We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the...We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.展开更多
Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of thes...Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of these measures over time remains understudied.This research explores the structural components of the Center for Epidemiological Studies Depression Scale(CES-D)and examines its consistency across various living environments and temporal stability in a cohort of Chinese teenagers.Method:In the initial phase,1,042 adolescents furnished demographic details and undertook the CES-D assessment.After a three-month interval,967 of these participants repeated the CES-D evaluation.The study employed Confirmatory factor analysis(CFA)to scrutinize the scale’s structural integrity.We investigated factorial invariance by conducting a twopronged CFA:one comparing urban vs.rural backgrounds,and another contrasting the results from the initial assessment with those from the follow-up.Results:The CES-D demonstrated adequate reliability in both rural and urban high school student samples.The preliminary four-factor model applied to the CES-D demonstrated a good fit with the collected data.Invariance tests,including multigroup analyses comparing rural and urban samples and longitudinal assessments,confirmed the scale’s invariance.Conclusions:The results suggest that the CES-D serves as a reliable instrument for evaluating depressive symptoms among Chinese adolescents.Its applicability is consistent across different living environments and remains stable over time.展开更多
We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 wit...We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).展开更多
The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first ...The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.展开更多
A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have...A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.展开更多
This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtaine...This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determinant in the process of solving. Then the invariant equation is solved by using the obtained partial derivatives. Finally, the solutions of invariant equations when the denominator functions satisfy the same simple harmonic oscillator equation or the denominator functions are power functions that have been obtained.展开更多
Optical-resolution photoacoustic microscopy(OR-PAM)has rapidly developed and is capable of characterizing optical absorption properties of biological tissue with high contrast and high resolution(micrometer-scale late...Optical-resolution photoacoustic microscopy(OR-PAM)has rapidly developed and is capable of characterizing optical absorption properties of biological tissue with high contrast and high resolution(micrometer-scale lateral resolution).However,the conventional excitation source of rapidly diverging Gaussian beam imposes limitations on the depth of focus(DOF)in OR-PAM,which in turn affects the depth-resolving ability and detection sensitivity.Here,we proposed a flexible DOF,depth-invariant resolution photoacoustic microscopy(FDIR-PAM)with nondiffraction of Airy beams.The spatial light modulator was incorporated into the optical pathway of the excitation source with matched switching phase patterns,achieving the flexibly adjustable modulation parameters of the Airy beam.We conducted experiments on phantoms and intravital tissue to validate the effectiveness of the proposed approach for high sensitivity and highresolution characterization of variable topology of tissue,offering a promising DOF of 926μm with an invariant lateral resolution of 3.2μm,which is more than 17-fold larger compared to the Gaussian beam.In addition,FDIR-PAM successfully revealed clear individual zebrafish larvae and the pigment pattern of adult zebrafishes,as well as fine morphology of cerebral vasculature in a large depth range with high resolution,which has reached an evident resolving capability improvement of 62%mean value compared with the Gaussian beam.展开更多
Structural reconstruction of electrocatalysts plays a pivotal role in catalytic performances for CO_(2)reduction reaction(CO_(2)RR),whereas the behavior is by far superficially understood.Here,we report that CO_(2)acc...Structural reconstruction of electrocatalysts plays a pivotal role in catalytic performances for CO_(2)reduction reaction(CO_(2)RR),whereas the behavior is by far superficially understood.Here,we report that CO_(2)accessibility results in a universal self-adaptive structural reconstruction from Cu_(2)O to Cu@CuxO composites,ending with feeding gas-dependent microstructures and catalytic performances.The CO_(2)-rich atmosphere favors reconstruction for CO_(2)RR,whereas the CO_(2)-deficient one prefers that for hydrogen evolution reaction.With the assistance of spectroscopic analysis and theoretical calculations,we uncover a CO_(2)-induced passivation behavior by identifying a reductionresistant but catalytic active Cu(I)-rich amorphous layer stabilized by*CO intermediates.Additionally,we find extra CO production is indispensable for the robust production of C2H4.An inverse correlation between durability and FECO/FEC2H4 is disclosed,suggesting that the selfstabilization process involving the absorption of*CO intermediates on Cu(I)sites is essential for durable electrolysis.Guided by this insight,we design hollow Cu_(2)O nanospheres for durable and selective CO_(2)RR electrolysis in producing C2H4.Our work recognizes the previously overlooked passivation reconstruction and self-stabilizing behavior and highlights the critical role of the local atmosphere in modulating reconstruction and catalytic processes.展开更多
The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation b...The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.展开更多
To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati...To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.展开更多
By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variab...By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C...To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model.展开更多
The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with ...The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.展开更多
In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and suffici...In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.展开更多
基金supported by the Natural Science Foundation of Beijing(Grant No.Z180007)the National Natural Science Foundation of China(Grant Nos.1157200511874003,and 51672018)。
文摘We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.
