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一类非线性优化的Canonical对偶函数
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作者 朱经浩 严旺光 《同济大学学报(自然科学版)》 EI CAS CSCD 北大核心 2010年第2期307-310,共4页
研究如何获取球体约束下非线性优化的全局最小点.通过引入常微分方程和构造Canonical对偶函数的局部形式,引入了相应的对偶定理,勾勒出了原问题的KKT点和对偶问题的KKT点两者之间的关系.给出了凸乘子定义,对偶定理和搜寻全局最优点的方... 研究如何获取球体约束下非线性优化的全局最小点.通过引入常微分方程和构造Canonical对偶函数的局部形式,引入了相应的对偶定理,勾勒出了原问题的KKT点和对偶问题的KKT点两者之间的关系.给出了凸乘子定义,对偶定理和搜寻全局最优点的方法,并通过一些例子加以演示. 展开更多
关键词 canonical对偶函数 canonical对偶变换 全局最优化
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CRABP1-mediated non-canonical retinoic acid signaling in motor neurons and neural stem cells
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作者 Li-Na Wei 《Neural Regeneration Research》 SCIE CAS CSCD 2024年第6期1169-1170,共2页
Retinoic acid(RA),the active metabolite of vitamin A(the retinoids),elicits a wide spectrum of biological activities critical to the development and health of most of the organ systems including the nervous systems(Co... Retinoic acid(RA),the active metabolite of vitamin A(the retinoids),elicits a wide spectrum of biological activities critical to the development and health of most of the organ systems including the nervous systems(Corcoran et al.,2002).The effects of RA are mediated by two very distinct pathways;the first is manifested in the nucleus by binding to a large family of nuclear RA receptors(RARs)to regulate proper expression of RAtargeted genes. 展开更多
关键词 canonical SPECTRUM CRITICAL
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Cross-Project Software Defect Prediction Based on SMOTE and Deep Canonical Correlation Analysis
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作者 Xin Fan Shuqing Zhang +2 位作者 Kaisheng Wu Wei Zheng Yu Ge 《Computers, Materials & Continua》 SCIE EI 2024年第2期1687-1711,共25页
Cross-Project Defect Prediction(CPDP)is a method that utilizes historical data from other source projects to train predictive models for defect prediction in the target project.However,existing CPDP methods only consi... Cross-Project Defect Prediction(CPDP)is a method that utilizes historical data from other source projects to train predictive models for defect prediction in the target project.However,existing CPDP methods only consider linear correlations between features(indicators)of the source and target projects.These models are not capable of evaluating non-linear correlations between features when they exist,for example,when there are differences in data distributions between the source and target projects.As a result,the performance of such CPDP models is compromised.In this paper,this paper proposes a novel CPDP method based on Synthetic Minority Oversampling Technique(SMOTE)and Deep Canonical Correlation Analysis(DCCA),referred to as S-DCCA.Canonical Correlation Analysis(CCA)is employed to address the issue of non-linear correlations between features of the source and target projects.S-DCCA extends CCA by incorporating the MlpNet model for feature extraction from the dataset.The redundant features are then eliminated by maximizing the correlated feature subset using the CCA loss function.Finally,cross-project defect prediction is achieved through the application of the SMOTE data sampling technique.Area Under Curve(AUC)and F1 scores(F1)are used as evaluation metrics.This paper conducted experiments on 27 projects from four public datasets to validate the proposed method.The results demonstrate that,on average,our method outperforms all baseline approaches by at least 1.2%in AUC and 5.5%in F1 score.This indicates that the proposed method exhibits favorable performance characteristics. 展开更多
关键词 Cross-project defect prediction deep canonical correlation analysis feature similarity
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Crosstalk among canonical Wnt and Hippo pathway members in skeletal muscle and at the neuromuscular junction
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作者 Said Hashemolhosseini Lea Gessler 《Neural Regeneration Research》 SCIE CAS 2025年第9期2464-2479,共16页
