This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--bre...This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--breaking bifurcation points. Two numerical examples are given. In addition, we show that there exist three quadratic pitchfork bifurcation point curves passing through corank-2 symmetry breaking bifurcation point.展开更多
A two-dimensional(2D)MA_(2)Z_(4)family with and phases has been attracting tremendous interest,the MoSi_(2)N_(4)and WSi_(2)N_(4)of which have been successfully fabricated(Science 369,670(2020)).Janus monolayers have b...A two-dimensional(2D)MA_(2)Z_(4)family with and phases has been attracting tremendous interest,the MoSi_(2)N_(4)and WSi_(2)N_(4)of which have been successfully fabricated(Science 369,670(2020)).Janus monolayers have been achieved in many 2D families,so it is interesting to construct a Janus monolayer from the MA_(2)Z_(4)family.In this work,Janus MSiGeN4(M=Zr and Hf)monolayers are predicted from-MA_(2)Z_(4),which exhibit dynamic,mechanical and thermal stabilities.It is found that they are indirect band-gap semiconductors by using generalized gradient approximation(GGA)plus spin-orbit coupling(SOC).With biaxial strain a/a0 from 0.90 to 1.10,the energy band gap shows a nonmonotonic behavior due to a change of conduction band minimum(CBM).A semiconductor to metal transition can be induced by both compressive and tensile strains,and the phase trans-formation point is about 0.96 for compressive strain and 1.10 for tensile strain.The tensile strain can change the positions of CBM and valence band maximum(VBM),and can also induce the weak Rashba-type spin splitting near CBM.For MSiGeN4(M=Zr and Hf)monolayers,both an in-plane and out-of-plane piezoelectric response can be produced,when a uniaxial strain in the basal plane is applied,which reveals the potential as piezoelectric 2D materials.The high absorption coefficients in the visible light region suggest that MSiGeN4(M=Zr and Hf)monolayers have potential photocatalytic applications.Our works provide an idea to achieve a Janus structure from the MA_(2)Z_(4)family,and can hopefully inspire further research exploring Janus MA_(2)Z_(4)monolayers.展开更多
Mangrove forests are under the stress of sea level rise(SLR)which would affect mangrove soil biogeochemistry.Mangrove soils are important sources of soil-atmosphere greenhouse gas(GHG)emissions,including carbon dioxid...Mangrove forests are under the stress of sea level rise(SLR)which would affect mangrove soil biogeochemistry.Mangrove soils are important sources of soil-atmosphere greenhouse gas(GHG)emissions,including carbon dioxide(CO_(2)),methane(CH_(4))and nitrous oxide(N_(2)O).Understanding how SLR influences GHG emissions is critical for evaluating mangrove blue carbon capability.In this study,potential effects of SLR on the GHG emissions were quantified through static closed chamber technique among three sites under different intertidal elevations,representing tidal flooding situation of SLR values of 0 cm,40 cm and 80 cm,respectively.Compared with Site SLR 0 cm,annual CO_(2) and N_(2)O fluxes decreased by approximately 75.0%and 27.3%due to higher soil water content,lower salinity and soil nutrient environments at Site SLR 80 cm.However,CH_(4) fluxes increased by approximately 13.7%at Site SLR 40 cm and 8.8%at Site SLR 80 cm because of lower salinity,higher soil water content and soil pH.CO_(2)-equivalent fluxes were 396.61 g/(m^(2)·a),1423.29 g/(m^(2)·a)and 1420.21 g/(m^(2)·a)at Sites SLR 80 cm,SLR 40 cm and SLR 0 cm,respectively.From Site SLR 0 cm to Site SLR 80 cm,contribution rate of N_(2)O and CH_(4) increased by approximately 7.42%and 3.02%,while contribution rate of CO_(2) decreased by approximately 10.44%.The results indicated that warming potential of trace CH_(4) and N_(2)O was non-negligible with SLR.Potential effects of SLR on the mangrove blue carbon capability should warrant attention due to changes of all three greenhouse gas fluxes with SLR.展开更多
This paper deals with the classification of the simple higher-order symmetry-breaking bifurcation in multiparameter nonlinear problems with Z2-symmetry. The regular extended systems for computing the simple higher-ord...This paper deals with the classification of the simple higher-order symmetry-breaking bifurcation in multiparameter nonlinear problems with Z2-symmetry. The regular extended systems for computing the simple higher-order symmetry-breaking bifurcation points with different singularities are proposed. An etficient algorithm for solving the extended systems is given. Finally, some numerical examples are shown to demonstrate the efficiency of the algorithm.展开更多
Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(...Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).展开更多
