In this paper, some theoretical mathematical aspects of the known predator-prey problem are considered by relaxing the assumptions that interaction of a predation leads to little or no effect on growth of the prey pop...In this paper, some theoretical mathematical aspects of the known predator-prey problem are considered by relaxing the assumptions that interaction of a predation leads to little or no effect on growth of the prey population and the prey growth rate parameter is a positive valued function of time. The predator growth model is derived considering that the prey follows a known growth models viz., Logistic and Von Bertalanffy. The result shows that the predator’s population growth models look to be new functions. For either models, the predator population size either converges to a finite positive limit or to 0 or diverges to +∞. It is shown algebraically and illustrated pictorially that there is a condition at which the predator-prey population models both converge to the same finite limit. Derivations and simulation studies are provided in the paper. Analysis of equilibrium points and stability is also included.展开更多
In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,...In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,and particularly,we obtain slant kink-wave solutions for the inhomogeneous Burgers(InhB)type equation.Next,we prove the integrability of the InhB equation in the sense of Lax pair.Furthermore,we study the spreading rate of the moving domain occupied by mass for the 1D Cauchy problem with compact support initial density.We find that the expanding domain grows exponentially in time,provided that the solutions exist and smooth at all time.Finally,we extend the corresponding results of the inhomogeneous pressureless Euler equations to the radially symmetric multi-dimensional case.展开更多
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokho...The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.展开更多
Vulnerability forecasting models help us to predict the number of vulnerabilities that may occur in the future for a given Operating System (OS). There exist few models that focus on quantifying future vulnerabilities...Vulnerability forecasting models help us to predict the number of vulnerabilities that may occur in the future for a given Operating System (OS). There exist few models that focus on quantifying future vulnerabilities without consideration of trend, level, seasonality and non linear components of vulnerabilities. Unlike traditional ones, we propose a vulnerability analytic prediction model based on linear and non-linear approaches via time series analysis. We have developed the models based on Auto Regressive Moving Average (ARIMA), Artificial Neural Network (ANN), and Support Vector Machine (SVM) settings. The best model which provides the minimum error rate is selected for prediction of future vulnerabilities. Utilizing time series approach, this study has developed a predictive analytic model for three popular Desktop Operating Systems, namely, Windows 7, Mac OS X, and Linux Kernel by using their reported vulnerabilities on the National Vulnerability Database (NVD). Based on these reported vulnerabilities, we predict ahead their behavior so that the OS companies can make strategic and operational decisions like secure deployment of OS, facilitate backup provisioning, disaster recovery, diversity planning, maintenance scheduling, etc. Similarly, it also helps in assessing current security risks along with estimation of resources needed for handling potential security breaches and to foresee the future releases of security patches. The proposed non-linear analytic models produce very good prediction results in comparison to linear time series models.展开更多
SAS and other popular statistical packages provide support for survey data with sampling weights. For example, PROC MEANS and PROC LOGISTIC in SAS have their counterparts PROC SURVEYMEANS and PROC SURVEYLOGISTIC to fa...SAS and other popular statistical packages provide support for survey data with sampling weights. For example, PROC MEANS and PROC LOGISTIC in SAS have their counterparts PROC SURVEYMEANS and PROC SURVEYLOGISTIC to facilitate analysis of data from complex survey studies. On the other hand, PROC MEANS and many other classic SAS procedures also provide an option for including weights and yield identical point estimates, but different standard errors (SEs), as their corresponding survey procedures. This paper takes an in-depth look at different types of weights and provides guidance on use of different SAS procedures.展开更多
Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model...Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L<sup>2</sup>-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.展开更多
In recent years, the use of cover crops is becoming a popular technology among growers in many regions of the United States, which is expected to deliver various benefits such as improving soil health, increasing soil...In recent years, the use of cover crops is becoming a popular technology among growers in many regions of the United States, which is expected to deliver various benefits such as improving soil health, increasing soil organic matter, controlling weeds, and helping conserve soil water and nutrients. Although expecting these benefits seems reasonable, it is challenging to know how much of these benefits to expect under specific situations. The potential effect of cover crops on soil water conservation is especially significant because of the documented impact of soil water on crop yield, especially for dryland cropping systems. Some researchers have found that planting a cover crop tended to increase soil water, while others have reported