Vibration detection using sensors with both wide working frequency range,good sensitivity,and other good performances is a topic of great interest in fields such as inertial navigation,deep-sea fishing boat engines co...Vibration detection using sensors with both wide working frequency range,good sensitivity,and other good performances is a topic of great interest in fields such as inertial navigation,deep-sea fishing boat engines condition monitoring,seismic monitoring,attitude,and heading reference system,etc.This paper investigates two 6H-SIC MEMS diaphragms,one triangular and the other square,used in a fiber optic Fabry–Perot(FP)accelerometer in an experimental scenario.The triangular chip shows a wide working frequency range of 630 Hz–5300 Hz,a natural frequency of 44.3 k Hz,and a mechanical sensitivity of 0.154 nm/g.An optimal structure of the square chip used in a probe such as a fiber optic FP accelerometer also shows a wide working frequency range of 120 Hz–2300 Hz;a good sensitivity of 31.5 m V/g,a resonance frequency of7873 Hz,an accuracy of 0.96%F.S.,a frequency measurement error of 1.15%,and an excellent linearity of 0.9995.展开更多
This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on ther...This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems.The controller parameters were tuned using the Integral Time Absolute Error(ITAE)objective function,which was also evaluated alongside other objective functions(IAE,ISE,and ITSE)to ensure high precision in frequency stabilization.To validate the effectiveness of the triangular membership function,comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions.Performance metrics,including ITAE,settling time,overshoot,and undershoot of frequency deviation,as well as tie-line power deviation,were evaluated.Robustness was established through a comprehensive sensitivity analysis with T_(G),T_(T),andT_(R) parameter variations(±50%),a non-linearity analysis incorporating Generation Rate Constraint(GRC)and Governor Deadband(GDB),a random Step Load Perturbation(SLP)over 0–100 s,and also Stability analysis of the proposed scheme is conducted using multiple approaches,including frequency-domain analysis,Lyapunov stability theory,and eigenvalue analysis.Additionally,the system incorporating thermal,hydro,and gas turbines,along with advanced components like CES and HVDC links,was analysed.Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm(MGOA),Honey Badger Algorithm(HBA),Particle Swarm Optimization(PSO),Artificial Bee Colony(ABC),and Spider Monkey Optimization(SMO)algorithms.Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives,exhibiting superior performance across all evaluated metrics.This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.展开更多
We optimized the gradation of cold recycled mixture(CRM)based on low-temperature performance.Firstly,the low-temperature crack resistance of CRM with different gradation and emulsified asphalt content was studied by i...We optimized the gradation of cold recycled mixture(CRM)based on low-temperature performance.Firstly,the low-temperature crack resistance of CRM with different gradation and emulsified asphalt content was studied by indirect tension(IDT)and semi-circular bending(SCB)test.Thereafter,the low-temperature performance evaluation index suitable for CRM was put forward.Then,the triangular coordinate statistical chart was used to analyze the optimal proportion of three grades of aggregate which are 2.36-4.75 mm,0.075-2.36 mm and below 0.075 mm.The results showed that the W_(f) and G_(f) could distinguish the low-temperature performance of CRM with different mixtures and emulsified asphalt dosage.For cold recycled fine aggregate,2.36-4.75 mm,0.075-2.36 mm and less than 0.075 mm account for 20%-25%,74.3%-80%and 5%-8%,respectively.The CRM with lower void fraction,higher W_(f) and G_(f) could be obtained.Based on the reported findings,it was suggested that the sieve passing percentage of 4.75,2.36,and 0.075 mm of CRM is 45%-55%,27%-52%and 1.5%-5%,respectively.展开更多
The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying t...The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying traditional maximum equivalent span beam(MESB)theory to determine deformation range,peak point,and angle influence poses a challenge.Considering the overall structure of the intersection roof,the maximum equivalent triangular plate(METP)theory is proposed,and its geometric parameter calculation formula and deflection calculation formula are obtained.The application of the two theories in 18 models with different intersection angles,roadway types,and surrounding rock lithology is verified by numerical analysis.The results show that:1)The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone;2)The area comparison method of the METP theory can be reasonably explained:①The roof subsidence of the intersection decreases with the increase of the intersection angle;②The roof subsidence at the intersection of different roadway types has a rectangular type>arch type>circular type;③The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock.According to the application results of the two theories,the four advantages of the METP theory are compared and clarified in the basic assumptions,mechanical models,main viewpoints,and mechanism analysis.The large deformation inducement of the intersection roof is then explored.The J 2 peak area of the roof drives the large deformation of the area,the peak point of which is consistent with the center of gravity position of the METP.Furthermore,the change in the range of this peak is consistent with the change law of the METP’s area.Hence,this theory clarifies the large deformation area of the intersection roof,which provides a clear guiding basis for its initial support design,mid-term monitoring,and late local reinforcement.展开更多
