Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
In recent years,the research on superconductivity in one-dimensional(1D)materials has been attracting increasing attention due to its potential applications in low-dimensional nanodevices.However,the critical temperat...In recent years,the research on superconductivity in one-dimensional(1D)materials has been attracting increasing attention due to its potential applications in low-dimensional nanodevices.However,the critical temperature(T_(c))of 1D superconductors is low.In this work,we theoretically investigate the possible high T_(c) superconductivity of(5,5)carbon nanotube(CNT).The pristine(5,5)CNT is a Dirac semimetal and can be modulated into a semiconductor by full hydrogenation.Interestingly,by further hole doping,it can be regulated into a metallic state with the sp3-hybridized𝜎electrons metalized,and a giant Kohn anomaly appears in the optical phonons.The two factors together enhance the electron–phonon coupling,and lead to high-T_(c) superconductivity.When the hole doping concentration of hydrogenated-(5,5)CNT is 2.5 hole/cell,the calculated T_(c) is 82.3 K,exceeding the boiling point of liquid nitrogen.Therefore,the predicted hole-doped hydrogenated-(5,5)CNT provides a new platform for 1D high-T_(c) superconductivity and may have potential applications in 1D nanodevices.展开更多
Compared to the well-studied two-dimensional(2D)ferroelectricity,the appearance of 2D antiferroelectricity is much rarer,where local dipoles from the nonequivalent sublattices within 2D monolayers are oppositely orien...Compared to the well-studied two-dimensional(2D)ferroelectricity,the appearance of 2D antiferroelectricity is much rarer,where local dipoles from the nonequivalent sublattices within 2D monolayers are oppositely oriented.Using NbOCl_(2) monolayer with competing ferroelectric(FE)and antiferroelectric(AFE)phases as a 2D material platform,we demonstrate the emergence of intrinsic antiferroelectricity in NbOCl_(2) monolayer under experimentally accessible shear strain,along with new functionality associated with electric field-induced AFE-to-FE phase transition.Specifically,the complex configuration space accommodating FE and AFE phases,polarization switching kinetics,and finite temperature thermodynamic properties of 2D NbOCl_(2) are all accurately predicted by large-scale molecular dynamics simulations based on deep learning interatomic potential model.Moreover,room temperature stable antiferroelectricity with low polarization switching barrier and one-dimensional collinear polarization arrangement is predicted in shear-deformed NbOCl_(2) monolayer.The transition from AFE to FE phase in 2D NbOCl_(2) can be triggered by a low critical electric field,leading to a double polarization–electric(P–E)loop with small hysteresis.A new type of optoelectronic device composed of AFE-NbOCl_(2) is proposed,enabling electric“writing”and nonlinear optical“reading”logical operation with fast operation speed and low power consumption.展开更多
[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the ...[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.展开更多
SrRuO_(3)is a canonical itinerant ferromagnet,yet its properties in the extreme two-dimensional limit on a(111)crystal plane remain largely unexplored.Here,we demonstrate a complete transformation of its ground state ...SrRuO_(3)is a canonical itinerant ferromagnet,yet its properties in the extreme two-dimensional limit on a(111)crystal plane remain largely unexplored.Here,we demonstrate a complete transformation of its ground state driven by dimensional reduction.As the thickness of(111)-oriented SrRuO_(3)films is reduced to a few unit cells,the system transitions from a metallic ferromagnet to a semiconducting antiferromagnet.This emergent antiferromagnetism is evidenced by a vanishing magnetic remanence and most strikingly,by the appearance of an unconventional twelve-fold anisotropic magnetoresistance.First-principles calculations confirm that an A-type antiferromagnetic order is the stable ground state in the ultrathin limit.Our findings establish(111)dimensional engineering as a powerful route to manipulate correlated electron states and uncover novel functionalities for antiferromagnetic spintronics.展开更多
Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by ...Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.展开更多
Fracture surface contour study is one of the important requirements for characterization and evaluation of the microstructure of rocks.Based on the improved cube covering method and the 3D contour digital reconstructi...Fracture surface contour study is one of the important requirements for characterization and evaluation of the microstructure of rocks.Based on the improved cube covering method and the 3D contour digital reconstruction model,this study proposes a quantitative microstructure characterization method combining the roughness evaluation index and the 3D fractal dimension to study the change rule of the fracture surface morphology after blasting.This method was applied and validated in the study of the fracture microstructure of the rock after blasting.The results show that the fracture morphology characteristics of the 3D contour digital reconstruction model have good correlation with the changes of