Simulation-Transactions of the Society for Modeling and Simulation International最新文献_第7页

Electromagnetic wave forward modeling of coal-gangue mixed model in top coal caving mining face 放顶煤矸石混合模型的电磁波正演模拟

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-12-01 DOI: 10.1177/00375497221105290

Lei Si, Feng Xing, Zhongbin Wang, Chao Tan

{"title":"Electromagnetic wave forward modeling of coal-gangue mixed model in top coal caving mining face","authors":"Lei Si, Feng Xing, Zhongbin Wang, Chao Tan","doi":"10.1177/00375497221105290","DOIUrl":"https://doi.org/10.1177/00375497221105290","url":null,"abstract":"The automatic control of top coal caving is of great significance to realize intelligent coal mining. In the process of top coal caving, a coal-gangue mixed area containing coal, gangue, and air is formed at the tail beam of the hydraulic support, which has different electromagnetic parameters, different volumes, and different shapes. To explore the transmission characteristics of electromagnetic wave in coal-gangue mixed model and the influence of different gangue ratios on electromagnetic wave propagation, the coal-gangue mixed model is established based on the random medium theory. Some electromagnetic forward modeling is carried out with different coal-gangue granularities, electromagnetic parameters, and gangue ratios based on finite-difference time-domain (FDTD) and finite-integration time-domain (FITD) methods. The results show that different granularities of coal and gangue will affect the amplitude of electromagnetic wave time-domain waveform. Under the same particle size, the equivalent electromagnetic parameters in the coal-gangue mixed medium will be larger with higher gangue ratio. Furthermore, the difference of transmitted wave signals between different gangue ratios will be larger with higher electromagnetic parameters difference of the coal and gangue. For higher refractive index, the propagation velocity of electromagnetic wave in the medium and the transmitted wave amplitude will be smaller. In addition, the comparison results illustrate that the rules of electromagnetic wave propagation obtained by FDTD and FITD methods are basically the same, which verifies the correctness of the simulations in this paper. The simulation results can lay a theoretical foundation for identifying the coal-gangue mixed degree in the process of top coal caving.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"25 1","pages":"1127 - 1142"},"PeriodicalIF":1.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78657405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Simulation study on the influence of wheel irregularity on the vertical dynamics of wheel–rail interaction for high-speed railway track using bond graph 基于键合图的高速铁路车轮不平顺度对轮轨相互作用垂直动力学影响的仿真研究

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-12-01 DOI: 10.1177/00375497221138943

Yamika Patel, V. Rastogi, W. Borutzky

{"title":"Simulation study on the influence of wheel irregularity on the vertical dynamics of wheel–rail interaction for high-speed railway track using bond graph","authors":"Yamika Patel, V. Rastogi, W. Borutzky","doi":"10.1177/00375497221138943","DOIUrl":"https://doi.org/10.1177/00375497221138943","url":null,"abstract":"Dynamic interaction between train wheel and high-speed slab is an important issue when evaluating the contact force at the wheel–rail interface under the influence of an irregularity either on the train wheel or on the rail. In this paper, an influence of amplitude of irregularity along with the vehicle speed on the dynamics of wheel–rail interaction for high-speed railway tracks is being analyzed. For this purpose, single-wheel high-speed railway (HSR) track interaction models are developed using the bond graph modeling technique. The HSR track model consists of two layers of beam, i.e., rail and concrete slab. Both the rail and slab track is modeled using the Euler–Bernoulli beam theory. The Hertzian contact theory at the wheel–rail interface has been considered for this analysis. The vertical dynamic interaction between a train wheel and a high-speed slab track is compiled in the time domain using a bond graph approach coupled with a technique known as modal superposition. Irregularity present on the wheel is characterized as smooth, moderate, and severe depending upon the variation of irregularity amplitude. An expeditious increase of maximum contact force has been observed between the speed range of 200 and 250 km/h. Beyond the speed of 250 km/h, there is a gradual increment of contact force up to its peak value. When the train speed is beyond 288 km/h, there is a gradual decrease in maximum contact force. This kind of several other useful dynamic responses in terms of wheel acceleration and wheel–rail overlap are also evaluated.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"1 1","pages":"643 - 656"},"PeriodicalIF":1.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90695804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Multi-Objective Patient Appointment Scheduling Framework (MO-PASS): a data-table input simulation–optimization approach 多目标患者预约调度框架(MO-PASS):一种数据表输入模拟优化方法

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-28 DOI: 10.1177/00375497221132574

