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协同拟凸函数的Riemann-Liouville分数阶积分不等式
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作者 郑茜 王淑红 《内蒙古民族大学学报(自然科学版)》 2024年第2期46-53,共8页
基于Riemann-Liouville分数阶积分,对协同拟凸函数的Hermite-Hadamard分数阶积分不等式进行了研究。剖析Riemann-Liouville分数阶积分的运算特点,深入探究SAR?KAYA给出的Riemann-Liouville分数阶积分恒等式。在该Riemann-Liouville分数... 基于Riemann-Liouville分数阶积分,对协同拟凸函数的Hermite-Hadamard分数阶积分不等式进行了研究。剖析Riemann-Liouville分数阶积分的运算特点,深入探究SAR?KAYA给出的Riemann-Liouville分数阶积分恒等式。在该Riemann-Liouville分数阶积分恒等式的基础上,利用二元函数的单调性和协同拟凸性,巧妙应用三角不等式和H?lder不等式等经典不等式,建立了若干个协同拟凸函数的Hermite-Hadamard分数阶积分不等式。 展开更多
关键词 协同拟凸函数 HERMITE-HADAMARD不等式 riemann-liouville分数阶积分
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基于Riemann-Liouville分数阶积分Bernstein-Kantorovich算子的逼近性质
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作者 汪洋 程文韬 +1 位作者 刘玉洁 刘磊 《淮北师范大学学报(自然科学版)》 CAS 2024年第1期27-32,共6页
文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐... 文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐进公式。该算子的构建使得在曲线曲面造型方面对于给定的函数将会有更小的近似误差。 展开更多
关键词 BERNSTEIN-KANTOROVICH算子 riemann-liouville分数阶积分 Peetre’-K泛函 Vorononskaja定理
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Riemann-Liouville型分数阶导数的非线性估计 被引量:1
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作者 郭玉祥 马保离 +1 位作者 张庆平 占生宝 《控制理论与应用》 EI CAS CSCD 北大核心 2023年第2期256-266,共11页
本文主要研究任意有界连续信号的Riemann-Liouville分数阶导数估计问题.当分数阶α属于0到1时,首先利用滑模技术提出一种有界连续信号分数阶导数的非线性估计方法;然后将其结果推广至分数阶α∈R+的情况,并给出相应的非线性估计方案.借... 本文主要研究任意有界连续信号的Riemann-Liouville分数阶导数估计问题.当分数阶α属于0到1时,首先利用滑模技术提出一种有界连续信号分数阶导数的非线性估计方法;然后将其结果推广至分数阶α∈R+的情况,并给出相应的非线性估计方案.借助Riemann-Liouville分数阶微积分频率分布模型,本文详细分析讨论了所给分数阶导数非线性估计的收敛性问题,并得到相应闭环系统是渐近稳定的结论.文中所提方法的主要优点是在事先未知给定信号分数阶导数上界的情况下,不仅能自适应地估计其Riemann-Liouville分数阶导数,而且当信号中含有随机噪声和不确定扰动时依然能正常工作.数值仿真实例验证了本文所给估计方法的可行性和有效性. 展开更多
关键词 分数阶微积分 riemann-liouville 非线性系统 自适应滑模 Gaussian白噪声
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一类Riemann-Liouville分数阶时滞随机发展方程的Ulam-Hyers稳定性 被引量:1
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作者 白玉洁 杨和 《吉林大学学报(理学版)》 CAS 北大核心 2023年第3期483-489,共7页
用不动点定理研究Hilbert空间中一类含α∈(0,1)阶Riemann-Liouville分数阶导数的时滞随机发展方程温和解的存在唯一性,并证明该解的Ulam-Hyers稳定性.最后举例说明所得结论的适用性.
