Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point...Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.展开更多
The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra sec...The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighborhopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamicalspin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spincorrelation in the t-t'-J model is the same as in the case of t-J model.展开更多
The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra sec...The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighborhopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamicalspin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spincorrelation in the t-t'-J model is the same as in the case of t-J model.展开更多
We investigate the magnetic ground state of Sm_(3)BWO_(9)with a distorted kagome lattice.A magnetic phase transition is identified at T_(N)=0.75 K from the temperature dependence of specific heat.From 11B nuclear magn...We investigate the magnetic ground state of Sm_(3)BWO_(9)with a distorted kagome lattice.A magnetic phase transition is identified at T_(N)=0.75 K from the temperature dependence of specific heat.From 11B nuclear magnetic resonance measurements,an incommensurate magnetic order is shown by the double-horn type spectra under a c-axis magnetic field,and absence of line splitting is observed for field oriented within the ab-plane,indicating the incommensurate modulation of the internal field strictly along𝑐c-axis.From the spin dynamics,the critical slowing-down behavior is observed in the temperature dependence of 1/T_(1)with𝜇_(μ0)H⊥c-axis,which is completely absent in the case with𝜇_(μ0)H||c-axis.Based on the local symmetry of 11B sites,we analyze the hyperfine coupling tensors and propose two constraints on the possible magnetic structure.The single ion anisotropy should play an important role in determination of contrasting ground states of Sm_(3)BWO_(9) and Pr_(3)BWO_(9).展开更多
Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,an...Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,and the second one due to the soft-mode of driving the martensitic transformation.The starting point,R_s,and finishing point,R_f,of the commensurate phase transition of the alloy have been determined.展开更多
We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability t...We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.展开更多
The microstructural characteristic of the misfit-layered compound PbTiS3 has been studied with transmission electron microscopy. All the incommensurate modulation-induced satellite spots and main diffraction spots of ...The microstructural characteristic of the misfit-layered compound PbTiS3 has been studied with transmission electron microscopy. All the incommensurate modulation-induced satellite spots and main diffraction spots of basic sublattices can be indexed systematically with a superspace group method. Finally, the relationship between the electronic transport properties and the crystal structure is discussed.展开更多
In this paper, we present Continuous Multiple Center(CMC) d-p πbond in TS_2 slabs on the basis of Extended Huckle calculation for incommensurate misfit compounds (MS)_xTS_2(where M=Pb, Sn and La; T=V,Nb,Ta, Cr), and ...In this paper, we present Continuous Multiple Center(CMC) d-p πbond in TS_2 slabs on the basis of Extended Huckle calculation for incommensurate misfit compounds (MS)_xTS_2(where M=Pb, Sn and La; T=V,Nb,Ta, Cr), and put forwards the trigonal prismatic coordination CMC d-p π conductive model. According to this model the conductivity of (MS)_xTS_2 series and the similarity between (MS)_xTS_2 and Na_xTS_2 series compounds in metallic behaviors can be explained successfully. Some relations between metallic behaviors and CMC d-p π bond (or band) are found.展开更多
The sample of cubic lazurite, collected in the Baikal region, with incommensurately 3D modulated (ITM) structure has been studied by the method of high-temperature X-ray powder diffraction. At short time of annealing ...The sample of cubic lazurite, collected in the Baikal region, with incommensurately 3D modulated (ITM) structure has been studied by the method of high-temperature X-ray powder diffraction. At short time of annealing in high-temperature diffraction experiment the modulation recovery proceeds during cooling down the sample to room temperature. The identity of the period of both initial and recovered modulation demonstrates that the system has a structural memory. The acquired results are interpreted through comparison of thermal behavior of lazurite, sodalite and quartz structures. It is supposed that two kinetically different and thermally activated processes proceed under heating: 1) reversible framework expansion due to Si-O-Al angle increase, and 2) equalizing of periodic local distortions via the diffusion-controlled transfer of cage ions between adjacent subcells. The second process seems to be much slower than the first one, especially at lower temperatures. With increasing temperature, both processes are activated. However, the framework expands more rapidly than the cage clusters migrate, and the periodic distortions of the framework are aligned. Under lower temperatures, the framework shrinks and again accommodates to the configuration of cage cations (clusters), which may be changed at high temperature and sufficient time or may not at lower temperature, short time, unfavorable SO2 fugacity values. In the first case the modulation disappears entirely, while in the second case it arises again. The probable reason for ITM formation is the balance of counteracting energetic terms: the elastic strain energy of structure deformation and the energy of cluster ordering providing the state of forced equilibrium. The excess free energy due to structure distortion is compensated by the increment associated with the cluster ordering process. However, no significant variations in sulphur anion speciation for different degrees of modulation retention were observed by XPS S 2p. This may be due to the ordering of Na- and Ca-containing clusters rather than the clusters with different sulphur species. ITM reversion is considered as an example of reversible forced equilibrium with completely reproducible forcing factor.展开更多