Skeletal muscles are essential for locomotion,posture,and metabolic regulation.To understand physiological processes,exercise adaptation,and muscle-related disorders,it is critical to understand the molecular pathways... Skeletal muscles are essential for locomotion,posture,and metabolic regulation.To understand physiological processes,exercise adaptation,and muscle-related disorders,it is critical to understand the molecular pathways that underlie skeletal muscle function.The process of muscle contra ction,orchestrated by a complex interplay of molecular events,is at the core of skeletal muscle function.Muscle contraction is initiated by an action potential and neuromuscular transmission requiring a neuromuscular junction.Within muscle fibers,calcium ions play a critical role in mediating the interaction between actin and myosin filaments that generate force.Regulation of calcium release from the sarcoplasmic reticulum plays a key role in excitation-contraction coupling.The development and growth of skeletal muscle are regulated by a network of molecular pathways collectively known as myogenesis.Myogenic regulators coordinate the diffe rentiation of myoblasts into mature muscle fibers.Signaling pathways regulate muscle protein synthesis and hypertrophy in response to mechanical stimuli and nutrient availability.Seve ral muscle-related diseases,including congenital myasthenic disorders,sarcopenia,muscular dystrophies,and metabolic myopathies,are underpinned by dys regulated molecular pathways in skeletal muscle.Therapeutic interventions aimed at preserving muscle mass and function,enhancing regeneration,and improving metabolic health hold promise by targeting specific molecular pathways.Other molecular signaling pathways in skeletal muscle include the canonical Wnt signaling pathway,a critical regulator of myogenesis,muscle regeneration,and metabolic function,and the Hippo signaling pathway.In recent years,more details have been uncovered about the role of these two pathways during myogenesis and in developing and adult skeletal muscle fibers,and at the neuromuscular junction.In fact,research in the last few years now suggests that these two signaling pathways are interconnected and that they jointly control physiological and pathophysiological processes in muscle fibers.In this review,we will summarize and discuss the data on these two pathways,focusing on their concerted action next to their contribution to skeletal muscle biology.However,an in-depth discussion of the noncanonical Wnt pathway,the fibro/a dipogenic precursors,or the mechanosensory aspects of these pathways is not the focus of this review. 展开更多
关键词 canonical Wnt"Wingless-related integration site"pathway beta-catenin(CTNNB1) Hippo pathway MYOGENESIS MYOTUBE neuromuscular junction satellite cell skeletal muscle fiber transcriptional co-activator with PDZ-binding motif(TAZ) T-cell-specific transcription factor/lymphoid enhancer-binding factor(TCF/LEF) TEA domain family member(TEAD) transducin-like enhancer of split(TLE) yes-associated protein 1(YAP1)
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Fe(Ⅱ)对CANON工艺处理城镇污水脱氮性能的影响
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作者 张倩倩 廖祖刚 +3 位作者 冯泽通 刘金泽 符文婧 赵剑强 《安全与环境工程》 CAS CSCD 北大核心 2024年第2期291-300,共10页
全程自养脱氮(CANON)工艺,作为新型脱氮工艺应用于城镇污水深度脱氮过程中,有望降低污水处理的运行费用。考察了亚铁离子[Fe(Ⅱ)]对CANON工艺启动及稳定运行时脱氮性能的影响。结果表明:15~23℃条件下投加6.3 mg/L Fe(Ⅱ)时,可有效启动... 全程自养脱氮(CANON)工艺,作为新型脱氮工艺应用于城镇污水深度脱氮过程中,有望降低污水处理的运行费用。考察了亚铁离子[Fe(Ⅱ)]对CANON工艺启动及稳定运行时脱氮性能的影响。结果表明:15~23℃条件下投加6.3 mg/L Fe(Ⅱ)时,可有效启动并稳定运行CANON工艺处理城镇污水,该工艺氮去除负荷(NRR)、总氮去除率(TNRE)和氨氮去除率(ARE)分别为(4.8±1.1)g-N/(L^(3)·d)、(97±1)%和(44.2±9.3)%;相关性分析表明,通过调控Fe(Ⅱ)投加量可有效抑制亚硝酸盐氧化菌(NOB)的活性;本次优化的Fe(Ⅱ)投加量为6.3 mg/L,其对CANON工艺脱氮性能的影响机制与CANON工艺中功能微生物活性的提高、Fe(Ⅱ)与进水氨氮及其他氮化合物的循环反应、铁型反硝化过程以及铁型厌氧氨氧化过程的耦合有关。 展开更多
关键词 canon工艺 城镇污水 Fe(Ⅱ) 脱氮效能
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“一招”解决函数f(ax+b)的奇偶性、对称性、周期性问题
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作者 霍忠林 《中学生数理化(高一数学)》 2024年第10期22-22,共1页
一、函数f(ax+b)的奇偶性问题例1设函数f(x)的定义域为R,且f(x+2)为偶函数,f(2x+1)为奇函数,则()。
关键词 函数 奇偶性 定义域 偶函数 对称性
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3-D Gait Identification Utilizing Latent Canonical Covariates Consisting of Gait Features 被引量:1
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作者 Ramiz Gorkem Birdal Ahmet Sertbas 《Computers, Materials & Continua》 SCIE EI 2023年第9期2727-2744,共18页