关键词 riemann-liouville分数阶导数 随机发展方程 时滞 Ulam-Hyers稳定性
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两类基于Riemann-Liouville分数阶导数的非线性偏微分方程的对称分析
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作者 张天棋 银山 《应用数学进展》 2023年第7期3436-3446,共11页
针对热传导类和扩散类这两类Riemann-Liouville分数阶微分方程,采用了Lie对称方法,研究了这两类分数阶微分方程所允许的Lie代数。给出两类方程拥有的对称,运用部分Lie对称变换把对应的偏微分方程化为新变量下的分数阶常微分方程,表明Li... 针对热传导类和扩散类这两类Riemann-Liouville分数阶微分方程,采用了Lie对称方法,研究了这两类分数阶微分方程所允许的Lie代数。给出两类方程拥有的对称,运用部分Lie对称变换把对应的偏微分方程化为新变量下的分数阶常微分方程,表明Lie对称方法适用于此类方程,可以使方程实现约化,进而更易求解,使得热传导类和扩散类Riemann-Liouville分数阶微分方程可以更加广泛地应用于对事物现象的描述。 展开更多
关键词 riemann-liouville分数阶微分方程 LIE对称 约化
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Calculus bovis inhibits M2 tumor-associated macrophage polarization via Wnt/β-catenin pathway modulation to suppress liver cancer 被引量:6
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作者 Zhen Huang Fan-Ying Meng +12 位作者 Lin-Zhu Lu Qian-Qian Guo Chang-Jun Lv Nian-Hua Tan Zhe Deng Jun-Yi Chen Zi-Shu Zhang Bo Zou Hong-Ping Long Qing Zhou Sha Tian Si Mei Xue-Fei Tian 《World Journal of Gastroenterology》 SCIE CAS 2024年第29期3511-3533,共23页
BACKGROUND Calculus bovis(CB),used in traditional Chinese medicine,exhibits anti-tumor effects in various cancer models.It also constitutes an integral component of a compound formulation known as Pien Tze Huang,which... BACKGROUND Calculus bovis(CB),used in traditional Chinese medicine,exhibits anti-tumor effects in various cancer models.It also constitutes an integral component of a compound formulation known as Pien Tze Huang,which is indicated for the treatment of liver cancer.However,its impact on the liver cancer tumor microenvironment,particularly on tumor-associated macrophages(TAMs),is not well understood.AIM To elucidate the anti-liver cancer effect of CB by inhibiting M2-TAM polarization via Wnt/β-catenin pathway modulation.METHODS This study identified the active components of CB using UPLC-Q-TOF-MS,evaluated its anti-neoplastic effects in a nude mouse model,and elucidated the underlying mechanisms via network pharmacology,transcriptomics,and molecular docking.In vitro assays were used to investigate the effects of CB-containing serum on HepG2 cells and M2-TAMs,and Wnt pathway modulation was validated by real-time reverse transcriptase-polymerase chain reaction and Western blot analysis.RESULTS This study identified 22 active components in CB,11 of which were detected in the bloodstream.Preclinical investigations have demonstrated the ability of CB to effectively inhibit liver tumor growth.An integrated approach employing network pharmacology,transcriptomics,and molecular docking implicated the Wnt signaling pathway as a target of the antineoplastic activity of CB by suppressing M2-TAM polarization.In vitro and in vivo experiments further confirmed that CB significantly hinders M2-TAM polarization and suppresses Wnt/β-catenin pathway activation.The inhibitory effect of CB on M2-TAMs was reversed when treated with the Wnt agonist SKL2001,confirming its pathway specificity.CONCLUSION This study demonstrated that CB mediates inhibition of M2-TAM polarization through the Wnt/β-catenin pathway,contributing to the suppression of liver cancer growth. 展开更多
关键词 calculus bovis M2 tumor-associated macrophage polarization Liver cancer Wnt/β-catenin pathway Tumor microenvironment
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一类Riemann-Liouville分数阶时滞发展方程解的存在性
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作者 杨和 白玉洁 《西北师范大学学报(自然科学版)》 CAS 北大核心 2023年第4期9-15,共7页
利用上下解单调迭代方法讨论了有序Banach空间中一类含Riemann-Liouville分数阶导数的时滞发展方程mild解的存在性,并通过一个具体的例子验证了抽象结论.