This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With...This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With the convex assumption,several elementary fractional difference inequalities on Lyapunov functions are developed.According to the essential features of nabla fractional calculus,the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method.To substantiate the efficacy and effectiveness of the theoretical results,four examples are elaborated.展开更多
The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)frac...The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.展开更多
The incommensurate modulated structure of the Bi2Sr2Ca1Cu2Oy high-Tc superocnductor has been studied by direct methods with X-ray diffraction data from a single crystal. The super-space group is N111Bbmb with three-di...The incommensurate modulated structure of the Bi2Sr2Ca1Cu2Oy high-Tc superocnductor has been studied by direct methods with X-ray diffraction data from a single crystal. The super-space group is N111Bbmb with three-dimensional unit cell parameters a = 0.54222 nm, b=0.5437 nm, c=3.0537 run, α=β=γ=90° andthemodula-tion wave vector q=(0, 0.22, 1). 543 main reflections, 867 first-order and 469 second-order satellite reflections have been observed. Phases of main reflections are derived by a conventional direct-method program SAPI91. The phases of satellite reflections are derived by the program DIMS running with default control based on the known phases of main reflections. The atomic parameters of the basic structure and of the modulation so obtained consist with the results from other authors. For the first time the structure details of the incommensurate modulation in the Bi-2212 phase are observed directly without relying on any assumed model of modulation.展开更多
Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered na...Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered nanocomposites, shear-lag analysis is usually implemented to evaluate the capability of interfacial loading transfer. Here, we introduce a multiscale shear-lag model that correlates macroscale mechanical properties with the molecular mechanisms to quantify the effects of interfacial configuration in graphene oxide(GO) layered nanocomposites. By investigating the mechanical responses of commensurate and incommensurate interfaces, we identify that the commensurate interface exhibits a pronounced size effect due to the nucleation and propagation of interfacial defects, whereas the incommensurate interface displays uniform deformation. Our predictions are further validated through large-scale molecular dynamics simulations for GO layered nanocomposites. This work demonstrates how size effects and interfacial configurations can be exploited to fabricate layered nanocomposites with superior mechanical properties despite relying on weak noncovalent interfaces.展开更多
A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatia...A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .展开更多
This paper mainly consists of the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes. An isomorphism class is defined by a type of finite mathemat...This paper mainly consists of the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes. An isomorphism class is defined by a type of finite mathematic group;for instance, the different types of mathematic groups have been well defined and studied by Coxeter. This classification may be used in the investigation of several domains of crystallography such as the study of the incommensurate phases, the quasi crystals … Indeed, each mathematic substitution group characterizes an isomorphism class of crystallographic point groups (spaces E2 or E3), of point groups of super crystals (spaces E4 or E5), and of molecular symmetry groups (spaces E2 or E3). This mathematic group gives interesting information about: 1) the incommensurate phase structures and their phase transitions according to the Landau’s theory in their super spaces E4, E5, E6, ···;2) the molecular symmetry group of chemisorbed molecules in space E2 (paragraph 2) or of the molecular crystal or solution in view of studying the molecule structure or its rotations or vibrationsin space E3;3) the geometric polyhedron symmetry groups as the regular rhombohedron in space E3, the rhombotope in space E4 or the rhombotope in space E5. Then, thanks to the isomorphism classes, we shall give properties of some crystal families that we have not published up to now. This formalism may be used to study crystal families in n-dimensional space with n > 6.展开更多
Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing...Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing from 0 and taking steps of length equal to <em>x</em>. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for <em>x</em> and <em>y</em>, whenever <em>y</em>/<em>x</em> is a rational number. In the case that <em>y</em>/<em>x</em> is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.展开更多
The paper discusses several wide-spread misunderstandings of Kuhn＇s theory of scientific development, most prominently the ascription that he conceives of scientific development as irrational. The core of this ascrip...The paper discusses several wide-spread misunderstandings of Kuhn＇s theory of scientific development, most prominently the ascription that he conceives of scientific development as irrational. The core of this ascription is an assessment of incommensurability as implying the lack of any rational possibility of theory comparison. This is supposed to be due to Gestalt switches and a quasi-religious element of conversion in theory change. Accordingly, scientific revolutions cannot be a serious matter for philosophical analysis; they furthermore foreclose any scientific progress. It is shown that such images of Kuhn＇s theory rest on deep misunderstandings that are partly due to Kuhn＇s writing style.展开更多
