Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

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.

Scalable Temporal Dimension Preserved Tensor Completion for Missing Traffic Data Imputation With Orthogonal Initialization

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.

An Exploration of the Three Dimensions and Epochal Strengths of Building a Human Community With a Shared Future

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.

Response of Rice Cultivars to Elevated Air Temperature and Soil Amendments: Implications towards Climate Change Adaptations and Mitigating Global Warming Potentials

Global mean surface air temperature is expected to increase 1.1˚C - 6.4˚C by the end of 21st century which may affect rice productivity and methane emissions in the future climate. This experiment was conducted to investigate the response of rice cultivars to elevated air temperature (+1.5˚C higher than ambient) and soil amendments in regards to rice yield, yield scaled methane emissions and global warming potentials. The experimental findings revealed that replacement of inorganic fertilizers (20% - 40% of recommended NPKS) with Vermicompost, Azolla biofertilizer, enriched sugarcane pressmud, rice husk biochar and silicate fertilization increased rice yield 13.0% - 23.0%, and 11.0% - 19.0% during wet aman and dry boro season, respectively. However, seasonal cumulative CH4 fluxes were decreased by 9.0% - 25.0% and 5.0% - 19.0% during rainfed wet aman and irrigated dry boro rice cultivation, respectively with selected soil amendments. The maximum reduction in seasonal cumulative CH4 flux (19.0% - 25.0%) was recorded with silicate fertilization and azolla biofertilizer amendments (9.0% - 13.0%), whereas maximum grain yield increment 10.0 % - 14.0% was found with Vermicompost and Sugarcane pressmud amendments compared to chemical fertilization (100% NPKS) treated soils at ambient air temperature. However, rice grain yield decreased drastically 43.0% - 50.0% at elevated air temperature (3˚C higher than ambient air temperature), eventhough accelerated the total cumulative CH4 flux as well as GWPs in all treatments. Maximum seasonal mean GWPs were calculated at 391.0 kg CO2 eq·ha−1 in rice husk biochar followed by sugarcane pressmud (mean GWP 387.0 kg CO2 eq·ha−1), while least GWPs were calculated at 285 - 305 kg CO2 eq·ha−1 with silicate fertilizer and Azolla biofertilizer amendments. Rice cultivar BRRI dhan 87 revealed comparatively higher seasonal cumulative CH4 fluxes, yield scaled CH4 flux and GWPs than BRRI dhan 71 during wet aman rice growing season;while BRRI dhan 89 showed higher cumulative CH4 flux and GWPs than BINA dhan 10 during irrigated boro rice cultivation. Conclusively, inorganic fertilizers may be partially (20% - 40% of the recommended NPKS) replaced with Vermicompost, azolla biofertilizer, silicate fertilizer and enriched sugarcane pressmud compost for sustainable rice production and decreasing GWPs under elevated air temperature condition.

Prospects and limitations of soil amendment and irrigation techniques for the water-saving public urban greenery and ephemeral weed management in the sandy soils of the United Arab Emirates

Public urban greenery greatly contributes to the residential and tourist value of cities in the Gulf Region,but due to the hyper-arid climatic conditions,the cost of irrigation and plant maintenance is very high.Existing strategies to reduce the monetary and ecological costs involve the cultivation of native xerophytic plantations,and/or the use of soil improvers to increase water-and nutrient-holding capacity of the sandy soils.Various soil improvers based on mineral,organic,or synthetic materials have entered the United Arab Emirates(UAE)market in recent years,but there is considerable uncertainty about how they should best be used in combination with ornamental plant stands involving xerophytic native plants.The present study investigated the effect of soil amendment and deep pipe irrigation on perennial ornamental plant stands involving native plants(Tephrosia appolinea(Gel.)Link in combination with Aerva javanica(Burm.f.)Juss.ex Schult.)and native-exotic plants(T.appolinea in combination with Ruelia simplex C.Wright)either or not topsoil and subsoil amendment with bentonite and hydrophobic sand under the irrigation water supply of less than 50%of reference evapotranspiration(ET0).After one year of cultivation,T.appolinea and A.javanica(native vs.native)produced high biomass and exhibited high water use efficiency(WUE)as compared with T.appolinea and R.simplex(native vs.exotic)combination given that no significant differences were found under the soil amendment treatments.All stands thrived under irrigation water supply far below what is usually supplied to exotic ornamental stands in public parks of the Al Ain City,the UAE.However,subsoil amendment in combination with deep pipe irrigation reduced the occurrence of weeds and increased the overall plant rooting depth.Our results suggest that subsoil amendment and irrigation up to 60-80 cm depth can potentially control ephemeral weed infestation,which is a great challenge in various plant production systems of the Gulf Region.The results of the present study suggest that the impact of soil amendment on the WUE of exotic plants is marginal and might not be economically justified.Replacing exotic with native ornamental plant species seems to have a far greater water-saving potential than the amendment of the soil,while weeds can be suppressed in the absence of topsoil moisture.

Fractal analysis of major faults and fractal dimension of lineaments in the Indo-Gangetic Plain on a regional scale

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.

A Dynamical System-Based Framework for Dimension Reduction

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.