Biometric gait recognition is a lesser-known but emerging and effective biometric recognition method which enables subjects’walking patterns to be recognized.Existing research in this area has primarily focused on fe... Biometric gait recognition is a lesser-known but emerging and effective biometric recognition method which enables subjects’walking patterns to be recognized.Existing research in this area has primarily focused on feature analysis through the extraction of individual features,which captures most of the information but fails to capture subtle variations in gait dynamics.Therefore,a novel feature taxonomy and an approach for deriving a relationship between a function of one set of gait features with another set are introduced.The gait features extracted from body halves divided by anatomical planes on vertical,horizontal,and diagonal axes are grouped to form canonical gait covariates.Canonical Correlation Analysis is utilized to measure the strength of association between the canonical covariates of gait.Thus,gait assessment and identification are enhancedwhenmore semantic information is available through CCA-basedmulti-feature fusion.Hence,CarnegieMellon University’s 3D gait database,which contains 32 gait samples taken at different paces,is utilized in analyzing gait characteristics.The performance of Linear Discriminant Analysis,K-Nearest Neighbors,Naive Bayes,Artificial Neural Networks,and Support Vector Machines was improved by a 4%average when the CCA-utilized gait identification approachwas used.Asignificant maximumaccuracy rate of 97.8%was achieved throughCCA-based gait identification.Beyond that,the rate of false identifications and unrecognized gaits went down to half,demonstrating state-of-the-art for gait identification. 展开更多
关键词 Gait identification canonical covariates multivariate data analysis gait determinant
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An Update Method of Decision Implication Canonical Basis on Attribute Granulating 被引量:1
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作者 Yanhui Zhai Rujie Chen Deyu Li 《Intelligent Automation & Soft Computing》 SCIE 2023年第8期1833-1851,共19页
Decision implication is a form of decision knowledge represen-tation,which is able to avoid generating attribute implications that occur between condition attributes and between decision attributes.Compared with other... Decision implication is a form of decision knowledge represen-tation,which is able to avoid generating attribute implications that occur between condition attributes and between decision attributes.Compared with other forms of decision knowledge representation,decision implication has a stronger knowledge representation capability.Attribute granularization may facilitate the knowledge extraction of different attribute granularity layers and thus is of application significance.Decision implication canonical basis(DICB)is the most compact set of decision implications,which can efficiently represent all knowledge in the decision context.In order to mine all deci-sion information on decision context under attribute granulating,this paper proposes an updated method of DICB.To this end,the paper reduces the update of DICB to the updates of decision premises after deleting an attribute and after adding granulation attributes of some attributes.Based on this,the paper analyzes the changes of decision premises,examines the properties of decision premises,designs an algorithm for incrementally generating DICB,and verifies its effectiveness through experiments.In real life,by using the updated algorithm of DICB,users may obtain all decision knowledge on decision context after attribute granularization. 展开更多
关键词 Decision context attribute granulating decision implication decision implication canonical basis
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Cohen-Macaulay局部环上的Canonical模
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作者 路姣姣 杨晓燕 《吉林大学学报(理学版)》 CAS 北大核心 2023年第1期61-65,共5页
令(R,m,k)是Cohen-Macaulay局部环,M,N是有限生成R-模.假设N∈ΩCM(R),且Ext_(R)^(1≤i≤d)(M,N)=0,证明HomR(M,N)∈ΩCM(R),并给出有限生成模N是canonical模的条件.
