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An Exploration of the Three Dimensions and Epochal Strengths of Building a Human Community With a Shared Future
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作者 Jiang Ruibing Liu Zongling 《Contemporary Social Sciences》 2024年第3期120-138,共19页
The idea of a human community with a shared future was proposed by the Communist Party of China(CPC)Central Committee with Comrade Xi Jinping at its core for the future development of human beings to face up to the mo... The idea of a human community with a shared future was proposed by the Communist Party of China(CPC)Central Committee with Comrade Xi Jinping at its core for the future development of human beings to face up to the most important question in today's world:“What is happening to the world and what should we do?”It profoundly answers the question of the world,history,and the times.The theory of a human community with a shared future is an innovative theory with a multidimensional formation logic that guides humanity toward continually seeking common interests and values.This paper dives into the profound motivations behind building a human community with a shared future from historical,cultural,and practical dimensions and analyzes its epochal value from both domestic and international perspectives.This not only helps exert China's role in the international community,contributing Chinese strength to the construction of a peaceful,stable,and prosperous human society,but also enhances the influence of the idea of a human community with a shared future in the international community,accelerating the building of a human community with a shared future that considers the legitimate concerns of all countries,and aiding in solving the crises facing the world. 展开更多
关键词 a human community with a shared future historical dimension cultural dimension practical dimension epochal strength
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The Historical Position and Value Dimensions of Human Rights Civilization
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作者 鲁广锦 PAN Yingzhao 《The Journal of Human Rights》 2024年第1期11-41,共31页
Human beings are the mainstay and the ultimate goal of civilization.The history of human civilization is a continuous struggle to realize the respect,liberation,protection,and development of humanity.Human rights are ... Human beings are the mainstay and the ultimate goal of civilization.The history of human civilization is a continuous struggle to realize the respect,liberation,protection,and development of humanity.Human rights are an achievement of humanity and a symbol of progress,and the human rights civilization is an important component of human civilization.Understanding and interpreting human rights from the perspective of human rights civilization means that human rights are not only a concept or an idea but also a grand historical and long-term social practice.Up to now,the development of human rights civilization has roughly experienced four awakening eras:initialization,revolution,popularization,and globalization.In terms of its value dimensions,it has the characteristics of progressiveness,diversity,commonality,inclusiveness,indivisibility,openness,and so on.The historical position of human rights civilization and the development of its value dimensions have shown to the world that human rights are the common wealth of humanity,and human rights belong to all mankind;human rights are historical,concrete,and developmental;the concept of human rights is constantly evolving,and its connotations and categories are constantly expanding;achieving the free and well-rounded development of every person is the highest value realm of human rights civilization.The Chinese modernization endows Chinese civilization with modern strength and opens up new horizons for human rights civilization.The new pattern of human rights civilization to be created by Chinese modernization not only possesses the common characteristics of human rights civilization but also enjoys Chinese characteristics based on its own national conditions,enriching and developing the diversity of human rights civilization for all mankind. 展开更多
关键词 human rights civilization four awakening eras of human rights value dimensions of human rights Chinese modernization new pattern of human rights civilization with Chinese characteristics
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Cosmological Model in Four Time and Four Space Dimensions
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作者 Juan Antonio Nieto 《Journal of Applied Mathematics and Physics》 2024年第3期829-840,共12页
We develop a cosmological model in a physical background scenario of four time and four space dimensions ((4+4)-dimensions or (4+4)-universe). We show that in this framework the (1+3)-universe is deeply connected with... We develop a cosmological model in a physical background scenario of four time and four space dimensions ((4+4)-dimensions or (4+4)-universe). We show that in this framework the (1+3)-universe is deeply connected with the (3+1)-universe. We argue that this means that in the (4+4)-universe there exists a duality relation between the (1+3)-universe and the (3+1)-universe. 展开更多
关键词 Cosmological Model (4+4)-dimensions Duality Symmetry
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Suppression of stimulated Raman scattering by angularly incoherent light, towards a laser system of incoherence in all dimensions of time, space, and angle 被引量:3
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作者 Yi Guo Xiaomei Zhang +3 位作者 Dirui Xu Xinju Guo Baifei Shen Ke Lan 《Matter and Radiation at Extremes》 SCIE EI CSCD 2023年第3期27-33,共7页
