The juvenile-to-adult phase change with first flowering as the indicator plays a crucial role in the lifecycle of fruit trees. However, the molecular mechanisms underlying phase change in fruit trees remain largely un...The juvenile-to-adult phase change with first flowering as the indicator plays a crucial role in the lifecycle of fruit trees. However, the molecular mechanisms underlying phase change in fruit trees remain largely unknown. Shikimic acid (ShA) pathway is a main metabolic pathway closely related to the synthesis of hormones and many important secondary metabolites participating in plant phase change. So,whether ShA regulates phase change in plants is worth clarifying. Here, the distinct morphological characteristics and the underlying mechanisms of phase change in jujube (Ziziphus jujuba Mill.), an important fruit tree native to China with nutritious fruit and outstanding tolerance abiotic stresses, were clarified. A combined transcriptome and metabolome analysis found that ShA is positively involved in jujube(Yuhong’×Xing 16’) phase change. The genes in the upstream of ShA synthesis pathway (ZjDAHPS, ZjDHQS and ZjSDH), the contents of ShA and the downstream secondary metabolites like phenols were significantly upregulated in the phase change period. Further, the treatment of spraying exogenous ShA verified that ShA at a very low concentration (60 mg·L^(-1)) can substantially speed up the phase change and flowering of jujube and other tested plants including Arabidopsis, tomato and wheat. The exogenous ShA (60 mg·L^(-1)) treatment in jujube seedlings could increase the accumulation of endogenous ShA, enhance leaf photosynthesis and the synthesis of phenols especially flavonoids and phenolic acids, and promote the expression of genes (ZjCOs, ZjNFYs and ZjPHYs) involved in flowering pathway. Basing on above results, we put forward a propose for the underlying mechanism of ShA regulating phase change, and a hypothesis that ShA could be considered a phytohormone-like substance because it is endogenous, ubiquitous, movable and highly efficient at very low concentrations. This study highlights the critical role of ShA in plant phase change and its phytohormone-like properties.展开更多
A time-resolved x-ray diffraction technique is employed to monitor the structural transformation of laser-shocked bismuth.Results reveal a retarded transformation from the shock-induced Bi-Ⅴphase to a metastable Bi-...A time-resolved x-ray diffraction technique is employed to monitor the structural transformation of laser-shocked bismuth.Results reveal a retarded transformation from the shock-induced Bi-Ⅴphase to a metastable Bi-Ⅳphase during the shock release,instead of the thermodynamically stable Bi-Ⅲphase.The emergence of the metastable Bi-Ⅳphase is understood by the competitive interplay between two transformation pathways towards the Bi-Ⅳand Bi-Ⅲ,respectively.The former is more rapid than the latter because the Bi-Ⅴto B-Ⅳtransformation is driven by interaction between the closest atoms while the Bi-Ⅴto B-Ⅲtransformation requires interaction between the second-closest atoms.The nucleation time for the Bi-Ⅴto Bi-Ⅳtransformation is determined to be 5.1±0.9 ns according to a classical nucleation model.This observation demonstrates the importance of the formation of the transient metastable phases,which can change the phase transformation pathway in a dynamic process.展开更多
Objective: The measurement of phase angles is an important monitoring parameter and supplementation with omega-3 could promote benefits by modulating the electrical potential of membranes and increasing body cell mass...Objective: The measurement of phase angles is an important monitoring parameter and supplementation with omega-3 could promote benefits by modulating the electrical potential of membranes and increasing body cell mass. This study aimed to evaluate the effectiveness of omega-3 fatty acid supplementation on the phase angle of people living with HIV/AIDS. Methods: In this study, 63 individuals of all genders who were undergoing outpatient follow-up and showed lipodystrophy due to highly active antiretroviral therapy were analyzed. Our sample consisted of two groups, one that received supplementation containing 2550 mg of omega-3/day (1080 mg of eicosapentaenoic acid and 720 mg of docosahexaenoic acid) for three months (n = 32) and another that underwent nutrition guidance (n = 31). Phase angle and body cell mass were assessed for both groups and compared at the beginning of research (T0) and after our intervention (T1) for each group separately. Results: Phase angle averaged 6.45° ± 1.06 SD. The comparison between T0 and T1 showed a significant increase in phase angle and body cell mass, whereas the guidance group showed a decrease in body cell mass at T1 in relation to T0, with a significant p-value. Variance in phase angle between moments showed significant values between T0 and T1 in the supplementation group for all genders. Conclusion: Omega-3 positively modulated patients phase angle and body cell mass, but we emphasize the need for other studies that can solidify knowledge about supplementation dosage and intervention time.展开更多
Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied...Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.展开更多
