In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of th...In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.展开更多
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
The difference between homogeneous and bubbling fluidization behaviors has been studied for the past 70 years, where several researchers have reported on the influence of interparticle forces in fluidization. Although...The difference between homogeneous and bubbling fluidization behaviors has been studied for the past 70 years, where several researchers have reported on the influence of interparticle forces in fluidization. Although interparticle forces such as van der Waals forces are evident in a real system, these forces are not the determinant in homogeneous fluidization, which can be simulated without any interparticle forces. In our previous study, the difference in fundamental mechanisms of the two fluidization states was analytically determined with a dimensionless gravity term, comprising the Reynolds number, Archimedes number, and density ratio. Nevertheless, some researchers insist that interparticle forces are dominant and a hydrodynamic force is not dominant. In this study, a dimensional analysis was applied to obtain a dominant parameter for distinguishing two fluidizations. Furthermore, some parameters were examined by comparing the experimental data in previous studies. The results indicated that hydrodynamic force is the dominant factor and the dimensionless gravity term is the dominant parameter in differentiating the two fluidized states.展开更多
Social interaction with peer pressure is widely studied in social network analysis.Game theory can be utilized to model dynamic social interaction,and one class of game network models assumes that people’s decision p...Social interaction with peer pressure is widely studied in social network analysis.Game theory can be utilized to model dynamic social interaction,and one class of game network models assumes that people’s decision payoff functions hinge on individual covariates and the choices of their friends.However,peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model.For this reason,we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks.The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios.To estimate peer pressure in the model,we first present two algorithms based on the initialize expand merge method and the polynomial-time twostage method to estimate homogeneity parameters.Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure.Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error.We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.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
The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been app...The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.展开更多
The photoinduced ligand-to-metal charge transfer(LMCT)process has been extensively investigated,however,the recovery of photocatalysts has remained a persistent challenge in the field.In light of this issue,a novel ap...The photoinduced ligand-to-metal charge transfer(LMCT)process has been extensively investigated,however,the recovery of photocatalysts has remained a persistent challenge in the field.In light of this issue,a novel approach involving the development of iron-based ionic liquids as photocatalysts has been pursued for the first time,with the goal of simultaneously facilitating the LMCT process and addressing the issue of photocatalyst recovery.Remarkably,the iron-based ionic liquid 1-butyl-3-methylimidazolium tetrachloroferrate(C_(4)mim-Fe Cl_(4))demonstrates exceptional recyclability and stability for the photocatalytic hydroacylation of olefins.This study will pave the way for new approaches to photocatalytic organic synthesis using ionic liquids as recyclable photocatalysts.展开更多
Currently,perovskite solar cells have achieved commendable progresses in power conversion efficiency(PCE)and operational stability.However,some conventional laboratory-scale fabrication methods become challenging when...Currently,perovskite solar cells have achieved commendable progresses in power conversion efficiency(PCE)and operational stability.However,some conventional laboratory-scale fabrication methods become challenging when scaling up material syntheses or device production.Particularly,the prolonged high-temperature annealing process for the crystallization of perovskites requires a substantial amount of energy consumption and impact the modules’throughput.Here,we report a modified near-infrared annealing(NIRA)process,which involves the excess PbI_(2)engineered crystallization,efficiently reduces the preparation time for perovskite active layer to within 20 s compared to dozens of min in conventional hot plate annealing(HPA)process.The study showed that the incorporated PbI_(2)promoted the consistent nucleation of the perovskite film,leading to the subsequent rapid and homogeneous crystallization at the NIRA stage.Thus,highly crystalized perovskite film was realized with even better crystallization performance than conventional HPA-based film.Ultimately,efficient perovskite solar modules of 36 and 100 cm^(2)were readily fabricated with the optimal PCEs of 22.03%and 20.18%,respectively.This study demonstrates,for the first time,the successful achievement of homogeneous and high-quality crystallization in large-area perovskite films through rapid NIRA processing.This approach not only significantly reduces energy consumption during production,but also substantially shortens the manufacturing cycle,paving a new path toward the commercial-scale application of perovskite solar modules.展开更多
Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)...Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.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
The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale dataset...The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.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
