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Examining the Use of Scott’s Formula and Link Expiration Time Metric for Vehicular Clustering
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作者 Fady Samann Shavan Askar 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期2421-2444,共24页
Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are sim... Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET. 展开更多
关键词 CLUsTERING vehicular network scott’s formula FastPAM
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Reciprocity Relation between Alternative Gravity Formulas
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作者 Hans Hermann Otto 《Journal of Applied Mathematics and Physics》 2024年第4期1432-1440,共9页
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw... We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter. 展开更多
关键词 Gravity formulas Reciprocity Distance Relation NEWTON EINsTEIN Bhandari Higgs Field Dirac’s Large Number
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A Construction That Produces Wallis-Type Formulas 被引量:1
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作者 Joshua M. Fitzhugh David L. Farnsworth 《Advances in Pure Mathematics》 2013年第6期579-585,共7页
Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myerson, are presented. The initial square is replaced with a rectangle, and also the dimensionality o... Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myerson, are presented. The initial square is replaced with a rectangle, and also the dimensionality of the construction is increased. By selecting values for the various parameters, such as the lengths of the sides of the original rectangle or rectangular box in dimensions more than two and their relationships to the size of the attached rectangles or rectangular boxes, some interesting formulas are found. Examples are Wallis-type infinite-product formulas for the areas of p-circles with p > 1. 展开更多
关键词 walliss formula Unit p-Circle INFINITE Product Π GAMMA Function
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Wallis不等式的一个推广 被引量:2
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作者 赵岳清 吴庆标 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2006年第4期372-375,共4页
针对著名的Wallis不等式,引入参数z,给出了Wallis不等式的一个推广结果.当0<z<1,n>1为正自然数时,1Γ(1-z)nz1+2(1n--z1)z<(1-z)(2-n!z)…(n-z)<Γ(1-z)nz11+21n-+z1z,1Γ(1-z)nz1+2(1n--z1)z<(1-z)(2-n!z)…(n-z)<... 针对著名的Wallis不等式,引入参数z,给出了Wallis不等式的一个推广结果.当0<z<1,n>1为正自然数时,1Γ(1-z)nz1+2(1n--z1)z<(1-z)(2-n!z)…(n-z)<Γ(1-z)nz11+21n-+z1z,1Γ(1-z)nz1+2(1n--z1)z<(1-z)(2-n!z)…(n-z)<Γ(1-z)nz11+12-nzz(n≥22),并改进了已有文献的结果. 展开更多
关键词 wallis不等式 Г-函数 泰勒展开
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Stirling公式与Wallis公式之间的关系 被引量:1
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作者 向日光 《长沙电力学院学报(自然科学版)》 2006年第4期95-96,100,共3页
Stirling公式为对于任意自然数n,n!=2nπnen.e12θn=(0<θ<1)及wa
关键词 sTIRLING公式 wallis公式 收敛级数
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关于含有Wallis公式的双边不等式及其应用 被引量:1
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作者 隆建军 《四川职业技术学院学报》 2012年第1期157-159,共3页
得到了含有Wallis公式的一个简洁而更为精细的双边不等式,作为应用有效地解决了一些幂级数的收敛性问题.
关键词 不等式 wallis公式 积分不等式 级数 收敛性
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Wallis数列推广的一个单调性结果 被引量:1
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作者 舒阳春 《高等数学研究》 2015年第6期12-12,35,共2页
讨论了推广的Wallis数列{n+c∫π/20sinnxdx}(n≥1,c为常数)单调性证明.所得结论是,当0≤c≤1/4时,数列为单调增加的;当c≥1时,该数列是单调减少的.
关键词 wallis公式 wallis数列 单调性
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Wallis公式与Stirling公式的推广
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作者 韩凯 《数学理论与应用》 2017年第2期73-78,共6页
Wallis公式和Stirling公式是高等数学中两个重要的公式.本文将Wallis公式和Stirling公式中的通项序数n推广为实数n+α,得到广义Wallis公式和广义Stirling公式,并讨论二者之间的内在联系.