the blasting action.The undulation rate of the three-dimensional surface profile of the rock is more prone to dramatic rise and dramatic fall morphology.In terms of tilting trend,the tilting direction also shows gradual disorder,with the tilting angle increasing correspondingly.All the roughness evaluation indexes of the rock fissure surface after blasting show a linear and gradually increasing trend as the distance to the bursting center increases;the difference between the two-dimensional roughness evaluation indexes and the three-dimensional ones of the same micro-area rock samples also becomes increasingly larger,among which the three-dimensional fissure roughness coefficient JRC and the surface roughness ratio Rs display better correlation.Compared with the linear fitting formula of the power function relationship,the three-dimensional fractal dimension of the postblast fissure surface is fitted with the values of JRC and Rs,which renders higher correlation coefficients,and the degree of linear fitting of JRC to the three-dimensional fractal dimension is higher.The fractal characteristics of the blast-affected region form a unity with the three-dimensional roughness evaluation of the fissure surface.展开更多
Background The patient-reported Dimensional Anhedonia Rating Scale(DARS)has been adapted into Chinese,so there is a need to evaluate its measurement properties in a Chinese population.Aims To evaluate the reliability ...Background The patient-reported Dimensional Anhedonia Rating Scale(DARS)has been adapted into Chinese,so there is a need to evaluate its measurement properties in a Chinese population.Aims To evaluate the reliability and validity of the DARS among Chinese individuals with major depressive disorder(MDD)and its treatment sensitivity in a prospective clinical study.Methods Data were from a multicentre,prospective clinical study(NCT03294525),which recruited both patients with MDD,who were followed for 8 weeks,and healthy controls(HCs),assessed at baseline only.The analysis included confirmatory factor analysis,validity and sensitivity to change.Results Patients’mean(standard deviation(SD))age was 34.8(11.0)years,with 68.7%being female.75.2%of patients with MDD had melancholic features,followed by 63.8%with anxious distress.Patients had experienced MDD for a mean(SD)of 9.2(18)months.DARS scores covered the full range of severity with no major floor or ceiling effects.Confirmatory factor analysis showed adequate fit statistics(comparative fit index 0.976,goodness-of-fit index 0.935 and root mean square error of approximation 0.055).Convergent validity with anhedonia-related measures was confirmed.While the correlation between the DARS and the Hamilton Depression Rating Scale was not strong(r=0.31,baseline),the DARS was found to differentiate between levels of depression.Greater improvements in DARS scores were seen with the Hamilton Rating Scale for Depression responder group(effect size 1.16)compared with the non-responder group(effect size 0.46).Conclusions This study comprehensively evaluated the measurement properties of the DARS using a Chinese population with MDD.Overall,the Chinese version of DARS demonstrates good psychometric properties and has been found to be responsive to change during antidepressant treatment.The DARS is a suitable scale for assessing patient-reported anhedonia in future clinical trials.展开更多
Low-dimensional physics provides profound insights into strongly correlated interactions,leading to enhancedquantum effects and the emergence of exotic quantum states.The Ln_(3)ScBi_(5)family stands out as a chemicall...Low-dimensional physics provides profound insights into strongly correlated interactions,leading to enhancedquantum effects and the emergence of exotic quantum states.The Ln_(3)ScBi_(5)family stands out as a chemicallyversatile kagome platform with mixed low-dimensional structural framework and tunable physical properties.Ourresearch initiates with a comprehensive evaluation of the currently known Ln_(3)ScBi_(5)(Ln=La-Nd,Sm)materials,providing a robust methodology for assessing their stability frontiers within this system.Focusing on Pr_(3)ScBi_(5),we investigate the influence of the zigzag chains of quasi-one-dimensional(Q1D)motifs and the distorted kagomelayers of quasi-two-dimensional(Q2D)networks in the mixed-dimensional structure on the intricate magneticground states and unique spin fluctuations.Our study reveals that the noncollinear antiferromagnetic(AFM)moments of Pr^(3+)ions are confined within the Q2D kagome planes,displaying minimal in-plane anisotropy.Incontrast,a strong AFM coupling is observed within the Q1D zigzag chains,significantly constraining spin motion.Notably,magnetic frustration is partially a consequence of coupling to conduction electrons via Ruderman-Kittel-Kasuya-Yosida interaction,highlighting a promising framework for future investigations into mixed-dimensional frustration in Ln_(3)ScBi_(5) systems.展开更多
