Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solve...Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.展开更多
The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier c...The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.展开更多
The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper...The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.展开更多
A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, an...A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.展开更多
The dynamic restoration behavior of 99.99% polycrystalline aluminum was investigated. The deformation was carried out by compression test at 533773 K and initial strain rate of 0.0022 s-1 to a true strain of （1.0） f...The dynamic restoration behavior of 99.99% polycrystalline aluminum was investigated. The deformation was carried out by compression test at 533773 K and initial strain rate of 0.0022 s-1 to a true strain of （1.0） followed by water quench. Polarized optical microscopy and transmission electron microscopy were applied to observe the deformation microstructure. It’s found that discontinuous dynamic recrystallization, which is commonly observed in lower stacking fault energy metals or ultra-high purity aluminum（≥99.999%）, occurs when Zenner-Hollomon parameter（Z parameter） is low, but the true stress—strain curve doesn’t accompany stress oscillation. Continuous dynamic recrystallization occurs when Z parameter is intermediate, and only dynamic recovery takes place if Z parameter is high.展开更多
This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous functions. Furthermore, the suf...This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous functions. Furthermore, the sufficient conditions for the continuity of the even order iterates with finitely many discontinuous points are obtained.展开更多
Apple replant disease(ARD)is a complex agricultural problem caused by multiple stressors that can lead to increased reactive oxygen species(ROS)levels and limited nutrient utilization in plants.However,existing counte...Apple replant disease(ARD)is a complex agricultural problem caused by multiple stressors that can lead to increased reactive oxygen species(ROS)levels and limited nutrient utilization in plants.However,existing countermeasures cannot effectively address this challenge.Here,we used Malus hupehensis as a test organism to investigate whether the pleiotropic molecule dopamine can alleviate ARD using pot experiments.Exogenous application of 100μmol L-1 dopamine significantly promoted the growth of apple seedlings in the replanted soil,with a relative growth rate increase of 17.44%.Our results revealed two major pathways by which dopamine regulates ARD resistance in apple trees.First,dopamine effectively reduces the level of ROS and activates the expression of genes related to nitrogen(N)transport and metabolism.Among those genes,MdNLP5,MdNRT1.1,MdNLP2,MdNRT2.5,MdNLP3,MdNRT2.4,MdNADH-GAGOT,and MdFd-GAGOT were strongly regulated by dopamine.These regulatory effects promoted the uptake and utilization of soil N by the plants.Second,dopamine improved the physical and chemical properties,enhanced microbial community diversity,and promoted mutual cooperation between microbial communities in the soil.Furthermore,dopamine altered the microbial structure of rhizosphere soil(upregulating Clostridiales,Gaiellales,Sordariales and Mortierellales;downregulating Micrococcales,Longimicrobiales,Hypocreales and Cystobasidiales).Notably,dopamine significantly upregulated the abundances of Gaiella and Mortierella,both of which were positively correlated with soil urease activity,soil available N content,plant growth and N uptake.Dopamine also significantly downregulated the abundance of the plant pathogen Gibberella(by 11.71-fold)in replant soil.Our results provide insights into the mechanisms by which dopamine promotes ARD resistance,and can promote the sustainable development of the apple industry.展开更多
In this study,the phase transformations,crystallization kinetics and dissolution mechanism ofβphase(Mg_(17)Al_(12))in magnesium alloy AZ91 were investigated by optical microscopy,X-ray diffraction,differential scanni...In this study,the phase transformations,crystallization kinetics and dissolution mechanism ofβphase(Mg_(17)Al_(12))in magnesium alloy AZ91 were investigated by optical microscopy,X-ray diffraction,differential scanning calorimetry and differential dilatometry.The results indicate that this AZ91 alloy undergoes a phase transformation during aging,a discontinuous precipitation of theβphase(Mg_(17)Al_(12))at 150℃at the grain boundaries and another continuous at 350℃within the grains.The activation energy of the dissolution reaction of theβphase(Mg_(17)Al_(12))under non-isothermal conditions is 116.781 kJ/mol,while it is 129.7383 kJ/mol under isothermal conditions.The Avrami coefficient,n,relevant for the dissolution kinetics of theβphase(Mg_(17)Al_(12))is 1.152 and 1.211 in the non-isothermal and isothermal conditions respectively.The numerical coefficients m and Avrami n are 0.993 and 1.152.展开更多