关键词 Cohen-Macaulay局部环 极大Cohen-Macaulay模 canonical
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Analysis of Differential Gene Expression and Core Canonical Pathways Involved in the Epithelial to Mesenchymal Transition of Triple Negative Breast Cancer Cells by Ingenuity Pathway Analysis
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作者 Elizabeth Cagle Brent Lake +10 位作者 Anasua Banerjee Jazmine Cuffee Narendra Banerjee Darla Gilmartin Makaiyah Liverman Shennel Brown Erik Armstrong Santanu Bhattacharya Somiranjan Ghosh Tanmoy Mandal Hirendra Banerjee 《Computational Molecular Bioscience》 2023年第2期21-34,共14页
Triple Negative Breast Cancer (TNBC) is a malignant form of cancer with very high mortality and morbidity. Epithelial to Mesenchymal Transition (EMT) is the most common pathophysiological change observed in cancer cel... Triple Negative Breast Cancer (TNBC) is a malignant form of cancer with very high mortality and morbidity. Epithelial to Mesenchymal Transition (EMT) is the most common pathophysiological change observed in cancer cells of epithelial origin that promotes metastasis, drug resistance and cancer stem cell formation. Since the information regarding differential gene expression in TNBC cells and cell signaling events leading to EMT is limited, this investigation was done by comparing transcriptomic data generated by RNA isolation and sequencing of a EMT model TNBC cell line in comparison to regular TNBC cells. RNA sequencing and Ingenuity Pathway Software Analysis (IPA) of the transcriptomic data revealed several upregulated and downregulated gene expressions along with novel core canonical pathways including Sirtuin signaling, Oxidative Phosphorylation and Mitochondrial dysfunction events involved in EMT changes of the TNBC cells. 展开更多
关键词 Triple Negative Breast Cancer Epithelial to Mesenchymal Transition Core canonical Pathways
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Grand canonical Monte Carlo simulation study of hydrogen storage by Li-decorated pha-graphene
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作者 张蒙蒙 张凤 +7 位作者 吴强 黄欣 闫巍 赵春梅 陈伟 杨志红 王允辉 武婷婷 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第6期476-480,共5页
Grand canonical Monte Carlo simulation(GCMCs)is utilized for studying hydrogen storage gravimetric density by pha-graphene at different metal densities,temperatures and pressures.It is demonstrated that the optimum ad... Grand canonical Monte Carlo simulation(GCMCs)is utilized for studying hydrogen storage gravimetric density by pha-graphene at different metal densities,temperatures and pressures.It is demonstrated that the optimum adsorbent location for Li atoms is the center of