the opposite effect. Information on the impact of cover crops on soil water in cotton (<em>Gossypium hirsutum</em> L.) production systems in South Carolina is currently lacking. Therefore, the objective of this study was to quantify the effect of cover crops on soil water and cotton yield. A field experiment was conducted in South Carolina during winter, spring, and summer of 2015, with three cover crop treatments. The treatments included: 1) rye (<em>Secale cereale </em>L.), planted alone;2) a mix of six cover crop species;and 3) a control treatment with no-cover. The cover crop was established in the winter, terminated in the spring, and cotton was grown during the summer. Soil water was measured at different depths using capacitance probes and a neutron probe. Our results showed no significant differences in soil water and cotton yield among the cover crop treatments. These results suggest that under the humid conditions of this study, any short-term effect of the cover crop on soil water was masked by timely rain.展开更多
We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems,...We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.展开更多
We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems.Based on properties of eigenvalue and adjoint eigenvalue prob...We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems.Based on properties of eigenvalue and adjoint eigenvalue problems,we solve the corresponding reflectionless Riemann-Hilbert problems,where eigenvalues could equal adjoint eigenvalues,and formulate their soliton solutions via those reflectionless Riemann-Hilbert problems.Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.展开更多
A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave solutions.It is proved that it is equivalent to a polynomial identity that an arbitrary linear combinati...A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave solutions.It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V equation.It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.展开更多
Computational gas dynamical simulations using the WENO-LF method are applied to modeling the high Mach number astrophysical jet XZ Tauri, including the effects of radiative cooling. Mach 55 simulations of the pulsed p...Computational gas dynamical simulations using the WENO-LF method are applied to modeling the high Mach number astrophysical jet XZ Tauri, including the effects of radiative cooling. Mach 55 simulations of the pulsed proto-jet are presented and analyzed in terms of interacting nonlinear waves： terminal Mach disks, bow shocks, and Meshkov-Richtmyer instabilities of the leading jet contact boundary.展开更多
In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown ...In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.展开更多
Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid na...Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's linearized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condition.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.展开更多
Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and stra...Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.展开更多
In this paper, a new numerical scheme for solving first-order hyperbolic partial differential equations is proposed and is implemented in the simulation study of macroscopic traffic flow model with constant velocity a...In this paper, a new numerical scheme for solving first-order hyperbolic partial differential equations is proposed and is implemented in the simulation study of macroscopic traffic flow model with constant velocity and linear velocity-density relationship. Macroscopic traffic flow model is first developed by Lighthill Whitham and Richards (LWR) and used to study traffic flow by collective variables such as flow rate, velocity and density. The LWR model is treated as an initial value problem and its numerical simulations are presented using numerical schemes. A variety of numerical schemes are available in literature to solve first order hyperbolic equations. Of these the well-known ones include one-dimensional explicit: Upwind, Downwind, FTCS, and Lax-Friedrichs schemes. Having been studied carefully the space and time mesh sizes, and the patterns of all these schemes, a new scheme has been developed and named as one-dimensional explicit Tolesa numerical scheme. Tolesa numerical scheme is one of the conditionally stable and highest rates of convergence schemes. All the said numerical schemes are applied to solve advection equation pertaining traffic flows. Also the one-dimensional explicit Tolesa numerical scheme is another alternative numerical scheme to solve advection equation and apply to traffic flows model like other well-known one-dimensional explicit schemes. The effect of density of cars on the overall interactions of the vehicles along a given length of the highway and time are investigated. Graphical representations of density profile, velocity profile, flux profile, and in general the fundamental diagrams of vehicles on the highway with different time levels are illustrated. These concepts and results have been arranged systematically in this paper.展开更多
In studies on psychiatry and neurodegenerative diseases,it is common to have data that are correlated due to the hierarchical structure in data collection or to repeated measures on the subject longitudinally.However,...In studies on psychiatry and neurodegenerative diseases,it is common to have data that are correlated due to the hierarchical structure in data collection or to repeated measures on the subject longitudinally.However,the feedback effect created due to time-dependent covariates in these studies is often overlooked and seldom modelled.This article reviews the methodological development of feedback effects with marginal models for longitudinal data and discusses their implementation.展开更多