Working memory is an executive memory process that includes encoding,maintenance,and retrieval.These processes can be modulated by transcranial alternating current stimulation(tACS)with sinusoidal waves.However,little...Working memory is an executive memory process that includes encoding,maintenance,and retrieval.These processes can be modulated by transcranial alternating current stimulation(tACS)with sinusoidal waves.However,little is known about the impact of the rate of current change on working memory.In this study,we aimed to investigate the effects of two types of tACS with different rates of current change on working memory performance and brain activity.We applied a randomized,single-blind design and divided 81 young participants who received triangular wave tACS,sinusoidal wave tACS,or sham stimulation into three groups.Participants performed n-back tasks,and electroencephalograms were recorded before,during,and after active or sham stimulation.Compared to the baseline,working memory performance(accuracy and response time)improved after stimulation under all stimulation conditions.According to drift-diffusion model analysis,triangular wave tACS significantly increased the efficiency of non-target information processing.In addition,compared with sham conditions,triangular wave tACS reduced alpha power oscillations in the occipital lobe throughout the encoding period,while sinusoidal wave tACS increased theta power in the central frontal region only during the later encoding period.The brain network connectivity results showed that triangular wave tACS improved the clustering coefficient,local efficiency,and node degree intensity in the early encoding stage,and these parameters were positively correlated with the non-target drift rate and decision starting point.Our findings on how tACS modulates working memory indicate that triangular wave tACS significantly enhances brain network connectivity during the early encoding stage,demonstrating an improvement in the efficiency of working memory processing.In contrast,sinusoidal wave tACS increased the theta power during the later encoding stage,suggesting its potential critical role in late-stage information processing.These findings provide valuable insights into the potential mechanisms by which tACS modulates working memory.展开更多
Objective:To explore the clinical effect of improved incision in the extraction of impacted mandibular wisdom teeth.Methods:160 patients who were treated in our hospital from October,2024 to April,2025 and had their m...Objective:To explore the clinical effect of improved incision in the extraction of impacted mandibular wisdom teeth.Methods:160 patients who were treated in our hospital from October,2024 to April,2025 and had their mandibular impacted wisdom teeth removed according to the doctor’s advice were randomly divided into observation group and control group.The observation group used modified incision,while the control group used traditional triangular incision.The operation time,intraoperative visual analogue scale(VAS)pain score,pain VAS score on the 1st,2nd and 3rd day after operation,facial swelling on the 2nd day after operation,mouth opening limitation on the 2nd day after operation and the incidence of dry socket after operation were recorded and compared between the two groups.Results:There was no significant difference in operation time between the two groups(p>0.05).The VAS score of pain in the observation group was significantly lower than that in the control group at each time point during and after operation(p<0.05).On the second day after operation,the facial swelling and mouth opening limitation in the observation group were significantly lighter than those in the control group(p<0.05).The incidence of dry socket in the observation group was 1.25%(1/80),which was significantly lower than that in the control group(8.75%,7/80),and the difference was statistically significant(p<0.05).Conclusion:The application of modified triangular incision in the extraction of impacted mandibular wisdom teeth can effectively relieve the pain during and after operation,reduce postoperative facial swelling and mouth opening limitation,and reduce the incidence of dry socket.展开更多
Software defect prediction(SDP)aims to find a reliable method to predict defects in specific software projects and help software engineers allocate limited resources to release high-quality software products.Software ...Software defect prediction(SDP)aims to find a reliable method to predict defects in specific software projects and help software engineers allocate limited resources to release high-quality software products.Software defect prediction can be effectively performed using traditional features,but there are some redundant or irrelevant features in them(the presence or absence of this feature has little effect on the prediction results).These problems can be solved using feature selection.However,existing feature selection methods have shortcomings such as insignificant dimensionality reduction effect and low classification accuracy of the selected optimal feature subset.In order to reduce the impact of these shortcomings,this paper proposes a new feature selection method Cubic TraverseMa Beluga whale optimization algorithm(CTMBWO)based on the improved Beluga whale optimization algorithm(BWO).The goal of this study is to determine how well the CTMBWO can extract the features that are most important for correctly predicting software defects,improve the accuracy of fault prediction,reduce the number of the selected feature and mitigate the risk of overfitting,thereby achieving more efficient resource utilization and better distribution of test workload.The CTMBWO comprises three main stages:preprocessing the dataset,selecting relevant features,and evaluating the classification performance of the model.The novel feature selection method can effectively improve the performance of SDP.This study performs experiments on two software defect datasets(PROMISE,NASA)and shows the method’s classification performance using four detailed evaluation metrics,Accuracy,F1-score,MCC,AUC and Recall.The results indicate that the approach presented in this paper achieves outstanding classification performance on both datasets and has significant improvement over the baseline models.展开更多
Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an a...Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.展开更多
Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urge...Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.展开更多
Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local ac...Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].展开更多
Background:An urban medical group in Dapeng New District was established in 2017 with the objective of enhancing outcomes for common diseases and reinforcing primary care by integrating high‐level hospitals with prim...Background:An urban medical group in Dapeng New District was established in 2017 with the objective of enhancing outcomes for common diseases and reinforcing primary care by integrating high‐level hospitals with primary health services.This study aimed to evaluate the performance of the urban medical group using the triangular value chain framework.Methods:The evaluation was conducted using the Donabedian model,focusing on three key dimensions:safety and quality,accessibility,and affordability.Longitudinal data were collected from 2016 to 2022 through government annual reports,the medical insurance bureau,and hospital information systems.Preprogram and postprogram outcome measurements were compared to assess differences and trends,providing a clear picture of the program's effectiveness.Results:Accessibility improved significantly,with the number of hospital beds per 1000 residents increasing from 2.62 in 2017 to 3.76 in 2022.The availability of general practitioners(GPs)also rose markedly,from 0 per 10,000 residents in 2017 to 6.27 in 2022.Regarding safety and quality,the proportion of complex medical procedures conducted within the New District expanded substantially,from 7.35%in 2017 to 38.11%in 2021.Additionally,there was an enhancement in the standardized management rate of chronic diseases.Affordability assessments showed that the proportion of medical income derived from the medical insurance fund increased by nearly 22.81 percentage points between 2012 and 2021.By 2021,75.02%of medical patients were covered by medical insurance,representing an increase of approximately 44 percentage points from 31.19%in 2012.Conclusions:The implementation of the urban medical group in Dapeng New District has led to substantial improvements in healthcare accessibility,safety and quality,and affordability.Future initiatives will focus on advancing the“Dapeng Mode”to generate exemplary healthcare outcomes and minimize disparities in basic health services and health status between urban and rural populations.The reform agenda includes piloting payment reforms and innovative payment models within the Dapeng group,complemented by a health assessment and performance incentive system aimed at encouraging healthcare institutions to prioritize health management.展开更多
This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stabl...This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stable configuration is essential for the continuous observation of gravitational waves(GWs).However,the motion near the collinear libration points is highly unstable.This problem is examined by output regulation theory.Using the tracking aspect,the equilateral triangular array formation is established in two periods and the fuel consumption is calculated.Furthermore,the natural evolution of the formation without control input is analyzed,and the effective stability duration is quantified to determine the timing of control interventions.Finally,to observe the GWs in same direction with different frequency bands,scale reconfiguration is employed.展开更多
Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are...Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.展开更多
This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and t...This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and the von Mises and two-surface yield criteria,a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates,and the C^(1)nodal NEM is adopted for discretization.Additionally,König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex.A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration.Kinematic shakedown load factors are directly calculated in a monotonically converging manner.Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.展开更多
BACKGROUND Extragastric lesions are typically not misdiagnosed as gastric submucosal tumor(SMT).However,we encountered two rare cases where extrinsic lesions were misdiagnosed as gastric SMTs.CASE SUMMARY We describe ...BACKGROUND Extragastric lesions are typically not misdiagnosed as gastric submucosal tumor(SMT).However,we encountered two rare cases where extrinsic lesions were misdiagnosed as gastric SMTs.CASE SUMMARY We describe two cases of gastric SMT-like protrusions initially misdiagnosed as gastric SMTs by the abdominal contrast-enhanced computed tomography(CT)and endoscopic ultrasound(EUS).Based on the CT and EUS findings,the patients underwent gastroscopy;however,no tumor was identified after incising the gastric wall.Subsequent surgical exploration revealed no gastric lesions in both patients,but a mass was found in the left triangular ligament of the liver.The patients underwent laparoscopic tumor resection,and the postoperative diagnosis was hepatic hemangiomas.CONCLUSION During EUS procedures,scanning across different layers and at varying degrees of gastric cavity distension,coupled with meticulous image analysis,has the potential to mitigate the likelihood of such misdiagnoses.展开更多