To explore the silicate lattice-based nanophosphors, a series of Eu3+-doped Z_(2)Si_(3)O_(8)(Z = Mg, Ca and Sr) materials were prepared by sol–gel procedure. The metal nitrates and silica powder were used as precurso...To explore the silicate lattice-based nanophosphors, a series of Eu3+-doped Z_(2)Si_(3)O_(8)(Z = Mg, Ca and Sr) materials were prepared by sol–gel procedure. The metal nitrates and silica powder were used as precursor components for the synthesis of these luminescent materials. Photoluminescence(PL) emission spectra, powder X-ray diffraction(PXRD), energy-dispersive X-ray spectroscopy(EDS), Fourier transform infrared spectroscopy(FTIR) and transmission electron microscopy(TEM)spectroscopic techniques were applied for the characterization of the fabricated materials. Three peaks were observed at 589, 613 and 650–652 nm corresponding to ^(5)D_(0)→^(7)F_(1-3) transition in PL emission spectra. Upon395 nm excitation and at 0.03 mol Eu3+, these nanophosphors displayed optimum photoluminescence with the most intense peak analogous to ^(5)D_(0)→^(7)F_(2)transition of dopant ion. The as-prepared phosphor materials were re-heated at1050 and 1150 ℃ to observe the consequences of higher temperatures on the emission intensity and crystal lattice.XRD analysis confirmed that all the synthesized materials were of crystalline nature, and the crystallinity was observed to be improved by increasing the temperature. In the FTIR spectrum, peaks at 483 and 610 cm^(-1) proved the existence of SiO_(4)group in Ca_(2)Si_(3)O_(8), and the peak centered at 417 cm^(-1) confirmed the presence of MgO6 octahedral in Mg_(2)Si_(3)O_(8) materials. TEM images were used to determine the particle size(13–35 nm) and to study the threedimensional structure of nanophosphor materials. The experimental studies indicate that these materials may be promising as red-emitting nanophosphors for white lightemitting diodes.展开更多
This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to ...This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the system.Hence standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.Keyworks: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system展开更多
We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems...We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems to determine double high order S-breaking bifurcation points. and we could also show that there exist two quadratic pitchfork bifurcation point paths passing through the point being considered.展开更多
Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of groups.Suppose that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoi...Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of groups.Suppose that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoint union of two real projective spaces with the same dimension.In this paper,the authors give a sufficient condition on the fixed data of the action for(M,Φ)bounding equivariantly.展开更多
文摘This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--breaking bifurcation points. Two numerical examples are given. In addition, we show that there exist three quadratic pitchfork bifurcation point curves passing through corank-2 symmetry breaking bifurcation point.
基金supported by Natural Science Basis Research Plan in Shaanxi Province of China(2021JM-456)。
文摘A two-dimensional(2D)MA_(2)Z_(4)family with and phases has been attracting tremendous interest,the MoSi_(2)N_(4)and WSi_(2)N_(4)of which have been successfully fabricated(Science 369,670(2020)).Janus monolayers have been achieved in many 2D families,so it is interesting to construct a Janus monolayer from the MA_(2)Z_(4)family.In this work,Janus MSiGeN4(M=Zr and Hf)monolayers are predicted from-MA_(2)Z_(4),which exhibit dynamic,mechanical and thermal stabilities.It is found that they are indirect band-gap semiconductors by using generalized gradient approximation(GGA)plus spin-orbit coupling(SOC).With biaxial strain a/a0 from 0.90 to 1.10,the energy band gap shows a nonmonotonic behavior due to a change of conduction band minimum(CBM).A semiconductor to metal transition can be induced by both compressive and tensile strains,and the phase trans-formation point is about 0.96 for compressive strain and 1.10 for tensile strain.The tensile strain can change the positions of CBM and valence band maximum(VBM),and can also induce the weak Rashba-type spin splitting near CBM.For MSiGeN4(M=Zr and Hf)monolayers,both an in-plane and out-of-plane piezoelectric response can be produced,when a uniaxial strain in the basal plane is applied,which reveals the potential as piezoelectric 2D materials.The high absorption coefficients in the visible light region suggest that MSiGeN4(M=Zr and Hf)monolayers have potential photocatalytic applications.Our works provide an idea to achieve a Janus structure from the MA_(2)Z_(4)family,and can hopefully inspire further research exploring Janus MA_(2)Z_(4)monolayers.
基金The National Natural Science Foundation of China under contract Nos 42076142 and 41776097the Provincial Natural Science Foundation of Fujian under contract No.2020J06030the Fund of Fujian Provincial Key Laboratory of Marine Ecological Conservation and Restoration under contract No.EPR2020003.