Two-dimensional energetic materials(2DEMs),characterized by their exceptional interlayer sliding properties,are recognized as exemplar of low-sensitivity energetic materials.However,the diversity of available 2DEMs is...Two-dimensional energetic materials(2DEMs),characterized by their exceptional interlayer sliding properties,are recognized as exemplar of low-sensitivity energetic materials.However,the diversity of available 2DEMs is severely constrained by the absence of efficient methods for rapidly predicting crystal packing modes from molecular structures,impeding the high-throughput rational design of such materials.In this study,we employed quantified indicators,such as hydrogen bond dimension and maximum planar separation,to quickly screen 172DEM and 16 non-2DEM crystal structures from a crystal database.They were subsequently compared and analyzed,focusing on hydrogen bond donor-acceptor combinations,skeleton features,and intermolecular interactions.Our findings suggest that theπ-πpacking interaction energy is a key determinant in the formation of layered packing modes by planar energetic molecules,with its magnitude primarily influenced by the strongest dimericπ-πinteraction(π-π2max).Consequently,we have delineated a critical threshold forπ-π2max to discern layered packing modes and formulated a theoretical model for predictingπ-π2max,grounded in molecular electrostatic potential and dipole moment analysis.The predictive efficacy of this model was substantiated through external validation on a test set comprising 31 planar energetic molecular crystals,achieving an accuracy of 84%and a recall of 75%.Furthermore,the proposed model shows superior classification predictive performance compared to typical machine learning methods,such as random forest,on the external validation samples.This contribution introduces a novel methodology for the identification of crystal packing modes in 2DEMs,potentially accelerating the design and synthesis of high-energy,low-sensitivity 2DEMs.展开更多
Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynam...Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynamic characteristics.Therefore,it is necessary to design a lowdimensional model that can well reflect the dynamic characteristics of high-dimensional system.To build such a low-dimensional model,this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory.First,sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted.Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced,and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined.Finally,the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method,and spectrum results were then compared experimentally.Numerical and experimental results demonstrate that,during the dimensionality reduction process,the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation.The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system.The larger the proportion of steady-state signals is,the closer the energy tends to accumulate towards lower orders.The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98%.The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of highdimensional systems coupled with strong nonlinearities under variable operating conditions.展开更多
“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that ...“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that balance global integration with local needs.This also includes management of global business operations across diverse cultures in a multipolar international landscape.The paper briefs the developed and already tested in numerous applications high-level Spatial Grasp Model and Technology(SGT),which can help investigate and manage complex systems with a holistic spatial approach effectively covering various physical and virtual dimensions,their interrelations,and integration as a whole.Different areas will be investigated with examples of practical solutions in them and their combinations in a high-level Spatial Grasp Language(SGL),the key element of SGT.This allows for the creation and distributed management of very large spatial networks with different orientation which can be self-spreading,self-analyzing,self-modifying,and self-recovering in complex terrestrial and celestial environments,and also organize dynamic multi-networking solutions supporting global evolution and integrity.展开更多
In the past decade, researchers in the fields of energy production have concentrated on the improvement of new energy storage devices. Lithium-ion batteries(LIBs) and faradaic supercapacitors(FSs) have attracted speci...In the past decade, researchers in the fields of energy production have concentrated on the improvement of new energy storage devices. Lithium-ion batteries(LIBs) and faradaic supercapacitors(FSs) have attracted special attention as a result of the rapid development of new electrode nanomaterials, especially hybrid nanomaterials, which can meet the increasingly higher requirements for future energy, such as the capability to deliver high-power performance and an extremely long life cycle. In these hybrid nanostructures, a series of synergistic effects and unique properties arising from the combination of individual components are a major factor leading to improved charge/discharge capability, energy density, and system lifetime. This paper describes the most recent progress in the growth of hybrid electrode materials for LIBs and FSs systems, focusing on the combination of zero-dimensional(0 D), one-dimensional(1 D), two-dimensional(2 D), and three-dimensional(3 D) nanomaterials, respectively.展开更多
Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the...Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the self-affine,self-similarity,and iterative generation characteristics of fractal geometry,the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane,facade,and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre.The research shows that the geometric complexity of Wuzhen Grand Theater in the“fifth façade”and multi-faceted façade is significantly higher than that of Harbin Grand Theater,and its morphological design is more inclined to echo the texture of the surrounding water towns.The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines.The research proves that fractal dimension can effectively quantify the complexity of architectural form,provide a scientific basis for the form design,environmental integration,and form interpretation of performance architecture,and expand the mathematical analysis dimension of architectural form design.展开更多
Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishe...Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.展开更多
In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existin...In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure.Despite continuing efforts,the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution’s internal data.We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction.To contribute to the field of financial innovation,this study proposes a Dimension Reduction Assisted Credit Scoring(DRA-CS)method via distance covariance-based sufficient dimension reduction(DCOV-SDR)in Majorization-Minimization(MM)algorithm.First,in the presence of a large number of variables,the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction.Second,when the DRA-CS method is employed with logistic regression,it outperforms existing methods based on different variable selection techniques.This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.展开更多
Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as o...Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as one of the most useful methods,has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems.However,this method often relies on manual inspection due to uncertainties from iden-tifying the scaling region,making the correlation dimension value calculation troublesome and subjective.Therefore,it is necessary to propose a fast and intelligent algorithm to solve the above problem.This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accu-rately identify the scaling range and estimate the correlation dimension values.The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province,China.The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values,and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.展开更多
The phenomenon of photothermally induced transparency(PTIT)arises from the nonlinear behavior of an optical cavity,resulting from the heating of mirrors.By introducing a coupling field in the form of a standing wave,P...The phenomenon of photothermally induced transparency(PTIT)arises from the nonlinear behavior of an optical cavity,resulting from the heating of mirrors.By introducing a coupling field in the form of a standing wave,PTIT can be transitioned into photothermally induced grating(PTIG).A two-dimensional(2D)diffraction pattern is achieved through the adjustment of key parameters such as coupling strength and effective detuning.Notably,we observe first,second,and third-order intensity distributions,with the ability to transfer probe energy predominantly to the third order by fine-tuning the coupling strength.The intensity distribution is characterized by(±m,±n),where m,n=1,2,3.This proposed 2D grating system offers a novel platform for manipulating PTIG,presenting unique possibilities for enhanced functionality and control.展开更多
In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown...In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.展开更多
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
基金supported by the National Natural Science Foundation of China (Grant Nos.12074213 and 11574108)the Major Basic Program of Natural Science Foundation of Shandong Province (Grant No.ZR2021ZD01)the Natural Science Foundation of Shandong Province (Grant No.ZR2023MA082)。
文摘In recent years,the research on superconductivity in one-dimensional(1D)materials has been attracting increasing attention due to its potential applications in low-dimensional nanodevices.However,the critical temperature(T_(c))of 1D superconductors is low.In this work,we theoretically investigate the possible high T_(c) superconductivity of(5,5)carbon nanotube(CNT).The pristine(5,5)CNT is a Dirac semimetal and can be modulated into a semiconductor by full hydrogenation.Interestingly,by further hole doping,it can be regulated into a metallic state with the sp3-hybridized𝜎electrons metalized,and a giant Kohn anomaly appears in the optical phonons.The two factors together enhance the electron–phonon coupling,and lead to high-T_(c) superconductivity.When the hole doping concentration of hydrogenated-(5,5)CNT is 2.5 hole/cell,the calculated T_(c) is 82.3 K,exceeding the boiling point of liquid nitrogen.Therefore,the predicted hole-doped hydrogenated-(5,5)CNT provides a new platform for 1D high-T_(c) superconductivity and may have potential applications in 1D nanodevices.