Optimization of Diesel and Crude Oil Degradation in a Ghanaian Soil Using Organic Wastes as Amendment

Soil contamination by hydrocarbons poses numerous environmental, health and agricultural problems. The degradation of these pollutants can occur naturally but very slowly. It is therefore generally necessary to stimulate this degradation by different means. Thus, this study aimed to improve the bio-degradation of diesel and crude oil in a Ghanaian soil by biostimulation. For this, the sampled soil was characterized by standard methods and contaminated with diesel and crude oil at a proportion of 1% (w/w). Then, contaminated soil samples were supplemented with biochar-compost, poultry manure or cow dung at the proportion of 10% (w/w). Periodically, fractions of these samples were taken to evaluate the density of hydrocarbon utilizing bacteria (HUB) and the residual quantities of diesel or crude oil. The characteristics of the soil used show the need for supplementation for better degradation of hydrocarbons. The results of the study show that supplementing the soil with organic substrates increases HUB loads in soils contaminated by diesel and crude oil. They also show that the residual quantities of diesel and crude oil are generally significantly lower in supplemented soils (p = 0.048 and p < 0.0001 respectively). In addition, the study shows that degradation was generally greater in soils contaminated by diesel compared to those contaminated by crude oil, especially at the end of the study.

A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

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.

The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation

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.

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

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.

Residual Effects of Phosphate Amendments on Rainfed Rice (Oryza sativa L.) Nutrition and Soil Properties in Three Agroecological Zones of Côte d’Ivoire

A study was conducted in Côte d’Ivoire to assess the after-effect of phosphate amendments on rice yields and soil properties. Eight types of amendments, composed of Moroccan phosphate rock (PRM) and triple superphosphate were tested in three agroecological zones over three consecutive years of cultivation. This study revealed that the application of Moroccan phosphate rock (PRM) and/or triple superphosphate (TSP) did not significantly affect soil cation exchange capacity (CEC) and organic carbon (Corg) content. However, there was a negative residual effect of PRM-rich treatments on soil pH and K and N content, but the impact varies depending on the characteristics of the soils studied. Furthermore, nutrient losses, notably nitrogen from −17.5 to −267.7 kg/ha and potassium (−0.1 to 0.7 kg/ha), were observed in all treatments. Only phosphorus showed a positive balance of +49.56 to +52 kg/ha in PRM-rich treatments. Treatment T3, composed of 80% RPM and 20% TSP, was the most effective in all zones, with a relative increase in grain yields of over 100% compared to the control. These results suggest that the input of natural phosphate rock can significantly improve rice yields and soil properties in the studied agroecological zones in Côte d’Ivoire.

Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

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.

A Study of the Teaching Effects of Case Analysis in Cross-Cultural Communication Class-Taking Individualism-Collectivism Cultural Dimension Class as an Example

This study introduces the individualism-collectivism dimension of the cultural dimension of cross-cultural communication initiated by Geert Hofstede.Different cultures must develop a way of correlating that strikes a balance between caring for themselves and showing concern for others.Individualist culture encourages uniqueness and independence while collectivist culture emphasizes conformity and mutual assistance.This article introduces how to use case analysis method to effectively carry out classroom teaching in this cultural dimension.

A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming

This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.

量化三维网格模型复杂度的Fractal Dimension^(+)方法

对三维网格模型复杂度的评估及应用进行研究,提出基于Fractal Dimension^(+)方法量化三维网格模型复杂度。该方法利用分形几何学的分形维度来确定三维网格模型的不规则性;为了全面量化复杂度并且提高量化的准确性和可信度,在分形维度算法中添加孔隙比和亏格数的概念,全面考虑介质内部空间分布和几何结构的连接性以及孔洞分布的信息。对大量三维网格模型进行实验,结果表明Fractal Dimension^(+)方法可以有效计算出准确的复杂度。

Rectangular tunnel heading stability in three dimensions and its predictive machine learning models

Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.

Measurement Uncertainty Analysis of the Rotary-scan Method for the Measurable Dimension of Cylindrical Workpieces

The measurement uncertainty analysis is carried out to investigate the measurable dimensions of cylindrical workpieces by the rotary-scan method in this paper.Due to the difficult alignment of the workpiece with a diameter of less than 3 mm by the rotary scan method,the measurement uncertainty of the cylindrical workpiece with a diameter of 3 mm and length of 50 mm which is measured by a roundness measuring machine,is evaluated according to GUM(Guide to the Expression of Uncertainty in Measurement)as an example.Since the uncertainty caused by the eccentricity of the measured workpiece is different with the dimension changing,the measurement uncertainty of cylindrical workpieces with other dimensions can be evaluated the same as the diameter of 3 mm but with different eccentricity.Measurement uncertainty caused by different eccentricities concerning the dimension of the measured cylindrical workpiece is set to simulate the evaluations.Compared to the target value of the measurement uncertainty of 0.1μm,the measurable dimensions of the cylindrical workpiece can be obtained.Experiments and analysis are presented to quantitatively evaluate the reliability of the rotary-scan method for the roundness measurement of cylindrical workpieces.

The Historical Position and Value Dimensions of Human Rights Civilization

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.

Cosmological Model in Four Time and Four Space Dimensions

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.