After the discovery of the ARECh_(2)(A=alkali or monovalent ions,RE=rare-earth,Ch=chalcogen)triangular lattice quantum spin liquid(QSL)family,a series of its oxide,sulfide,and selenide counterparts has been consistent...After the discovery of the ARECh_(2)(A=alkali or monovalent ions,RE=rare-earth,Ch=chalcogen)triangular lattice quantum spin liquid(QSL)family,a series of its oxide,sulfide,and selenide counterparts has been consistently reported and extensively investigated.While KErTe_(2) represents the initial synthesized telluride member,preserving its triangular spin lattice,it was anticipated that the substantial tellurium ions could impart more pronounced magnetic attributes and electronic structures to this material class.This study delves into the magnetism of KErTe_(2) at finite temperatures through magnetization and electron spin resonance(ESR)measurements.Based on the angular momentum J after spin-orbit coupling(SOC)and symmetry analysis,we obtain the magnetic effective Hamiltonian to describe the magnetism of Er^(3+)in R3m space group.Applying the mean-field approximation to the Hamiltonian,we can simulate the magnetization and magnetic heat capacity of KErTe_(2) in paramagnetic state and determine the crystalline electric field(CEF)parameters and partial exchange interactions.The relatively narrow energy gaps between the CEF ground state and excited states exert a significant influence on the magnetism.For example,small CEF excitations can result in a significant broadening of the ESR linewidth at 2 K.For the fitted exchange interactions,although the values are small,given a large angular momentum J=15/2 after SOC,they still have a noticeable effect at finite temperatures.Notably,the heat capacity data under different magnetic fields along the𝑐axis direction also roughly match our calculated results,further validating the reliability of our analytical approach.These derived parameters serve as crucial tools for future investigations into the ground state magnetism of KErTe_(2).The findings presented herein lay a foundation for exploration of the intricate magnetism within the triangular-lattice delafossite family.展开更多
As a typical two-dimensional frustrated quantum magnet,the triangular-lattice antiferromagnet exhibits a series of exotic states from the complicated interplay of the lattice,spin,electron,and orbit with quantum and t...As a typical two-dimensional frustrated quantum magnet,the triangular-lattice antiferromagnet exhibits a series of exotic states from the complicated interplay of the lattice,spin,electron,and orbit with quantum and thermal fluctuations.From the ground state of a triangular-lattice Heisenberg antiferromagnet with coplanar 120o ordering,a series of magnetization anomalies can manifest under a magnetic field,such as the 1/3 magnetization plateau(Ms/3)and umbrella-shaped phase.This Ms/3 plateau state is recognized as an up-up-down structure stabilized by the quantum effect.By surveying theoretical research and experimental measurements on triangularlattice antiferromagnets,this review article describes the current understanding of the magnetic properties of triple-perovskite antiferromagnets A_(3)MB_(2)O_(9)(A=Ba,Ca,and Sr;M=Co,Ni,and Mn;B=Sb,Nb).Through examining both the bulk properties and spin dynamics,fascinating insights into the quantum effect on the triangular lattice are discussed.展开更多
We demonstrate the flexible tunability of excitation transport in Rydberg atoms,under the interplay of controlled dissipation and interaction-induced synthetic flux.Considering a minimum four-site setup,i.e.,a triangu...We demonstrate the flexible tunability of excitation transport in Rydberg atoms,under the interplay of controlled dissipation and interaction-induced synthetic flux.Considering a minimum four-site setup,i.e.,a triangular configuration with an additional output site,we study the transport of a single excitation.展开更多
Heat in solids can be transported by various quasiparticles, making low-temperature heat transport a powerfultool for probing charge-neutral excitations in quantum materials. In recent years, ultralow-temperature heat...Heat in solids can be transported by various quasiparticles, making low-temperature heat transport a powerfultool for probing charge-neutral excitations in quantum materials. In recent years, ultralow-temperature heattransport has been instrumental in detecting exotic excitations in quantum spin liquids (QSLs). A non-zeroresidual thermal conductivity, κ0/T, serves as compelling evidence for the presence of itinerant spinons andthe gapless nature of a disordered state. Additionally, the thermal Hall effect (THE) in QSLs can arise fromcontributions by spinons or Majorana fermions. In this review, we summarize key thermal conductivity findingsfrom various QSL candidates, focusing on the role of spinons in both heat transport and phonon scattering.We also examine different experimental observations and the underlying mechanisms of THE in QSL candidateswith three-dimensional pyrochlore structures, as well as two-dimensional honeycomb and triangular lattices. Thisreview offers valuable insights and guidance for understanding ultralow-temperature heat transport in QSLs.展开更多
In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state pr...In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.32473216)Ningbo Youth Science and Technology Innovation Leading Talent Project(Grant No.2023QL004)。
文摘Vibration detection using sensors with both wide working frequency range,good sensitivity,and other good performances is a topic of great interest in fields such as inertial navigation,deep-sea fishing boat engines condition monitoring,seismic monitoring,attitude,and heading reference system,etc.This paper investigates two 6H-SIC MEMS diaphragms,one triangular and the other square,used in a fiber optic Fabry–Perot(FP)accelerometer in an experimental scenario.The triangular chip shows a wide working frequency range of 630 Hz–5300 Hz,a natural frequency of 44.3 k Hz,and a mechanical sensitivity of 0.154 nm/g.An optimal structure of the square chip used in a probe such as a fiber optic FP accelerometer also shows a wide working frequency range of 120 Hz–2300 Hz;a good sensitivity of 31.5 m V/g,a resonance frequency of7873 Hz,an accuracy of 0.96%F.S.,a frequency measurement error of 1.15%,and an excellent linearity of 0.9995.