Mohammad Dehghanimohammadabadi, Mandana Rezaeiahari, Javad Seif

{"title":"Multi-Objective Patient Appointment Scheduling Framework (MO-PASS): a data-table input simulation–optimization approach","authors":"Mohammad Dehghanimohammadabadi, Mandana Rezaeiahari, Javad Seif","doi":"10.1177/00375497221132574","DOIUrl":"https://doi.org/10.1177/00375497221132574","url":null,"abstract":"Appointment scheduling is one of the critical factors for improving patient satisfaction with healthcare services. A practical and robust appointment scheduling solution allows clinics to efficiently utilize medical devices, equipment, and other resources. This study introduces a Multi-Objective Patient Appointment Scheduling (MO-PASS) framework to enhance clinic operations and quality of care. The proposed framework integrates three modules: (1) Optimization (using MATLAB), (2) Data-Exchange (MS Excel), and (3) Simulation (Simio). To implement MO-PASS, the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is coded in MATLAB, and a Simio API is developed, which exchanges simulated scenarios with MOPSO via Excel. The efficiency of the proposed framework is evaluated in a breast cancer clinic with multiple physicians and patient types. Two objective functions are defined for evaluating the solutions of the AS problem: (1) minimizing the total service time and (2) maximizing the number of (admitted) patients with zero overtime. Finally, the performance of MO-PASS is tested against three heuristic approaches with respect to objective functions. The computational experiment results show that the proposed MO-PASS outperforms the existing heuristic benchmarks. Also, the framework is accompanied by all the necessary details to make it practical and easy to implement.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"22 1","pages":"363 - 383"},"PeriodicalIF":1.6,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84674956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Combination of anti-PD-L1 and radiotherapy in hepatocellular carcinoma: a mathematical model with uncertain parameters 抗pd - l1联合放疗治疗肝癌:一个参数不确定的数学模型

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-19 DOI: 10.1177/00375497221133846

Sajad Shafiekhani, N. Gheibi, Azam Janati Esfahani

{"title":"Combination of anti-PD-L1 and radiotherapy in hepatocellular carcinoma: a mathematical model with uncertain parameters","authors":"Sajad Shafiekhani, N. Gheibi, Azam Janati Esfahani","doi":"10.1177/00375497221133846","DOIUrl":"https://doi.org/10.1177/00375497221133846","url":null,"abstract":"Blockade of programmed death-ligand-1 (PD-L1) as a new method of immunotherapy for cancers has shown limited efficacy in hepatocellular carcinoma (HCC). The combination of anti-PD-L1 and radiotherapy (RT) enhances the antitumor effect in HCC cancer. The efficacy and interactions of these treatments can be addressed by a mathematical model. We developed a mathematical model using a set of ordinary differential equations (ODEs). The variables include cancer cells, cytotoxic T lymphocytes (CTLs), programmed cell death-1 (PD-1), PD-L1, anti-PD-L1, and ionizing radiation. The model is parameterized with imprecise data set of murine HCC model and the effect of parametric uncertainty is assessed by the fuzzy theorem. The global sensitivity analysis (GSA) is performed to assess model robustness against perturbation in parameters and to identify the most influential parameters on the dynamics of cells and proteins. In silico predictions are consistent with experimental data. The model simulation shows that anti-PD-L1 and RT have a synergistic effect. In silico assessment of treatments’ efficacy in the fuzzy setting of parameters revealed that anti-PD-L1 therapy, RT, and combination treatment caused the uncertainty band of tumor cells to lead to lower populations. This model as a validated rigorous simulation framework can be used to deepen our understanding of tumor and immune cell interactions and helps clinicians to investigate the efficacy of different time schedules of anti-PD-L1, RT, and combination therapy. The fuzzy theorem in conjunction with the classical ODE model that is parameterized by imprecise data was used to predict reliable outcomes of treatment.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"15 1","pages":"313 - 325"},"PeriodicalIF":1.6,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75277596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Race conditions and data partitioning: risks posed by common errors to reproducible parallel simulations 竞争条件和数据分区:常见错误给可重复并行模拟带来的风险

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-19 DOI: 10.1177/00375497221132566

