Applied Stochastic Models in Business and Industry最新文献

筛选
英文 中文
The Analysis of Association Rules: Sensitivity Analysis 关联规则分析:敏感性分析
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-06-09 DOI: 10.1002/asmb.70022
Ron S. Kenett, Chris Gotwalt
{"title":"The Analysis of Association Rules: Sensitivity Analysis","authors":"Ron S. Kenett,&nbsp;Chris Gotwalt","doi":"10.1002/asmb.70022","DOIUrl":"https://doi.org/10.1002/asmb.70022","url":null,"abstract":"<div>\u0000 \u0000 <p>Association rules are extracting information from transactional databases of documents with a collection of items also called “tokens” or “words”. The approach is used in the analysis of text records, of social media and of consumer behaviour. We present an innovative sensitivity analysis of association rules (AR) measures of interest. In text analytics, a document term matrix (DTM) consists of rows referring to documents and columns corresponding to items. In binary weights, “1” indicates the presence of a term in a document and “0” otherwise. From a DTM one computes measures of interest characterising ARs. The approach we introduce is based on the application of befitting cross validation (BCV) principles to ARs. The sensitivity analysis of ARs is based on computer generated repeated shuffling of training and validation sets that provide an assessment of the uncertainty of AR measures of interest. We demonstrate this methodology with reports of symptoms associated with a Nicardipine drug product used in the treatment of high blood pressure and angina. Patients self-reports on side effect events are analysed. Association rules, derived from these reports, describe combinations of terms in these reports. AR measures of interest are defined in section 1. In section 2 we introduce the case study that motivates the method we propose. In section 3 we apply BCV principles by concatenating side effect events of Nicardipine by patient. Sensitivity analysis (SA) of ARs is introduced and demonstrated in section 4. The sensitivity analysis method presented here is discussed in section 5 where we formulate general data analysis considerations on how to organise and analyse semantic data.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144244146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Framework to Estimate Return on Investment for Player Salaries in the National Basketball Association 一个估算nba球员工资投资回报的新框架
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-31 DOI: 10.1002/asmb.70020
Jackson P. Lautier
{"title":"A New Framework to Estimate Return on Investment for Player Salaries in the National Basketball Association","authors":"Jackson P. Lautier","doi":"10.1002/asmb.70020","DOIUrl":"https://doi.org/10.1002/asmb.70020","url":null,"abstract":"<div>\u0000 \u0000 <p>An essential component of financial analysis is a comparison of realized returns. These calculations are straightforward when all cash flows have dollar values. Complexities arise if some flows are nonmonetary, however, such as on-court basketball activities. To our knowledge, this problem remains open. We thus present the first known framework to estimate a return on investment for player salaries in the National Basketball Association (NBA). It is a flexible five-part procedure that includes a novel player credit estimator, the Wealth Redistribution Merit Share (WRMS). The WRMS is a per-game wealth redistribution estimator that allocates fractional performance-based credit to players standardized and centered to uniformity. We show it is asymptotically unbiased to the natural share and simultaneously more robust. The per-game approach allows for break-even analysis between high-performing players with frequent missed games and average-performing players with consistent availability. The WRMS may be used to allocate revenue from a single game to each of its players. Using a player's salary as an initial investment, this creates a sequence of cash flows that may be evaluated using traditional financial analysis. We illustrate all methods with empirical estimates from the 2022–2023 NBA regular season. All data and replication code are made available.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144179402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparisons of Coherent Systems' Lifetimes in the Increasing Convex Order 渐增凸序相干系统寿命的比较
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-31 DOI: 10.1002/asmb.70021
Francesco Buono, Franco Pellerey
{"title":"Comparisons of Coherent Systems' Lifetimes in the Increasing Convex Order","authors":"Francesco Buono,&nbsp;Franco Pellerey","doi":"10.1002/asmb.70021","DOIUrl":"https://doi.org/10.1002/asmb.70021","url":null,"abstract":"<p>Stochastic orders have been widely used in reliability literature to compare the performances of coherent systems, and various criteria have been provided on this purpose. In particular, sufficient conditions have been found for the lifetime of a system to be stochastically larger than that of another system having the same components with identically distributed lifetimes but a different structure function. Known results of this kind concern some of the most relevant stochastic orders, but in the literature no conditions have been provided for the well-known increasing convex order (icx). Here we describe conditions such that two lifetimes of coherent systems are comparable in this stochastic sense when conditions for other stronger orders do not apply. Illustrative examples are also given.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.70021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144179403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Modeling and Time-Frequency Analysis for Predictive Maintenance of Automotive Suspension Systems 汽车悬架系统预测性维修的随机建模与时频分析
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-26 DOI: 10.1002/asmb.70013
Livio Fenga, Luca Biazzo