The Mn-based oxide cathode with enriched crystal phase structure and component diversity can provide the excellent chemistry structure for Na-ion batteries.Nevertheless,the broad application prospect is obstructed by ...The Mn-based oxide cathode with enriched crystal phase structure and component diversity can provide the excellent chemistry structure for Na-ion batteries.Nevertheless,the broad application prospect is obstructed by the sluggish Na^(+)kinetics and the phase transitions upon cycling.Herein,we establish the thermodynamically stable phase diagram of various Mn-based oxide composites precisely controlled by sodium content tailoring strategy coupling with co-doping and solid-state reaction.The chemical environment of the P2/P'3 and P2/P3 biphasic composites indicate that the charge compensation mechanism stems from the cooperative contribution of anions and cations.Benefiting from the no phase transition to scavenge the structure strain,P2/P'3 electrode can deliver long cycling stability(capacity retention of 73.8%after 1000 cycles at 10 C)and outstanding rate properties(the discharge capacity of 84.08 mA h g^(-1)at 20 C)than P2/P3 electrode.Furthermore,the DFT calculation demonstrates that the introducing novel P'3 phase can significantly regulate the Na^(+)reaction dynamics and modify the local electron configuration of Mn.The effective phase engineering can provide a reference for designing other high-performance electrode materials for Na-ion batteries.展开更多
Phase transitions involving oxygen ion extraction within the framework of the crystallographic relevance have been widely exploited for sake of superconductivity,ferromagnetism,and ion conductivity in perovskiterelate...Phase transitions involving oxygen ion extraction within the framework of the crystallographic relevance have been widely exploited for sake of superconductivity,ferromagnetism,and ion conductivity in perovskiterelated oxides.However,atomic-scale pathways of phase transitions and ion extraction threshold are inadequately understood.Here we investigate the atomic structure evolution of LaCoO_(3) films upon oxygen extraction and subsequent Co migration,focusing on the key role of epitaxial strain.The brownmillerite to Ruddlesden-Popper phase transitions are discovered to stabilize at distinct crystal orientations in compressive-and tensile-strained cobaltites,which could be attributed to in-plane and out-of-plane Ruddlesden-Popper stacking faults,respectively.A two-stage process from exterior to interior phase transition is evidenced in compressive-strained LaCoO_(2.5),while a single-step nucleation process leaving bottom layer unchanged in tensile-strained situation.Strain analyses reveal that the former process is initiated by an expansion in Co layer at boundary,whereas the latter one is associated with an edge dislocation combined with antiphase boundary.These findings provide a chemomechanical perspective on the structure regulation of perovskite oxides and enrich insights into strain-dependent phase diagram in epitaxial oxides films.展开更多
Evidence for metallization in dense oxygen has been reported for over 30 years[Desgreniers et al.,J.Phys.Chem.94,1117(1990)]at a now routinely accessible 95 GPa[Shimizu et al.,Nature 393,767(1998)].However,despite the...Evidence for metallization in dense oxygen has been reported for over 30 years[Desgreniers et al.,J.Phys.Chem.94,1117(1990)]at a now routinely accessible 95 GPa[Shimizu et al.,Nature 393,767(1998)].However,despite the longevity of this result and the technological advances since,the nature of the metallic phase remains poorly constrained[Akahama et al.,Phys.Rev.Lett.74,4690(1995);Goncharov et al.,Phys.Rev.B 68,224108(2003);Ma,Phys.Rev.B 76,064101(2007);and Weck et al.,Phys.Rev.Lett.102,255503(2009)].In this work,through Raman spectroscopy,we report the distinct vibrational characteristics of metallicζ-O_(2) from 85 to 225 GPa.In comparison with numerical simulations,wefind reasonable agreement with the candidate structure up to about 150 GPa.At higher pressures,the C2/mstructure is found to be unstable and incompatible with experimental observations.Alternative candidate structures,and Ci,with C2/m C2/conly two molecules in the primitive unit cell,are found to be stable and more compatible with measurements above 175 GPa,indicative of the dissociation of(O_(2))4 units.Further,we report and discuss a strong hysteresis and metastability with the precursory phaseϵ-O_(2).Thesefindings will reinvigorate experimental and theoretical work into the dense oxygen system,which will have importance for oxygen-bearing chemistry,prevalent in the deep Earth,as well as fundamental physics.展开更多
The hydrothermal synthesis of In_(2)O_(3)and CeO_(2)–In_(2)O_(3)is investigated as well as the properties of sensor layers based on these compounds.During the synthesis of In_(2)O_(3),intermediate products In(OH)_(3)...The hydrothermal synthesis of In_(2)O_(3)and CeO_(2)–In_(2)O_(3)is investigated as well as the properties of sensor layers based on these compounds.During the synthesis of In_(2)O_(3),intermediate products In(OH)_(3)and InOOH are formed,which are the precursors of stable cubic(c-In_(2)O_(3))and metastable rhombohedral(rh-In_(2)O_(3))phases,respectively.A transition from c-In_(2)O_(3)to rh-In_(2)O_(3)is observed with the addition of CeO_(2).The introduction of cerium into rh-In_(2)O_(3)results in a decrease in the sensor response to hydrogen,while it increases in composites based on c-In_(2)O_(3).The data on the sensor activity of the composites correlate with XPS results in which CeO_(2)causes a decrease in the concentrations of chemisorbed oxygen and oxygen vacancies in rh-In_(2)O_(3).The reverse situation is observed in composites based on c-In_(2)O_(3).Compared to In_(2)O_(3)and CeO_(2)–In_(2)O_(3)obtained by other methods,the synthesized composites demonstrate maximum response to H_(2)at low temperatures by 70–100℃,and have short response time(0.2–0.5 s),short recovery time(6–7 s),and long-term stability.A model is proposed for the dependence of sensitivity on the direction of electron transfer between In_(2)O_(3)and CeO_(2).展开更多
The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order...The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.展开更多
Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted ...Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.展开更多
A new robust bio-inspired route by using lysozyme aqueous solution for surface modification on 1,3,5,7-tetranitro-1,3,5,7-tetrazocane(HMX)was described in this paper.HMX crystals were coated by in situ phase transitio...A new robust bio-inspired route by using lysozyme aqueous solution for surface modification on 1,3,5,7-tetranitro-1,3,5,7-tetrazocane(HMX)was described in this paper.HMX crystals were coated by in situ phase transition of lysozyme(PTL)molecules.The HMX decorated by PTL was characterized by SEM,XRD,FTIR and XPS,demonstrating a dense core-shell coating layer.The coverage of lysozyme on HMX crystal was calculated by the ratio of sulfur content.The surface coverage increased from 60.5% to 93.5% when the content of PTL was changed from 0.5 wt% to 2.0 wt%,indicating efficient coating.The thermal stability of HMX was investigated by in situ XRD and DSC.The thermal phase transition temperature of HMX(β to δ phase)was delayed by 42℃ with 2.0 wt% PTL coating,which prevented HMX from thermal damage and sensitivity by the effect of PTL coating.After heating at 215℃,large cracks appeared in the naked HMX crystal,while the PTL coated HMX still maintained intact,with the impact energy of HMX dropped dramatically from 5 J to 2 J.However,the impact energy of HMX with 1.0 wt% and 2.0 wt% coating content(HMX@PTL-1.0 and HMX@PTL-2.0)was unchanged(5 J).Present results potentially enable large-scale fabrication of polymorphic energetic materials with outstanding thermal stability by novel lysozyme coating.展开更多
Dendrite growth is a complex liquid-solid phase transition process involving multiple physical factors.A phase-field lattice-Boltzmann method was developed to simulate the two-and three-dimension dendrite growth of Al...Dendrite growth is a complex liquid-solid phase transition process involving multiple physical factors.A phase-field lattice-Boltzmann method was developed to simulate the two-and three-dimension dendrite growth of Al-Cu alloy.The effect of fully coupled thermal-solute-convection interaction on the dendrite growth was investigated by incorporating a parallel-adaptive mesh refinement algorithm into the numerical model.By accurately reproducing the latent heat release,solute diffusion and convective transport behaviors at the liquidsolid interface,the interaction mechanism among thermal-solute-convection transport as well as their coupling effects on the dendrite growth dynamics were discussed.The simulation results show that the release of latent heat slows down the dendrite growth rate,and both natural and forced convection disrupt the symmetrical growth of dendrites.Their combination makes the growth of dendrites more complex,capturing important physical aspects such as recalescence,dendrite tip splitting,dendrite tilting,dendrite remelting,and solute plume in the simulation case.Based on the robustness and powerful ability of the numerical model,the formation mechanisms of these physical aspects were revealed.展开更多
Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent prob...Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.展开更多
Objective This study aimed to evaluate whether the onset of the plateau phase of slow hepatitis B surface antigen decline in patients with chronic hepatitis B treated with intermittent interferon therapy is related to...Objective This study aimed to evaluate whether the onset of the plateau phase of slow hepatitis B surface antigen decline in patients with chronic hepatitis B treated with intermittent interferon therapy is related to the frequency of dendritic cell subsets and expression of the costimulatory molecules CD40,CD80,CD83,and CD86.Method This was a cross-sectional study in which patients were divided into a natural history group(namely NH group),a long-term oral nucleoside analogs treatment group(namely NA group),and a plateau-arriving group(namely P group).The percentage of plasmacytoid dendritic cell and myeloid dendritic cell subsets in peripheral blood lymphocytes and monocytes and the mean fluorescence intensity of their surface costimulatory molecules were detected using a flow cytometer.Results In total,143 patients were enrolled(NH group,n=49;NA group,n=47;P group,n=47).The results demonstrated that CD141/CD1c double negative myeloid dendritic cell(DNmDC)/lymphocytes and monocytes(%)in P group(0.041[0.024,0.069])was significantly lower than that in NH group(0.270[0.135,0.407])and NA group(0.273[0.150,0.443]),and CD86 mean fluorescence intensity of DNmDCs in P group(1832.0[1484.0,2793.0])was significantly lower than that in NH group(4316.0[2958.0,5169.0])and NA group(3299.0[2534.0,4371.0]),Adjusted P all<0.001.Conclusion Reduced DNmDCs and impaired maturation may be associated with the onset of the plateau phase during intermittent interferon therapy in patients with chronic hepatitis B.展开更多
Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±...Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| |≤ε.The mapping g is said to be a phase isometry provided that ε=0.In this paper,we show the following universal inequality of g:for each u^(*) ∈ w^(*)-exp ‖u^(*)‖B_(x^(*)),there exist a phase function σ_(u^(*)):X→{-1,1} and φ ∈ Y^(*) with ‖φ‖=‖u^(*)‖≡α satisfying that|(u^(*),u)-σ_(u^(*))(u)<φ,g(u)>)|≤5/2εα,for all u ∈ X.In particular,let X be a smooth Banach space.Then we show the following:(1) the universal inequality holds for all u^(*) ∈ X^(*);(2) the constant 5/2 can be reduced to 3/2 provided that Y~*is strictly convex;(3) the existence of such a g implies the existence of a phase isometryΘ:X→Y such that■ provided that Y^(**) has the w^(*)-Kadec-Klee property(for example,Y is both reflexive and locally uniformly convex).展开更多
