A Teaching Experiment in Modelling through Scale Reduction Methods： A Bridge to Later Trigonometric Methods

In a teaching experiment, Japanese Grade 9 students investigated how to measure the height of an aerial balloon using different models involving angles and distances, and also to evaluate the models they developed. As novices to mathematical modelling, they needed to decide which of several possible models were both valid and practicable, and the errors in measurement that are likely to arise. Opportunities to construct and use paper models, as scale reductions of the real situation, and discussing their results in small groups were effective in moving forward the thinking of many students on the dimensions mentioned above. While students were less able to identify different sources of errors, many came to appreciate the need to learn trigonometric techniques that are more suitable in dealing with problems of this kind.

Static output feedback stabilization for second-order singular systems using model reduction methods

In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm.

Effect of different reduction methods on Pd/Al_(2)O_(3) for o-xylene oxidation at low temperature

Pd/Al_(2)O_(3)was pretreated by CO,H_(2)and NaBH_(4)reduction,respectively.The reduced catalysts were tested for o-xylene oxidation and characterized by power X-ray diffraction(XRD),transmission electron microscopy (TEM),X-ray photoelectron spectroscopy (XPS) and temperature-programmed decomposition of palladium hydride (TPDH).The characterizations indicate the pretreatments lead to distinct Pd particle sizes and amount of surface activated oxygen species,which are responsible for the catalytic performance.Compared with H_(2)and NaBH_(4)reduction methods,CO reduction shows a strong interaction between Pd and Al_(2)O_(3)with smaller Pd particle size and more surface activated oxygen.It exhibited excellent catalytic performance,complete oxidation of 50 ppmV o-xylene at 85℃with a WHSV of 60,000 mL/(g·hr).

A numerical framework for underground structures in layered ground under inclined P-SV waves using stiffness matrix and domain reduction methods

A numerical framework was proposed for the seismic analysis of underground structures in layered ground under inclined P-SV waves.The free-field responses are first obtained using the stiffness matrix method based on plane-wave assumptions.Then,the domain reduction method was employed to reproduce the wavefield in the numerical model of the soil–structure system.The proposed numerical framework was verified by providing comparisons with analytical solutions for cases involving free-field responses of homogeneous ground,layered ground,and pressure-dependent heterogeneous ground,as well as for an example of a soil–structure interaction simulation.Compared with the viscous and viscous-spring boundary methods adopted in previous studies,the proposed framework exhibits the advantage of incorporating oblique incident waves in a nonlinear heterogeneous ground.Numerical results show that SV-waves are more destructive to underground structures than P-waves,and the responses of underground structures are significantly affected by the incident angles.

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis(DEA).In this study,we focus on a“big data”problem related to the considerably large dimensions of the input-output data.The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation,including principal component analysis(PCA-DEA),which is based on the idea of aggregating input and output,efficiency contribution measurement(ECM),average efficiency measure(AEC),and regression-based detection(RB),which is based on the idea of variable selection.We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test.In addition,we discuss the effect of initial variable selection in RB for the first time.Based on the results,we offer guidelines that are more reliable on how to choose an appropriate method.

Investigation of β-Ga_(2)O_(3) thick films grown on c-plane sapphire via carbothermal reduction

We investigated the influence of the growth temperature, O_(2) flow, molar ratio between Ga_(2)O_(3) powder and graphite powder on the structure and morphology of the films grown on the c-plane sapphire(0001) substrates by a carbothermal reduction method. Experimental results for the heteroepitaxial growth of β-Ga_(2)O_(3) illustrate that β-Ga_(2)O_(3) growth by the carbothermal reduction method can be controlled. The optimal result was obtained at a growth temperature of 1050 °C. The fastest growth rate of β-Ga_(2)O_(3) films was produced when the O_(2) flow was 20 sccm. To guarantee that β-Ga_(2)O_(3) films with both high-quality crystal and morphology properties, the ideal molar ratio between graphite powder and Ga_(2)O_(3) powder should be set at 10 : 1.

Preparation of TiC powders by carbothermal reduction method in vacuum

The preparation of fine TiC powders by carbothermal reduction of TiO2 in vacuum was investigated by XRD,SEM,XRF and laser particle sizer.Thermodynamic analysis indicates that it is easy to prepare TiC in vacuum and the formation sequence of products are Ti4O7（Magneli phase）,Ti3O5,Ti2O3,TiCxO1-x and TiC with the increase of reaction temperature.Experimental results demonstrate that TiC powders with single phase are obtained with molar ratio of TiO2 to C ranging from 1：3.2 to 1：6 at 1 550 ℃ for 4 h when the system pressure is 50 Pa,and TiC1.0 is gained when the molar ratio of TiO2 to C is 1：4 and 1：5.In addition,fine TiC1.0 powders（D50 equals 3.04 μm） with single phase and low impurities are obtained when the molar ratio of TiO2 to C is 1：4.SEM observation shows that uniform shape,low agglomeration,and loose structure are observed on the surface of block product.