关键词 wallis公式 sTIRLING公式 伽马函数Γ(x) 贝塔函数B(p q)
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Wallis公式新证明
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作者 屈芝莲 《科学技术与工程》 2011年第3期548-550,共3页
借助于类比思维,利用根与系数关系类似联想的思维方法及差分方程解的收敛性,给出了沃利斯(Wallis)公式的新证明。旨在借鉴模仿创新思想,利用新视角方法,促进工程数学与实际问题的融合,打通复杂计算的瓶颈,建立快速通道。
关键词 沃利斯公式 根与系数关系 差分方程 收敛
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含Wallis公式的双边不等式的一个新证明 被引量:1
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作者 应玮婷 《台州学院学报》 2008年第3期1-3,23,共4页
利用数列的单调收敛性得到一个含Wallis公式的更精细的双边不等式.
关键词 wallis公式 不等式 单调数列
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对wallis双边不等式的一个改进及应用
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作者 池爱子 郑米海 郑鹏飞 《佳木斯大学学报(自然科学版)》 CAS 2013年第3期438-440,共3页
通过改进文献[5]的方法,本文得到了关于Wallis双边不等式的加强,其结果更加精细,同时利用这个新结果改进了一些其他结论.
关键词 wallis公式 wallis不等式 单调数列
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Bushen Yizhi Formula regulates the IRE1αpathway to alleviate endoplasmic reticulum stress in an Alzheimer’s disease rat model
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作者 XIRU XU YUAN FANG +5 位作者 BIAO ZHANG SHICHAO TENG XIANG WU JING ZHANG XIAOQUN GU MEIXIA MA 《BIOCELL》 SCIE 2023年第7期1595-1609,共15页
While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amylo... While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amyloid-beta peptide(Aβ)were used to treat rat pheochromocytoma cells(P12)and human neuroblastoma cells(SH-SY5Y).Cell morphological changes were observed to determine the in vitro cell damage.Cell Counting Kit(CCK)-8 assay and flow cytometry were employed to identify cell viability and apoptosis/cell cycle,respectively.Western blotting and immunohistochemistry were employed to measure the expressions of endoplasmic reticulum stress(ERS)-related proteins(GRP78 and CHOP),p-IRE1α,IRE1α,ASK1,p-JNK,JNK,Bax,Bcl-2,XBP-1,and Bim.Fura 2-acetoxymethyl ester(Fura-2/AM)was used to determine the intracellular calcium(Ca^(2+))concentration.Also,an AD model was constructed by injecting Aβinto the CA1 area of the hippocampus in Sprague Dawley rats.AD model rats were gavaged with different concentrations of Bushen Yizhi Formula for 14 consecutive days.The Morris water maze experiment was conducted to test the learning and memory of rats.Hematoxylin&Eosin(H&E)and Terminal-deoxynucleotidyl Transferase(TdT)-mediated dUTP Nick-End Labeling(TUNEL)staining were done to determine histopathological changes in the brain.Results:Bushen Yizhi Formula relieved the Aβ-induced effects including cell injury,decreased viability,increased apoptosis,G0/G1 phase cell cycle arrest,upregulation of GRP78,CHOP,p-IRE1α,p-JNK,Bax,XBP-1 and Bim,as well as down-regulation of Bcl-2.These results were also seen with IRE1αsilencing.While Aβsuppressed the learning and memory abilities of rats,the Bushen Yizhi Formula alleviated these effects of Aβ.Brain nerve cell injury induced by Aβcould also be treated with Bushen Yizhi Formula.Conclusion:Bushen Yizhi Formula could influence ERS through the IRE1αsignaling pathway to achieve its therapeutic effects on AD. 展开更多
关键词 Bushen Yizhi formula Alzheimer’s disease Endoplasmic reticulum stress IRE1α
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一种含参数的Wallis公式与Stirling公式 被引量:1
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作者 李建军 贾恬 《数学理论与应用》 2008年第1期52-54,共3页
利用离散变量连续化的思想,得到了含参数的Wallis公式与Stirling公式,它们是对这两个经典公式的一种推广形式。
关键词 wallis公式与stirling公式 高斯-欧拉公式 参数
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含连续参数的Wallis公式
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作者 徐军 《高等数学研究》 2017年第6期32-33,共2页
以Wallis积分为基础,构造含连续参数的积分函数,利用该函数的递推性质和取极限的方法,最终得到含连续参数的Wallis公式.