Nickel-manganese binary layered oxides with high working potential and low cost are potential candidates for sodium-ion batteries,but their electrochemical properties are highly related to compositional diversity.Dive...Nickel-manganese binary layered oxides with high working potential and low cost are potential candidates for sodium-ion batteries,but their electrochemical properties are highly related to compositional diversity.Diverse composite materials with various phase structures of P3,P2/P3,P2,P2/O3,and P2/P3/O3 were synthesized by manipulating the sodium content and calcination conditions,leading to the construction of a synthetic phase diagram for Na_(x)Ni_(0.25)Mn_(0.75)O_(2)(0.45≤x≤1.1).Then,we compared the electrochemical characteristics and structural evolution during the desodiation/sodiation process of P2,P2/P3,P2/03,and P2/P3/O3-Na_(x)Ni_(0.25)Mn_(0.75)O_(2).Among them,P2/P3-Na0.75Ni0.25Mn0.75O2exhibits the best rate capability of 90.9 mA h g^(-1)at 5 C,with an initial discharge capacity of 142.62 mA h g^(-1)at 0.1 C and a capacity retention rate of 78.25%after 100 cycles at 1 C in the voltage range of 2-4.3 V.The observed superior sodium storage performance of P2/P3 hybrids compared to other composite phases can be attributed to the enhanced Na^(+)transfer dynamic,reduction of the Jahn-teller effect,and improved reaction reversibility induced by the synergistic effect of P2 and P3 phases.The systematic research and exploration of phases in Na_(x)Ni_(0.25)Mn_(0.75)O_(2)provide new sights into high-performance nickel-manganese binary layered oxide for sodium-ion batteries.展开更多
By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic Ad S black holes(BHs) with quasitopological electromagnet...By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic Ad S black holes(BHs) with quasitopological electromagnetism in Einstein–Gauss–Bonnet(EGB) gravity. The results indicate that the small/large BH phase transition that is similar to the van der Waals(vdW) liquid/gas phase transition always exists for any spacetime dimensions. Interestingly, we then find that this BH system exhibits a more complex phase structure in 6-dimensional case that is missed in other dimensions.Specifically, it shows for D = 6 that we observed the small/intermediate/large BH phase transitions in a specific parameter region with the triple point naturally appeared. Moreover, when the magnetic charge turned off, we still observed the small/intermediate/large BH phase transitions and triple point only in 6-dimensional spacetime, which is consistent with the previous results. However, for the dyonic Ad S BHs with quasitopological electromagnetism in Einstein–Born–Infeld(EBI) gravity, the novel phase structure composed of two separate coexistence curves observed by Li et al. [Phys. Rev. D105 104048(2022)] disappeared in EGB gravity. This implies that this novel phase structure is closely related to gravity theories, and seems to have nothing to do with the effect of quasitopological electromagnetism. In addition, it is also true that the critical exponents calculated near the critical points possess identical values as mean field theory. Finally, we conclude that these findings shall provide some deep insights into the intriguing thermodynamic properties of the dyonic Ad S BHs with quasitopological electromagnetism in EGB gravity.展开更多
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur...The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.展开更多
基金partially supported by the National Natural Science Foundation of China (Grant No.31772285)the National Key R&D Program Project Funding (Grant No.2018YFD1000607)Foundation for 100 Innovative Talents of Hebei Province(Grant No.SLRC2019031)。
文摘The juvenile-to-adult phase change with first flowering as the indicator plays a crucial role in the lifecycle of fruit trees. However, the molecular mechanisms underlying phase change in fruit trees remain largely unknown. Shikimic acid (ShA) pathway is a main metabolic pathway closely related to the synthesis of hormones and many important secondary metabolites participating in plant phase change. So,whether ShA regulates phase change in plants is worth clarifying. Here, the distinct morphological characteristics and the underlying mechanisms of phase change in jujube (Ziziphus jujuba Mill.), an important fruit tree native to China with nutritious fruit and outstanding tolerance abiotic stresses, were clarified. A combined transcriptome and metabolome analysis found that ShA is positively involved in jujube(Yuhong’×Xing 16’) phase change. The genes in the upstream of ShA synthesis pathway (ZjDAHPS, ZjDHQS and ZjSDH), the contents of ShA and the downstream secondary metabolites like phenols were significantly upregulated in the phase change period. Further, the treatment of spraying exogenous ShA verified that ShA at a very low concentration (60 mg·L^(-1)) can substantially speed up the phase change and flowering of jujube and other tested plants including Arabidopsis, tomato and wheat. The exogenous ShA (60 mg·L^(-1)) treatment in jujube seedlings could increase the accumulation of endogenous ShA, enhance leaf photosynthesis and the synthesis of phenols especially flavonoids and phenolic acids, and promote the expression of genes (ZjCOs, ZjNFYs and ZjPHYs) involved in flowering pathway. Basing on above results, we put forward a propose for the underlying mechanism of ShA regulating phase change, and a hypothesis that ShA could be considered a phytohormone-like substance because it is endogenous, ubiquitous, movable and highly efficient at very low concentrations. This study highlights the critical role of ShA in plant phase change and its phytohormone-like properties.