Researchers in the field of Second Language Acquisition （SLA） have been taking different routes. Some researchers make linguistic-cognitive issues their inquire object and pursue objectivity with quantitative resear...Researchers in the field of Second Language Acquisition （SLA） have been taking different routes. Some researchers make linguistic-cognitive issues their inquire object and pursue objectivity with quantitative research methods. Other researchers regard the social context of activity as an essential characteristic of learning and teaching. These groups of researchers make use of qualitative research methods like case study, grounded theory, narrative inquiry, and ethnography. There are many other routes that SLA researchers have taken, but the two just mentioned are perhaps the most predominant ones and the ones that are most easily contrasted. The present paper explores the disparity between the different research paths from the perspective of philosophy of science echoing the notion of incommensurability. In this paper the author argues that the differences between different SLA perspectives are not only commensurable but wholesome for the development of SLA.展开更多
This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 ...This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 investigate the consequences in relation to reflexivity, justification, and paradox for Kuhn＇s account of science. I want to do this on two levels, firstly looking at different possibilities for characterising individual paradigms. I will look at some examples from ancient and early modem astronomy as here it is clearest that paradigms can be characterised in different ways and that this has important consequences. I will argue in particular that Kuhn＇s characterisation of the paradigm for astronomy which emerges from antiquity （geocentrism） is favourable to his general account of the history of science, but that there is a very plausible and extremely damaging alternative. I argue that these differing characterisations generate differing, incommensurable taxonomies of the history of astronomy, with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice. If so, Kuhn then has problems with generating an adequate decision making protocol for choosing between the two paradigm characterisations. That is problematic in itself, but I also argue this problem is systemic and affects the evidence needed for Kuhn to justify his general account of the history of science. I also want to investigate the implications of differing taxonomies of the history of science at a more abstract level. Kuhn＇s general theory of the history of science generates a taxonomy of the history of science, as do other theories such as those of Popper and of gradualism. If so, the incommensurability involved here, again with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice, leads to issues of paradox and justification for Kuhn＇s general account of the history of science. With this broader understanding of taxonomic issues, some important Kuhn statements about scientific theories become self-referential, again generating problems of paradox and justification.展开更多
基金the National Natural Science Foundation of China(Grant No.11805285)the Natural Science Foundation of Shaanxi Province of China(Grant No.2022JM-033)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN 201900703)。
文摘Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10125415, 10074007, 90103024, and NationalScience Council under Grant No. NSC 90-2816-M-032-0001-6
文摘The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighborhopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamicalspin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spincorrelation in the t-t'-J model is the same as in the case of t-J model.
文摘The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighborhopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamicalspin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spincorrelation in the t-t'-J model is the same as in the case of t-J model.
基金supported by the National Natural Science Foundation of China (Grants No.11874057,11874158,U1732273,and 21927814)the High Magnetic Field Laboratory of Anhui Province
文摘We investigate the magnetic ground state of Sm_(3)BWO_(9)with a distorted kagome lattice.A magnetic phase transition is identified at T_(N)=0.75 K from the temperature dependence of specific heat.From 11B nuclear magnetic resonance measurements,an incommensurate magnetic order is shown by the double-horn type spectra under a c-axis magnetic field,and absence of line splitting is observed for field oriented within the ab-plane,indicating the incommensurate modulation of the internal field strictly along𝑐c-axis.From the spin dynamics,the critical slowing-down behavior is observed in the temperature dependence of 1/T_(1)with𝜇_(μ0)H⊥c-axis,which is completely absent in the case with𝜇_(μ0)H||c-axis.Based on the local symmetry of 11B sites,we analyze the hyperfine coupling tensors and propose two constraints on the possible magnetic structure.The single ion anisotropy should play an important role in determination of contrasting ground states of Sm_(3)BWO_(9) and Pr_(3)BWO_(9).
文摘Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,and the second one due to the soft-mode of driving the martensitic transformation.The starting point,R_s,and finishing point,R_f,of the commensurate phase transition of the alloy have been determined.
基金Project supported by the Natural Science Foundation of Hebei Province, China （Grant No. A2010000343）.