基金supported by the National Natural Science Foundation of China (Grant No.11574244 for G.Y.G.)the XJTU Research Fund for AI Science (Grant No.2025YXYC011 for G.Y.G.)the Hong Kong Global STEM Professorship Scheme (for X.C.Z.)。
文摘Compared to the well-studied two-dimensional(2D)ferroelectricity,the appearance of 2D antiferroelectricity is much rarer,where local dipoles from the nonequivalent sublattices within 2D monolayers are oppositely oriented.Using NbOCl_(2) monolayer with competing ferroelectric(FE)and antiferroelectric(AFE)phases as a 2D material platform,we demonstrate the emergence of intrinsic antiferroelectricity in NbOCl_(2) monolayer under experimentally accessible shear strain,along with new functionality associated with electric field-induced AFE-to-FE phase transition.Specifically,the complex configuration space accommodating FE and AFE phases,polarization switching kinetics,and finite temperature thermodynamic properties of 2D NbOCl_(2) are all accurately predicted by large-scale molecular dynamics simulations based on deep learning interatomic potential model.Moreover,room temperature stable antiferroelectricity with low polarization switching barrier and one-dimensional collinear polarization arrangement is predicted in shear-deformed NbOCl_(2) monolayer.The transition from AFE to FE phase in 2D NbOCl_(2) can be triggered by a low critical electric field,leading to a double polarization–electric(P–E)loop with small hysteresis.A new type of optoelectronic device composed of AFE-NbOCl_(2) is proposed,enabling electric“writing”and nonlinear optical“reading”logical operation with fast operation speed and low power consumption.
基金Supported by National Natural Science Fund Program(40705038)~~
文摘[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.
基金supported by the National Natural Science Foundation of China(Grant Nos.12204521,12250710675,and 12504198)the National Key R&D Program of China(Grant No.2022YFA1403000)。
文摘SrRuO_(3)is a canonical itinerant ferromagnet,yet its properties in the extreme two-dimensional limit on a(111)crystal plane remain largely unexplored.Here,we demonstrate a complete transformation of its ground state driven by dimensional reduction.As the thickness of(111)-oriented SrRuO_(3)films is reduced to a few unit cells,the system transitions from a metallic ferromagnet to a semiconducting antiferromagnet.This emergent antiferromagnetism is evidenced by a vanishing magnetic remanence and most strikingly,by the appearance of an unconventional twelve-fold anisotropic magnetoresistance.First-principles calculations confirm that an A-type antiferromagnetic order is the stable ground state in the ultrathin limit.Our findings establish(111)dimensional engineering as a powerful route to manipulate correlated electron states and uncover novel functionalities for antiferromagnetic spintronics.
基金supported by the Key Program of the National Natural Science Foundation of China(Grant No.62031013)Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project(Grant No.2022ZDJS117).
文摘Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.