We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived...We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived,and characterization of SSP IMEX methods is provided following the recent work by Spijker.Stability properties of these methods with respect to the decoupled linear system with a complex parameter,and a coupled linear system with real parameters are also investigated.Examples of methods up to the order p=4 and stage order q—p are provided.Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration,and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes.展开更多
If you don’t use it,you lose it.School breaks,during which students do not regularly participate in instruction,can therefore have negative consequences on learning.This is especially true for mathematics learning si...If you don’t use it,you lose it.School breaks,during which students do not regularly participate in instruction,can therefore have negative consequences on learning.This is especially true for mathematics learning since skills build progressively on earlier materials.How can we bridge these gaps in formal instruction?The Keeping in School Shape(KisSS)program is a mobile,engaging,innovative,and cost-effective way of using technology to help students who have time off between related math courses stay fresh on prerequisite knowledge and skills.Founded on learning theory and designed on a model of behavioral change,the KiSS program embodies retrieval practice and nudges by sending students a daily multiple-choice review problem via text messaging over school break.After rating their confidence in solving the daily problem students receive feedback and a solution.This study explores measures of participation,accuracy,and confidence in an implementation of the KiSS program over winter break between two sequential introductory engineering courses at a large state university in the Southwest United States.Results indicate that careful attention should be paid to the construction of the first few days of the program,and that encouragement,problem difficulty may improve participation.展开更多
The COVID-19 pandemic has ravaged global health and national economies worldwide.Testing and isolation are effective control strategies to mitigate the transmission of COVID-19,especially in the early stage of the dis...The COVID-19 pandemic has ravaged global health and national economies worldwide.Testing and isolation are effective control strategies to mitigate the transmission of COVID-19,especially in the early stage of the disease outbreak.In this paper,we develop a deterministic model to investigate the impact of testing and compliance with isolation on the transmission of COVID-19.We derive the control reproduction number R_(C),which gives the threshold for disease elimination or prevalence.Using data from New York State in the early stage of the disease outbreak,we estimate R_(C)=7:989.Both elasticity and sensitivity analyses show that testing and compliance with isolation are significant in reducing R_(C) and disease prevalence.Simulation reveals that only high testing volume combined with a large proportion of individuals complying with isolation have great impact on mitigating the transmission.The testing starting date is also crucial:the earlier testing is implemented,the more impact it has on reducing the infection.The results obtained here would also be helpful in developing guidelines of early control strategies for pandemics similar to COVID-19.展开更多
The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these...The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these interventions is now being threatened by numerous factors,such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening(when humans are not protected by the bednets).This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics.A notable feature of the model is that it stratifies the mosquito population in terms of type(wild or resistant to insecticides)and feeding preference(indoor or outdoor).The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial diseasefree equilibrium,the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist).Simulations of the model,using data relevant to malaria transmission dynamics in Ethiopia(a malaria-endemic nation),show that the use of optimal ITNs alone,or in combination with optimal IRS,is more effective than the singular implementation of an optimal IRS-only strategy.Further,when the effect of the fitness cost of insecticide resistance with respect to fecundity(i.e.,assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes)is accounted for,numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease,and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.展开更多
文摘In this paper, some theoretical mathematical aspects of the known predator-prey problem are considered by relaxing the assumptions that interaction of a predation leads to little or no effect on growth of the prey population and the prey growth rate parameter is a positive valued function of time. The predator growth model is derived considering that the prey follows a known growth models viz., Logistic and Von Bertalanffy. The result shows that the predator’s population growth models look to be new functions. For either models, the predator population size either converges to a finite positive limit or to 0 or diverges to +∞. It is shown algebraically and illustrated pictorially that there is a condition at which the predator-prey population models both converge to the same finite limit. Derivations and simulation studies are provided in the paper. Analysis of equilibrium points and stability is also included.