文摘We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB932302)the National Natural Science Foundation of China(Grant No.50921091)the Specific Funding of the Discipline and Graduate Education Project of Beijing Municipal Commission of Education,China
文摘The microstructural characteristic of the misfit-layered compound PbTiS3 has been studied with transmission electron microscopy. All the incommensurate modulation-induced satellite spots and main diffraction spots of basic sublattices can be indexed systematically with a superspace group method. Finally, the relationship between the electronic transport properties and the crystal structure is discussed.
文摘In this paper, we present Continuous Multiple Center(CMC) d-p πbond in TS_2 slabs on the basis of Extended Huckle calculation for incommensurate misfit compounds (MS)_xTS_2(where M=Pb, Sn and La; T=V,Nb,Ta, Cr), and put forwards the trigonal prismatic coordination CMC d-p π conductive model. According to this model the conductivity of (MS)_xTS_2 series and the similarity between (MS)_xTS_2 and Na_xTS_2 series compounds in metallic behaviors can be explained successfully. Some relations between metallic behaviors and CMC d-p π bond (or band) are found.
文摘The sample of cubic lazurite, collected in the Baikal region, with incommensurately 3D modulated (ITM) structure has been studied by the method of high-temperature X-ray powder diffraction. At short time of annealing in high-temperature diffraction experiment the modulation recovery proceeds during cooling down the sample to room temperature. The identity of the period of both initial and recovered modulation demonstrates that the system has a structural memory. The acquired results are interpreted through comparison of thermal behavior of lazurite, sodalite and quartz structures. It is supposed that two kinetically different and thermally activated processes proceed under heating: 1) reversible framework expansion due to Si-O-Al angle increase, and 2) equalizing of periodic local distortions via the diffusion-controlled transfer of cage ions between adjacent subcells. The second process seems to be much slower than the first one, especially at lower temperatures. With increasing temperature, both processes are activated. However, the framework expands more rapidly than the cage clusters migrate, and the periodic distortions of the framework are aligned. Under lower temperatures, the framework shrinks and again accommodates to the configuration of cage cations (clusters), which may be changed at high temperature and sufficient time or may not at lower temperature, short time, unfavorable SO2 fugacity values. In the first case the modulation disappears entirely, while in the second case it arises again. The probable reason for ITM formation is the balance of counteracting energetic terms: the elastic strain energy of structure deformation and the energy of cluster ordering providing the state of forced equilibrium. The excess free energy due to structure distortion is compensated by the increment associated with the cluster ordering process. However, no significant variations in sulphur anion speciation for different degrees of modulation retention were observed by XPS S 2p. This may be due to the ordering of Na- and Ca-containing clusters rather than the clusters with different sulphur species. ITM reversion is considered as an example of reversible forced equilibrium with completely reproducible forcing factor.
基金supported by the National Natural Science Foundation of China under Grant No.62273092the Science Climbing Project under Grant No.4307012166+3 种基金the Anhui Provincial Natural Science Foundation under Grant No.1708085QF141the Fundamental Research Funds for the Central Universities under Grant No.WK2100100028the General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2016M602032the fund of China Scholarship Council under Grant No.201806345002。
文摘This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With the convex assumption,several elementary fractional difference inequalities on Lyapunov functions are developed.According to the essential features of nabla fractional calculus,the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method.To substantiate the efficacy and effectiveness of the theoretical results,four examples are elaborated.
文摘The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.
文摘The incommensurate modulated structure of the Bi2Sr2Ca1Cu2Oy high-Tc superocnductor has been studied by direct methods with X-ray diffraction data from a single crystal. The super-space group is N111Bbmb with three-dimensional unit cell parameters a = 0.54222 nm, b=0.5437 nm, c=3.0537 run, α=β=γ=90° andthemodula-tion wave vector q=(0, 0.22, 1). 543 main reflections, 867 first-order and 469 second-order satellite reflections have been observed. Phases of main reflections are derived by a conventional direct-method program SAPI91. The phases of satellite reflections are derived by the program DIMS running with default control based on the known phases of main reflections. The atomic parameters of the basic structure and of the modulation so obtained consist with the results from other authors. For the first time the structure details of the incommensurate modulation in the Bi-2212 phase are observed directly without relying on any assumed model of modulation.