Microstructural evolution and dynamic recrystallization(DRX)mechanisms of a Ti-48Al-2Cr-2Nb(at.%)alloy prepared by selective electron beam melting(SEBM)during hot deformation at 1150℃and 0.1 s^(-1)were investigated b...Microstructural evolution and dynamic recrystallization(DRX)mechanisms of a Ti-48Al-2Cr-2Nb(at.%)alloy prepared by selective electron beam melting(SEBM)during hot deformation at 1150℃and 0.1 s^(-1)were investigated by hot compression tests,optical microscope(OM),scanning electron microscope(SEM),electron back-scattered diffraction(EBSD)and transmission electron microscope(TEM).The results show that the initial microstructure of the as-SEBMed alloy exhibits layers of coarseγgrains and fineγ+α_(2)+(α_(2)/γ)lamellar mixture grains alternately along the building direction.During the early stage of hot deformation,deformation twins tend to form within the coarse grains,facilitating subsequent deformation,and a small number of DRX grains appear in the fine-grained regions.With the increase of strain,extensive DRX grains are formed through different DRX mechanisms in both coarse and fine-grained regions,involving discontinuous dynamic recrystallization mechanism(DDRX)in the fine-grained regions and a coexistence of DDRX and continuous dynamic recrystallization(CDRX)in the coarsegrained regions.展开更多
In this paper we embark on the study of Dynamic Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system. We give a formal definition of a topological dynamic system in th...In this paper we embark on the study of Dynamic Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system. We give a formal definition of a topological dynamic system in the space of piece-wise continuous functions and show, by way of an example, stability in the sense of Poisson discontinuous function. We prove that a fixed discontinuous function, f, is discontinuous for all its shifts, whereas the trajectory of discontinuous function is not a compact set.展开更多
文摘Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.
文摘The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.
基金Supported by the National Natural Science Foundation of China(10771171)Supported by the 555 Innovation Talent Project of Gansu Province(GS-555-CXRC)+1 种基金Supported by the Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)
文摘The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.
基金supported by the National Key Basic Research Program of China(2013CB036405)the National Natural Science Foundation of China(11002154,41272349,and 41372315)the CAS/SAFEA International Partnership Program for Creative Research Teams(KZCX2-YW-T12)
文摘A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.
基金Project (G1999064908) supported by the National Key Fundamental Research & Development Program of China
文摘The dynamic restoration behavior of 99.99% polycrystalline aluminum was investigated. The deformation was carried out by compression test at 533773 K and initial strain rate of 0.0022 s-1 to a true strain of （1.0） followed by water quench. Polarized optical microscopy and transmission electron microscopy were applied to observe the deformation microstructure. It’s found that discontinuous dynamic recrystallization, which is commonly observed in lower stacking fault energy metals or ultra-high purity aluminum（≥99.999%）, occurs when Zenner-Hollomon parameter（Z parameter） is low, but the true stress—strain curve doesn’t accompany stress oscillation. Continuous dynamic recrystallization occurs when Z parameter is intermediate, and only dynamic recovery takes place if Z parameter is high.
文摘This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous functions. Furthermore, the sufficient conditions for the continuity of the even order iterates with finitely many discontinuous points are obtained.
基金supported by National Natural Science Foundation of China(31901964)the Science and Technology Project of Hebei Education Department,China(BJK2022012)+3 种基金the Innovation Ability Training Project for Graduate Student of Hebei Province,China(CXZZBS2023071)the Introduced Talents Project of Hebei Agricultural University,China(YJ201904)the Key Research and Development Project of Hebei Province,China(21326308D-02-03)the Earmarked Fund for the China Agricultural Research System,China(CARS-27).