With the rapid advancement of global socio-economy and mounting environmental and ecological risks,China faces challenges in ensuring its food security and sustainable development,which further affects global food tra...With the rapid advancement of global socio-economy and mounting environmental and ecological risks,China faces challenges in ensuring its food security and sustainable development,which further affects global food trade and security.This study aims to identify the supply-demand match between cropland supply and food consumption and to evaluate sustainable cropland zoning in multiple scenarios and multidimensional assessments.This study uses ecological,environmental and socioeconomic data to quantify diverse food demand patterns into corresponding cropland demands,further mapping the spatio-temporal characteristics of China's cropland supply-demand matches.By utilizing shared socioeconomic pathways(SSPs),this study delineates multiple scenarios to determine the supply-demand of cropland across different Chinese regions from 2030 to 2050.On the basis of ecological,geographical and socioeconomic datasets,this study constructs a multidimensional and multiscenario framework for sustainable agricultural zoning from 2030 to 2050 and proposes a future sustainable agricultural development strategy for each region in different periods.The results indicate that between 2002 and 2022,there was a significant gap between cropland supply and demand.Moreover,an obvious spatial mismatch is observed between cropland supply and demand across various Chinese regions.From 2030 to 2050,there is a noticeable shift in the spatial distribution of cropland supply and demand,with the supply-demand match becoming more strained and varying considerably under different development scenarios.With significant differences between different development scenarios,different regions will have to adopt different development strategies at different periods.This study proposes a multiscenario and multidimensional simulation framework for future agricultural sustainable zoning,which aims to provide scientific insights and policy improvements to promote sustainable agricultural development.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
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
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 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
We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in l...We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory(LEFT).The on-shell method significantly simplifies the construction of scattering amplitudes.By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals,we bypass the need for direct loop integral calculations.The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients,which will aid in precision experimental fitting of these coefficients.展开更多
Against the backdrop of intensified global cultural collisions and ideological competition,deeply integrating excellent traditional Chinese culture(ETCC)into university ideological and political courses(IPCs)has becom...Against the backdrop of intensified global cultural collisions and ideological competition,deeply integrating excellent traditional Chinese culture(ETCC)into university ideological and political courses(IPCs)has become an imperative of our times.Guided by General Secretary Xi Jinping’s methodology of“Two Integrations,”this paper examines the pathways for this integration from three dimensions:value,theory,and practice.The value dimension emphasizes fostering moral conviction and strengthening the spiritual foundation to meet needs such as safeguarding cultural security,preserving the spiritual lineage,and constructing a spiritual framework.The theoretical dimension reveals the mutually constitutive breakthroughs between Marxism and traditional Chinese dialectical thinking,encompassing methodological complementarity,logical coherence of values,and discursive system innovation.The practical dimension involves constructing a comprehensive educational ecosystem by localizing teaching content,modernizing traditional resources,and fostering inter-platform collaborative education,thereby internalizing the value of traditional culture.These three dimensions synergize and co-constitute each other,collectively providing methodological support and practical paradigms for cultivating cultural confidence among youth and forging a new generation capable of shouldering the mission of national rejuvenation.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
基金supported by the NSFC(12461012)and the NSF of Chongqing(CSTB2024NSCQ-MSX1246).
文摘In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.
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.
文摘The difference between homogeneous and bubbling fluidization behaviors has been studied for the past 70 years, where several researchers have reported on the influence of interparticle forces in fluidization. Although interparticle forces such as van der Waals forces are evident in a real system, these forces are not the determinant in homogeneous fluidization, which can be simulated without any interparticle forces. In our previous study, the difference in fundamental mechanisms of the two fluidization states was analytically determined with a dimensionless gravity term, comprising the Reynolds number, Archimedes number, and density ratio. Nevertheless, some researchers insist that interparticle forces are dominant and a hydrodynamic force is not dominant. In this study, a dimensional analysis was applied to obtain a dominant parameter for distinguishing two fluidizations. Furthermore, some parameters were examined by comparing the experimental data in previous studies. The results indicated that hydrodynamic force is the dominant factor and the dimensionless gravity term is the dominant parameter in differentiating the two fluidized states.