基金supported by the National Natural Science Foundation of China (Grant No.12072331)the Science Challenge Project (Grant No.TZ2018001)+2 种基金the Japan Society for the Promotion of Science (Grant Nos.17H04820 and 21H01677)the Foundation of the United Laboratory of High-Pressure Physics and Earthquake Scienceperformed under the approval of the Photon Factory Program Advisory Committee (Proposal Nos.2016S2-006 and 2020G680)。
文摘A time-resolved x-ray diffraction technique is employed to monitor the structural transformation of laser-shocked bismuth.Results reveal a retarded transformation from the shock-induced Bi-Ⅴphase to a metastable Bi-Ⅳphase during the shock release,instead of the thermodynamically stable Bi-Ⅲphase.The emergence of the metastable Bi-Ⅳphase is understood by the competitive interplay between two transformation pathways towards the Bi-Ⅳand Bi-Ⅲ,respectively.The former is more rapid than the latter because the Bi-Ⅴto B-Ⅳtransformation is driven by interaction between the closest atoms while the Bi-Ⅴto B-Ⅲtransformation requires interaction between the second-closest atoms.The nucleation time for the Bi-Ⅴto Bi-Ⅳtransformation is determined to be 5.1±0.9 ns according to a classical nucleation model.This observation demonstrates the importance of the formation of the transient metastable phases,which can change the phase transformation pathway in a dynamic process.
文摘Objective: The measurement of phase angles is an important monitoring parameter and supplementation with omega-3 could promote benefits by modulating the electrical potential of membranes and increasing body cell mass. This study aimed to evaluate the effectiveness of omega-3 fatty acid supplementation on the phase angle of people living with HIV/AIDS. Methods: In this study, 63 individuals of all genders who were undergoing outpatient follow-up and showed lipodystrophy due to highly active antiretroviral therapy were analyzed. Our sample consisted of two groups, one that received supplementation containing 2550 mg of omega-3/day (1080 mg of eicosapentaenoic acid and 720 mg of docosahexaenoic acid) for three months (n = 32) and another that underwent nutrition guidance (n = 31). Phase angle and body cell mass were assessed for both groups and compared at the beginning of research (T0) and after our intervention (T1) for each group separately. Results: Phase angle averaged 6.45° ± 1.06 SD. The comparison between T0 and T1 showed a significant increase in phase angle and body cell mass, whereas the guidance group showed a decrease in body cell mass at T1 in relation to T0, with a significant p-value. Variance in phase angle between moments showed significant values between T0 and T1 in the supplementation group for all genders. Conclusion: Omega-3 positively modulated patients phase angle and body cell mass, but we emphasize the need for other studies that can solidify knowledge about supplementation dosage and intervention time.
基金Project supported by LingChuang Research Project of China National Nuclear Corporationthe National Natural Science Foundation of China(Grant No.12027812)。
文摘Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.
基金supported by the National Natural Science Foundation of China (52173273)Fundamental Research Funds for the Central Universities (2022CX11013)+2 种基金Shanxi Province Science Foundation for Youths (No.202203021212391)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No.2022L253)Institute Foundation Project of China Academy of Railway Sciences Corporation Limited Metals and Chemistry Research Institute (No.2023SJ02)。
文摘The Mn-based oxide cathode with enriched crystal phase structure and component diversity can provide the excellent chemistry structure for Na-ion batteries.Nevertheless,the broad application prospect is obstructed by the sluggish Na^(+)kinetics and the phase transitions upon cycling.Herein,we establish the thermodynamically stable phase diagram of various Mn-based oxide composites precisely controlled by sodium content tailoring strategy coupling with co-doping and solid-state reaction.The chemical environment of the P2/P'3 and P2/P3 biphasic composites indicate that the charge compensation mechanism stems from the cooperative contribution of anions and cations.Benefiting from the no phase transition to scavenge the structure strain,P2/P'3 electrode can deliver long cycling stability(capacity retention of 73.8%after 1000 cycles at 10 C)and outstanding rate properties(the discharge capacity of 84.08 mA h g^(-1)at 20 C)than P2/P3 electrode.Furthermore,the DFT calculation demonstrates that the introducing novel P'3 phase can significantly regulate the Na^(+)reaction dynamics and modify the local electron configuration of Mn.The effective phase engineering can provide a reference for designing other high-performance electrode materials for Na-ion batteries.