基金Supported by the Henan Natural Science Foundation(242300421397)the Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions(25ZX013)+2 种基金the Scientific Research Team Plan of Zhengzhou University of Aeronautics(23ZHTD01003)the National Natural Science Foundation of China(11971475)the FLASS Internationalization and Exchange Scheme(FLASS/IE−D09/19-20−FLASS).
文摘In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,and particularly,we obtain slant kink-wave solutions for the inhomogeneous Burgers(InhB)type equation.Next,we prove the integrability of the InhB equation in the sense of Lax pair.Furthermore,we study the spreading rate of the moving domain occupied by mass for the 1D Cauchy problem with compact support initial density.We find that the expanding domain grows exponentially in time,provided that the solutions exist and smooth at all time.Finally,we extend the corresponding results of the inhomogeneous pressureless Euler equations to the radially symmetric multi-dimensional case.
基金supported in part by NSFC(11975145 and 11972291)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.
文摘Vulnerability forecasting models help us to predict the number of vulnerabilities that may occur in the future for a given Operating System (OS). There exist few models that focus on quantifying future vulnerabilities without consideration of trend, level, seasonality and non linear components of vulnerabilities. Unlike traditional ones, we propose a vulnerability analytic prediction model based on linear and non-linear approaches via time series analysis. We have developed the models based on Auto Regressive Moving Average (ARIMA), Artificial Neural Network (ANN), and Support Vector Machine (SVM) settings. The best model which provides the minimum error rate is selected for prediction of future vulnerabilities. Utilizing time series approach, this study has developed a predictive analytic model for three popular Desktop Operating Systems, namely, Windows 7, Mac OS X, and Linux Kernel by using their reported vulnerabilities on the National Vulnerability Database (NVD). Based on these reported vulnerabilities, we predict ahead their behavior so that the OS companies can make strategic and operational decisions like secure deployment of OS, facilitate backup provisioning, disaster recovery, diversity planning, maintenance scheduling, etc. Similarly, it also helps in assessing current security risks along with estimation of resources needed for handling potential security breaches and to foresee the future releases of security patches. The proposed non-linear analytic models produce very good prediction results in comparison to linear time series models.
文摘SAS and other popular statistical packages provide support for survey data with sampling weights. For example, PROC MEANS and PROC LOGISTIC in SAS have their counterparts PROC SURVEYMEANS and PROC SURVEYLOGISTIC to facilitate analysis of data from complex survey studies. On the other hand, PROC MEANS and many other classic SAS procedures also provide an option for including weights and yield identical point estimates, but different standard errors (SEs), as their corresponding survey procedures. This paper takes an in-depth look at different types of weights and provides guidance on use of different SAS procedures.
文摘Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L<sup>2</sup>-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.