基金supported by the National Nature Science Foundation of China(71771201,72531009,71973001)the USTC Research Funds of the Double First-Class Initiative(FSSF-A-240202).
文摘Social interaction with peer pressure is widely studied in social network analysis.Game theory can be utilized to model dynamic social interaction,and one class of game network models assumes that people’s decision payoff functions hinge on individual covariates and the choices of their friends.However,peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model.For this reason,we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks.The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios.To estimate peer pressure in the model,we first present two algorithms based on the initialize expand merge method and the polynomial-time twostage method to estimate homogeneity parameters.Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure.Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error.We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.
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Rami Ahmad El-Nabulsi has received funding from the Czech National Agency of Agricultural 533 Research,project QK22020134“Innovative fisheries management of a large reservoir”.
文摘The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.
基金financial support from the National Natural Science Foundation of China(Nos.22071222,22171249)the Natural Science Foundation of Henan Province(Nos.232300421363,242300420526)+2 种基金Key Research Projects of Universities in Henan Province(No.23A180010)Science&Technology Innovation Talents in Universities of Henan Province(No.23HASTIT003)Science and Technology Research and Development Plan Joint Fund of Henan Province(No.242301420006)。
文摘The photoinduced ligand-to-metal charge transfer(LMCT)process has been extensively investigated,however,the recovery of photocatalysts has remained a persistent challenge in the field.In light of this issue,a novel approach involving the development of iron-based ionic liquids as photocatalysts has been pursued for the first time,with the goal of simultaneously facilitating the LMCT process and addressing the issue of photocatalyst recovery.Remarkably,the iron-based ionic liquid 1-butyl-3-methylimidazolium tetrachloroferrate(C_(4)mim-Fe Cl_(4))demonstrates exceptional recyclability and stability for the photocatalytic hydroacylation of olefins.This study will pave the way for new approaches to photocatalytic organic synthesis using ionic liquids as recyclable photocatalysts.
基金supported by China Huaneng Group Key R&D Program(HNKJ22-H104)the Science and Technology Programs of Fujian Province(2022H0005)+1 种基金the Fundamental Research Funds for the Central Universities(20720240067)Technology Projects of Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province(RD2020020101 and RD2022040601).
文摘Currently,perovskite solar cells have achieved commendable progresses in power conversion efficiency(PCE)and operational stability.However,some conventional laboratory-scale fabrication methods become challenging when scaling up material syntheses or device production.Particularly,the prolonged high-temperature annealing process for the crystallization of perovskites requires a substantial amount of energy consumption and impact the modules’throughput.Here,we report a modified near-infrared annealing(NIRA)process,which involves the excess PbI_(2)engineered crystallization,efficiently reduces the preparation time for perovskite active layer to within 20 s compared to dozens of min in conventional hot plate annealing(HPA)process.The study showed that the incorporated PbI_(2)promoted the consistent nucleation of the perovskite film,leading to the subsequent rapid and homogeneous crystallization at the NIRA stage.Thus,highly crystalized perovskite film was realized with even better crystallization performance than conventional HPA-based film.Ultimately,efficient perovskite solar modules of 36 and 100 cm^(2)were readily fabricated with the optimal PCEs of 22.03%and 20.18%,respectively.This study demonstrates,for the first time,the successful achievement of homogeneous and high-quality crystallization in large-area perovskite films through rapid NIRA processing.This approach not only significantly reduces energy consumption during production,but also substantially shortens the manufacturing cycle,paving a new path toward the commercial-scale application of perovskite solar modules.