基金supported by the National Natural Science Foundation of China(Grant Nos.52322212,52072400,52025025,and 52250402)。
文摘Phase transitions involving oxygen ion extraction within the framework of the crystallographic relevance have been widely exploited for sake of superconductivity,ferromagnetism,and ion conductivity in perovskiterelated oxides.However,atomic-scale pathways of phase transitions and ion extraction threshold are inadequately understood.Here we investigate the atomic structure evolution of LaCoO_(3) films upon oxygen extraction and subsequent Co migration,focusing on the key role of epitaxial strain.The brownmillerite to Ruddlesden-Popper phase transitions are discovered to stabilize at distinct crystal orientations in compressive-and tensile-strained cobaltites,which could be attributed to in-plane and out-of-plane Ruddlesden-Popper stacking faults,respectively.A two-stage process from exterior to interior phase transition is evidenced in compressive-strained LaCoO_(2.5),while a single-step nucleation process leaving bottom layer unchanged in tensile-strained situation.Strain analyses reveal that the former process is initiated by an expansion in Co layer at boundary,whereas the latter one is associated with an edge dislocation combined with antiphase boundary.These findings provide a chemomechanical perspective on the structure regulation of perovskite oxides and enrich insights into strain-dependent phase diagram in epitaxial oxides films.
基金The computational resources were provided by the Cambridge Tier-2 sys-tem operated by the University of Cambridge Research Computing Service and funded by the UK EPSRC(Grant No.EP/P020259/1).
文摘Evidence for metallization in dense oxygen has been reported for over 30 years[Desgreniers et al.,J.Phys.Chem.94,1117(1990)]at a now routinely accessible 95 GPa[Shimizu et al.,Nature 393,767(1998)].However,despite the longevity of this result and the technological advances since,the nature of the metallic phase remains poorly constrained[Akahama et al.,Phys.Rev.Lett.74,4690(1995);Goncharov et al.,Phys.Rev.B 68,224108(2003);Ma,Phys.Rev.B 76,064101(2007);and Weck et al.,Phys.Rev.Lett.102,255503(2009)].In this work,through Raman spectroscopy,we report the distinct vibrational characteristics of metallicζ-O_(2) from 85 to 225 GPa.In comparison with numerical simulations,wefind reasonable agreement with the candidate structure up to about 150 GPa.At higher pressures,the C2/mstructure is found to be unstable and incompatible with experimental observations.Alternative candidate structures,and Ci,with C2/m C2/conly two molecules in the primitive unit cell,are found to be stable and more compatible with measurements above 175 GPa,indicative of the dissociation of(O_(2))4 units.Further,we report and discuss a strong hysteresis and metastability with the precursory phaseϵ-O_(2).Thesefindings will reinvigorate experimental and theoretical work into the dense oxygen system,which will have importance for oxygen-bearing chemistry,prevalent in the deep Earth,as well as fundamental physics.
基金supported by the Russian Science Foundation(grant No.22-19-00037),https://rscf.ru/project/22-19-00037/.
文摘The hydrothermal synthesis of In_(2)O_(3)and CeO_(2)–In_(2)O_(3)is investigated as well as the properties of sensor layers based on these compounds.During the synthesis of In_(2)O_(3),intermediate products In(OH)_(3)and InOOH are formed,which are the precursors of stable cubic(c-In_(2)O_(3))and metastable rhombohedral(rh-In_(2)O_(3))phases,respectively.A transition from c-In_(2)O_(3)to rh-In_(2)O_(3)is observed with the addition of CeO_(2).The introduction of cerium into rh-In_(2)O_(3)results in a decrease in the sensor response to hydrogen,while it increases in composites based on c-In_(2)O_(3).The data on the sensor activity of the composites correlate with XPS results in which CeO_(2)causes a decrease in the concentrations of chemisorbed oxygen and oxygen vacancies in rh-In_(2)O_(3).The reverse situation is observed in composites based on c-In_(2)O_(3).Compared to In_(2)O_(3)and CeO_(2)–In_(2)O_(3)obtained by other methods,the synthesized composites demonstrate maximum response to H_(2)at low temperatures by 70–100℃,and have short response time(0.2–0.5 s),short recovery time(6–7 s),and long-term stability.A model is proposed for the dependence of sensitivity on the direction of electron transfer between In_(2)O_(3)and CeO_(2).
基金Project supported by the National Natural Science Foundation of China (Grants Nos.12375031 and 11905068)the Natural Science Foundation of Fujian Province, China (Grant No.2023J01113)the Scientific Research Funds of Huaqiao University (Grant No.ZQN-810)。
文摘The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 92065113, 11904357, 62075208, and 12174367)the Innovation Programme for Quantum Science and Technology (Grant No. 2021ZD0301604)+1 种基金the National Key Research and Development Program of China (Grant No. 2021YFE0113100)supported by Beijing Academy of Quantum Information Sciences
文摘Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.