关键词 riemann-liouville分数阶导数 上下解 单调迭代技巧 时滞 加权函数
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Riemann-Liouville分数阶半线性发展型H-半变分不等式的可解性和最优控制
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作者 施翠云 《数学杂志》 2023年第4期307-322,共16页
本文研究了Hilbert空间中半线性Riemann-Liouville分数阶发展型H-半变分不等式的可解性和最优控制.首先,利用不动点理论和Clarke广义次微分性质得到半线性Riemann-Liouville分数阶发展型H-半变分不等式解的存在性.其次,在一般假设条件... 本文研究了Hilbert空间中半线性Riemann-Liouville分数阶发展型H-半变分不等式的可解性和最优控制.首先,利用不动点理论和Clarke广义次微分性质得到半线性Riemann-Liouville分数阶发展型H-半变分不等式解的存在性.其次,在一般假设条件下证明系统的最优控制存在性.最后,给出一个例子来验证本文的主要结果. 展开更多
关键词 发展型H-半变分不等式 最优控制 Clarke广义次微分 riemann-liouville分数阶导数
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Promise and challenges of traditional Chinese medicine,specifically Calculus bovis,in liver cancer treatment
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作者 Ao-Xi Xu Zhi-Feng Zhao +8 位作者 Li Zhu Yi-Heng Zhang Yan Li Yu-Fan Wei Bo-Ya Zhang Bin Jiang Tian-Ze Gao Meng-Si Li Jia-Yu Liu 《World Journal of Gastroenterology》 SCIE CAS 2024年第40期4380-4385,共6页
Liver cancer,one of the most common malignancies worldwide,ranks sixth in incidence and third in mortality.Liver cancer treatment options are diverse,inclu-ding surgical resection,liver transplantation,percutaneous ab... Liver cancer,one of the most common malignancies worldwide,ranks sixth in incidence and third in mortality.Liver cancer treatment options are diverse,inclu-ding surgical resection,liver transplantation,percutaneous ablation,transarterial chemoembolization,radiotherapy,chemotherapy,targeted therapy,immuno-therapy,and traditional Chinese medicine(TCM).A multidisciplinary team(MDT)is essential to customize treatment plans based on tumor staging,liver function,and performance status(PS),ensuring individualized patient care.Treatment decisions require a MDT to tailor strategies based on tumor staging,liver function,and PS,ensuring personalized care.The approval of new first-line and second-line drugs and the establishment of standard treatments based on immune checkpoint inhibitors have significantly expanded treatment options for advanced liver cancer,improving overall prognosis.However,many patients do not respond effectively to these treatments and ultimately succumb to the disease.Modern oncology treatments,while extending patient survival,often come with severe side effects,resistance,and damage to the body,negatively impacting quality of life.Huang et al's study published at World Journal of Gastroenterology rigorously validates the anticancer properties of Calculus bovis,enhancing our understanding of TCM and contributing to new liver cancer treatment strategies.For over 5000 years,TCM has been used in East Asian countries like China to treat various diseases,including liver conditions.Analysis of real-world clinical data suggests that for patients with advanced-stage tumors lacking effective treatments,integrated TCM therapies could provide significant breakthroughs. 展开更多
关键词 Traditional Chinese medicine Liver cancer calculus bovis TREATMENT PROMISE CHALLENGES
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Calculus bovis in hepatocellular carcinoma:Tumor molecular basis,Wnt/β-catenin pathway role,and protective mechanism
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作者 Khaled Mohamed Mohamed Koriem 《World Journal of Gastroenterology》 SCIE CAS 2024年第35期3959-3964,共6页
In this editorial,we comment on the recent article by Huang et al.The editorial focuses specifically on the molecular mechanisms of hepatocellular carcinoma(HCC),mechanism of Wnt/β-catenin pathway in HCC,and protecti... In this editorial,we comment on the recent article by Huang et al.The editorial focuses specifically on the molecular mechanisms of hepatocellular carcinoma(HCC),mechanism of Wnt/β-catenin pathway in HCC,and protective mechanism of Calculus bovis(CB)in HCC.Liver cancer is the fourth most common cause of cancer-related deaths globally.The most prevalent kind of primary liver cancer,HCC,is typically brought on by long-term viral infections(hepatitis B and C),non-alcoholic steatohepatitis,excessive alcohol consumption,and other conditions that can cause the liver to become chronically inflamed and cirrhotic.CB is a wellknown traditional remedy in China and Japan and has been used extensively to treat a variety of diseases,such as high fever,convulsions,and stroke.Disturbances in lipid metabolism,cholesterol metabolism,bile acid metabolism,alcohol metabolism,and xenobiotic detoxification lead to fatty liver disease and liver cirrhosis.Succinate,which is a tricarboxylic acid cycle intermediate,is vital to energy production and mitochondrial metabolism.It is also thought to be a signaling molecule in metabolism and in the development