基金supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)the China Postdoctoral Science Foundation(2023M743878)+2 种基金the Postdoctoral Fellowship Program of CPSF(GZB20240848)supported partially by the NSFC(12271176)the Guangdong Natural Science Foundation(2024A1515010946).
文摘Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
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partly supported by Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City(2021JJLH0052)National Natural Science Foundation of China(42274154,42304116)+2 种基金Natural Science Foundation of Heilongjiang Province,China(LH2024D013)Heilongjiang Postdoctoral Fund(LBHZ23103)Hainan Yazhou Bay Science and Technology City Jingying Talent Project(SKJC-JYRC-2024-05)。
文摘The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.
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Zhejiang Provincial Sannong-Jiufang Science and Technology Collaboration Initiative,No.2025SNJF012。
文摘With the rapid advancement of global socio-economy and mounting environmental and ecological risks,China faces challenges in ensuring its food security and sustainable development,which further affects global food trade and security.This study aims to identify the supply-demand match between cropland supply and food consumption and to evaluate sustainable cropland zoning in multiple scenarios and multidimensional assessments.This study uses ecological,environmental and socioeconomic data to quantify diverse food demand patterns into corresponding cropland demands,further mapping the spatio-temporal characteristics of China's cropland supply-demand matches.By utilizing shared socioeconomic pathways(SSPs),this study delineates multiple scenarios to determine the supply-demand of cropland across different Chinese regions from 2030 to 2050.On the basis of ecological,geographical and socioeconomic datasets,this study constructs a multidimensional and multiscenario framework for sustainable agricultural zoning from 2030 to 2050 and proposes a future sustainable agricultural development strategy for each region in different periods.The results indicate that between 2002 and 2022,there was a significant gap between cropland supply and demand.Moreover,an obvious spatial mismatch is observed between cropland supply and demand across various Chinese regions.From 2030 to 2050,there is a noticeable shift in the spatial distribution of cropland supply and demand,with the supply-demand match becoming more strained and varying considerably under different development scenarios.With significant differences between different development scenarios,different regions will have to adopt different development strategies at different periods.This study proposes a multiscenario and multidimensional simulation framework for future agricultural sustainable zoning,which aims to provide scientific insights and policy improvements to promote sustainable agricultural development.
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.
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.
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}.
基金supported by the National Science Foundation of China under Grants Nos.12347145,12347105,12375099,and 12047503the National Key Research and Development Program of China Grant Nos.2020YFC2201501 and 2021YFA0718304。
文摘We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory(LEFT).The on-shell method significantly simplifies the construction of scattering amplitudes.By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals,we bypass the need for direct loop integral calculations.The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients,which will aid in precision experimental fitting of these coefficients.
基金Center for Sinicized Marxism and Traditional Culture,Sichuan University of Science&Engineering(Project No.:ZMCY202410)。
文摘Against the backdrop of intensified global cultural collisions and ideological competition,deeply integrating excellent traditional Chinese culture(ETCC)into university ideological and political courses(IPCs)has become an imperative of our times.Guided by General Secretary Xi Jinping’s methodology of“Two Integrations,”this paper examines the pathways for this integration from three dimensions:value,theory,and practice.The value dimension emphasizes fostering moral conviction and strengthening the spiritual foundation to meet needs such as safeguarding cultural security,preserving the spiritual lineage,and constructing a spiritual framework.The theoretical dimension reveals the mutually constitutive breakthroughs between Marxism and traditional Chinese dialectical thinking,encompassing methodological complementarity,logical coherence of values,and discursive system innovation.The practical dimension involves constructing a comprehensive educational ecosystem by localizing teaching content,modernizing traditional resources,and fostering inter-platform collaborative education,thereby internalizing the value of traditional culture.These three dimensions synergize and co-constitute each other,collectively providing methodological support and practical paradigms for cultivating cultural confidence among youth and forging a new generation capable of shouldering the mission of national rejuvenation.
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.