{"title":"Stochastic Modeling and Time-Frequency Analysis for Predictive Maintenance of Automotive Suspension Systems","authors":"Livio Fenga,&nbsp;Luca Biazzo","doi":"10.1002/asmb.70013","DOIUrl":"https://doi.org/10.1002/asmb.70013","url":null,"abstract":"<p>This article presents a real-time predictive maintenance model of vehicle suspensions based on vibration signal analysis. The study is grounded in the observation that suspension wear and failure are primarily driven by cumulative stresses and external shocks encountered during vehicle operation. We use a wavelet-based technique integrated with stochastic modeling and lifetime data analysis to predict the remaining useful life (RUL) of the suspension. The proposed framework provides a decision-making tool for determining whether and when suspension systems should be subjected to inspection, replacement, or overhaul. An empirical application, using vibration data from a uniaxial accelerometer mounted on a vehicle suspension under varying road conditions, validates the theoretical model and estimation procedure.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.70013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Foreword to the Special Issue on Data Science in Business and Industry 商业和工业数据科学特刊前言
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-22 DOI: 10.1002/asmb.70019
David Banks, Alba Martínez-Ruiz, David F. Muñoz, Javier Trejos-Zelaya
{"title":"Foreword to the Special Issue on Data Science in Business and Industry","authors":"David Banks,&nbsp;Alba Martínez-Ruiz,&nbsp;David F. Muñoz,&nbsp;Javier Trejos-Zelaya","doi":"10.1002/asmb.70019","DOIUrl":"https://doi.org/10.1002/asmb.70019","url":null,"abstract":"","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144118040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Feature Selection for Stock Movement Direction Prediction Using Sparse Support Vector Machine 基于稀疏支持向量机的股票运动方向预测特征选择
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-19 DOI: 10.1002/asmb.70011
Maoxuan Miao, Jinran Wu, Fengjing Cai, Liya Fu, Shurong Zheng, You-Gan Wang
{"title":"Feature Selection for Stock Movement Direction Prediction Using Sparse Support Vector Machine","authors":"Maoxuan Miao,&nbsp;Jinran Wu,&nbsp;Fengjing Cai,&nbsp;Liya Fu,&nbsp;Shurong Zheng,&nbsp;You-Gan Wang","doi":"10.1002/asmb.70011","DOIUrl":"https://doi.org/10.1002/asmb.70011","url":null,"abstract":"&lt;p&gt;In financial markets, accurate stock price movement prediction can significantly enhance investors' profits. However, the stock price is a highly complex dynamic system with considerable fluctuations, and the accuracy of direction prediction can be improved by selecting appropriate technical indicators. In this work, we propose a novel sparse support vector machines (SVMs) that combines recursive feature elimination (RFE) and ReliefF using a weight parameter. Unlike traditional RFE-based SVMs, our approach constructs a nested feature subset structure, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;mi&gt;⋯&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {F}_1subset {F}_2subset cdots subset {F}_p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, using a new filter algorithm that combines backward sacrifice and ReliefF by weighting. This new filter algorithm can capture relevant features and feature interactions simultaneously and is crucial in preventing valuable features from being removed at each iteration. Moreover, the ReliefF algorithm combined with RFE can identify more discriminative feature subsets by reordering the features such that valuable ones are ranked higher than valueless ones, and removing valueless features sequentially through iterative processes. Our experimental results on nine stock datasets from the liquor and spirits concept demonstrate that our proposed method outperforms baseline sparse SVMs and SVM models in terms of accuracy and F-test, while also producing a desirable number of features and automatically eliminating redundancy among technical indicators. We also show that on most stock datasets, the ReliefF algorithm combined with RFE can effectively identify discriminative feature subsets for cases of linear and Gaussian kernel SVMs and our proposed filter method can prevent valuable features from being removed at each iteration. In addition, our experimental findings reveal that feature subsets generated by technical indicators are more discriminative while feature subsets generated by technical i","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.70011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bayesian Hierarchical Modeling of Noisy Gamma Processes: Formulation and Extensions for Unit-To-Unit Variability 噪声伽马过程的贝叶斯分层建模:单位到单位可变性的公式和扩展
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-15 DOI: 10.1002/asmb.70014
Ryan Leadbetter, Gabriel González Cáceres, Aloke Phatak
{"title":"Bayesian Hierarchical Modeling of Noisy Gamma Processes: Formulation and Extensions for Unit-To-Unit Variability","authors":"Ryan Leadbetter,&nbsp;Gabriel González Cáceres,&nbsp;Aloke Phatak","doi":"10.1002/asmb.70014","DOIUrl":"https://doi.org/10.1002/asmb.70014","url":null,"abstract":"<p>The gamma process is a natural model for monotonic degradation processes. In practice, it is desirable to extend the single gamma process to incorporate measurement error and to construct models for the degradation of several nominally identical units. In this paper, we show how these extensions are easily facilitated through the Bayesian hierarchical modeling framework. Following the precepts of the Bayesian statistical workflow, we show the principled construction of a noisy gamma process model. We also reparameterise the gamma process to simplify the specification of priors and make it obvious how the single gamma process model can be extended to include unit-to-unit variability or covariates. We first fit the noisy gamma process model to a single simulated degradation trace. In doing so, we find an identifiability problem between the volatility of the gamma process and the measurement error when there are only a few noisy degradation observations. However, this lack of identifiability can be resolved by including extra information in the analysis through a stronger prior or extra data that informs one of the non-identifiable parameters, or by borrowing information from multiple units. We then explore extensions of the model to account for unit-to-unit variability and demonstrate them using a crack-propagation data set with added measurement error. Lastly, we perform model selection in a fully Bayesian framework by using cross-validation to approximate the expected log probability density of a new observation. We also show how failure time distributions with uncertainty intervals can be calculated for new units or units that are currently under test but have yet to fail.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Industrial Statistics in the Knowledge Economy 知识经济中的工业统计