基金jointly supported by the National Natural Science Foundation of China(Nos.11872063 and 12172346)the University of Science and Technology of China(USTC)Research Funds of the Double First-Class Initiative(No.YD2480002002)China Postdoctoral Science Foundation(No.2021TQ0323)。
文摘Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered nanocomposites, shear-lag analysis is usually implemented to evaluate the capability of interfacial loading transfer. Here, we introduce a multiscale shear-lag model that correlates macroscale mechanical properties with the molecular mechanisms to quantify the effects of interfacial configuration in graphene oxide(GO) layered nanocomposites. By investigating the mechanical responses of commensurate and incommensurate interfaces, we identify that the commensurate interface exhibits a pronounced size effect due to the nucleation and propagation of interfacial defects, whereas the incommensurate interface displays uniform deformation. Our predictions are further validated through large-scale molecular dynamics simulations for GO layered nanocomposites. This work demonstrates how size effects and interfacial configurations can be exploited to fabricate layered nanocomposites with superior mechanical properties despite relying on weak noncovalent interfaces.
文摘A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .
文摘This paper mainly consists of the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes. An isomorphism class is defined by a type of finite mathematic group;for instance, the different types of mathematic groups have been well defined and studied by Coxeter. This classification may be used in the investigation of several domains of crystallography such as the study of the incommensurate phases, the quasi crystals … Indeed, each mathematic substitution group characterizes an isomorphism class of crystallographic point groups (spaces E2 or E3), of point groups of super crystals (spaces E4 or E5), and of molecular symmetry groups (spaces E2 or E3). This mathematic group gives interesting information about: 1) the incommensurate phase structures and their phase transitions according to the Landau’s theory in their super spaces E4, E5, E6, ···;2) the molecular symmetry group of chemisorbed molecules in space E2 (paragraph 2) or of the molecular crystal or solution in view of studying the molecule structure or its rotations or vibrationsin space E3;3) the geometric polyhedron symmetry groups as the regular rhombohedron in space E3, the rhombotope in space E4 or the rhombotope in space E5. Then, thanks to the isomorphism classes, we shall give properties of some crystal families that we have not published up to now. This formalism may be used to study crystal families in n-dimensional space with n > 6.
文摘Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing from 0 and taking steps of length equal to <em>x</em>. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for <em>x</em> and <em>y</em>, whenever <em>y</em>/<em>x</em> is a rational number. In the case that <em>y</em>/<em>x</em> is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.
文摘The paper discusses several wide-spread misunderstandings of Kuhn＇s theory of scientific development, most prominently the ascription that he conceives of scientific development as irrational. The core of this ascription is an assessment of incommensurability as implying the lack of any rational possibility of theory comparison. This is supposed to be due to Gestalt switches and a quasi-religious element of conversion in theory change. Accordingly, scientific revolutions cannot be a serious matter for philosophical analysis; they furthermore foreclose any scientific progress. It is shown that such images of Kuhn＇s theory rest on deep misunderstandings that are partly due to Kuhn＇s writing style.
文摘Researchers in the field of Second Language Acquisition （SLA） have been taking different routes. Some researchers make linguistic-cognitive issues their inquire object and pursue objectivity with quantitative research methods. Other researchers regard the social context of activity as an essential characteristic of learning and teaching. These groups of researchers make use of qualitative research methods like case study, grounded theory, narrative inquiry, and ethnography. There are many other routes that SLA researchers have taken, but the two just mentioned are perhaps the most predominant ones and the ones that are most easily contrasted. The present paper explores the disparity between the different research paths from the perspective of philosophy of science echoing the notion of incommensurability. In this paper the author argues that the differences between different SLA perspectives are not only commensurable but wholesome for the development of SLA.
文摘This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 investigate the consequences in relation to reflexivity, justification, and paradox for Kuhn＇s account of science. I want to do this on two levels, firstly looking at different possibilities for characterising individual paradigms. I will look at some examples from ancient and early modem astronomy as here it is clearest that paradigms can be characterised in different ways and that this has important consequences. I will argue in particular that Kuhn＇s characterisation of the paradigm for astronomy which emerges from antiquity （geocentrism） is favourable to his general account of the history of science, but that there is a very plausible and extremely damaging alternative. I argue that these differing characterisations generate differing, incommensurable taxonomies of the history of astronomy, with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice. If so, Kuhn then has problems with generating an adequate decision making protocol for choosing between the two paradigm characterisations. That is problematic in itself, but I also argue this problem is systemic and affects the evidence needed for Kuhn to justify his general account of the history of science. I also want to investigate the implications of differing taxonomies of the history of science at a more abstract level. Kuhn＇s general theory of the history of science generates a taxonomy of the history of science, as do other theories such as those of Popper and of gradualism. If so, the incommensurability involved here, again with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice, leads to issues of paradox and justification for Kuhn＇s general account of the history of science. With this broader understanding of taxonomic issues, some important Kuhn statements about scientific theories become self-referential, again generating problems of paradox and justification.