the seven-membered ring of pha-graphene.The binding energy of Li-decorated phagraphene is larger than the cohesive energy of Li atoms,implying that Li can be distributed on the surface of pha-graphene without forming metal clusters.We fitted the force field parameters of Li and C atoms at different positions and performed GCMCs to study the absorption capacity of H_(2).The capacity of hydrogen storage was studied by the differing density of Li decoration.The maximum hydrogen storage capacity of 4Li-decorated pha-graphene was 15.88 wt%at 77 K and100 bar.The enthalpy values of adsorption at the three densities are in the ideal range of 15 kJ·mol^(-1)-25 kJ·mol^(-1).The GCMC results at different pressures and temperatures show that with the increase in Li decorative density,the hydrogen storage gravimetric ratio of pha-graphene decreases but can reach the 2025 US Department of Energy's standard(5.5 wt%).Therefore,pha-graphene is considered to be a potential hydrogen storage material. 展开更多
关键词 hydrogen storage pha-graphene grand canonical Monte Carlo simulation(GCMCs) force field
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东北长白山泥炭地硅藻−水位埋深转换函数
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作者 徐双余 卜兆君 +3 位作者 黄咸雨 彭佳 李俊璐 陈旭 《地理科学》 CSSCI CSCD 北大核心 2024年第8期1459-1469,共11页
本研究基于2016、2019和2021年夏季在东北长白山地区7处泥炭地采集的160个表层样品和环境因子数据,结合表层样品硅藻分析,构建了硅藻属种与环境因子数据库,该数据库包括64个硅藻属种和11个环境变量。优势硅藻属种组合沿水位埋深梯度(0~6... 本研究基于2016、2019和2021年夏季在东北长白山地区7处泥炭地采集的160个表层样品和环境因子数据,结合表层样品硅藻分析,构建了硅藻属种与环境因子数据库,该数据库包括64个硅藻属种和11个环境变量。优势硅藻属种组合沿水位埋深梯度(0~66 cm)呈现明显分异,偏典范对应分析结果表明,水位埋深单独解释了硅藻组合数据总方差的8.4%,远大于其他环境因子的单独解释份额。基于此,选取加权平均模型和最大似然估计模型构建硅藻−水位转换函数。不同模型分析结果显示,典型回归耐受值降权加权平均模型构建的硅藻−水位转换函数表现最佳,剔除残差大于20%水位梯度(13.2 cm)的样品后进行留一法交叉检验,该模型的推导值与实测值相关系数最大和推导误差最小。本文构建的硅藻−水位转换函数为定量反演长白山地区泥炭地过去水位变化提供了新的有效方法。 展开更多
关键词 硅藻指标 典范对应分析 加权平均模型 水位埋深 定量重建
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基于Canonical最小二乘蒙特卡罗法的可转债定价
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作者 殷炼乾 皮蓉 《债券》 2023年第12期91-97,共7页
区别于传统的最小二乘蒙特卡罗方法,本文利用标的资产收益率生成Canonical风险中性概率计算累计概率分布函数进行抽样,以此生成标的资产价格的蒙特卡罗路径。同时,运用平赌过程适配法对蒙特卡罗模拟进行改进,以提高模型的收敛速度并降... 区别于传统的最小二乘蒙特卡罗方法,本文利用标的资产收益率生成Canonical风险中性概率计算累计概率分布函数进行抽样,以此生成标的资产价格的蒙特卡罗路径。同时,运用平赌过程适配法对蒙特卡罗模拟进行改进,以提高模型的收敛速度并降低其误差。针对可转债的特殊条款,本文按照市场惯例及逻辑,将回售条款与下修条款结合处理,以提高模型的可行性和运算效率。最后,使用传统的参数化方法进行对比实验。结果表明,本文所设计方法的模拟路径比传统方法更能体现标的资产的运动特性,定价结果优于传统的参数化方法。 展开更多
关键词 可转债定价 最小二乘蒙特卡罗 canonical风险中性概率 平赌过程适配法
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由“函数奇偶性”的概念教学引发的思考
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作者 于伟 《数学教学通讯》 2024年第3期40-41,49,共3页
文章从“旧知回顾,知识梳理”“情境创设,激发认知冲突”“深入探究,理解偶函数”“问题启发,辨析偶函数”“类比分析,探寻奇函数”五方面展开“函数奇偶性”的概念教学,并从以下三方面谈一些思考:放低教学起点,创设合理情境,经历探究过程.