文摘This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems.The controller parameters were tuned using the Integral Time Absolute Error(ITAE)objective function,which was also evaluated alongside other objective functions(IAE,ISE,and ITSE)to ensure high precision in frequency stabilization.To validate the effectiveness of the triangular membership function,comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions.Performance metrics,including ITAE,settling time,overshoot,and undershoot of frequency deviation,as well as tie-line power deviation,were evaluated.Robustness was established through a comprehensive sensitivity analysis with T_(G),T_(T),andT_(R) parameter variations(±50%),a non-linearity analysis incorporating Generation Rate Constraint(GRC)and Governor Deadband(GDB),a random Step Load Perturbation(SLP)over 0–100 s,and also Stability analysis of the proposed scheme is conducted using multiple approaches,including frequency-domain analysis,Lyapunov stability theory,and eigenvalue analysis.Additionally,the system incorporating thermal,hydro,and gas turbines,along with advanced components like CES and HVDC links,was analysed.Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm(MGOA),Honey Badger Algorithm(HBA),Particle Swarm Optimization(PSO),Artificial Bee Colony(ABC),and Spider Monkey Optimization(SMO)algorithms.Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives,exhibiting superior performance across all evaluated metrics.This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.
基金Funded by the Key Research and Development Plan of Jiangxi Province (No. 20223BBG74002)the Natural Science Foundation of China (Nos. 51778483, 51978521)the Fundamental Research Funds for the Central Universities (No. DUT24RC (3)100)。
文摘We optimized the gradation of cold recycled mixture(CRM)based on low-temperature performance.Firstly,the low-temperature crack resistance of CRM with different gradation and emulsified asphalt content was studied by indirect tension(IDT)and semi-circular bending(SCB)test.Thereafter,the low-temperature performance evaluation index suitable for CRM was put forward.Then,the triangular coordinate statistical chart was used to analyze the optimal proportion of three grades of aggregate which are 2.36-4.75 mm,0.075-2.36 mm and below 0.075 mm.The results showed that the W_(f) and G_(f) could distinguish the low-temperature performance of CRM with different mixtures and emulsified asphalt dosage.For cold recycled fine aggregate,2.36-4.75 mm,0.075-2.36 mm and less than 0.075 mm account for 20%-25%,74.3%-80%and 5%-8%,respectively.The CRM with lower void fraction,higher W_(f) and G_(f) could be obtained.Based on the reported findings,it was suggested that the sieve passing percentage of 4.75,2.36,and 0.075 mm of CRM is 45%-55%,27%-52%and 1.5%-5%,respectively.
基金Project(52204164)supported by the National Natural Science Foundation of ChinaProject(2021QNRC001)supported by the Young Elite Scientists Sponsorship Program by CAST,China。
文摘The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying traditional maximum equivalent span beam(MESB)theory to determine deformation range,peak point,and angle influence poses a challenge.Considering the overall structure of the intersection roof,the maximum equivalent triangular plate(METP)theory is proposed,and its geometric parameter calculation formula and deflection calculation formula are obtained.The application of the two theories in 18 models with different intersection angles,roadway types,and surrounding rock lithology is verified by numerical analysis.The results show that:1)The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone;2)The area comparison method of the METP theory can be reasonably explained:①The roof subsidence of the intersection decreases with the increase of the intersection angle;②The roof subsidence at the intersection of different roadway types has a rectangular type>arch type>circular type;③The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock.According to the application results of the two theories,the four advantages of the METP theory are compared and clarified in the basic assumptions,mechanical models,main viewpoints,and mechanism analysis.The large deformation inducement of the intersection roof is then explored.The J 2 peak area of the roof drives the large deformation of the area,the peak point of which is consistent with the center of gravity position of the METP.Furthermore,the change in the range of this peak is consistent with the change law of the METP’s area.Hence,this theory clarifies the large deformation area of the intersection roof,which provides a clear guiding basis for its initial support design,mid-term monitoring,and late local reinforcement.