and spread of liver malignancies.The Wnt/β-catenin pathway is made up of a group of proteins that are essential for both adult tissue homeostasis and embryonic development.Cancer is frequently caused by the dysregulation of the Wnt/β-catenin signaling pathway.In HCC liver carcinogenesis,Wnt/β-catenin signaling is activated by the expression of downstream target genes.Communication between the liver and the gut exists via the portal vein,biliary tract,and systemic circulation.This"gutliver axis"controls intestinal physiology.One of the main factors contributing to the development,progression,and treatment resistance of HCC is the abnormal activation of the Wnt/β-Catenin signaling pathway.Therefore,understanding this pathway is essential to treating HCC.Eleven ingredients of CB,particularly oleanolic acid,ergosterol,and ursolic acid,have anti-primary liver cancer properties.Additionally,CB is important in the treatment of primary liver cancer through pathways linked to immune system function and apoptosis.CB also inhibits the proliferation of cancer stem cells and tumor cells and controls the tumor microenvironment.In the future,clinicians may be able to recommend one of many potential new drugs from CB ingredients to treat HCC expression,development,and progress. 展开更多
关键词 Hepatocellular carcinoma MICRORNAS Wnt/β-catenin pathway calculus bovis APOPTOSIS
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Harnessing the power of Calculus bovis:Anti-cancer properties and Wnt pathway modulation in hepatocellular carcinoma
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作者 Himanshi Goyal Sachin Parwani +1 位作者 Kaneez Fatima Jyotdeep Kaur 《World Journal of Gastroenterology》 SCIE CAS 2024年第41期4496-4502,共7页
In this manuscript,we comment on the article,which explores the anti-cancer effects of Calculus bovis(CB)in tumor biology.We highlight its potential,particularly in hepatocellular carcinoma(HCC),where it inhibits the ... In this manuscript,we comment on the article,which explores the anti-cancer effects of Calculus bovis(CB)in tumor biology.We highlight its potential,particularly in hepatocellular carcinoma(HCC),where it inhibits the phosphatidylinositol 3-kinase/protein kinase B/mammalian target of rapamycin pathways and induces apoptosis.CB contains compounds such as oleanolic acid and ursolic acid that target interleukin-6,mitogen-activated protein kinase 8,vascular endothelial growth factor,and caspase-3,offering anti-inflammatory and hepatoprotective benefits.The manuscript also discusses CB sativus(CBS),an artificial substitute,which has shown efficacy in reducing hepatic inflammation and oxidative stress in animal models.We emphasize the need for further research on the effects of CBS on the gut-liver axis and gut microbiota,and on targeting Wnt signaling and M2 tumor-associated macrophage as potential therapeutic strategies against HCC. 展开更多
关键词 calculus bovis Liver cancer Tumor-associated macrophages M2 polarization Wnt signaling pathway
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Anti-tumor efficacy of Calculus bovis: Suppressing liver cancer by targeting tumor-associated macrophages
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作者 Ishita Kathuria Bhupesh Singla 《World Journal of Gastroenterology》 SCIE CAS 2024年第38期4249-4253,共5页
Despite significant advances in our understanding of the molecular pathogenesis of liver cancer and the availability of novel pharmacotherapies,liver cancer remains the fourth leading cause of cancer-related mortality... Despite significant advances in our understanding of the molecular pathogenesis of liver cancer and the availability of novel pharmacotherapies,liver cancer remains the fourth leading cause of cancer-related mortality worldwide.Tumor relapse,resistance to current anti-cancer drugs,metastasis,and organ toxicity are the major challenges that prevent considerable improvements in patient survival and quality of life.Calculus bovis(CB),an ancient Chinese medicinal drug,has been used to treat various pathologies,including stroke,convulsion,epilepsy,pain,and cancer.In this editorial,we discuss the research findings recently published by Huang et al on the therapeutic effects of CB in inhibiting the development of liver cancer.Utilizing the comprehensive transcriptomic analyses,in vitro experiments,and in vivo studies,the authors demonstrated that CB treatment inhibits the tumor-promoting M2 phenotype of tumor-associated macrophages via downregulating Wnt pathway.While multiple studies have been performed to explore the molecular mechanisms regulated by CB,this study uniquely shows its role in modulating the M2 phenotype of macrophages present within the tumor microenvironment.This study opens new avenues of future investigations aimed at investigating this drug’s efficacy in various mouse models including the effects of combination therapy,and against drug-resistant tumors. 展开更多