文摘Mangrove forests are under the stress of sea level rise(SLR)which would affect mangrove soil biogeochemistry.Mangrove soils are important sources of soil-atmosphere greenhouse gas(GHG)emissions,including carbon dioxide(CO_(2)),methane(CH_(4))and nitrous oxide(N_(2)O).Understanding how SLR influences GHG emissions is critical for evaluating mangrove blue carbon capability.In this study,potential effects of SLR on the GHG emissions were quantified through static closed chamber technique among three sites under different intertidal elevations,representing tidal flooding situation of SLR values of 0 cm,40 cm and 80 cm,respectively.Compared with Site SLR 0 cm,annual CO_(2) and N_(2)O fluxes decreased by approximately 75.0%and 27.3%due to higher soil water content,lower salinity and soil nutrient environments at Site SLR 80 cm.However,CH_(4) fluxes increased by approximately 13.7%at Site SLR 40 cm and 8.8%at Site SLR 80 cm because of lower salinity,higher soil water content and soil pH.CO_(2)-equivalent fluxes were 396.61 g/(m^(2)·a),1423.29 g/(m^(2)·a)and 1420.21 g/(m^(2)·a)at Sites SLR 80 cm,SLR 40 cm and SLR 0 cm,respectively.From Site SLR 0 cm to Site SLR 80 cm,contribution rate of N_(2)O and CH_(4) increased by approximately 7.42%and 3.02%,while contribution rate of CO_(2) decreased by approximately 10.44%.The results indicated that warming potential of trace CH_(4) and N_(2)O was non-negligible with SLR.Potential effects of SLR on the mangrove blue carbon capability should warrant attention due to changes of all three greenhouse gas fluxes with SLR.
文摘This paper deals with the classification of the simple higher-order symmetry-breaking bifurcation in multiparameter nonlinear problems with Z2-symmetry. The regular extended systems for computing the simple higher-order symmetry-breaking bifurcation points with different singularities are proposed. An etficient algorithm for solving the extended systems is given. Finally, some numerical examples are shown to demonstrate the efficiency of the algorithm.
基金Supported by the National Natural Sciences Foundation of P.R.China(No.10371029)the Natural Sciences Foundation of Hebei Province(No.103144)the Doctoral Foundation of Hebei Normal University(No.103257)
文摘Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).
基金supported by the National Key Research and Development Program of China(2021YFA1400900)the National Natural Science Foundation of China(11825401 and 11921005)+1 种基金the Open Project of Shenzhen Institute of Quantum Science and Engineering(SIQSE202003)the Strategic Priority Research Program of Chinese Academy of Sciences(XDB28000000)。
文摘To explore the silicate lattice-based nanophosphors, a series of Eu3+-doped Z_(2)Si_(3)O_(8)(Z = Mg, Ca and Sr) materials were prepared by sol–gel procedure. The metal nitrates and silica powder were used as precursor components for the synthesis of these luminescent materials. Photoluminescence(PL) emission spectra, powder X-ray diffraction(PXRD), energy-dispersive X-ray spectroscopy(EDS), Fourier transform infrared spectroscopy(FTIR) and transmission electron microscopy(TEM)spectroscopic techniques were applied for the characterization of the fabricated materials. Three peaks were observed at 589, 613 and 650–652 nm corresponding to ^(5)D_(0)→^(7)F_(1-3) transition in PL emission spectra. Upon395 nm excitation and at 0.03 mol Eu3+, these nanophosphors displayed optimum photoluminescence with the most intense peak analogous to ^(5)D_(0)→^(7)F_(2)transition of dopant ion. The as-prepared phosphor materials were re-heated at1050 and 1150 ℃ to observe the consequences of higher temperatures on the emission intensity and crystal lattice.XRD analysis confirmed that all the synthesized materials were of crystalline nature, and the crystallinity was observed to be improved by increasing the temperature. In the FTIR spectrum, peaks at 483 and 610 cm^(-1) proved the existence of SiO_(4)group in Ca_(2)Si_(3)O_(8), and the peak centered at 417 cm^(-1) confirmed the presence of MgO6 octahedral in Mg_(2)Si_(3)O_(8) materials. TEM images were used to determine the particle size(13–35 nm) and to study the threedimensional structure of nanophosphor materials. The experimental studies indicate that these materials may be promising as red-emitting nanophosphors for white lightemitting diodes.
文摘This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the system.Hence standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.Keyworks: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system
文摘We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems to determine double high order S-breaking bifurcation points. and we could also show that there exist two quadratic pitchfork bifurcation point paths passing through the point being considered.
基金supported by the National Natural Science Foundation of China(No.11771116)。
文摘Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of groups.Suppose that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoint union of two real projective spaces with the same dimension.In this paper,the authors give a sufficient condition on the fixed data of the action for(M,Φ)bounding equivariantly.