基金National Key Research and Development Program of China,Grant/Award Number:2021YFC2902103National Natural Science Foundation of China,Grant/Award Number:51934001Fundamental Research Funds for the Central Universities,Grant/Award Number:2023JCCXLJ02。
文摘Fracture surface contour study is one of the important requirements for characterization and evaluation of the microstructure of rocks.Based on the improved cube covering method and the 3D contour digital reconstruction model,this study proposes a quantitative microstructure characterization method combining the roughness evaluation index and the 3D fractal dimension to study the change rule of the fracture surface morphology after blasting.This method was applied and validated in the study of the fracture microstructure of the rock after blasting.The results show that the fracture morphology characteristics of the 3D contour digital reconstruction model have good correlation with the changes of the blasting action.The undulation rate of the three-dimensional surface profile of the rock is more prone to dramatic rise and dramatic fall morphology.In terms of tilting trend,the tilting direction also shows gradual disorder,with the tilting angle increasing correspondingly.All the roughness evaluation indexes of the rock fissure surface after blasting show a linear and gradually increasing trend as the distance to the bursting center increases;the difference between the two-dimensional roughness evaluation indexes and the three-dimensional ones of the same micro-area rock samples also becomes increasingly larger,among which the three-dimensional fissure roughness coefficient JRC and the surface roughness ratio Rs display better correlation.Compared with the linear fitting formula of the power function relationship,the three-dimensional fractal dimension of the postblast fissure surface is fitted with the values of JRC and Rs,which renders higher correlation coefficients,and the degree of linear fitting of JRC to the three-dimensional fractal dimension is higher.The fractal characteristics of the blast-affected region form a unity with the three-dimensional roughness evaluation of the fissure surface.
基金supported by the National Natural Science Foundation of China(No.82371530,82171529)the Capital Health Development Special Research Project(2022-1-4111)the National Key Technology R and D Program(No.2015BAI13B01).
文摘Background The patient-reported Dimensional Anhedonia Rating Scale(DARS)has been adapted into Chinese,so there is a need to evaluate its measurement properties in a Chinese population.Aims To evaluate the reliability and validity of the DARS among Chinese individuals with major depressive disorder(MDD)and its treatment sensitivity in a prospective clinical study.Methods Data were from a multicentre,prospective clinical study(NCT03294525),which recruited both patients with MDD,who were followed for 8 weeks,and healthy controls(HCs),assessed at baseline only.The analysis included confirmatory factor analysis,validity and sensitivity to change.Results Patients’mean(standard deviation(SD))age was 34.8(11.0)years,with 68.7%being female.75.2%of patients with MDD had melancholic features,followed by 63.8%with anxious distress.Patients had experienced MDD for a mean(SD)of 9.2(18)months.DARS scores covered the full range of severity with no major floor or ceiling effects.Confirmatory factor analysis showed adequate fit statistics(comparative fit index 0.976,goodness-of-fit index 0.935 and root mean square error of approximation 0.055).Convergent validity with anhedonia-related measures was confirmed.While the correlation between the DARS and the Hamilton Depression Rating Scale was not strong(r=0.31,baseline),the DARS was found to differentiate between levels of depression.Greater improvements in DARS scores were seen with the Hamilton Rating Scale for Depression responder group(effect size 1.16)compared with the non-responder group(effect size 0.46).Conclusions This study comprehensively evaluated the measurement properties of the DARS using a Chinese population with MDD.Overall,the Chinese version of DARS demonstrates good psychometric properties and has been found to be responsive to change during antidepressant treatment.The DARS is a suitable scale for assessing patient-reported anhedonia in future clinical trials.
基金supported by the National Key R&D Program of China(Grant Nos.2024YFA1408400 and 2021YFA1400401)the National Natural Science Foundation of China(Grant Nos.U22A6005 and 52271238)+2 种基金the China Postdoctoral Science Foundation(Grant No.2025M770186)the Center for Materials Genome,and the Synergetic Extreme Condition User Facility(SECUF)supported by the AI-driven experiments,simulations and model training on the robotic AI-Scientist platform from Chinese Academy of Sciences and the Research Funds for the Central Universities(Grant No.N25ZLE007).
