In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified ...In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.展开更多
In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unif...In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.展开更多
In order to investigate and predict the material properties of curved surface AISI 1045 steel component during spot continual induction hardening(SCIH),a 3D model for curved surface workpieces which coupled electromag...In order to investigate and predict the material properties of curved surface AISI 1045 steel component during spot continual induction hardening(SCIH),a 3D model for curved surface workpieces which coupled electromagnetic,temperature and phase transformation fields was built by finite element software ANSYS.A small size inductor and magnetizer were used in this model,which can move along the top surface of workpiece flexibly.The effect of inductor moving velocity and workpiece radius on temperature field was analyzed and the heating delay phenomenon was found through comparing the simulated results.The temperature field results indicate that the heating delay phenomenon is more obvious under high inductor moving velocity condition.This trend becomes more obvious if the workpiece radius becomes larger.The predictions of microstructure and micro-hardness distribution were also carried out via this model.The predicted results show that the inductor moving velocity is the dominated factor for the distribution of 100% martensite region and phase transformation region.The influencing factor of workpiece radius on 100% martensite region and phase transformation region distribution is obvious under relatively high inductor moving velocity but inconspicuous under relatively low inductor moving velocity.展开更多
For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consid...For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.展开更多
Devising an electrocatalyst with brilliant efficiency and satisfactory durability for hydrogen production is of considerable demand,especially for large-scale application.Herein,we adopt a multi-step consequential ind...Devising an electrocatalyst with brilliant efficiency and satisfactory durability for hydrogen production is of considerable demand,especially for large-scale application.Herein,we adopt a multi-step consequential induced strategy to construct a bifunctional electrocatalyst for the overall water splitting.Graphene oxide(GO)was used as a carbon matrix and in situ oxygen source,which was supported by the octahedral PtNi alloy to form the PtxNiy-GO precursor.When calcinating in Ar atmosphere,the oxygen in GO induced the surface segregation of Ni from the PtNi octahedron to form a core-shell structure of Ptx@Niy.Then,the surface-enriched Ni continuously induced the reformation of C in reduced graphene oxide(rGO)to enhance the degree of graphitization.This multi-step induction formed a nanocatalyst Pt_(x)@Ni_(y)-rGO which has very high catalytic efficiency and stability.By optimizing the feeding ratio of PtNi(Pt:Ni=1:2),the electrolytic overall water splitting at 10 mA·cm^(-2) can be driven by an electrolytic voltage of as low as 1.485 V,and hydrogen evolution reaction(HER)only needs an overpotential of 37 mV in 1.0 M KOH aqueous solution.Additionally,the catalyst exhibited consistent existence form in both HER and oxygen evolution reaction(OER),which was verified by switching the anode and cathode of the cell in the electrolysis of water.This work provides a new idea for the synthesis and evaluation of the bifunctional catalysts for water splitting.展开更多
文摘In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.
文摘In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.
基金Project (51175392) supported by the National Natural Science Foundation of ChinaProject (2014BAA012) supported by the Key Project of Hubei Province Science & Technology Pillar Program,ChinaProjects (2012-IV-067,2013-VII-020) supported by the Fundamental Research Funds for the Central Universities of China
文摘In order to investigate and predict the material properties of curved surface AISI 1045 steel component during spot continual induction hardening(SCIH),a 3D model for curved surface workpieces which coupled electromagnetic,temperature and phase transformation fields was built by finite element software ANSYS.A small size inductor and magnetizer were used in this model,which can move along the top surface of workpiece flexibly.The effect of inductor moving velocity and workpiece radius on temperature field was analyzed and the heating delay phenomenon was found through comparing the simulated results.The temperature field results indicate that the heating delay phenomenon is more obvious under high inductor moving velocity condition.This trend becomes more obvious if the workpiece radius becomes larger.The predictions of microstructure and micro-hardness distribution were also carried out via this model.The predicted results show that the inductor moving velocity is the dominated factor for the distribution of 100% martensite region and phase transformation region.The influencing factor of workpiece radius on 100% martensite region and phase transformation region distribution is obvious under relatively high inductor moving velocity but inconspicuous under relatively low inductor moving velocity.
基金partially supported by the NSFC(11571177)the Priority Academic Program Development of Jiangsu Higher Education Institutionspartially funded by the DFG through the Sino-German Project "Analysis of PDEs and Applications"
文摘For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.
基金supported by the National Natural Science Foundation of China(No.21872020)1226 Engineering Health Major Project(Nos.BWS17J028 and AWS16J018)Fundamental Research Funds for the Central Universities(No.N180705004).
文摘Devising an electrocatalyst with brilliant efficiency and satisfactory durability for hydrogen production is of considerable demand,especially for large-scale application.Herein,we adopt a multi-step consequential induced strategy to construct a bifunctional electrocatalyst for the overall water splitting.Graphene oxide(GO)was used as a carbon matrix and in situ oxygen source,which was supported by the octahedral PtNi alloy to form the PtxNiy-GO precursor.When calcinating in Ar atmosphere,the oxygen in GO induced the surface segregation of Ni from the PtNi octahedron to form a core-shell structure of Ptx@Niy.Then,the surface-enriched Ni continuously induced the reformation of C in reduced graphene oxide(rGO)to enhance the degree of graphitization.This multi-step induction formed a nanocatalyst Pt_(x)@Ni_(y)-rGO which has very high catalytic efficiency and stability.By optimizing the feeding ratio of PtNi(Pt:Ni=1:2),the electrolytic overall water splitting at 10 mA·cm^(-2) can be driven by an electrolytic voltage of as low as 1.485 V,and hydrogen evolution reaction(HER)only needs an overpotential of 37 mV in 1.0 M KOH aqueous solution.Additionally,the catalyst exhibited consistent existence form in both HER and oxygen evolution reaction(OER),which was verified by switching the anode and cathode of the cell in the electrolysis of water.This work provides a new idea for the synthesis and evaluation of the bifunctional catalysts for water splitting.