基金the China National Nature Science Foundation(Grant No.12102404)。
文摘A new robust bio-inspired route by using lysozyme aqueous solution for surface modification on 1,3,5,7-tetranitro-1,3,5,7-tetrazocane(HMX)was described in this paper.HMX crystals were coated by in situ phase transition of lysozyme(PTL)molecules.The HMX decorated by PTL was characterized by SEM,XRD,FTIR and XPS,demonstrating a dense core-shell coating layer.The coverage of lysozyme on HMX crystal was calculated by the ratio of sulfur content.The surface coverage increased from 60.5% to 93.5% when the content of PTL was changed from 0.5 wt% to 2.0 wt%,indicating efficient coating.The thermal stability of HMX was investigated by in situ XRD and DSC.The thermal phase transition temperature of HMX(β to δ phase)was delayed by 42℃ with 2.0 wt% PTL coating,which prevented HMX from thermal damage and sensitivity by the effect of PTL coating.After heating at 215℃,large cracks appeared in the naked HMX crystal,while the PTL coated HMX still maintained intact,with the impact energy of HMX dropped dramatically from 5 J to 2 J.However,the impact energy of HMX with 1.0 wt% and 2.0 wt% coating content(HMX@PTL-1.0 and HMX@PTL-2.0)was unchanged(5 J).Present results potentially enable large-scale fabrication of polymorphic energetic materials with outstanding thermal stability by novel lysozyme coating.
基金financially supported by the National Natural Science Foundation of China(Grant No.52275370)the Key R&D Program of Hubei Province,China(Grant No.2022BAD100 and No.2021BAA048)the Open Fund of Hubei Longzhong Laboratory,China(Grant No.2022ZZ-04)。
文摘Dendrite growth is a complex liquid-solid phase transition process involving multiple physical factors.A phase-field lattice-Boltzmann method was developed to simulate the two-and three-dimension dendrite growth of Al-Cu alloy.The effect of fully coupled thermal-solute-convection interaction on the dendrite growth was investigated by incorporating a parallel-adaptive mesh refinement algorithm into the numerical model.By accurately reproducing the latent heat release,solute diffusion and convective transport behaviors at the liquidsolid interface,the interaction mechanism among thermal-solute-convection transport as well as their coupling effects on the dendrite growth dynamics were discussed.The simulation results show that the release of latent heat slows down the dendrite growth rate,and both natural and forced convection disrupt the symmetrical growth of dendrites.Their combination makes the growth of dendrites more complex,capturing important physical aspects such as recalescence,dendrite tip splitting,dendrite tilting,dendrite remelting,and solute plume in the simulation case.Based on the robustness and powerful ability of the numerical model,the formation mechanisms of these physical aspects were revealed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52204258 and 52106099)the Postdoctoral Research Foundation of China (Grant No.2023M743779)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No.2022QN1017)the Key Research Development Projects in Xinjiang Uygur Autonomous Region (Grant No.2022B03003-3)the Shandong Provincial Natural Science Foundation (Grant No.ZR2020LLZ004)。
文摘Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.
基金supported by the National Key Research and Development Program[2022YFC2603500,2022YFC2603505]Capital Clinical Diagnostic Techniques and Translational Application Projects(Z211100002921059)+2 种基金Capital’s Funds for Health Improvement and Research[2022-1-2172]Beijing Hospitals Authority Clinical Medicine Development of Special Funding Support[XMLX 202127]National Science and Technology Major Project of China[2017ZX10203202-003]。
文摘Objective This study aimed to evaluate whether the onset of the plateau phase of slow hepatitis B surface antigen decline in patients with chronic hepatitis B treated with intermittent interferon therapy is related to the frequency of dendritic cell subsets and expression of the costimulatory molecules CD40,CD80,CD83,and CD86.Method This was a cross-sectional study in which patients were divided into a natural history group(namely NH group),a long-term oral nucleoside analogs treatment group(namely NA group),and a plateau-arriving group(namely P group).The percentage of plasmacytoid dendritic cell and myeloid dendritic cell subsets in peripheral blood lymphocytes and monocytes and the mean fluorescence intensity of their surface costimulatory molecules were detected using a flow cytometer.Results In total,143 patients were enrolled(NH group,n=49;NA group,n=47;P group,n=47).The results demonstrated that CD141/CD1c double negative myeloid dendritic cell(DNmDC)/lymphocytes and monocytes(%)in P group(0.041[0.024,0.069])was significantly lower than that in NH group(0.270[0.135,0.407])and NA group(0.273[0.150,0.443]),and CD86 mean fluorescence intensity of DNmDCs in P group(1832.0[1484.0,2793.0])was significantly lower than that in NH group(4316.0[2958.0,5169.0])and NA group(3299.0[2534.0,4371.0]),Adjusted P all<0.001.Conclusion Reduced DNmDCs and impaired maturation may be associated with the onset of the plateau phase during intermittent interferon therapy in patients with chronic hepatitis B.