关键词 wallis积分 wallis公式 极限
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On the Weyl’s Lemma for Triharmonic Functions
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作者 ZHENG Run-jie ZENG Jia-min FANG Yi 《Chinese Quarterly Journal of Mathematics》 2024年第3期288-294,共7页
In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
关键词 Weyl’s lemma Harmonic functions Triharmonic functions Test functions Mean value formulas
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New Color-Difference Formula Based on CIECAM97s 被引量:1
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作者 宦晖 李为 赵达尊 《Journal of Beijing Institute of Technology》 EI CAS 2001年第2期149-152,共4页
To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new f... To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new formula is then deduced in the space and named CDF CIECAM97s. The factors for lightness, chroma and hue correction in the formula are derived by linear regression according to BFD? CP data sets. It is found by statistical analysis that CDF CIECAM97s is in closer accordance with the visual assessments when compared with CMC(1∶1), CIE94 and CIE L *a *b * color difference formulae. Based on color appearance model, the new color difference formula can be used to predict color difference perception in a varity of different viewing conditions. 展开更多
关键词 CIECAM97s color difference formulae color space
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基于Ackermann's formula的类反斜线回滞系统滑模控制 被引量:1
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作者 张达科 胡跃明 郭华芳 《机械工程学报》 EI CAS CSCD 北大核心 2005年第1期11-15,共5页
回滞现象广泛地存在于许多机械控制领域。由于回滞特性具有不可微性,从而使得对回滞系统的控制变得困难和复杂,同时由于回滞可能引起系统的振荡,甚至造成系统的不稳定,因此有必要对回滞系统的有效控制进行研究。考虑到回滞系统建模仍然... 回滞现象广泛地存在于许多机械控制领域。由于回滞特性具有不可微性,从而使得对回滞系统的控制变得困难和复杂,同时由于回滞可能引起系统的振荡,甚至造成系统的不稳定,因此有必要对回滞系统的有效控制进行研究。考虑到回滞系统建模仍然是个研究的领域,针对类反斜线回滞系统进行研究。把类反斜线回滞模型分解为确定的线性部分和已知上界的不确定非线性部分,利用Ackermann's formula给出了类反斜线回滞系统的滑模控制律。仿真表明此滑模控制律是有效的,同时此滑模控制保证了整个系统的稳定性。 展开更多
关键词 类反斜线回滞 滑模控制 Ackermann’s formula
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S4B-2 Bushen-Yizhi Formula Inhibits the NLRP3/NFκB Mediated Neuroinflammation and Improves the Motor Dysfunction in a Mouse Model of Parkinson’s Disease
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作者 王奇 《神经药理学报》 2018年第4期71-72,共2页
Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TC... Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TCM theory understanding,so we can learn from each other in the process of drug discovery.The clinical results showed that Bushen-Yizhi formula(BSYZ)could effectively improve the neurological function score of senile dementia patients and had a better anti-dementia effect.Further pharmacological studies showed that BSYZ had neuroprotective effects,such as anti-inflammatory,anti-oxidation,anti-apoptosis and neurotrophic effects.In this study,the therapeutic effect of BSYZ on PD was evaluated in vivo and in vivo,and its molecular mechanism was discussed in order to expand the scope of application of BSYZ and to provide strategies for drug discovery of related neurodegenerative diseases.Methods:C57 BL/6 mice were injected intraperitoneally with MPTP to construct a PD mouse model.BSYZ(1.46,2.92,5.84 mg·kg-1)was administered for two weeks,and the positive control group was given a NSAID,piroxicam(12.5 mg·kg-1).After 1 week of pretreatment,MPTP was used to construct a PD mouse model.The mice were subjected to Rotation test on days 1,3 and 5,6th day.and the movement coordination and exercise ability of the drug on PD mice were observed on theThe number of TH-positive cells,Iba1 and CD68-labeled microglial cells in SNpc region were observed by immunofluorescence to observe the proliferation and activation of microglial cells and GFAP-labeled astrocytes.Western blotting was used to detect the nuclear transfer of NLRP3,Caspase-1,ASC,pro-IL-1β,IL-1βand NF-κB in the midbrain.Results:1.BSYZ could