average MLD was shallowest(22.77 m)in summer;it deepened through autumn and reached a winter maximum(41.12 m).

Mixed Method in Language Learner Cognition

Research on mixed method has made great development.In order to explore the practical application of mixed method,this article starts from the perspective of language learner cognition and selects The Modern Language Journal and Language Teaching Research as the research journals.It explores some empirical papers that used mixed method to learn the specific research designs of mixed method as well as the main means of its application.The study finds that mixed method has been applied in several fields and is more scientifically reliable than qualitative and quantitative methods especially in language learner cognition,and the different research tools used in the field of language learner cognition demonstrate the flexibility and relevance of mixed method data collection.

Factors Related to Engaging in Physical Activity: A Mixed Methods Study of Female University Students

Objective: As a needs assessment for intervention, quantitative and qualitative methods were used to examine attitude, subjective norms, perceived behavioral control, intention, knowledge, and weight control status related to physical activity in female university students within the Theory of Planned Behavior (TPB). Methods: A two-phase mixed method design was used. In Phase I, 362 students participated in an online survey, and in Phase II, 33 students participated in five focus group discussions. Ages of participants ranged from 18 to 45 years old, with 18 - 25 year olds making up over 74% of the sample. Results: Attitude, subjective norms, and perceived behavioral control, along with weight control status of trying to lose weight, were found to be significant predictors of intention to follow physical activity recommendations, which in turn were the strongest predictor of physical activity. Knowledge was not found to be significant. Group discussions revealed barriers to meeting physical activity recommendations, which included lack of companionship and social support, lack of motivation, time and cost restrictions, and lack of privacy in the gym. Social norms exerted both positive and negative influences. Conclusion: The mixed method approach provided a deeper insight into the influential factors pertaining to physical activity among female students, and results could be used in further research to develop effective interventions.

Testing a mobile app for child abuse treatment: A mixed methods study

Objective:This study provides a preliminary evaluation of the usability and acceptability of a mobile application(sexual assault care algorithm,SACA).Methods:An explanatory sequential mixed methods research was used.A quantitative survey was followed up by a qualitative study.A convenience sample of participants(n=4)was recruited.The research was conducted on a one-on-one basis.In the quantitative phase,a random assignment technique was used to divide four participants into two groups of two participants each.Post-Study System Usability Questionnaire(PSSUQ)and Acceptability e-Scale were used to collect quantitative data.In the qualitative phase,interview,observation,and documentation were used to collect qualitative data.Data were analyzed both quantitative and qualitatively.The qualitative data were linked with the initial quantitative data to determine how the follow-up qualitative data helped explain the initial quantitative results.Results:The quantitative results suggested that SACA has high usability(5.05±1.83)and acceptability(3.81±1.22).The qualitative results further indicate that the participants thought SACA was easy to use and useful,and most of them would recommend it to others.Areas of improvement include adding features that would calculate and validate the elapsed time since the sexual assault,adding explanations to some buttons,and providing training.Conclusions:Our findings highlight the value of using a mixed methods research design to conduct a usability and acceptability test.Nurses are more likely to adopt a new technology for their evidencebased practice when the technology is easy to use and useful and requires less time to find the right piece of guideline evidence.Individualized training needs to be designed based on users'characteristics.

Error Estimates of H^1-Galerkin Mixed Methods for the Viscoelasticity Wave Equation

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.

TWO LEVEL SCHWARZ METHODS OF MIXED FINITE ELEMENT APPROXIMATION OF BIHARMONIC PROBLEM

In this paper,the two level additive Schwarz algorithm of mixed finite element.dts-cretization of Inharmonic problem is presented,the rate of convergenece is obtained.Moreover,the two level multiplicative Schwarz algorithm is considered.

IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.

MIXED COMPATIBLE ELEMENT AND MIXED HYBRID INCOMPATIBLE ELEMENT VARIATIONAL METHODS IN DYNAMICS OF VISCOUS BAROTROPIC FLUIDS

This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTA-TION (Ⅰ)-THE CONTINUOUS-TIME CASE

An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element(MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal.

Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations

The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.

Emerging HIV Epidemic in the North-Eastern State of Assam, India: An Exploratory Study Using Mixed-Methods Approach

Background: The national HIV scenario in India has improved impressively during past two decades. Contrastingly, the State-level HIV sentinel surveil-lance and routine programme data from various testing facilities indicated an increasing HIV prevalence among antenatal clinic attendees and female sex workers (FSWs) in three districts of Assam. Objectives: 1) To explore the reasons behind increasing adult HIV prevalence and 2) To understand the role of FSW and Migrants/long distance truckers as drivers of the HIV epi-demic in these districts. Methodology: Three sources of data were utilized in this concurrent mixed methods study—1) existing programme data for past three years;2) questionnaire-based data for a case-control study, where dur-ing past six months at designated testing facilities HIV(+) married women were “cases” and age-matched HIV(?) women from the same district were “controls”. Spouses of these women were also interviewed separately;and 3) a qualitative study, where focus group discussions were conducted among FSWs, outgoing male migrant labourers and long-distance truckers. Results: The study revealed high levels of unsafe sexual practices among the FSWs. Sometimes in poverty-struck areas, women, not identifying themselves as sex workers, sold sex on a part-time basis to earn extra money for financial sup-port and often remained invisible to the programme. The clients of the sex workers, male migrants and truckers also revealed various risk behaviours for contracting and transmitting HIV infection. Conclusion: Population and context specific programme strategies are required to halt the rising trend of HIV infection in the general population in Assam.

Determinants of Risky Sexual Behaviour among Inmates in Katsina Correctional Service: A Mixed Methods Study

Background: Incarceration does not vitiate sexual desire. Therefore, sexual activities occur behind bars, regardless of the stringent rules in correctional institutions. However, little has been documented about risky sexual behaviors, determinants, and experiences among inmates of correctional institutions in Katsina State, Nigeria. The study determined the sexual practices, prevalence, and determinants of risky sexual behaviors among prison inmates in Katsina. Methodology: A descriptive cross-sectional design with concurrent mixed methods of data collection was used to interview 216 inmates using a semi-structured questionnaire supplemented with 22 in-depth interviews. Result: Most (94%) respondents were male, almost half (44.4%) had secondary education, more than half (55.1%) were engaged in business or trading before incarceration, and the majority (75.9%) were awaiting trial. Nearly all inmates (98.6%) reported having sexual desire. Drug use (80.1%) and unprotected sex (79.2%) were quite common but sexual violence was low (7.4%). The number of sexual partners of respondents remained a significant predictor of sexual activity. Inmates who had one (1) or no sexual partner were 64% less likely to engage in risky sexual activity within the confines of the prison (AOR = 0.36, 95% CI = 0.20 - 0.63, p = 0.01). Qualitative interviews revealed the denial of occurrence of sexual activity in prison despite sexual desire felt by inmates;loneliness, poverty, and curiosity as motives for sexual relations;denial of occurrence of sexual violence in prison;and drug use and use of unsterilized sharps as risky sexual behaviors. Conclusion: Despite the disciplinary action meted out on inmates, prisoners still engaged in a range of risky sexual behaviors. Conjugal visitations for married inmates could be considered to reduce sexually deviant and risky alternatives of relieving sexual desire among prisoners.