Laser–plasma instability(LPI)is one of the main obstacles to achieving predictable and reproducible fusion at high gain through laser-driven inertial confinement fusion(ICF).In this paper,for the first time,we show a... Laser–plasma instability(LPI)is one of the main obstacles to achieving predictable and reproducible fusion at high gain through laser-driven inertial confinement fusion(ICF).In this paper,for the first time,we show analytically and confirm with three-dimensional particle-incell simulations that angular incoherence provides suppression of the instability growth rate that is additional to and much stronger than that provided by the well-known temporal and spatial incoherence usually used in ICF studies.For the model used in our calculations,the maximum field ratio between the stimulated Raman scattering and the driving pulses drops from 0.2 for a Laguerre–Gaussian pulse with a single nonzero topological charge to 0.05 for a super light spring with an angular momentum spread and random relative phases.In particular,angular incoherence does not introduce extra undesirable hot electrons.This provides a novel method for suppressing LPI by using light with an angular momentum spread and paves the way towards a low-LPI laser system for inertial fusion energy with a super light spring of incoherence in all dimensions of time,space,and angle,and may open the door to the use of longer-wavelength lasers for inertial fusion energy. 展开更多
关键词 SCATTERING dimensions ANGULAR
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ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS
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作者 刘佳 石赛赛 张远 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2483-2492,共10页
In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C... In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14]. 展开更多
关键词 Hausdorff dimension packing dimension graph of function product of functions
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Adding dimensions with Lucy-Richardson-Rosen algorithm to incoherent imaging
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作者 Tatsuki Tahara 《Opto-Electronic Advances》 SCIE EI CAS CSCD 2023年第5期7-9,共3页
A novel computational reconstruction method called the Lucy–Richardson–Rosen algorithm(LRRA)for the construction of a single-shot infrared 3D imaging microscope was reported in Opto-Electronic Science.In that study,... A novel computational reconstruction method called the Lucy–Richardson–Rosen algorithm(LRRA)for the construction of a single-shot infrared 3D imaging microscope was reported in Opto-Electronic Science.In that study,a commonly available optical element,the Cassegrain objective lens,was used as a coded aperture for 3D imaging using LRRA.Unlike regular coded aperture imaging systems,achieving 3D imaging using commonly available imaging devices leads to the development of hybrid imaging systems where direct and indirect imaging concepts coexist.The development above will make 3D imaging more commonly used in daily life. 展开更多
关键词 RICHARDSON dimensions ALGORITHM
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Early selection efficiency for fiber dimensions and their relationships with growth and wood quality for Pinus elliotth Engelm.in southern China
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作者 Jing Wen Min Yi +5 位作者 Leiming Dong Lu Zhang Siyu Liu Shenggui Yuan Xiaoxiao Tao Meng Lai 《Journal of Forestry Research》 SCIE CAS CSCD 2023年第6期1951-1962,共12页
A solid understanding of the efficiency of early selection for fiber dimensions is a prerequisite for breeding slash pine(Pinus elliottii Engelm.)with improved properties for pulp and paper products.Genetic correlatio... A solid understanding of the efficiency of early selection for fiber dimensions is a prerequisite for breeding slash pine(Pinus elliottii Engelm.)with improved properties for pulp and paper products.Genetic correlations between size of fibers,wood quality and growth properties are also important.To accomplish effective early selection for size of fibers and evaluate the impact for wood quality traits and ring widths,core samples were collected from360 trees of 20 open-pollinated Pinus elliottii families from three genetic trials.Cores were measured by SilviScan,and the age trends for phenotypic values,heritability,early-late genetic correlations,and early selection efficiency for fiber dimensions,such as tangential and radial fiber widths,fiber wall thickness and fiber coarseness,and their correlations with microfibril angle(MFA),modulus of elasticity(MOE),wood density and ring width were investigated.Different phenotypic trends were found for tangential and radial fiber widths while fiber coarseness and wall thickness curves were similar.Age trends of heritability based on area-weighted fiber dimensions were different.Low to moderate heritability from pith to bark(~0.5)was found for all fiber dimension across the three sites except for tangential fiber width and wall thickness at the Ganzhou site.Early-late genetic correlations were 0.9 after age of 9 years,and early selection for fiber dimensions could be effective due to strong genetic correlations.Our results showed moderate to strong positive genetic correlations for modulus of elasticity and density with fiber dimensions.The effects on fiber dimensions were weak or moderate when ring width or wood quality traits were selected alone.Estimates of efficiency for early selection indicated that the optimal age for radial fiber width and fiber coarseness was 6-7 years,while for tangential fiber width and wall thickness was 9-10 years. 展开更多
关键词 Pinus elliottii Early selection efficiency Genetic correlation HERITABILITY Fiber dimensions