关键词 calculus bovis Liver cancer M2-like tumor associated macrophages Wnt/β-catenin pathway Tumor environment
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From traditional Chinese medicine formulations to effective anticancer agents:Insights from Calculus bovis
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作者 He-Tong Zhao 《World Journal of Gastroenterology》 SCIE CAS 2024年第35期4011-4013,共3页
This editorial examines the therapeutic potential of traditional Chinese medicine(TCM)for aggressive cancers,particularly liver cancer.It highlights the study by Huang et al,which shows how Calculus bovis,a component ... This editorial examines the therapeutic potential of traditional Chinese medicine(TCM)for aggressive cancers,particularly liver cancer.It highlights the study by Huang et al,which shows how Calculus bovis,a component of the TCM Pien Tze Huang,suppresses liver cancer by inhibiting M2 macrophage polarization via the Wnt/β-catenin pathway.This research emphasizes the importance of transitioning from effective TCM formulations to isolating active components and understanding their mechanisms.While the study provides valuable insights,it primarily focuses on the Wnt/β-catenin pathway and does not delve deeply into the mechanisms of individual components.Future research should aim to comprehensively study these components,explore their interactions,and validate findings through clinical trials.This approach will integrate traditional wisdom with modern scientific validation,advancing the development of innovative cancer treatments based on TCM formulations. 展开更多
关键词 calculus bovis Traditional Chinese medicine Liver cancer Tumor microenvironment M2 tumor-associated macrophages Wnt/β-catenin pathway
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Exploring a new chapter in traditional Chinese medicine:The potential of Calculus bovis in liver cancer treatment
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作者 Huang Du Hong-Bin Chen Yu Zhao 《World Journal of Clinical Oncology》 2024年第12期1520-1527,共8页
In the ongoing quest for new treatments in medicine,traditional Chinese medicine offers unique insights and potential.Recently,studies on the ability of Calculus bovis to inhibit M2-type tumour-associated macrophage p... In the ongoing quest for new treatments in medicine,traditional Chinese medicine offers unique insights and potential.Recently,studies on the ability of Calculus bovis to inhibit M2-type tumour-associated macrophage polarisation by modulating the Wnt/β-catenin signalling pathway to suppress liver cancer have undoubtedly revealed new benefits and hope for this field of research.The purpose of this article is to comment on this study and explore its strengths and weaknesses,thereby providing ideas for the future treatment of liver cancer. 展开更多
关键词 calculus bovis M2 tumor-associated macrophage polarization Liver cancer Wnt/β-catenin pathway The tumor microenvironment
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数字图像的Riemann-Liouville分数阶微分增强方法 被引量:8
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作者 牛为华 李宝树 梁贵书 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 2014年第12期2189-2195,共7页
针对传统图像增强过程中存在丢失细节且容易出现欠增强或过增强的不足,提出一种基于RiemannLiouville分数阶微分的图像增强方法.该方法利用基本分数阶微积分的形式,根据数字图像的自相关性对RiemannLiouville分数阶微分中常数分数阶微... 针对传统图像增强过程中存在丢失细节且容易出现欠增强或过增强的不足,提出一种基于RiemannLiouville分数阶微分的图像增强方法.该方法利用基本分数阶微积分的形式,根据数字图像的自相关性对RiemannLiouville分数阶微分中常数分数阶微分不为0的情况进行改进;定义了新的微分增强模板系数,构造了8个方向的分数阶微分卷积模板,并将其应用于图像增强.实验结果表明,文中方法在对图像高频信息进行提升的同时能够有效地提升图像的中低频信息,使得图像的纹理细节,特别是边缘信息更加突出,图像的清晰度及信息熵等图像质量指标有明显的提高,增强后图像的视觉效果良好. 展开更多
关键词 分数阶微分 改进riemann-liouville微分 图像增强 微分卷积模板 边界点
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Riemann-Liouville分数阶微积分的定义及其性质 被引量:8
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作者 靳丹丹 马芳芳 么焕民 《哈尔滨师范大学自然科学学报》 CAS 2011年第3期20-22,共3页
作为微积分理论的发展,分数阶微积分的概念早已提出,实际应用的介入为它注入了新的生机.分数阶微积分成为研究分数阶微分方程,分形函数的有力工具,它被应用于分形集合、分形函数、分形PDE、函数空间等领域,近年来分数阶微积分被广泛的... 作为微积分理论的发展,分数阶微积分的概念早已提出,实际应用的介入为它注入了新的生机.分数阶微积分成为研究分数阶微分方程,分形函数的有力工具,它被应用于分形集合、分形函数、分形PDE、函数空间等领域,近年来分数阶微积分被广泛的应用到建立各种数学模型. 展开更多
关键词 riemann-liouville分数阶微积分 分数阶微分 分数阶积分
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凸函数的关于Riemann-Liouville分式积分的Hermite-Hadamard型不等式 被引量:4
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作者 白淑萍 石德平 谷桂花 《湖北民族学院学报(自然科学版)》 CAS 2015年第4期384-387,共4页
凸函数的Hermite-Hadamard型不等式具有重要的理论意义,并且有着广泛的应用.首先建立了一个关于Riemann-Liouville分式积分的等式,然后讨论凸函数的关于Riemann-Liouville分式积分的Hermite-Hadamard型积分不等式,得到了若干个结果.