Preparation of V-Ti-Fe master alloys by metallothermic reduction method

V-Ti-Fe master alloys were prepared by metaUothermic reduction method, and the influences of the mass ratio of V205 to TiO2, Al and Al-Mg alloy addition amounts on the metal recovery rates and alloy compositions were investigated. The results show that appropriate technological parameters are： the mass ratio of V205 to TiO2 is 0.5：1, Al addition represents 95% of the theoretical value, and the Al-Mg alloy addition amount is one third that of the Al addition. The results from energy spectrum analysis show that V and Fe distribute uniformly in the prepared alloy, while the segregation for Ti, i.e. Ti-rich phase is detected. A spray refming process was carried out to reduce the impurity contents of Al and O in the prepared alloys. The Al content drops from 4.27% to 1.86%, and the O content drops from 2.10% to 0.91% after the refining process.

Preparation of Cu nanoparticles with ascorbic acid by aqueous solution reduction method

Cu nanoparticles were prepared by reducing Cu2＋ ions with ascorbic acid through aqueous solution reduction method. The effects of solution pH and average size of Cu2O particles on the preparation of Cu nanoparticles were investigated. Cu particles were prepared at pH 3, 5 or 7, with the smallest Cu particles obtained at pH 7. However, Cu particles could not be prepared at pH 9 or 11. The average size of Cu2O particles can affect that of Cu particles. Larger Cu2O particles result in larger Cu particles. In addition, experiments were conducted to explore the reaction process by measuring the X-ray diffraction （XRD） patterns of specimens collected at different time points during the reaction. It was found that Cu（OH）2 was initially formed as a precursor, followed by the formation of Cu2O, which was finally reduced to Cu particles.

Effects of reaction parameters on preparation of Cu nanoparticles via aqueous solution reduction method with NaBH_4

The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution.

Physics-based seismic analysis of ancient wood structure:fault-to-structure simulation

Based on the domain reduction method,this study employs an SEM-FEM hybrid workflow which integrates the advantages of the spectral element method(SEM)for flexible and highly efficient simulation of seismic wave propagation in a three-dimensional(3D)regional-scale geophysics model and the finite element method(FEM)for fine simulation of structural response including soil-structure interaction,and performs a physics-based simulation from initial fault rupture on an ancient wood structure.After verification of the hybrid workflow,a large-scale model of an ancient wood structure in the Beijing area,The Tower of Buddhist Incense,is established and its responses under the 1665 Tongxian earthquake and the 1730 Yiheyuan earthquake are simulated.The results from the simulated ground motion and seismic response of the wood structure under the two earthquakes demonstrate that this hybrid workflow can be employed to efficiently provide insight into the relationships between geophysical parameters and the structural response,and is of great significance toward accurate input for seismic simulation of structures under specific site and fault conditions.

Optimal mining sequence for coal faces under a bedding slope:insight from landslide prevention

Repetitive mining beneath bedding slopes is identified as a critical factor in geomorphic disturbances, especially landslides and surface subsidence. Prior research has largely concentrated on surface deformation in plains due to multi-seam coal mining and the instability of natural bedding slopes, yet the cumulative impact of different mining sequences on bedding slopes has been less explored. This study combines drone surveys and geological data to construct a comprehensive three-dimensional model of bedding slopes. Utilizing FLAC3D and PFC2D models, derived from laboratory experiments, it simulates stress, deformation, and failure dynamics of slopes under various mining sequences. Incorporating fractal dimension analysis, the research evaluates the stability of slopes in relation to different mining sequences. The findings reveal that mining in an upslope direction minimizes disruption to overlying strata. Initiating extraction from lower segments increases tensile-shear stress in coal pillar overburdens, resulting in greater creep deformation towards the downslope than when starting from upper segments, potentially leading to localized landslides and widespread creep deformation in mined-out areas. The downslope upward mining sequence exhibits the least fractal dimensions, indicating minimal disturbance to both strata and surface. While all five mining scenarios maintain good slope stability under normal conditions, recalibrated stability assessments based on fractal dimensions suggest that downslope upward mining offers the highest stability under rainfall, contrasting with the lower stability and potential instability risks of upslope downward mining. These insights are pivotal for mining operations and geological hazard mitigation in multi-seam coal exploitation on bedding slopes.

