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ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS
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作者 Maoan HAN Yan YE 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1524-1535,共12页
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol... In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications. 展开更多
关键词 periodic solution Poincarémap periodic equation stability
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Ultrafast dynamics of femtosecond laser-induced high spatial frequency periodic structures on silicon surfaces
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作者 Ruozhong Han Yuchan Zhang +6 位作者 Qilin Jiang Long Chen Kaiqiang Cao Shian Zhang Donghai Feng Zhenrong Sun Tianqing Jia 《Opto-Electronic Science》 2024年第3期33-46,共14页
Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than t... Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL. 展开更多
关键词 laser-induced periodic surface structures(LIPSS) local field enhancement collinear pump-probe imaging silicon high spatial frequency periodic structures
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Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis
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作者 Chenfeng Li Peibing Yang +1 位作者 Tengxu Zhang Jiachun Guo 《Geodesy and Geodynamics》 EI CSCD 2024年第1期50-60,共11页
Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection... Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites. 展开更多
关键词 GNSS Time series Singular spectrum analysis Trace matrix periodic signal
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Optimal design for rubber concrete layered periodic foundations based on the analytical approximations of band gaps and mapping relations
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作者 Wu Qiaoyun Xu Zhifeng +2 位作者 Xu Peishan Zeng Wenxuan Chen Xuyong 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2024年第3期593-608,共16页
The seismic performance of rubber concrete-layered periodic foundations are significantly influenced by their design,in which the band gaps play a paramount role.Aiming at providing better designs for these foundation... The seismic performance of rubber concrete-layered periodic foundations are significantly influenced by their design,in which the band gaps play a paramount role.Aiming at providing better designs for these foundations,this study first proposes and validates the analytical formulas to approximate the bounds of the first few band gaps.In addition,the mapping relations linking the frequencies of different band gaps are presented.Furthermore,an optimal design method for these foundations is developed,which is validated through an engineering example.It is demonstrated that ensuring the superstructure’s resonance zones are completely covered by the corresponding periodic foundation’s band gaps can achieve satisfactory vibration attenuation effects,which is a good strategy for the design of rubber concrete layered periodic foundations. 展开更多
关键词 periodic foundation band gap vibration attenuation seismic isolation optimal design
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3D Printing of Periodic Porous Metamaterials for Tunable Electromagnetic Shielding Across Broad Frequencies
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作者 Qinniu Lv Zilin Peng +5 位作者 Haoran Pei Xinxing Zhang Yinghong Chen Huarong Zhang Xu Zhu Shulong Wu 《Nano-Micro Letters》 SCIE EI CAS CSCD 2024年第12期533-552,共20页
The new-generation electronic components require a balance between electromagnetic interference shielding efficiency and open structure factors such as ventilation and heat dissipation.In addition,realizing the tunabl... The new-generation electronic components require a balance between electromagnetic interference shielding efficiency and open structure factors such as ventilation and heat dissipation.In addition,realizing the tunable shielding of porous shields over a wide range of wavelengths is even more challenging.In this study,the well-prepared thermoplastic polyurethane/carbon nanotubes composites were used to fabricate the novel periodic porous flexible metamaterials using fused deposition modeling 3D printing.Particularly,the investigation focuses on optimization of pore geometry,size,dislocation configuration and material thickness,thus establishing a clear correlation between structural parameters and shielding property.Both experimental and simulation results have validated the superior shielding performance of hexagon derived honeycomb structure over other designs,and proposed the failure shielding size(D_(f)≈λ/8-λ/5)and critical inclined angle(θf≈43°-48°),which could be used as new benchmarks for tunable electromagnetic shielding.In addition,the proper regulation of the material thickness could remarkably enhance the maximum shielding capability(85-95 dB)and absorption coefficient A(over 0.83).The final innovative design of the porous shielding box also exhibits good shielding effectiveness across a broad frequency range(over 2.4 GHz),opening up novel pathways for individualized and diversified shielding solutions. 展开更多