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-15 DOI: 10.1002/asmb.70018
David Banks, Yue Li
{"title":"Industrial Statistics in the Knowledge Economy","authors":"David Banks,&nbsp;Yue Li","doi":"10.1002/asmb.70018","DOIUrl":"https://doi.org/10.1002/asmb.70018","url":null,"abstract":"<div>\u0000 \u0000 <p>Industrial statistics grew up in an era when manufacturing was the primary engine of commerce. Today, the driver is information technology. This paper discusses how statisticians need to adapt to contribute to this new business model, with particular emphasis upon computational advertising, autonomous vehicles, operations management, and large language models. Remarkably, many of our old tools are still relevant, even as the new problem space poses fresh research challenges for our employment and educational systems.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Multistate Markovian Model of the Economic Burden for Allergy Immunotherapy 变态反应免疫治疗经济负担的多态马尔可夫模型
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-15 DOI: 10.1002/asmb.70017
Massimo Bilancia, Gaetano Serviddio
{"title":"A Multistate Markovian Model of the Economic Burden for Allergy Immunotherapy","authors":"Massimo Bilancia,&nbsp;Gaetano Serviddio","doi":"10.1002/asmb.70017","DOIUrl":"https://doi.org/10.1002/asmb.70017","url":null,"abstract":"<div>\u0000 \u0000 <p>The incidence of allergic rhinoconjunctivitis due to pollinosis is increasing in Western countries. The first-line therapy (No-AIT) typically involves the administration of antihistamines and corticosteroid sprays to manage symptoms. Immunotherapy represents an alternative treatment option, as it promotes desensitization to allergens. However, it is associated with significant costs. Currently, two types of allergen immunotherapy (AIT) are prescribed: subcutaneous immunotherapy and sublingual immunotherapy. This article compares these two therapeutic options with No-AIT. The comparison is conducted through a cost-effectiveness analysis (CEA), which evaluates health-related outcomes by estimating the incremental cost per unit of change in a composite outcome that combines morbidity and quality-of-life metrics. To perform the analysis, we developed a realistic multistate model describing the progression of a cohort of patients undergoing the three therapeutic approaches. The model was designed to be sufficiently flexible to account for treatment-related challenges commonly observed in real-world settings, which are often inadequately represented in randomized controlled trials. By employing a novel two-dimensional framework, we tracked the proportion of the cohort transitioning between health states during each cycle while simultaneously capturing the origin and destination of each transition. This approach enabled the integration of structural features that are typically overlooked, such as early treatment discontinuation, transition rewards, nonstationarities associated with the usual termination of immunotherapy after three years, and differential protection against severe complications (e.g., asthma) depending on whether immunotherapy was completed or not. Deterministic simulations were conducted using standard input parameters, supplemented by probabilistic simulations to generate CEACs for each of the three strategies. The results from our model indicate that AIT is not cost-effective unless the payer exhibits a moderately high willingness-to-pay. These findings have important implications for the pharmaceutical industry involved in the production of AIT drugs.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Soft-Clipping Autoregressive Models for Ordinal Time Series 有序时间序列的软裁剪自回归模型
IF 1.3 4区 数学
Applied Stochastic Models in Business and Industry Pub Date : 2025-05-05 DOI: 10.1002/asmb.70015
Christian H. Weiß, Osama Swidan
{"title":"Soft-Clipping Autoregressive Models for Ordinal Time Series","authors":"Christian H. Weiß,&nbsp;Osama Swidan","doi":"10.1002/asmb.70015","DOIUrl":"https://doi.org/10.1002/asmb.70015","url":null,"abstract":"<p>The linear autoregressive models are among the most popular models in the practice of time series analysis, which constitutes an incentive to adapt them to ordinal time series as well. Our starting point for modeling ordinal time series data is the latent variable approach to define a generalized linear model. This method, however, typically leads to a non-linear relationship between the past observations and the current conditional cumulative distribution function (cdf). To overcome this problem, we use the soft-clipping link to obtain an approximately linear model structure and propose a wide and flexible class of soft-clipping autoregressive (scAR) models. The constraints imposed on the model parameters allow us to identify relevant special cases of the scAR model family. We study the calculation of transition probabilities as well as approximate formulae for the CDF. Our proposals are illustrated by numerical examples and simulation experiments, where the performance of maximum likelihood estimation as well as model selection is analyzed. The novel model family is successfully applied to a real-world ordinal time series from finance.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.70015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信