文摘Low-dimensional physics provides profound insights into strongly correlated interactions,leading to enhancedquantum effects and the emergence of exotic quantum states.The Ln_(3)ScBi_(5)family stands out as a chemicallyversatile kagome platform with mixed low-dimensional structural framework and tunable physical properties.Ourresearch initiates with a comprehensive evaluation of the currently known Ln_(3)ScBi_(5)(Ln=La-Nd,Sm)materials,providing a robust methodology for assessing their stability frontiers within this system.Focusing on Pr_(3)ScBi_(5),we investigate the influence of the zigzag chains of quasi-one-dimensional(Q1D)motifs and the distorted kagomelayers of quasi-two-dimensional(Q2D)networks in the mixed-dimensional structure on the intricate magneticground states and unique spin fluctuations.Our study reveals that the noncollinear antiferromagnetic(AFM)moments of Pr^(3+)ions are confined within the Q2D kagome planes,displaying minimal in-plane anisotropy.Incontrast,a strong AFM coupling is observed within the Q1D zigzag chains,significantly constraining spin motion.Notably,magnetic frustration is partially a consequence of coupling to conduction electrons via Ruderman-Kittel-Kasuya-Yosida interaction,highlighting a promising framework for future investigations into mixed-dimensional frustration in Ln_(3)ScBi_(5) systems.
基金support from National Natural Science Foundation of China(Grant Nos.22275145,22305189and 21875184)Natural Science Foundation of Shaanxi Province(Grant Nos.2022JC-10 and 2024JC-YBQN-0112).
文摘Two-dimensional energetic materials(2DEMs),characterized by their exceptional interlayer sliding properties,are recognized as exemplar of low-sensitivity energetic materials.However,the diversity of available 2DEMs is severely constrained by the absence of efficient methods for rapidly predicting crystal packing modes from molecular structures,impeding the high-throughput rational design of such materials.In this study,we employed quantified indicators,such as hydrogen bond dimension and maximum planar separation,to quickly screen 172DEM and 16 non-2DEM crystal structures from a crystal database.They were subsequently compared and analyzed,focusing on hydrogen bond donor-acceptor combinations,skeleton features,and intermolecular interactions.Our findings suggest that theπ-πpacking interaction energy is a key determinant in the formation of layered packing modes by planar energetic molecules,with its magnitude primarily influenced by the strongest dimericπ-πinteraction(π-π2max).Consequently,we have delineated a critical threshold forπ-π2max to discern layered packing modes and formulated a theoretical model for predictingπ-π2max,grounded in molecular electrostatic potential and dipole moment analysis.The predictive efficacy of this model was substantiated through external validation on a test set comprising 31 planar energetic molecular crystals,achieving an accuracy of 84%and a recall of 75%.Furthermore,the proposed model shows superior classification predictive performance compared to typical machine learning methods,such as random forest,on the external validation samples.This contribution introduces a novel methodology for the identification of crystal packing modes in 2DEMs,potentially accelerating the design and synthesis of high-energy,low-sensitivity 2DEMs.
基金supported by the China Postdoctoral Science Foundation(No.2024M764171)the Postdoctoral Research Start-up Funds,China(No.AUGA5710027424)+1 种基金the National Natural Science Foundation of China(No.U2341237)the Development and construction funds for the School of Mechatronics Engineering of HIT,China(No.CBQQ8880103624)。
文摘Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynamic characteristics.Therefore,it is necessary to design a lowdimensional model that can well reflect the dynamic characteristics of high-dimensional system.To build such a low-dimensional model,this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory.First,sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted.Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced,and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined.Finally,the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method,and spectrum results were then compared experimentally.Numerical and experimental results demonstrate that,during the dimensionality reduction process,the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation.The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system.The larger the proportion of steady-state signals is,the closer the energy tends to accumulate towards lower orders.The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98%.The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of highdimensional systems coupled with strong nonlinearities under variable operating conditions.