关键词 Polymeric component 3D printing Tunable electromagnetic shielding periodic porous metamaterials Honeycomb pore structure
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A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties
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作者 Yanda WANG Yanping LIAN +2 位作者 Zhidong WANG Chunpeng WANG Daining FANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第2期217-238,共22页
Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM... Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures. 展开更多
关键词 lattice structure triple periodic minimal surface(TPMS) plate lattice structural optimization machine learning
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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS
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作者 Zhenhai LIU Nikolaos S.PAPAGEORGIOU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1280-1300,共21页
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con... We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems. 展开更多
关键词 periodic boundary condition time-dependent maximal monotone operator convex and nonconvex problems extremal solutions strong relaxation
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Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations
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作者 M.SAFI M.VAKILIFARD M.J.MAHMOODI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第3期407-424,共18页
In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6... In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz. 展开更多
关键词 layered metamaterial periodic foundation complex dispersion curve wave transmission diagram
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Tuning Second Chern Number in a Four-Dimensional Topological Insulator by High-Frequency Time-Periodic Driving
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作者 刘峥嵘 陈锐 周斌 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第4期77-89,共13页
Floquet engineering has attracted considerable attention as a promising approach for tuning topological phase transitions.We investigate the effects of high-frequency time-periodic driving in a four-dimensional(4D)top... Floquet engineering has attracted considerable attention as a promising approach for tuning topological phase transitions.We investigate the effects of high-frequency time-periodic driving in a four-dimensional(4D)topological insulator,focusing on topological phase transitions at the off-resonant quasienergy gap.The 4D topological insulator hosts gapless three-dimensional boundary states,characterized by the second Chern number C_(2).We demonstrate that the second Chern number of 4D topological insulators can be modulated by tuning the amplitude of time-periodic driving.This includes transitions from a topological phase with C_(2)=±3 to another topological phase with C_(2)=±1,or to a topological phase with an even second Chern number C_(2)=±2,which is absent in the 4D static system.Finally,the approximation theory in the high-frequency limit further confirms the numerical conclusions. 展开更多
关键词 TOPOLOGICAL TRANSITIONS periodic
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Solitons and Their Biperiodic Pulsation in Ultrafast Fiber Lasers Based on CB/GO
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作者 Zhen-Tao Ju Zhi-Zeng Si +1 位作者 Xin Yan Chao-Qing Dai 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第8期28-32,共5页
The carbon black(CB)is introduced to manufacture CB/graphene oxide(GO)composite material to mitigate limitations of GO as a saturable absorber with the excellent performance in ultrafast fiber lasers.At a central wave... The carbon black(CB)is introduced to manufacture CB/graphene oxide(GO)composite material to mitigate limitations of GO as a saturable absorber with the excellent performance in ultrafast fiber lasers.At a central wavelength of 1555.5 nm,the stable mode-locked pulse with width of 656 fs,repetition rate of 20.16 MHz,and high signal-to-noise ratio of 82.07 dB is experimentally obtained.Additionally,experimental observations for pulsation phenomena of vector biperiodic solitons combining period-1 and period-17,period-2 and period-32,period-3 and period-36 are verified via simulations. 展开更多
关键词 fiber periodic ABSORBER
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Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material
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作者 Yali ZHANG Yueting ZHOU Shenghu DING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期179-196,共18页
Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical... Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads. 展开更多
关键词 wavy surface periodic contact thermoelectric(TE)material Hilbert integral kernel
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Self-propelled Leidenfrost droplets on femtosecond-laser-induced surface with periodic hydrophobicity gradient
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作者 Bohong Li Lan Jiang +2 位作者 Xiaowei Li Zhipeng Wang Peng Yi 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2024年第2期502-509,共8页
The controllable transfer of droplets on the surface of objects has a wide application prospect in the fields of microfluidic devices,fog collection and so on.The Leidenfrost effect can be utilized to significantly re... The controllable transfer of droplets on the surface of objects has a wide application prospect in the fields of microfluidic devices,fog collection and so on.The Leidenfrost effect can be utilized to significantly reduce motion resistance.However,the use of 3D structures limits the widespread application of self-propulsion based on Leidenfrost droplets in microelectromechanical system.To manipulate Leidenfrost droplets,it is necessary to create 2D or quasi-2D geometries.In this study,femtosecond laser is applied to fabricate a surface with periodic hydrophobicity gradient(SPHG),enabling directional self-propulsion of Leidenfrost droplets.Flow field analysis within the Leidenfrost droplets reveals that the vapor layer between the droplets and the hot surface can be modulated by the SPHG,resulting in directional propulsion of the inner gas.The viscous force between the gas and liquid then drives the droplet to move. 展开更多
关键词 SELF-PROPELLED Leidenfrost droplets periodic hydrophobicity gradient femtosecond laser fabrication
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Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites
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作者 Chengkan Xu Xiaofei Wang +2 位作者 Yixuan Li Guannan Wang He Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期957-974,共18页
Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstru... Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites. 展开更多
关键词 periodic composites localized stress recovery conditional generative adversarial network
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Impact of Alcian blue and periodic acid Schiff expression on the prognosis of gastric signet ring cell carcinoma
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作者 Juan Lin Zhu-Feng Chen +1 位作者 Guo-Dong Guo Xin Chen 《World Journal of Gastrointestinal Oncology》 SCIE 2024年第3期687-698,共12页
BACKGROUND The Alcian blue(AB)and periodic acid Schiff(PAS)stains are representative mucus markers in gastric signet ring cell carcinoma(SRCC).They are low-cost special staining methods used to detect acidic mucus and... BACKGROUND The Alcian blue(AB)and periodic acid Schiff(PAS)stains are representative mucus markers in gastric signet ring cell carcinoma(SRCC).They are low-cost special staining methods used to detect acidic mucus and neutral mucus,respectively.However,the clinical importance of the special combined AB and PAS stain is unclear.AIM To investigate AB expression,PAS expression and the AB-to-PAS(A/P)ratio in gastric SRCC patients and to assess patient prognosis.METHODS Paraffin-embedded sections from 83 patients with gastric SRCC were stained with AB and PAS,and signet ring cell positivity was assessed quantitatively.Immuno-histochemical staining for Ki67,protein 53(P53)and human epidermal growth factor receptor 2(HER2)was performed simultaneously.The cancer-specific survival(CSS)rate was estimated via Kaplan-Meier analysis.Cox proportional hazards models were used for univariate and multivariate survival analyses.RESULTS Kaplan-Meier survival analysis revealed that the 3-year CSS rate was significantly greater in the high-PAS-expression subgroup than in the low-PAS-expression subgroup(P<0.001).The 3-year CSS rate in the A/P≤0.5 group was significantly greater than that in the A/P>0.5 group(P=0.042).Univariate Cox regression analysis revealed that the factors affecting prognosis included tumor diameter,lymph node metastasis,vessel carcinoma embolus,tumor stage,the A/P ratio and the expression of Ki67,P53 and the PAS.Cox multivariate regression analysis confirmed that low PAS expression[hazard ratio(HR)=3.809,95%confidence interval(CI):1.563-9.283,P=0.003]and large tumor diameter(HR=2.761,95%CI:1.086-7.020,P=0.033)were independent risk factors for poor prognosis.CONCLUSION A/P>0.5 is potentially a risk factor for prognosis,and low PAS expression is an independent risk factor in the prognosis of gastric SRCC.PAS expression and the A/P ratio could help in predicting the clinical prognosis of patients with SRCC. 展开更多