文摘Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of these measures over time remains understudied.This research explores the structural components of the Center for Epidemiological Studies Depression Scale(CES-D)and examines its consistency across various living environments and temporal stability in a cohort of Chinese teenagers.Method:In the initial phase,1,042 adolescents furnished demographic details and undertook the CES-D assessment.After a three-month interval,967 of these participants repeated the CES-D evaluation.The study employed Confirmatory factor analysis(CFA)to scrutinize the scale’s structural integrity.We investigated factorial invariance by conducting a twopronged CFA:one comparing urban vs.rural backgrounds,and another contrasting the results from the initial assessment with those from the follow-up.Results:The CES-D demonstrated adequate reliability in both rural and urban high school student samples.The preliminary four-factor model applied to the CES-D demonstrated a good fit with the collected data.Invariance tests,including multigroup analyses comparing rural and urban samples and longitudinal assessments,confirmed the scale’s invariance.Conclusions:The results suggest that the CES-D serves as a reliable instrument for evaluating depressive symptoms among Chinese adolescents.Its applicability is consistent across different living environments and remains stable over time.
基金Supported by the National Natural Science Foundation of China(11671373).
文摘We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).
文摘The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.
文摘A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.
文摘This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determinant in the process of solving. Then the invariant equation is solved by using the obtained partial derivatives. Finally, the solutions of invariant equations when the denominator functions satisfy the same simple harmonic oscillator equation or the denominator functions are power functions that have been obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.62105255 and 62275210)the Xidian University Specially Funded Project for Interdisciplinary Exploration(Grant No.TZJH2024043)+1 种基金the Key Research and Development Program of Shaanxi Province(Grant No.2023-YBSF-293)the National Young Talent Program and Shaanxi Young Top-notch Talent Program,and the Fundamental Research Funds for CentralUniversities(Grant No.ZYTS23187).
文摘Optical-resolution photoacoustic microscopy(OR-PAM)has rapidly developed and is capable of characterizing optical absorption properties of biological tissue with high contrast and high resolution(micrometer-scale lateral resolution).However,the conventional excitation source of rapidly diverging Gaussian beam imposes limitations on the depth of focus(DOF)in OR-PAM,which in turn affects the depth-resolving ability and detection sensitivity.Here,we proposed a flexible DOF,depth-invariant resolution photoacoustic microscopy(FDIR-PAM)with nondiffraction of Airy beams.The spatial light modulator was incorporated into the optical pathway of the excitation source with matched switching phase patterns,achieving the flexibly adjustable modulation parameters of the Airy beam.We conducted experiments on phantoms and intravital tissue to validate the effectiveness of the proposed approach for high sensitivity and highresolution characterization of variable topology of tissue,offering a promising DOF of 926μm with an invariant lateral resolution of 3.2μm,which is more than 17-fold larger compared to the Gaussian beam.In addition,FDIR-PAM successfully revealed clear individual zebrafish larvae and the pigment pattern of adult zebrafishes,as well as fine morphology of cerebral vasculature in a large depth range with high resolution,which has reached an evident resolving capability improvement of 62%mean value compared with the Gaussian beam.
基金supported by the National Natural Science Foundation of China(Grant No.22479097)the Shanghai Science and Technology Committee(Grant No.23ZR1433000)the National High-Level Talent Program for Young Scholars,the Start-up Fund(F.S.)from Shanghai Jiao Tong University.
文摘Structural reconstruction of electrocatalysts plays a pivotal role in catalytic performances for CO_(2)reduction reaction(CO_(2)RR),whereas the behavior is by far superficially understood.Here,we report that CO_(2)accessibility results in a universal self-adaptive structural reconstruction from Cu_(2)O to Cu@CuxO composites,ending with feeding gas-dependent microstructures and catalytic performances.The CO_(2)-rich atmosphere favors reconstruction for CO_(2)RR,whereas the CO_(2)-deficient one prefers that for hydrogen evolution reaction.With the assistance of spectroscopic analysis and theoretical calculations,we uncover a CO_(2)-induced passivation behavior by identifying a reductionresistant but catalytic active Cu(I)-rich amorphous layer stabilized by*CO intermediates.Additionally,we find extra CO production is indispensable for the robust production of C2H4.An inverse correlation between durability and FECO/FEC2H4 is disclosed,suggesting that the selfstabilization process involving the absorption of*CO intermediates on Cu(I)sites is essential for durable electrolysis.Guided by this insight,we design hollow Cu_(2)O nanospheres for durable and selective CO_(2)RR electrolysis in producing C2H4.Our work recognizes the previously overlooked passivation reconstruction and self-stabilizing behavior and highlights the critical role of the local atmosphere in modulating reconstruction and catalytic processes.
文摘The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.
文摘To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.
文摘By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
文摘To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model.
文摘The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.
文摘In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.