文摘“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that balance global integration with local needs.This also includes management of global business operations across diverse cultures in a multipolar international landscape.The paper briefs the developed and already tested in numerous applications high-level Spatial Grasp Model and Technology(SGT),which can help investigate and manage complex systems with a holistic spatial approach effectively covering various physical and virtual dimensions,their interrelations,and integration as a whole.Different areas will be investigated with examples of practical solutions in them and their combinations in a high-level Spatial Grasp Language(SGL),the key element of SGT.This allows for the creation and distributed management of very large spatial networks with different orientation which can be self-spreading,self-analyzing,self-modifying,and self-recovering in complex terrestrial and celestial environments,and also organize dynamic multi-networking solutions supporting global evolution and integrity.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education(NRF-2017R1D1A1A09000642)by a grant from the R&D Program of the Korea Railroad Research Institute (KRRI), Republic of Korea
文摘In the past decade, researchers in the fields of energy production have concentrated on the improvement of new energy storage devices. Lithium-ion batteries(LIBs) and faradaic supercapacitors(FSs) have attracted special attention as a result of the rapid development of new electrode nanomaterials, especially hybrid nanomaterials, which can meet the increasingly higher requirements for future energy, such as the capability to deliver high-power performance and an extremely long life cycle. In these hybrid nanostructures, a series of synergistic effects and unique properties arising from the combination of individual components are a major factor leading to improved charge/discharge capability, energy density, and system lifetime. This paper describes the most recent progress in the growth of hybrid electrode materials for LIBs and FSs systems, focusing on the combination of zero-dimensional(0 D), one-dimensional(1 D), two-dimensional(2 D), and three-dimensional(3 D) nanomaterials, respectively.
基金Jiangxi Province Intelligent Building Engineering Research Center Open Fund Project,Fractal Theory of Performing Architectural Form Design Research(Project No.:EZ202111440).
文摘Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the self-affine,self-similarity,and iterative generation characteristics of fractal geometry,the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane,facade,and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre.The research shows that the geometric complexity of Wuzhen Grand Theater in the“fifth façade”and multi-faceted façade is significantly higher than that of Harbin Grand Theater,and its morphological design is more inclined to echo the texture of the surrounding water towns.The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines.The research proves that fractal dimension can effectively quantify the complexity of architectural form,provide a scientific basis for the form design,environmental integration,and form interpretation of performance architecture,and expand the mathematical analysis dimension of architectural form design.
基金funded by the National Key R&D Program of China,China(Grant No.2023YFB4005500)National Natural Science Foundation of China,China(Grant Nos.52379113 and 52379114).
文摘Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.
文摘In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure.Despite continuing efforts,the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution’s internal data.We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction.To contribute to the field of financial innovation,this study proposes a Dimension Reduction Assisted Credit Scoring(DRA-CS)method via distance covariance-based sufficient dimension reduction(DCOV-SDR)in Majorization-Minimization(MM)algorithm.First,in the presence of a large number of variables,the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction.Second,when the DRA-CS method is employed with logistic regression,it outperforms existing methods based on different variable selection techniques.This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.
基金IWHR Basic Scientific Research Project,Grant/Award Number:JZ110145B0072024IWHR Internationally-Oriented Talent for International Academic Leader Program,Grant/Award Number:0203982012National Natural Science Foundation of China,Grant/Award Number:51609257。
文摘Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as one of the most useful methods,has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems.However,this method often relies on manual inspection due to uncertainties from iden-tifying the scaling region,making the correlation dimension value calculation troublesome and subjective.Therefore,it is necessary to propose a fast and intelligent algorithm to solve the above problem.This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accu-rately identify the scaling range and estimate the correlation dimension values.The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province,China.The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values,and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.
文摘The phenomenon of photothermally induced transparency(PTIT)arises from the nonlinear behavior of an optical cavity,resulting from the heating of mirrors.By introducing a coupling field in the form of a standing wave,PTIT can be transitioned into photothermally induced grating(PTIG).A two-dimensional(2D)diffraction pattern is achieved through the adjustment of key parameters such as coupling strength and effective detuning.Notably,we observe first,second,and third-order intensity distributions,with the ability to transfer probe energy predominantly to the third order by fine-tuning the coupling strength.The intensity distribution is characterized by(±m,±n),where m,n=1,2,3.This proposed 2D grating system offers a novel platform for manipulating PTIG,presenting unique possibilities for enhanced functionality and control.
基金Supported by the National Natural Science Foundation of China(12061061)Young Talents Team Project of Gansu Province(2025QNTD49)+1 种基金Lanshan Talents Project of Northwest Minzu University(Xbmulsrc202412)Longyuan Young Talents of Gansu Province。
文摘In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.