基金supported by the NSFC(12126329,12171266,12126346)the NSF of Fujian Province of China(2023J01805)+5 种基金the Research Start-Up Fund of Jimei University(ZQ2021017)supported by the NSFC(12101234)the NSF of Hebei Province(A2022502010)the Fundamental Research Funds for the Central Universities(2023MS164)the China Scholarship Councilsupported by the Simons Foundation(585081)。
文摘Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| |≤ε.The mapping g is said to be a phase isometry provided that ε=0.In this paper,we show the following universal inequality of g:for each u^(*) ∈ w^(*)-exp ‖u^(*)‖B_(x^(*)),there exist a phase function σ_(u^(*)):X→{-1,1} and φ ∈ Y^(*) with ‖φ‖=‖u^(*)‖≡α satisfying that|(u^(*),u)-σ_(u^(*))(u)<φ,g(u)>)|≤5/2εα,for all u ∈ X.In particular,let X be a smooth Banach space.Then we show the following:(1) the universal inequality holds for all u^(*) ∈ X^(*);(2) the constant 5/2 can be reduced to 3/2 provided that Y~*is strictly convex;(3) the existence of such a g implies the existence of a phase isometryΘ:X→Y such that■ provided that Y^(**) has the w^(*)-Kadec-Klee property(for example,Y is both reflexive and locally uniformly convex).
基金supported by project from the National Natural Science Foundation of China(21805018)by the Sichuan Science and Technology Program(2022ZHCG0018,2023NSFSC0117,2023ZHCG0060)+1 种基金the Yibin Science and Technology Program(2022JB005)project funded by the China Postdoctoral Science Foundation(2022M722704)。
文摘Nickel-manganese binary layered oxides with high working potential and low cost are potential candidates for sodium-ion batteries,but their electrochemical properties are highly related to compositional diversity.Diverse composite materials with various phase structures of P3,P2/P3,P2,P2/O3,and P2/P3/O3 were synthesized by manipulating the sodium content and calcination conditions,leading to the construction of a synthetic phase diagram for Na_(x)Ni_(0.25)Mn_(0.75)O_(2)(0.45≤x≤1.1).Then,we compared the electrochemical characteristics and structural evolution during the desodiation/sodiation process of P2,P2/P3,P2/03,and P2/P3/O3-Na_(x)Ni_(0.25)Mn_(0.75)O_(2).Among them,P2/P3-Na0.75Ni0.25Mn0.75O2exhibits the best rate capability of 90.9 mA h g^(-1)at 5 C,with an initial discharge capacity of 142.62 mA h g^(-1)at 0.1 C and a capacity retention rate of 78.25%after 100 cycles at 1 C in the voltage range of 2-4.3 V.The observed superior sodium storage performance of P2/P3 hybrids compared to other composite phases can be attributed to the enhanced Na^(+)transfer dynamic,reduction of the Jahn-teller effect,and improved reaction reversibility induced by the synergistic effect of P2 and P3 phases.The systematic research and exploration of phases in Na_(x)Ni_(0.25)Mn_(0.75)O_(2)provide new sights into high-performance nickel-manganese binary layered oxide for sodium-ion batteries.
基金supported by the National Natural Science Foundation of China (Grant No. 11903025)the Starting Fund of China West Normal University (Grant No. 18Q062)+2 种基金the Sichuan Science and Technology Program (Grant No. 2023ZYD0023)the Sichuan Youth Science and Technology Innovation Research Team (Grant No. 21CXTD0038)the Natural Science Foundation of Sichuan Province (Grant No. 2022NSFSC1833)。
文摘By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic Ad S black holes(BHs) with quasitopological electromagnetism in Einstein–Gauss–Bonnet(EGB) gravity. The results indicate that the small/large BH phase transition that is similar to the van der Waals(vdW) liquid/gas phase transition always exists for any spacetime dimensions. Interestingly, we then find that this BH system exhibits a more complex phase structure in 6-dimensional case that is missed in other dimensions.Specifically, it shows for D = 6 that we observed the small/intermediate/large BH phase transitions in a specific parameter region with the triple point naturally appeared. Moreover, when the magnetic charge turned off, we still observed the small/intermediate/large BH phase transitions and triple point only in 6-dimensional spacetime, which is consistent with the previous results. However, for the dyonic Ad S BHs with quasitopological electromagnetism in Einstein–Born–Infeld(EBI) gravity, the novel phase structure composed of two separate coexistence curves observed by Li et al. [Phys. Rev. D105 104048(2022)] disappeared in EGB gravity. This implies that this novel phase structure is closely related to gravity theories, and seems to have nothing to do with the effect of quasitopological electromagnetism. In addition, it is also true that the critical exponents calculated near the critical points possess identical values as mean field theory. Finally, we conclude that these findings shall provide some deep insights into the intriguing thermodynamic properties of the dyonic Ad S BHs with quasitopological electromagnetism in EGB gravity.
基金supported as part of the Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0020145Y.Z.would like to acknowledge support for his effort by the Simons Foundation through Grant No.357963 and NSF grant DMS-2142500.
文摘The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.