关键词 概念教学 偶函数 函数
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The Publication of the Piling Canon in the Late Qing
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作者 LIU Yi 《Cultural and Religious Studies》 2024年第9期566-574,共9页
Piling Canon refers to a woodblock-printed Chinese Buddhist Canon during the late Qing Dynasty.Despite its historical significance,it has received limited attention from the academia,as its discovery took place after ... Piling Canon refers to a woodblock-printed Chinese Buddhist Canon during the late Qing Dynasty.Despite its historical significance,it has received limited attention from the academia,as its discovery took place after the turn of the 21st century.This study explores the background,supervisor,proofreader,engravers,donors,and other factors that contributed to the publication of the Piling Canon.It was supervised by Buddhist monk Qingrong in Changzhou Tianning Monastery from 1908 to 1926,due to the commission of Yang Wenhui.By investigating the historical records in the colophons of Piling Canon,we found that engraving locations are distributed in Hubei,Yangzhou,and Danyang which engravers operated in groups;the majority of donors were found to be individuals and group forms,social fundraising was included as well.It is noteworthy that Sheng Xuanhuai made a significant contribution in terms of funding.Furthermore,the production of the Piling Canon confirms to the commence of Buddhism revival,as Buddhist scriptures in Jiangnan regions were almost destroyed after the Taiping Rebellion.The research shed light on extensive participation of cultural celebrities,diverse donation forms,and excellent engraving,offering a vivid depiction of Buddhist belief and social landscape in Jiangnan region. 展开更多
关键词 Piling canon Buddhist scriptures Tianning Monastery DONORS Jiangnan
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采用奇偶函数法的平面面形绝对测量技术仿真分析 被引量:7
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作者 贾辛 邢廷文 +1 位作者 魏豪明 李云 《红外与激光工程》 EI CSCD 北大核心 2012年第2期500-505,共6页
随着现代工业和科学技术的飞速发展,特别是近代大规模集成电路技术的不断提高,对系统精度的要求日益提高。在光刻系统中,越来越短的特征尺寸要求我们使用更高精度的光刻物镜。在这之前我们需要更高精度的检测技术来满足加工及系统集成... 随着现代工业和科学技术的飞速发展,特别是近代大规模集成电路技术的不断提高,对系统精度的要求日益提高。在光刻系统中,越来越短的特征尺寸要求我们使用更高精度的光刻物镜。在这之前我们需要更高精度的检测技术来满足加工及系统集成的需要。高精度移相干涉仪的测量结果包含了待测面和参考面的误差,移相干涉测量法的测量精度受限于参考面的精度。绝对测量方法通过移除参考面的误差,从而达到提高测量精度的目的。回顾了光学平面面形绝对测量方法,重点描述了基于奇偶函数的绝对测量方法。分析了旋转角度误差对测量结果的影响,通过旋转更小的角度求出了高阶面形拟合分量,给出了求高阶面形拟合分量的通项公式。 展开更多
关键词 光学检测 绝对测量 偶函数 面形检测