Highly Defective Dark TiO_(2) Modified with Pt: Effects of Precursor Nature and Preparation Method on Photocatalytic Properties

The study focused on the modification with platinum of dark defective titania obtained via pulsed laser ablation. Both the method of Pt introduction and the nature of the Pt precursor were varied. All samples exhibited similar phase compositions, specific surface areas, and Pt contents. High-resolution transmission electron microscopy coupled with pulsed CO adsorption revealed increased dispersity when photoreduction and the hydroxonitrate complex (Me _(4) N) _(2) [Pt _(2) (OH) _(2) (NO _(3) ) _(8) ] were used. The sample featured a high content of single-atom species and subnano-sized Pt clusters. The X-ray photoelectron spectroscopy results showed that the photoreduction method facilitated the appearance of a larger number of Pt ^(2+) states, which appeared owing to the strong metal-support interaction (SMSI) eff ect of the transfer of electron density from the electron-saturated defects on the TiO _(2) surface to Pt ^(4+) . In the hydrogen evolution reaction, samples with a significant fraction of the Pt ^(2+) ionic component, capable of generating short-lived Pt^(0) single-atom sites under irradiation due to the SMSI eff ect, exhibited the highest photocatalytic activity. The 0.5Pt(C)/TiO_(2) -Ph sample exhibited the highest hydrogen yield with a quantum efficiency of 0.53, retaining its activity even after 8 h of operation.

A Pioneering Approach to the Synthesis of Silver Nanoparticles

Our research introduces a groundbreaking chemical reduction method for synthesizing silver nanoparticles, marking a significant advancement in the field. The nanoparticles were meticulously characterized using various techniques, including optical analysis, structural analysis, transmission electron microscopy (TEM), and field-emission scanning electron microscope (FESEM). This thorough process instills confidence in the accuracy of our findings. The results unveiled that the silver nanoparticles had a diameter of less than 20 nm, a finding of great importance. The absorption spectrum decreased in the peak wavelength range (405 - 394 mm) with increasing concentrations of Ag nanoparticles in the range (1 - 5%). The XRD results indicated a cubic crystal structure for silver nanoparticles with the lattice constant (a = 4.0855 Å), and Miller indices were (111), (002), (002), and (113). The simulation on the XRD pattern showed a face center cubic phase with space group Fm-3m, providing valuable insights into the structure of the nanoparticles.

A strength reduction method based on double reduction parameters and its application

In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described as η.With the increase in the slopeangle,ηincreases; in particular,when the slope angle is 45°,tηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.

A new double reduction method for slope stability analysis

The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

Limit analysis of vertical anti-pulling screw pile group under inclined loading on 3D elastic-plastic finite element strength reduction method

Based on the functional theory, catastrophe theory, simultaneity principle and the idea of strength reduction method （SRM）, the bearing capacity functional anti SRM of pile group foundation were established, and the criteria of ultimate load and the concept of safety storage coefficient （Css） were advanced. The inclined ultimate loads by the static loading test, load increment method （LIM） and SRM are compared. Theoretically, the ultimate load of piles does not change with the loading levels when it is calculated by SRM. When the one strength reduction parameter is applied in the calculation boundary, there are calculating errors because the bearing capacity action of soils happened in the finite zone. The inclined 10adings are 108, 132 and 144 kN, and SSC are 1.07, 0.94 and 0.79, respectively, so the calculation values of ultimate loads are about 115.56, 124.08 and 113.76 kN, respectively. The error between calculations and observation values is less than 6%. But .the error between calculations of LIM and observations is 20%. Because of the effect of inclined loading, the push-rotation phenomenon of screw pile group appears. Under this testing, the ultimate bearing capacity of piles is mostly determined by the horizontal ultimate bearing capacity, and the effect of the vertical component of inclined load should also be considered.

Evaluation of regional water resources carrying capacity based on binary index method and reduction index method

Based on the regional water resources carrying capacity(WRCC)evaluation principles and evaluation index system in the National Technical Outline of Water Resources Carrying Capacity Monitoring and Early Warning(hereafter referred to as the Technical Outline),this paper elaborates on the collection and sorting of the basic data of water resources conditions,water resources development and utilization status,social and economic development in basins,analysis and examination of integrity,consistency,normativeness,and rationality of the basic data,and the necessity of WRCC evaluation.This paper also describes the technique of evaluating the WRCC in prefecture-level cities and city-level administrative divisions in the District of the Taihu Lake Basin,which is composed of the Taihu Lake Basin and the Southeastern River Basin.The evaluation process combines the binary index evaluation method and reduction index evaluation method.The former,recommended by the Technical Outline,uses the total water use and the amount of exploited groundwater as evaluation indices,showing stronger operability,while the latter is developed by simplifying and optimizing the comprehensive index system with greater systematicness and completeness.The mutual validation and adjustment of the results of the above-mentioned two evaluation methods indicate that the WRCC of the District of the Taihu Lake Basin is overloaded in general because some prefecture-level cities and city-level administrative divisions in the Taihu Lake Basin and the Southeastern River Basin are in a severely overloaded state.In order to explain this conclusion,this paper analyzes the causes of WRCC overloading from the aspects of basin water environment,water resources development and utilization,water resources regulation and control ability,water resources utilization efficiency,and water resources management.