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Validation of a Characteristics Dimensions for Transfers during Convective Drying of Sweet Potato Cubic, Cylindrical and Spherical Shapes
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作者 Ouoba Kondia Honore Ganame Abdou-Salam +2 位作者 Ibrango Abdoul Salam Bama Désiré Zougmore François 《Open Journal of Applied Sciences》 2023年第10期1714-1722,共9页
This present work solves the problem of initial shape influence on transfer during convective drying. A characteristic dimension is found for the cubic, cylindrical and spherical-shaped samples of the sweet potato. Th... This present work solves the problem of initial shape influence on transfer during convective drying. A characteristic dimension is found for the cubic, cylindrical and spherical-shaped samples of the sweet potato. This characteristic dimension corresponds to the diameter D for the sphere, to the edge a for the cube and the diameter = height D = H for the cylinder. Unlike the sphere where this characteristic dimension is perfect, the cubic and cylindrical shapes have space factors which are, among other things, angles and borders. By fixing the same characteristic dimensions, we end up with overlapping curves, showing identical and uniform transfers. 展开更多
关键词 DRYING Initial Size Characteristic dimension FORMS
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Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws
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作者 Feng Zheng Jianxian Qiu 《Communications on Applied Mathematics and Computation》 EI 2024年第1期605-624,共20页
In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy ... In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme. 展开更多
关键词 Finite volume dimension by dimension HWENO Hyperbolic conservation laws
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A Retrodirective Array Enabled by CMOS Chips for Two-Way Wireless Communication with Automatic Beam Tracking
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作者 Jiacheng Guo Yizhu Shen +2 位作者 Guoqing Dong Zhuang Han Sanming Hu 《Engineering》 SCIE EI CAS CSCD 2024年第6期196-207,共12页
This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic comple... This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic complementary metal-oxide semiconductor(CMOS)process.The highly integrated CMOS chip includes a receiving(Rx)chain,a transmitting(Tx)chain,and a unique tracking phaselocked loop(PLL)for the crucial conjugated phase recovery in the RDA.This article also proposes a method to reduce the beam pointing error(BPE)in a conventional RDA.To validate the above ideas simply yet without loss of generality,a 2.4 GHz RDA is demonstrated through two-way communication links between the Rx and Tx chains,and an on-chip quadrature coupler is designed to achieve a nonretrodirective signal suppression of 23 dBc.The experimental results demonstrate that the proposed RDA,which incorporates domestically manufactured low-cost 0.18 lm CMOS chips,is capable of automatically tracking beams covering±40with a reduced BPE.Each CMOS chip in the RDA has a compact size of 4.62 mm^(2) and a low power consumption of 0.15 W.To the best of the authors’knowledge,this is the first research to demonstrate an RDA with a fully customized CMOS chip for wireless communication with automatic beam tracking。 展开更多
关键词 Automatic beam tracking CMOS Retrodirective array two-way communication
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Scalable Temporal Dimension Preserved Tensor Completion for Missing Traffic Data Imputation With Orthogonal Initialization
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作者 Hong Chen Mingwei Lin +1 位作者 Jiaqi Liu Zeshui Xu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第10期2188-2190,共3页
Dear Editor,This letter puts forward a novel scalable temporal dimension preserved tensor completion model based on orthogonal initialization for missing traffic data(MTD)imputation.The MTD imputation acts directly on... Dear Editor,This letter puts forward a novel scalable temporal dimension preserved tensor completion model based on orthogonal initialization for missing traffic data(MTD)imputation.The MTD imputation acts directly on accessing the traffic state,and affects the traffic management. 展开更多
关键词 dimensION management traffic
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Reference-frame-independent quantum key distribution with two-way classical communication
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作者 Chun Zhou Hai-Tao Wang +9 位作者 Yi-Fei Lu Xiao-Lei Jiang Yan-Mei Zhao Yu Zhou Yang Wang Jia-Ji Li Yan-Yang Zhou Xiang Wang Hong-Wei Li Wan-Su Bao 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第10期146-152,共7页
The data post-processing scheme based on two-way classical communication(TWCC)can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution(QKD)system.In... The data post-processing scheme based on two-way classical communication(TWCC)can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution(QKD)system.In this study,we apply the TWCC method to improve the performance of reference-frame-independent quantum key distribution(RFI-QKD),and analyze the influence of the TWCC method on the performance of decoy-state RFI-QKD in both asymptotic and non-asymptotic cases.Our numerical simulation results show that the TWCC method is able to extend the maximal transmission distance from 175 km to 198 km and improve the tolerable bit error rate from 10.48%to 16.75%.At the same time,the performance of RFI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are considered.We conclude that RFI-QKD with the TWCC method is of practical interest. 展开更多
关键词 quantum key distribution reference-frame-independent two-way classical communication