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基于奇偶函数法的绝对检测实验研究 被引量:7
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作者 李宇琛 韩森 +3 位作者 吴泉英 唐寿鸿 李雪园 王全召 《应用光学》 CAS CSCD 北大核心 2017年第3期469-475,共7页
针对平面干涉检测技术的检测精度受限于参考面面形精度的问题,提出使用基于奇偶函数的高精度绝对检测方法消除干涉系统中参考面面形误差的影响。对旋转角度误差与旋转偏心误差对绝对检测方法测量精度的影响进行了仿真分析。利用商用菲... 针对平面干涉检测技术的检测精度受限于参考面面形精度的问题,提出使用基于奇偶函数的高精度绝对检测方法消除干涉系统中参考面面形误差的影响。对旋转角度误差与旋转偏心误差对绝对检测方法测量精度的影响进行了仿真分析。利用商用菲索干涉仪,设计和分析了绝对检测精度实验及重复性实验。仿真结果显示:旋转角度误差在达到0.13°时,测量误差PV值为0.000 1λ;旋转偏心误差达到3pixel时,测量误差PV值为0.005λ。实验结果显示:测得实际样品的绝对检测精度PV_(10)值为0.041 5λ,RMS值为0.008 7λ,小于常规干涉检测所得结果;对同一平面两次独立的绝对检测结果进行点对点作差处理,从而获得残差图,其残差图PV_(10)值为0.004λRMS值为0.000 5λ。实验结果表明了该方法的高重复性和有效性。 展开更多
关键词 光学干涉测量 绝对检测 偶函数 面形精度
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Canonical对偶理论在一类多项式全局优化中的应用 被引量:1
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作者 朱经浩 谭素娥 《同济大学学报(自然科学版)》 EI CAS CSCD 北大核心 2011年第9期1373-1376,共4页
用Canonical对偶理论,讨论一类高阶多项式全局最优化问题的求解.首先将无约束多项式全局优化问题转换成箱体约束下的多项式全局优化问题,之后通过构造非线性变换对偶函数及相应的共轭函数,得到原问题的Canonical对偶问题.进一步通过求... 用Canonical对偶理论,讨论一类高阶多项式全局最优化问题的求解.首先将无约束多项式全局优化问题转换成箱体约束下的多项式全局优化问题,之后通过构造非线性变换对偶函数及相应的共轭函数,得到原问题的Canonical对偶问题.进一步通过求解对偶问题的最优解,导出原多项式全局优化问题的最优解,并给出对偶问题是凹函数的证明.最后应用所得方法,计算一个二元6次多项式全局最优化实例. 展开更多
关键词 canonical对偶理论 全局优化 高阶多元多项式
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关于Smarandache对偶函数 被引量:6
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作者 苟素 杜晓英 《纯粹数学与应用数学》 CSCD 北大核心 2008年第1期17-20,共4页
定义Smarandache对偶函数S~*(n)为最大的正整数m使得m!|n.定义另一种双阶乘函数S^(**)(n)为最大的正整数2m-1使得(2m-1)!!|n,其中2+n;且当2|n时,为最大的正整数2m使得(2m)!!|n.本文的主要目的是利用初等方法研究一个包含S^(**)(n)的无... 定义Smarandache对偶函数S~*(n)为最大的正整数m使得m!|n.定义另一种双阶乘函数S^(**)(n)为最大的正整数2m-1使得(2m-1)!!|n,其中2+n;且当2|n时,为最大的正整数2m使得(2m)!!|n.本文的主要目的是利用初等方法研究一个包含S^(**)(n)的无穷级数的收敛性,并给出一个有趣的恒等式. 展开更多
关键词 SMARANDACHE对偶函数 无穷级数 恒等式
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钢柱脚抗剪键埋深的对偶函数积分变换解法 被引量:3
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作者 肖南 顾强强 《浙江大学学报(工学版)》 EI CAS CSCD 北大核心 2009年第2期353-359,共7页
为解决钢结构柱脚抗剪键埋深的设计难题,基于Timoshenko梁理论,利用奇异函数表示抗剪键所受力的分布,通过积分变换、逆变换和对偶函数求解微分方程,分别采用混凝土应力-应变关系的理想弹塑性模型和非线性弹塑性模型推导了抗剪键的变形... 为解决钢结构柱脚抗剪键埋深的设计难题,基于Timoshenko梁理论,利用奇异函数表示抗剪键所受力的分布,通过积分变换、逆变换和对偶函数求解微分方程,分别采用混凝土应力-应变关系的理想弹塑性模型和非线性弹塑性模型推导了抗剪键的变形曲线方程,得到了抗剪键埋深的计算公式并建立了可供实际应用的表格.计算结果表明,依据理想弹塑性理论计算得到的抗剪键埋深稍大,偏于安全;抗剪键设计埋深主要与抗剪键承受的剪力、泊松比、抗弯刚度、剪切刚度4个因素有关.抗剪键所受分布力的合力会对柱脚产生附加弯矩,从而影响钢柱脚底板尺寸及锚栓面积等其他参数的设计. 展开更多
关键词 钢柱脚 抗剪键 奇异函数 对偶函数 积分变换 Timoshenko梁 附加弯矩
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