J. Nutaro, Ozgur Ozmen

{"title":"Race conditions and data partitioning: risks posed by common errors to reproducible parallel simulations","authors":"J. Nutaro, Ozgur Ozmen","doi":"10.1177/00375497221132566","DOIUrl":"https://doi.org/10.1177/00375497221132566","url":null,"abstract":"When parallel algorithms for simulation were introduced in the 1970s, their development and use interested only experts in parallel computation. This circumstance changed as multi-core processors became commonplace, putting a parallel computer into the hands of every modeler. A natural outcome is growing interest in parallel simulation among persons not intimately familiar with parallel computing. At the same time, parallel simulation tools continue to be developed with the implicit assumption that the modeler is knowledgeable about parallel programming. The unintended consequence is a rapidly growing number of users of parallel simulation tools that are unlikely to recognize when the interaction of race conditions, partitioning strategies, and simultaneous action in their simulation models make results non-reproducible, thereby calling into question the validity of conclusions drawn from the simulation data. We illustrate the potential dangers of exposing parallel algorithms to users who are not experts in parallel computation with example models constructed using existing parallel simulation tools. By doing so, we hope to refocus tool developers on usability, even if this new focus incurs loss of some performance.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"63 1","pages":"417 - 427"},"PeriodicalIF":1.6,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83843025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Modeling and interactive simulation of measures against infection transmission 预防感染传播措施的建模和交互模拟

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-19 DOI: 10.1177/00375497221133849

M. Abadeer, Sameh Magharious, S. Gorlatch

{"title":"Modeling and interactive simulation of measures against infection transmission","authors":"M. Abadeer, Sameh Magharious, S. Gorlatch","doi":"10.1177/00375497221133849","DOIUrl":"https://doi.org/10.1177/00375497221133849","url":null,"abstract":"In this paper we develop an approach to modeling and simulating the process of infection transmission among individuals and the effectiveness of protective counter-measures. We base our approach on pedestrian dynamics and we implement it as an extension of the Vadere simulation framework. In order to enable a convenient simulation process for a variety of scenarios, we allow the user to interact with the simulated virtual environment (VE) during run time, for example, by dynamically opening/closing doors for room ventilation and moving/stopping agents for re-positioning their locations. We calibrate and evaluate our approach on a real-life case study—simulating COVID-19 infection transmission in two kinds of scenarios: large-scale (such as the city of Münster, Germany) and small-scale (such as the most common indoor environments—classrooms, restaurants, etc.). By using the tunable parameters of our modeling approach, we can simulate and predict the effectiveness of specific anti-COVID protective measures, such as social distancing, wearing masks, self-isolation, schools closing, etc.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"10 1","pages":"327 - 346"},"PeriodicalIF":1.6,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78574026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

HLA-based time management and synchronization framework for lean manufacturing tools evaluation 基于hla的时间管理和同步框架的精益制造工具评价

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-19 DOI: 10.1177/00375497221132577

J. Possik, G. Zacharewicz, Anne Zouggar, B. Vallespir

引用次数: 2

In silico analysis of optimum photon energy spectra and beam parameters for iodine nanoparticle–aided orthovoltage radiation therapy of brain tumors 碘纳米粒子辅助正电压放射治疗脑肿瘤的最佳光子能谱和光束参数的硅分析

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-18 DOI: 10.1177/00375497221135630

A. Mesbahi, Maryam Sadeghian, Aisan Mesbahi, H. Smilowitz, J. Hainfeld

{"title":"In silico analysis of optimum photon energy spectra and beam parameters for iodine nanoparticle–aided orthovoltage radiation therapy of brain tumors","authors":"A. Mesbahi, Maryam Sadeghian, Aisan Mesbahi, H. Smilowitz, J. Hainfeld","doi":"10.1177/00375497221135630","DOIUrl":"https://doi.org/10.1177/00375497221135630","url":null,"abstract":"In this study, the effect of photon energy spectra on the dose enhancement factor (DEF) and other influencing parameters such as skull–tumor dose ratios were estimated for a confined tumor loaded with iodine nanoparticles (INPs). A mathematical brain phantom with a brain tumor was simulated by the MCNP6 Monte Carlo code. A validated commercial computed tomography model consisting of an X-ray tube, Al–Cu filters, and collimators was used to simulate the rotational conformal treatment of the tumor. INPs with a diameter of 20 nm and concentrations of 10–50 mg/g were introduced inside the tumor as homogenously distributed spherical particles. The dose distribution inside the phantom was scored for several orthovoltage beams with the peak voltages of 140, 200, and 320 kVp as well as two 3.5 and 6 MV megavoltage beams. A significant rise of DEF values with nanoparticle (NP) concentration for orthovoltage beams is revealed; no significant dose enhancement was obtained for megavoltage beams. The highest DEF and skull–tumor dose ratio were obtained for the 140 kVp beam which decreased with the number of directional fields. The clinically optimal plan for a brain tumor, with high DEFs of 2.81–2.24 and acceptable skull–tumor dose ratios of 0.61–0.51, would be feasible for treatment using 200 and 320 kVp beams, an iodine concentration of 20 mg/g, and 8–15 fields. Our calculations show that clinically significant radiation dose enhancements can be obtained for tumors loaded with INPs using orthovoltage beams. Optimal treatment regimens are feasible using a proper selection of photon beam spectrum and sufficient numbers of cross-firing beams. The limiting effect of skull bone could be minimized by increasing the number of radiation fields and the use of higher quality of orthovoltage beams.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"16 1","pages":"539 - 552"},"PeriodicalIF":1.6,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73022248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