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Beamforming Design for IRS-and-UAV-Aided Two-Way Amplify-and-Forward Relay Networks in Maritime IoT
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作者 Wang Xuehui Shu Feng +6 位作者 Wu Yuanyuan Shi Weiping Yan Shihao Zhao Yifan Cheng Qiankun Sun Zhongwen Wang Jiangzhou 《China Communications》 SCIE CSCD 2024年第8期45-61,共17页
In this paper,an intelligent reflecting surface(IRS)-and-unmanned aerial vehicle(UAV)-assisted two-way amplify-and-forward(AF)relay network in maritime Internet of Things(IoT)is proposed,where ship1(S1)and ship2(S2)ca... In this paper,an intelligent reflecting surface(IRS)-and-unmanned aerial vehicle(UAV)-assisted two-way amplify-and-forward(AF)relay network in maritime Internet of Things(IoT)is proposed,where ship1(S1)and ship2(S2)can be viewed as data collecting centers.To enhance the message exchange rate between S1 and S2,a problem of maximizing minimum rate is cast,where the variables,namely AF relay beamforming matrix and IRS phase shifts of two time slots,need to be optimized.To achieve a maximum rate,a low-complexity alternately iterative(AI)scheme based on zero forcing and successive convex approximation(LC-ZF-SCA)algorithm is presented.To obtain a significant rate enhancement,a high-performance AI method based on one step,semidefinite programming and penalty SCA(ONSSDP-PSCA)is proposed.Simulation results show that by the proposed LC-ZF-SCA and ONS-SDP-PSCA methods,the rate of the IRS-and-UAV-assisted AF relay network surpass those of with random phase and only AF relay networks.Moreover,ONS-SDP-PSCA perform better than LC-ZF-SCA in aspect of rate. 展开更多
关键词 BEAMFORMING maritime Internet of Things phase shift rate performance two-way amplify-and-forward relay unmanned aerial vehicle
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Fractal analysis of major faults and fractal dimension of lineaments in the Indo-Gangetic Plain on a regional scale
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作者 Vipin Chauhan Jagabandhu Dixit 《Earthquake Science》 2024年第2期107-121,共15页
The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the... The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones. 展开更多
关键词 geospatial analysis fractal modeling seismicity pattern fractal dimension
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A Dynamical System-Based Framework for Dimension Reduction
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作者 Ryeongkyung Yoon Braxton Osting 《Communications on Applied Mathematics and Computation》 EI 2024年第2期757-789,共33页
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a... We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap. 展开更多
关键词 dimension reduction Equation discovery Dynamical systems Adjoint method Optimal transportation
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A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone
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作者 Huiqing Liu Heping Xie +2 位作者 Fei Wu Cunbao Li Renbo Gao 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2024年第4期479-489,共11页
Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media withi... Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks. 展开更多
关键词 3D fractal analysis Fractal dimension Rock pore structure Box-counting method Permeability simulation Computational geosciences
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Mean Dimension for Non-autonomous Iterated Function Systems
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作者 Meng Deyu Zhao Cao 《数学理论与应用》 2024年第3期119-129,共11页
In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations... In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension. 展开更多
关键词 Non-autonomous iterated function system Mean dimension Metric mean dimension
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The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation
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作者 Yuhuai Liao 《Journal of Applied Mathematics and Physics》 2024年第4期1178-1187,共10页
In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set ar... In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained. 展开更多
关键词 Generalized Kolmogorov-Petrovlkii-Piskunov Equation Existence of Solution Hausdorff dimension Fractal dimension
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Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems
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作者 Paula Chen Jerome Darbon Tingwei Meng 《Communications on Applied Mathematics and Computation》 EI 2024年第2期1428-1471,共44页
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we p... Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control.We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians.Additionally,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of dimensionality.Using existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial costs.We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can achieve.Our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time. 展开更多
关键词 Optimal control Hamilton-Jacobi partial differential equations Grid-free numerical methods High dimensions Field-programmable gate arrays(FPGAs)
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Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines
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作者 Franklin Lee 《Journal of Applied Mathematics and Physics》 2024年第5期1890-1903,共14页
Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short w... Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections. 展开更多
关键词 Map Projection Distortion COASTLINE Fractal dimension CARTOGRAPHY Geographic Information Systems
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