基金supported by the Key-Area Research and Development Program of Guangdong Province(2023B0303030002)the Beijing Natural Science Foundation(IS23114,7242274)+4 种基金the China Postdoctoral Science Foundation(2023TQ0027 and 2024M754099)the STI 2030-Major Projects(2022ZD0208500)the National Natural Science Foundation of China(62336002,82071912,62406025,82202291,62373056,62306035)the Beijing Nova Program(20230484465)the Shenzhen Basic Research Program(JCYJ20241202124804007).
文摘Working memory is an executive memory process that includes encoding,maintenance,and retrieval.These processes can be modulated by transcranial alternating current stimulation(tACS)with sinusoidal waves.However,little is known about the impact of the rate of current change on working memory.In this study,we aimed to investigate the effects of two types of tACS with different rates of current change on working memory performance and brain activity.We applied a randomized,single-blind design and divided 81 young participants who received triangular wave tACS,sinusoidal wave tACS,or sham stimulation into three groups.Participants performed n-back tasks,and electroencephalograms were recorded before,during,and after active or sham stimulation.Compared to the baseline,working memory performance(accuracy and response time)improved after stimulation under all stimulation conditions.According to drift-diffusion model analysis,triangular wave tACS significantly increased the efficiency of non-target information processing.In addition,compared with sham conditions,triangular wave tACS reduced alpha power oscillations in the occipital lobe throughout the encoding period,while sinusoidal wave tACS increased theta power in the central frontal region only during the later encoding period.The brain network connectivity results showed that triangular wave tACS improved the clustering coefficient,local efficiency,and node degree intensity in the early encoding stage,and these parameters were positively correlated with the non-target drift rate and decision starting point.Our findings on how tACS modulates working memory indicate that triangular wave tACS significantly enhances brain network connectivity during the early encoding stage,demonstrating an improvement in the efficiency of working memory processing.In contrast,sinusoidal wave tACS increased the theta power during the later encoding stage,suggesting its potential critical role in late-stage information processing.These findings provide valuable insights into the potential mechanisms by which tACS modulates working memory.
文摘Objective:To explore the clinical effect of improved incision in the extraction of impacted mandibular wisdom teeth.Methods:160 patients who were treated in our hospital from October,2024 to April,2025 and had their mandibular impacted wisdom teeth removed according to the doctor’s advice were randomly divided into observation group and control group.The observation group used modified incision,while the control group used traditional triangular incision.The operation time,intraoperative visual analogue scale(VAS)pain score,pain VAS score on the 1st,2nd and 3rd day after operation,facial swelling on the 2nd day after operation,mouth opening limitation on the 2nd day after operation and the incidence of dry socket after operation were recorded and compared between the two groups.Results:There was no significant difference in operation time between the two groups(p>0.05).The VAS score of pain in the observation group was significantly lower than that in the control group at each time point during and after operation(p<0.05).On the second day after operation,the facial swelling and mouth opening limitation in the observation group were significantly lighter than those in the control group(p<0.05).The incidence of dry socket in the observation group was 1.25%(1/80),which was significantly lower than that in the control group(8.75%,7/80),and the difference was statistically significant(p<0.05).Conclusion:The application of modified triangular incision in the extraction of impacted mandibular wisdom teeth can effectively relieve the pain during and after operation,reduce postoperative facial swelling and mouth opening limitation,and reduce the incidence of dry socket.
文摘Software defect prediction(SDP)aims to find a reliable method to predict defects in specific software projects and help software engineers allocate limited resources to release high-quality software products.Software defect prediction can be effectively performed using traditional features,but there are some redundant or irrelevant features in them(the presence or absence of this feature has little effect on the prediction results).These problems can be solved using feature selection.However,existing feature selection methods have shortcomings such as insignificant dimensionality reduction effect and low classification accuracy of the selected optimal feature subset.In order to reduce the impact of these shortcomings,this paper proposes a new feature selection method Cubic TraverseMa Beluga whale optimization algorithm(CTMBWO)based on the improved Beluga whale optimization algorithm(BWO).The goal of this study is to determine how well the CTMBWO can extract the features that are most important for correctly predicting software defects,improve the accuracy of fault prediction,reduce the number of the selected feature and mitigate the risk of overfitting,thereby achieving more efficient resource utilization and better distribution of test workload.The CTMBWO comprises three main stages:preprocessing the dataset,selecting relevant features,and evaluating the classification performance of the model.The novel feature selection method can effectively improve the performance of SDP.This study performs experiments on two software defect datasets(PROMISE,NASA)and shows the method’s classification performance using four detailed evaluation metrics,Accuracy,F1-score,MCC,AUC and Recall.The results indicate that the approach presented in this paper achieves outstanding classification performance on both datasets and has significant improvement over the baseline models.