关键词 riemann-liouville分式积分 凸函数 Hermite-Hadamard型积分不等式
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Riemann-Liouville分数阶图像增强算法及其电路实现 被引量:5
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作者 陈庆利 黄果 +1 位作者 蒲亦非 周激流 《沈阳工业大学学报》 EI CAS 北大核心 2012年第5期549-555,共7页
为了解决整数阶微分对图像纹理增强效果不明显及Grümwald-Letnikov(G-L)微分后会使RGB彩色图像边缘色彩失真的问题,提出了一种Riemann-Liouville(R-L)分数阶图像增强算法并讨论了该算法的电路实现.从R-L定义出发,推导出分数阶微分... 为了解决整数阶微分对图像纹理增强效果不明显及Grümwald-Letnikov(G-L)微分后会使RGB彩色图像边缘色彩失真的问题,提出了一种Riemann-Liouville(R-L)分数阶图像增强算法并讨论了该算法的电路实现.从R-L定义出发,推导出分数阶微分方程,构造了数字图像8个方向上的0~1阶分数阶微分模板并讨论了其数值运算规则,在此基础上构造并实现了数字图像的R-L分数阶微分电路,并在HSI空间对I分量进行分数阶微分实现彩色图像增强.实验结果表明,该算法能比较明显地增强图像的纹理和边缘细节,增强后的图像清晰度和对比度提高,图像视觉效果明显,具有非线性增强灰度图像和彩色图像的复杂纹理特征及边缘信息的独特优势和良好效果. 展开更多
关键词 图像增强 分数阶微分 分数阶微分算子 riemann-liouville分数阶微分 HSI色彩空间 分数阶微分卷积模板 空间滤波 分数阶数字微分电路
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基于Riemann-Liouville导数的分数阶Pfaff-Birkhoff原理和分数阶Birkhoff方程 被引量:4
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作者 周燕 张毅 《科技通报》 北大核心 2013年第3期4-10,共7页
研究分数阶Pfaff-Birkhoff变分问题。列写出Riemann-Liouville分数阶导数的定义及其有关性质。建立了基于Riemann-Liuville分数阶导数的分数阶Pfaff-Birkhoff原理,并由分数阶Pfaff-Birkhoff原理推导出了分数阶Birkhoff方程及其横截性条... 研究分数阶Pfaff-Birkhoff变分问题。列写出Riemann-Liouville分数阶导数的定义及其有关性质。建立了基于Riemann-Liuville分数阶导数的分数阶Pfaff-Birkhoff原理,并由分数阶Pfaff-Birkhoff原理推导出了分数阶Birkhoff方程及其横截性条件。研究表明:整数阶Pfaff-Birkhoff原理和Birkhoff方程是本文结果的特例。文末举例说明结果的应用。 展开更多
关键词 riemann-liouville分数阶导数 分数阶Pfaff-Birkhoff原理 分数阶Birkhoff方程 横截性条件
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基于Riemann-Liouville分数阶微分的图像增强 被引量:3
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作者 勾荣 《制造业自动化》 北大核心 2013年第16期1-4,共4页
根据Riemann-Liouville分数阶微分的定义,推导了分数阶微分的差分表达式,考虑中心像素邻域八个方向像素点的影响,构造了5×5大小的分数阶微分图像增强算子模板。对灰度图像和彩色图像进行了增强处理,并与传统整数阶微分图像锐化增... 根据Riemann-Liouville分数阶微分的定义,推导了分数阶微分的差分表达式,考虑中心像素邻域八个方向像素点的影响,构造了5×5大小的分数阶微分图像增强算子模板。对灰度图像和彩色图像进行了增强处理,并与传统整数阶微分图像锐化增强算子的增强效果进行了比较。结果表明,分数阶微分算子在提升图像高频分量的同时,也能有效地保留图像的中低频细节纹理信息,图像增强视觉效果明显优于传统图像锐化增强算子,且分数阶微分阶次可调,是一种灵活有效的图像增强算法。 展开更多
关键词 数字图像处理 图像增强 分数阶微分 riemann-liouville 微分阶次
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