TRAILS mobility model TRAILS机动性模型

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-11-14 DOI: 10.1177/00375497221133847

Leonardo Sarmiento, Anna Förster

{"title":"TRAILS mobility model","authors":"Leonardo Sarmiento, Anna Förster","doi":"10.1177/00375497221133847","DOIUrl":"https://doi.org/10.1177/00375497221133847","url":null,"abstract":"According to state-of-the-art research, mobile network simulation is preferred over real testbeds, especially to evaluate communication protocols used in Opportunistic Networks (OppNet) or Mobile Ad hoc NETworks (MANET). The main reason behind it is the difficulty of performing experiments in real scenarios. However, in a simulation, a mobility model is required to define users’ mobility patterns. Trace-based models can be used for this purpose, but they are difficult to obtain, and they are not flexible or scalable. Another option is TRAce-based ProbabILiStic (TRAILS). TRAILS mimics the spatial dependency, geographic restrictions, and temporal dependency from real scenarios. In addition, with TRAILS, it is possible to scale the number of mobile users and simulation time. In this paper, we dive into the algorithms used by TRAILS to generate mobility graphs from real scenarios and simulate human mobility. In addition, we compare mobility metrics of TRAILS simulations, real traces, and another synthetic mobility model such as Small Worlds in Motion (SWIM). Finally, we analyze the performance of an implementation of the TRAILS model in computation time and memory consumption. We observed that TRAILS simulations represent the interaction among users of real scenarios with higher accuracy than SWIM simulations. Furthermore, we found that a simulation with TRAILS requires less computation time than a simulation with real traces and that a TRAILS graph consumes less memory than traces.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"55 1","pages":"385 - 402"},"PeriodicalIF":1.6,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88249661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Simulation of disequilibrium and chaos in aggregates of disposable income, wealth, and consumption in EU macroeconomics using nonlinear dynamic analysis 用非线性动态分析模拟欧盟宏观经济中可支配收入、财富和消费总量的不平衡和混乱

IF 1.6 4区工程技术

Simulation-Transactions of the Society for Modeling and Simulation International Pub Date : 2022-10-29 DOI: 10.1177/00375497221130100

Damir V Sindik, Vladimir Kašćelan, Ljiljana Kašćelan

{"title":"Simulation of disequilibrium and chaos in aggregates of disposable income, wealth, and consumption in EU macroeconomics using nonlinear dynamic analysis","authors":"Damir V Sindik, Vladimir Kašćelan, Ljiljana Kašćelan","doi":"10.1177/00375497221130100","DOIUrl":"https://doi.org/10.1177/00375497221130100","url":null,"abstract":"Economic disequilibrium theory (DT) more realistically represents modern macroeconomic systems than general equilibrium theory. DT coupled with applied mathematical economics and nonlinear dynamical analysis generates multi-dimensional phase spaces. Interdependencies of endogenous variables in state space create a flow of different and “parallel economic realities,” which depend on the initial conditions. By modeling variable changes using the nonlinear least squares (NLLS) method, we define the first-order nonlinear ordinary differential equation (NODE) system. The NODE system is impossible to solve analytically. The numerical solution and visualization requires the MATLAB software package, combined with its specialized applications pplane (two-dimensional (2D)) and MATCONT (three-dimensional (3D)). By analyzing the evolution of flow operators, we can predict the future qualitative behavior of the entire system, determine the model-optimal values, and perform inverse modeling for variables. The obtained data advocate better and more stable macroeconomic paths that economic policymakers can pursue. The proposed methodology’s boundaries have strong links to chaos theory. Chaotic behavior can arise after a certain number of periods. We found very high computation accuracy, transformation of discrete variables to continuous functions, and the implementation of high-order polynomial data fitting offset its effects in part and to some reasonable degree.","PeriodicalId":49516,"journal":{"name":"Simulation-Transactions of the Society for Modeling and Simulation International","volume":"24 1","pages":"137 - 167"},"PeriodicalIF":1.6,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75457839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1