关键词 Alcian blue periodic acid-Schiff PROGNOSIS GASTRIC Signet ring cell carcinoma
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Effect of temperature gradientinduced periodic deformation of CRTS Ⅲ slab track on dynamic responses of the train-track system
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作者 Wang Jijun Zhang Huanxin +1 位作者 Shi Cheng Wang Meng 《Railway Sciences》 2024年第4期437-452,共16页
Purpose-Temperature is an important load for a ballastless track.However,little research has been conducted on the dynamic responses when a train travels on a ballastless track under the temperature gradient.The dynam... Purpose-Temperature is an important load for a ballastless track.However,little research has been conducted on the dynamic responses when a train travels on a ballastless track under the temperature gradient.The dynamic responses under different temperature gradients of the slab are theoretically investigated in this work.Design/methodology/approach-Considering the moving train,the temperature gradient of the slab,and the gravity of the slab track,a dynamic model for a high-speed train that runs along the CRTS Ⅲ slab track on subgrade is developed by a nonlinear coupled way in Abaqus.Findings-The results are as follows:(1)The upward transmission of the periodic deformation of the slab causes periodic track irregularity.(2)Because of the geometric constraint of limiting structures,the maximum bending stresses of the slab occur near the end of the slab under positive temperature gradients,but in the middle of the slab under negative temperature gradients.(3)The periodic deformation of the slab can induce periodic changes in the interlayer stiffness and contact status,leading to a large vibration of the slab.Because of the vibration-reduction capacity of the fastener and the larger mass of the concrete base,the accelerations of both the slab and concrete base are far less than the acceleration of the rail.Originality/value-This study reveals the influence mechanism of temperature gradient-induced periodic deformation in the dynamic responses of the train-track system,and it also provides a guide for the safe service of CRTS Ⅲ slab track. 展开更多
关键词 Ballastless track CRTSⅢslab track Temperature gradient periodic deformation Train performance
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A Brief Introduction to the English Periodical of Contemporary Social Sciences
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《Contemporary Social Sciences》 2024年第2期F0002-F0002,共1页
The English periodical of Contemporary Social Sciences is an English periodical founded by Sichuan Academy of Social Sciences and is published every two months.It was approved by the National Radio and Television Admi... The English periodical of Contemporary Social Sciences is an English periodical founded by Sichuan Academy of Social Sciences and is published every two months.It was approved by the National Radio and Television Administration of the People’s Republic of China(formerly the State Administration of Press,Publication,Radio,Film and Television of the People’s Republic of China)in March 2016. 展开更多
关键词 periodicAL SHE CONTEMPORARY
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Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations
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作者 Terry E. Moschandreou 《Advances in Pure Mathematics》 2024年第2期118-138,共21页
This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the perio... This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v<sub>3</sub> is continuous and {C, y<sub>1</sub>, y<sub>1</sub><sup>2</sup>}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y<sub>1</sub><sup>2</sup>=y<sub>2</sub>, C∈R) together with the condition v<sub>2</sub>=-2y<sub>1</sub>v<sub>1</sub>. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v<sub>1</sub> and v<sub>2</sub> and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y<sub>3</sub> component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v<sub>3 </sub>only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v<sub>3</sub> reaches a peak in the third component y<sub>3</sub>. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y<sub>3</sub>, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]<sup>3</sup> is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v<sub>3</sub> wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v<sub>3</sub> is spatially finite on the Riemann Sphere and the forcing is oscillatory in y<sub>3</sub> component if the velocity v3</sub> is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3</sub> is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball. 展开更多
关键词 Navier-Stokes PNS 3-Torus periodic Ball Sphere Hölder CONTINUOUS Riemann-Surface Uniqueness
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Effective Elimination of Hazardous Chromium (VI) Using Periodic Elements and Contemporary Adsorption Methods by Using Magnesium Ferrite Nanoparticle: A Review