基金supported by the National Key R&D Program of China(Grant No.2022YFC3003601)Joint Funds of the National Natural Science Foundation of China Project on Earthquake Science(Grant No.U2239252)the program of the Innovative Research Team in China Earthquake Administration.
文摘Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.
文摘Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.
基金Supported by Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].
文摘Background:An urban medical group in Dapeng New District was established in 2017 with the objective of enhancing outcomes for common diseases and reinforcing primary care by integrating high‐level hospitals with primary health services.This study aimed to evaluate the performance of the urban medical group using the triangular value chain framework.Methods:The evaluation was conducted using the Donabedian model,focusing on three key dimensions:safety and quality,accessibility,and affordability.Longitudinal data were collected from 2016 to 2022 through government annual reports,the medical insurance bureau,and hospital information systems.Preprogram and postprogram outcome measurements were compared to assess differences and trends,providing a clear picture of the program's effectiveness.Results:Accessibility improved significantly,with the number of hospital beds per 1000 residents increasing from 2.62 in 2017 to 3.76 in 2022.The availability of general practitioners(GPs)also rose markedly,from 0 per 10,000 residents in 2017 to 6.27 in 2022.Regarding safety and quality,the proportion of complex medical procedures conducted within the New District expanded substantially,from 7.35%in 2017 to 38.11%in 2021.Additionally,there was an enhancement in the standardized management rate of chronic diseases.Affordability assessments showed that the proportion of medical income derived from the medical insurance fund increased by nearly 22.81 percentage points between 2012 and 2021.By 2021,75.02%of medical patients were covered by medical insurance,representing an increase of approximately 44 percentage points from 31.19%in 2012.Conclusions:The implementation of the urban medical group in Dapeng New District has led to substantial improvements in healthcare accessibility,safety and quality,and affordability.Future initiatives will focus on advancing the“Dapeng Mode”to generate exemplary healthcare outcomes and minimize disparities in basic health services and health status between urban and rural populations.The reform agenda includes piloting payment reforms and innovative payment models within the Dapeng group,complemented by a health assessment and performance incentive system aimed at encouraging healthcare institutions to prioritize health management.
基金supported by the China Scholarship Council(CSC)(No.202206290131)。
文摘This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stable configuration is essential for the continuous observation of gravitational waves(GWs).However,the motion near the collinear libration points is highly unstable.This problem is examined by output regulation theory.Using the tracking aspect,the equilateral triangular array formation is established in two periods and the fuel consumption is calculated.Furthermore,the natural evolution of the formation without control input is analyzed,and the effective stability duration is quantified to determine the timing of control interventions.Finally,to observe the GWs in same direction with different frequency bands,scale reconfiguration is employed.
基金Supported by the National Natural Science Foundation of China(Grant No.12301041)the Science Foundation for Distinguished Young Scholars of Anhui Province(Grant No.2108085J01)。
文摘Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.
基金supported by the Chinese Postdoctoral Science Foundation(2013M540934).
文摘This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and the von Mises and two-surface yield criteria,a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates,and the C^(1)nodal NEM is adopted for discretization.Additionally,König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex.A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration.Kinematic shakedown load factors are directly calculated in a monotonically converging manner.Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.
基金Supported by the Natural Science Foundation of Zhejiang Province,No.LQ20H030007 and No.LY20H030010the Zhejiang Medical Health Technology Project,No.2019KY393.
文摘BACKGROUND Extragastric lesions are typically not misdiagnosed as gastric submucosal tumor(SMT).However,we encountered two rare cases where extrinsic lesions were misdiagnosed as gastric SMTs.CASE SUMMARY We describe two cases of gastric SMT-like protrusions initially misdiagnosed as gastric SMTs by the abdominal contrast-enhanced computed tomography(CT)and endoscopic ultrasound(EUS).Based on the CT and EUS findings,the patients underwent gastroscopy;however,no tumor was identified after incising the gastric wall.Subsequent surgical exploration revealed no gastric lesions in both patients,but a mass was found in the left triangular ligament of the liver.The patients underwent laparoscopic tumor resection,and the postoperative diagnosis was hepatic hemangiomas.CONCLUSION During EUS procedures,scanning across different layers and at varying degrees of gastric cavity distension,coupled with meticulous image analysis,has the potential to mitigate the likelihood of such misdiagnoses.