文摘Apple replant disease(ARD)is a complex agricultural problem caused by multiple stressors that can lead to increased reactive oxygen species(ROS)levels and limited nutrient utilization in plants.However,existing countermeasures cannot effectively address this challenge.Here,we used Malus hupehensis as a test organism to investigate whether the pleiotropic molecule dopamine can alleviate ARD using pot experiments.Exogenous application of 100μmol L-1 dopamine significantly promoted the growth of apple seedlings in the replanted soil,with a relative growth rate increase of 17.44%.Our results revealed two major pathways by which dopamine regulates ARD resistance in apple trees.First,dopamine effectively reduces the level of ROS and activates the expression of genes related to nitrogen(N)transport and metabolism.Among those genes,MdNLP5,MdNRT1.1,MdNLP2,MdNRT2.5,MdNLP3,MdNRT2.4,MdNADH-GAGOT,and MdFd-GAGOT were strongly regulated by dopamine.These regulatory effects promoted the uptake and utilization of soil N by the plants.Second,dopamine improved the physical and chemical properties,enhanced microbial community diversity,and promoted mutual cooperation between microbial communities in the soil.Furthermore,dopamine altered the microbial structure of rhizosphere soil(upregulating Clostridiales,Gaiellales,Sordariales and Mortierellales;downregulating Micrococcales,Longimicrobiales,Hypocreales and Cystobasidiales).Notably,dopamine significantly upregulated the abundances of Gaiella and Mortierella,both of which were positively correlated with soil urease activity,soil available N content,plant growth and N uptake.Dopamine also significantly downregulated the abundance of the plant pathogen Gibberella(by 11.71-fold)in replant soil.Our results provide insights into the mechanisms by which dopamine promotes ARD resistance,and can promote the sustainable development of the apple industry.
基金founded by Taif University,Taif,Saudi Arabia (TU-DSPP-2024-63).
文摘In this study,the phase transformations,crystallization kinetics and dissolution mechanism ofβphase(Mg_(17)Al_(12))in magnesium alloy AZ91 were investigated by optical microscopy,X-ray diffraction,differential scanning calorimetry and differential dilatometry.The results indicate that this AZ91 alloy undergoes a phase transformation during aging,a discontinuous precipitation of theβphase(Mg_(17)Al_(12))at 150℃at the grain boundaries and another continuous at 350℃within the grains.The activation energy of the dissolution reaction of theβphase(Mg_(17)Al_(12))under non-isothermal conditions is 116.781 kJ/mol,while it is 129.7383 kJ/mol under isothermal conditions.The Avrami coefficient,n,relevant for the dissolution kinetics of theβphase(Mg_(17)Al_(12))is 1.152 and 1.211 in the non-isothermal and isothermal conditions respectively.The numerical coefficients m and Avrami n are 0.993 and 1.152.
基金the financial supports from the Shaanxi Province Key Research and Development Projects,China(No.2023KXJ-071)the National Natural Science Foundation of China(Nos.52274402,52174381)。
文摘Microstructural evolution and dynamic recrystallization(DRX)mechanisms of a Ti-48Al-2Cr-2Nb(at.%)alloy prepared by selective electron beam melting(SEBM)during hot deformation at 1150℃and 0.1 s^(-1)were investigated by hot compression tests,optical microscope(OM),scanning electron microscope(SEM),electron back-scattered diffraction(EBSD)and transmission electron microscope(TEM).The results show that the initial microstructure of the as-SEBMed alloy exhibits layers of coarseγgrains and fineγ+α_(2)+(α_(2)/γ)lamellar mixture grains alternately along the building direction.During the early stage of hot deformation,deformation twins tend to form within the coarse grains,facilitating subsequent deformation,and a small number of DRX grains appear in the fine-grained regions.With the increase of strain,extensive DRX grains are formed through different DRX mechanisms in both coarse and fine-grained regions,involving discontinuous dynamic recrystallization mechanism(DDRX)in the fine-grained regions and a coexistence of DDRX and continuous dynamic recrystallization(CDRX)in the coarsegrained regions.
文摘In this paper we embark on the study of Dynamic Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system. We give a formal definition of a topological dynamic system in the space of piece-wise continuous functions and show, by way of an example, stability in the sense of Poisson discontinuous function. We prove that a fixed discontinuous function, f, is discontinuous for all its shifts, whereas the trajectory of discontinuous function is not a compact set.