significantly improve the expression of MPTP model mice in the experiment of fatigue and Y-maze,increase the number of neurons in SNpc region and the positive expression of TH protein.2.BSYZ significantly inhibited the number of Iba1/CD68-positive microglial cells in MPTP-model mice and decreased the number of GFAP-positive astrocytes.3.BSYZ significantly inhibited the expression of NLRP3-associated protein in BV2 microglial cells induced by LPS+ATP and inhibited the nuclear transfer of NF-κB.Conclusion:BSYZ can effectively relieve the motor dysfunction of PD model mice,improve the damage of dopaminergic neurons,inhibit the proliferation and activation of microglial cells and astrocytes,and have good anti-MPTPinduced neuroinflammation and neuroinflammation mediated by nuclear transfer of NF-κB.The results show that BSYZ has a good prospect of anti-Parkinson’s disease and provides valuable drug discovery strategies for the related neurodegenerative diseases. 展开更多
关键词 Parkinson’s disease Drug Discovery Bushen-Yizhi formula neuroinfl ammation
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基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方改善CSE诱导小鼠肺泡巨噬细胞炎症反应的作用机制
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作者 王卉 杨勤军 +3 位作者 周凡超 杨程 童佳兵 李泽庚 《海南医学院学报》 2023年第17期1295-1301,共7页
目的:基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方(SQTS)改善香烟烟雾提取物(Cigarette smoking extract,CSE)诱导小鼠肺泡巨噬细胞(MH-S)炎症反应的作用机制。方法:以MH-S细胞为研究对象,通过CCK-8法分析SQTS对MH-S细胞的安全性及药效浓... 目的:基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方(SQTS)改善香烟烟雾提取物(Cigarette smoking extract,CSE)诱导小鼠肺泡巨噬细胞(MH-S)炎症反应的作用机制。方法:以MH-S细胞为研究对象,通过CCK-8法分析SQTS对MH-S细胞的安全性及药效浓度;随后MH-S分为空白组、模型组(8%CSE)和SQTS低、中、高剂量组(40、80、160 mg/L)。ELISA检测细胞上清TNF-α、IL-1β和IL-6含量;DCFH-DA荧光探针法检测细胞中ROS水平;Westernblot检测TLR4/NF-κB/NLRP3通路蛋白的表达,使用TLR4抑制剂TAK-242验证SQTS在TLR4/NF-κB/NLRP3通路上的作用。结果:与空白组比较,CSE组细胞活力降低,炎症因子TNF-α、IL-1β和IL-6的含量增加(P<0.05),ROS荧光表达水平显著升高(P<0.01),TLR4/NF-κB/NLRP3通路蛋白表达明显增加(P<0.05);与模型组比较,参芪调肾方各剂量组细胞活力升高,以上各指标表达水平均有所降低(P<0.05),且TAK-242各组细胞TLR4/NF-κB/NLRP3通路蛋白减少(P<0.05)。结论:参芪调肾方可减轻CSE诱导的MH-S细胞的炎症反应,其机制可能与抑制TLR4/NF-κB/NLRP3通路有关。 展开更多
关键词 参芪调肾方 CsE MH-s细胞 TLR4/NF-κB/NLRP3信号通路 炎症
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Compound Formula Rehmannia alleviates levodopainduced dyskinesia in Parkinson's disease 被引量:9
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作者 Long Teng Fang Hong +2 位作者 Chenguang Zhang Jiancheng He Haiying Wang 《Neural Regeneration Research》 SCIE CAS CSCD 2014年第4期407-412,共6页
Compound Formula Rehmannia has been shown to be clinically effective in treating Parkinson's disease and levodopa-induced dyskinesia; however, the mechanisms remain unclear. In this study, we established a model of P... Compound Formula Rehmannia has been shown to be clinically effective in treating Parkinson's disease and levodopa-induced dyskinesia; however, the mechanisms remain unclear. In this study, we established a model of Parkinson's disease dyskinesia in rats, and treated these animals with Compound Formula Rehmannia. Compound Formula Rehmannia inhibited the increase in mRNA expression of N-methyl-D-aspartate receptor subunits 1 and 2 and excitatory amino acid neurotransmitter genes, and it inhibited the reduction in expression of γ-aminobutyric acid receptor B1, an inhibitory amino acid neurotransmitter gene, in the corpus striatum. In addition, Compound Formula Rehmannia alleviated dyskinesia symptoms in the Parkinson's disease rats. These experimental findings indicate that Compound Formula Rehmannia alleviates levodopa-induced dyskinesia in Parkinson's disease by modulating neurotransmitter signaling in the corpus striatum. 展开更多
关键词 nerve regeneration traditional Chinese medicine Parkinson's disease DYsKINEsIA excitato-ry amino acid inhibitory amino acid NEUROBEHAVIOR Compound formula Rehmannia NsFC grant neural regeneration
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