基金supported by the National Science Foundation of China(Grant Nos.U1932215 and 12274186)the National Key Research and Development Program of China(Grant No.2022YFA1402704)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB33010100)the Synergetic Extreme Condition User Facility(SECUF)。
文摘After the discovery of the ARECh_(2)(A=alkali or monovalent ions,RE=rare-earth,Ch=chalcogen)triangular lattice quantum spin liquid(QSL)family,a series of its oxide,sulfide,and selenide counterparts has been consistently reported and extensively investigated.While KErTe_(2) represents the initial synthesized telluride member,preserving its triangular spin lattice,it was anticipated that the substantial tellurium ions could impart more pronounced magnetic attributes and electronic structures to this material class.This study delves into the magnetism of KErTe_(2) at finite temperatures through magnetization and electron spin resonance(ESR)measurements.Based on the angular momentum J after spin-orbit coupling(SOC)and symmetry analysis,we obtain the magnetic effective Hamiltonian to describe the magnetism of Er^(3+)in R3m space group.Applying the mean-field approximation to the Hamiltonian,we can simulate the magnetization and magnetic heat capacity of KErTe_(2) in paramagnetic state and determine the crystalline electric field(CEF)parameters and partial exchange interactions.The relatively narrow energy gaps between the CEF ground state and excited states exert a significant influence on the magnetism.For example,small CEF excitations can result in a significant broadening of the ESR linewidth at 2 K.For the fitted exchange interactions,although the values are small,given a large angular momentum J=15/2 after SOC,they still have a noticeable effect at finite temperatures.Notably,the heat capacity data under different magnetic fields along the𝑐axis direction also roughly match our calculated results,further validating the reliability of our analytical approach.These derived parameters serve as crucial tools for future investigations into the ground state magnetism of KErTe_(2).The findings presented herein lay a foundation for exploration of the intricate magnetism within the triangular-lattice delafossite family.
文摘As a typical two-dimensional frustrated quantum magnet,the triangular-lattice antiferromagnet exhibits a series of exotic states from the complicated interplay of the lattice,spin,electron,and orbit with quantum and thermal fluctuations.From the ground state of a triangular-lattice Heisenberg antiferromagnet with coplanar 120o ordering,a series of magnetization anomalies can manifest under a magnetic field,such as the 1/3 magnetization plateau(Ms/3)and umbrella-shaped phase.This Ms/3 plateau state is recognized as an up-up-down structure stabilized by the quantum effect.By surveying theoretical research and experimental measurements on triangularlattice antiferromagnets,this review article describes the current understanding of the magnetic properties of triple-perovskite antiferromagnets A_(3)MB_(2)O_(9)(A=Ba,Ca,and Sr;M=Co,Ni,and Mn;B=Sb,Nb).Through examining both the bulk properties and spin dynamics,fascinating insights into the quantum effect on the triangular lattice are discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.11974331 and 12374479)。
文摘We demonstrate the flexible tunability of excitation transport in Rydberg atoms,under the interplay of controlled dissipation and interaction-induced synthetic flux.Considering a minimum four-site setup,i.e.,a triangular configuration with an additional output site,we study the transport of a single excitation.
文摘Heat in solids can be transported by various quasiparticles, making low-temperature heat transport a powerfultool for probing charge-neutral excitations in quantum materials. In recent years, ultralow-temperature heattransport has been instrumental in detecting exotic excitations in quantum spin liquids (QSLs). A non-zeroresidual thermal conductivity, κ0/T, serves as compelling evidence for the presence of itinerant spinons andthe gapless nature of a disordered state. Additionally, the thermal Hall effect (THE) in QSLs can arise fromcontributions by spinons or Majorana fermions. In this review, we summarize key thermal conductivity findingsfrom various QSL candidates, focusing on the role of spinons in both heat transport and phonon scattering.We also examine different experimental observations and the underlying mechanisms of THE in QSL candidateswith three-dimensional pyrochlore structures, as well as two-dimensional honeycomb and triangular lattices. Thisreview offers valuable insights and guidance for understanding ultralow-temperature heat transport in QSLs.
基金supported by the NSFC Grant No.11872210 and Grant No.MCMS-I-0120G01Chi-Wang Shu:Research is supported by the AFOSR Grant FA9550-20-1-0055 and the NSF Grant DMS-2010107Jianxian Qiu:Research is supported by the NSFC Grant No.12071392.
文摘In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.