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作者 Nazmun Nahar Mahabub Hossain Swaron +1 位作者 Md. Aliuzzaman Sheik Md. Jamal Uddin 《Journal of Environmental Protection》 2024年第5期596-619,共24页
A well-known hazardous metal and top contaminant in wastewater is hexavalent chromium. The two forms of most commonly found chromium are chromate ( CrO 4 2− ) and dichromate ( Cr 2 O 7 2− ). Leather tanning, cooling t... A well-known hazardous metal and top contaminant in wastewater is hexavalent chromium. The two forms of most commonly found chromium are chromate ( CrO 4 2− ) and dichromate ( Cr 2 O 7 2− ). Leather tanning, cooling tower blow-down, plating, electroplating, rinse water sources, anodizing baths etc. are the main sources of Cr (VI) contamination. The Cr (VI) is not only non-biodegradable in the environment but also carcinogenic to living population. It is still difficult to treat Cr contaminated waste water effectively, safely, eco-friendly, and economically. As a result, many techniques have been used to treat Cr (VI)-polluted wastewater, including adsorption, chemical precipitation, coagulation, ion-exchange, and filtration. Among these practices, the most practical method is adsorption for the removal of Cr (VI) from aqueous solutions, which has gained widespread acceptance due to the ease of use and affordability of the equipment and adsorbent. It has been revealed that Fe-based adsorbents’ oxides and hydroxides have high adsorptive potential to lower Cr (VI) content below the advised threshold. Fe-based adsorbents were also discovered to be relatively cheap and toxic-free in Cr (VI) treatment. Fe-based adsorbents are commonly utilized in industry. It has been discovered that nanoparticles of Fe-, Ti-, and Cu-based adsorbents have a better capacity to remove Cr (VI). Cr (VI) was effectively removed from contaminated water using mixed element-based adsorbents (Fe-Mn, Fe-Ti, Fe-Cu, Fe-Zr, Fe-Cu-Y, Fe-Mg, etc.). Initial findings suggest that Cr (VI) removal from wastewater may be accomplished by using magnesium ferrite nanomaterials as an efficient adsorbent. 展开更多
关键词 Chromium (VI) periodic Elements Adsorption ELIMINATION Magnesium Ferrite
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Calibration of CO and CO2 Monitors Used in Periodic Inspection of Vehicles at Fixed Stations for Environmental Control
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作者 Adel Bassuoni Shehata Abdulrahman Rashed Al Askar +2 位作者 Najjy Hamad Al Yami Abdullah Suleiman Al Owaysi Sultan K. Alharbi 《Green and Sustainable Chemistry》 2024年第2期29-41,共13页
Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuri... Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuring the quantitative assessment of emissions for informed decisions on environmental treatments. This paper describes a method for the calibration of CO/CO<sub>2</sub> monitors used for periodic inspections of vehicles in cites. The calibration was performed in the selected ranges: 900 - 12,000 µmol/mol for CO and 2000 - 20,000 µmol/mol for CO<sub>2</sub>. The traceability of the measurement results to the SI units was ensured by using certified reference materials from CO/N<sub>2</sub> and CO<sub>2</sub>/N<sub>2</sub> primary gas mixtures. The method performance was evaluated by assessing its linearity, accuracy, precision, bias, and uncertainty of the calibration results. The calibration data exhibited a strong linear trend with R² values close to 1, indicating an excellent fit between the measured values and the calibration lines. Precision, expressed as relative standard deviation (%RSD), ranged from 0.48 to 4.56% for CO and from 0.97 to 3.53% for CO<sub>2</sub>, staying well below the 5% threshold for reporting results at a 95% confidence level. Accuracy measured as percent recovery, was consistently high (≥ 99.1%) for CO and ranged from 84.90% to 101.54% across the calibration range for CO<sub>2</sub>. In addition, the method exhibited minimal bias for both CO and CO<sub>2</sub> calibrations and thus provided a reliable and accurate approach for calibrating CO/CO<sub>2</sub> monitors used in vehicle inspections. Thus, it ensures the effectiveness of exhaust emission control for better environment. 展开更多
关键词 MONITORS periodic Inspection CO/CO2 Calibration LINEARITY Precision Accuracy
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The Periodic Table of Primes
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作者 Han-Lin Li Shu-Cherng Fang Way Kuo 《Advances in Pure Mathematics》 2024年第5期394-419,共26页
Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers... Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes. 展开更多
关键词 PRIMES COMPOSITES the periodic Table of Primes
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