文摘In recent years, the use of cover crops is becoming a popular technology among growers in many regions of the United States, which is expected to deliver various benefits such as improving soil health, increasing soil organic matter, controlling weeds, and helping conserve soil water and nutrients. Although expecting these benefits seems reasonable, it is challenging to know how much of these benefits to expect under specific situations. The potential effect of cover crops on soil water conservation is especially significant because of the documented impact of soil water on crop yield, especially for dryland cropping systems. Some researchers have found that planting a cover crop tended to increase soil water, while others have reported the opposite effect. Information on the impact of cover crops on soil water in cotton (<em>Gossypium hirsutum</em> L.) production systems in South Carolina is currently lacking. Therefore, the objective of this study was to quantify the effect of cover crops on soil water and cotton yield. A field experiment was conducted in South Carolina during winter, spring, and summer of 2015, with three cover crop treatments. The treatments included: 1) rye (<em>Secale cereale </em>L.), planted alone;2) a mix of six cover crop species;and 3) a control treatment with no-cover. The cover crop was established in the winter, terminated in the spring, and cotton was grown during the summer. Soil water was measured at different depths using capacitance probes and a neutron probe. Our results showed no significant differences in soil water and cotton yield among the cover crop treatments. These results suggest that under the humid conditions of this study, any short-term effect of the cover crop on soil water was masked by timely rain.
基金supported in part by the National Natural Science Foundation of China (Grant Nos. 11975145, 11972291, and 51771083)the Ministry of Science and Technology of China (Grant No. G2021016032L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant No. 17 KJB 110020)。
文摘We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12271488,11975145,11972291,and 51771083)the Ministry of Science and Technology of China(Grant No.G2021016032L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(Grant No.17 KJB 110020).
文摘We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems.Based on properties of eigenvalue and adjoint eigenvalue problems,we solve the corresponding reflectionless Riemann-Hilbert problems,where eigenvalues could equal adjoint eigenvalues,and formulate their soliton solutions via those reflectionless Riemann-Hilbert problems.Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.
基金supported in part by NSFC under the Grant Nos.11975145 and 11972291。
文摘A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave solutions.It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V equation.It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.
文摘Computational gas dynamical simulations using the WENO-LF method are applied to modeling the high Mach number astrophysical jet XZ Tauri, including the effects of radiative cooling. Mach 55 simulations of the pulsed proto-jet are presented and analyzed in terms of interacting nonlinear waves： terminal Mach disks, bow shocks, and Meshkov-Richtmyer instabilities of the leading jet contact boundary.
文摘In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.
文摘Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's linearized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condition.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.
基金funded by King Saud University,Riyadh,Saudi Arabia.
文摘Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.
文摘In this paper, a new numerical scheme for solving first-order hyperbolic partial differential equations is proposed and is implemented in the simulation study of macroscopic traffic flow model with constant velocity and linear velocity-density relationship. Macroscopic traffic flow model is first developed by Lighthill Whitham and Richards (LWR) and used to study traffic flow by collective variables such as flow rate, velocity and density. The LWR model is treated as an initial value problem and its numerical simulations are presented using numerical schemes. A variety of numerical schemes are available in literature to solve first order hyperbolic equations. Of these the well-known ones include one-dimensional explicit: Upwind, Downwind, FTCS, and Lax-Friedrichs schemes. Having been studied carefully the space and time mesh sizes, and the patterns of all these schemes, a new scheme has been developed and named as one-dimensional explicit Tolesa numerical scheme. Tolesa numerical scheme is one of the conditionally stable and highest rates of convergence schemes. All the said numerical schemes are applied to solve advection equation pertaining traffic flows. Also the one-dimensional explicit Tolesa numerical scheme is another alternative numerical scheme to solve advection equation and apply to traffic flows model like other well-known one-dimensional explicit schemes. The effect of density of cars on the overall interactions of the vehicles along a given length of the highway and time are investigated. Graphical representations of density profile, velocity profile, flux profile, and in general the fundamental diagrams of vehicles on the highway with different time levels are illustrated. These concepts and results have been arranged systematically in this paper.
文摘In studies on psychiatry and neurodegenerative diseases,it is common to have data that are correlated due to the hierarchical structure in data collection or to repeated measures on the subject longitudinally.However,the feedback effect created due to time-dependent covariates in these studies is often overlooked and seldom modelled.This article reviews the methodological development of feedback effects with marginal models for longitudinal data and discusses their implementation.
文摘We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived,and characterization of SSP IMEX methods is provided following the recent work by Spijker.Stability properties of these methods with respect to the decoupled linear system with a complex parameter,and a coupled linear system with real parameters are also investigated.Examples of methods up to the order p=4 and stage order q—p are provided.Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration,and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes.
文摘If you don’t use it,you lose it.School breaks,during which students do not regularly participate in instruction,can therefore have negative consequences on learning.This is especially true for mathematics learning since skills build progressively on earlier materials.How can we bridge these gaps in formal instruction?The Keeping in School Shape(KisSS)program is a mobile,engaging,innovative,and cost-effective way of using technology to help students who have time off between related math courses stay fresh on prerequisite knowledge and skills.Founded on learning theory and designed on a model of behavioral change,the KiSS program embodies retrieval practice and nudges by sending students a daily multiple-choice review problem via text messaging over school break.After rating their confidence in solving the daily problem students receive feedback and a solution.This study explores measures of participation,accuracy,and confidence in an implementation of the KiSS program over winter break between two sequential introductory engineering courses at a large state university in the Southwest United States.Results indicate that careful attention should be paid to the construction of the first few days of the program,and that encouragement,problem difficulty may improve participation.
基金The authors thank the Department of Mathematics at the University of Central Florida,which received funding through the NSF Grant DMS-2132585 to provide support to organize and participate in the“CBMS Conference:Interface of Mathe-matical Biology and linear Algebra"where this research was initiated and developedLN.was partially funded by the Charles Phelps Taft Research Center at the University of Cincinnati,the research of PvdD is partially supported by an NSERC DiscoveryGrant 2016-03677the research ofW.Z.is supported by Simons Foundation,Award Number:714029.
文摘The COVID-19 pandemic has ravaged global health and national economies worldwide.Testing and isolation are effective control strategies to mitigate the transmission of COVID-19,especially in the early stage of the disease outbreak.In this paper,we develop a deterministic model to investigate the impact of testing and compliance with isolation on the transmission of COVID-19.We derive the control reproduction number R_(C),which gives the threshold for disease elimination or prevalence.Using data from New York State in the early stage of the disease outbreak,we estimate R_(C)=7:989.Both elasticity and sensitivity analyses show that testing and compliance with isolation are significant in reducing R_(C) and disease prevalence.Simulation reveals that only high testing volume combined with a large proportion of individuals complying with isolation have great impact on mitigating the transmission.The testing starting date is also crucial:the earlier testing is implemented,the more impact it has on reducing the infection.The results obtained here would also be helpful in developing guidelines of early control strategies for pandemics similar to COVID-19.
基金The authors are grateful to National Institute for Mathematical and Biological Synthesis(NIMBioS)for funding theWorking Group on Climate Change and Vector-borne Diseases(VBDs)held from 2013 to 2015.NIMBioS is an Institute sponsored by the National Science Foundation,the U.S.Department of Homeland Security,and the U.S.Department of Agriculture through NSF Award#EF-0832858with additional support from The University of Tennessee,Knoxville.The authors are grateful to the anonymous reviewers for their constructive comments.
文摘The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these interventions is now being threatened by numerous factors,such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening(when humans are not protected by the bednets).This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics.A notable feature of the model is that it stratifies the mosquito population in terms of type(wild or resistant to insecticides)and feeding preference(indoor or outdoor).The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial diseasefree equilibrium,the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist).Simulations of the model,using data relevant to malaria transmission dynamics in Ethiopia(a malaria-endemic nation),show that the use of optimal ITNs alone,or in combination with optimal IRS,is more effective than the singular implementation of an optimal IRS-only strategy.Further,when the effect of the fitness cost of insecticide resistance with respect to fecundity(i.e.,assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes)is accounted for,numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease,and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.
