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Infrared small target detection algorithm via partial sum of the tensor nuclear norm and direction residual weighting
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作者 SUN Bin XIA Xing-Ling +1 位作者 FU Rong-Guo SHI Liang 《红外与毫米波学报》 北大核心 2025年第2期277-288,共12页
Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small targe... Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target. 展开更多
关键词 infrared small target detection infrared patch tensor model partial sum of the tensor nuclear norm direction residual weighting
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Asymptotics of the Maximum Sum of Randomly Stopped Finite Random Walks with Subexponential Distribution
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作者 CAO Shuxia LIU Zixin ZHANG Shuguang 《应用概率统计》 北大核心 2026年第1期75-89,共15页
We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the ... We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the distribution of the lengths of these intervals is relatively light compared to the distribution of the increments of the random walks,we derive the asymptotic tail distribution of the partial maximum sum over the random time interval. 展开更多
关键词 subexponential distribution maximum sum random walk ASYMPTOTICS
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Some Reciprocity Formulas for Generalized Dedekind-Rademacher Sums
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作者 HE Yuan SHI Yongguo 《数学进展》 北大核心 2026年第1期85-102,共18页
In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's... In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases. 展开更多
关键词 Bernoulli function Dedekind sum Hurwitz and Lerch zeta function reciprocity formula
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A Novel Improved Puma Optimizer to Boost Photovoltaic Array Production in Partially Shaded Environments
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作者 Nagwan Abdel Samee Ahmed Fathy +2 位作者 Mohamed A.Mahdy Maali Alabdulhafith Essam H.Houssein 《Computer Modeling in Engineering & Sciences》 2026年第2期737-771,共35页
This research proposes an improved Puma optimization algorithm(IPuma)as a novel dynamic recon-figuration tool for a photovoltaic(PV)array linked in total-cross-tied(TCT).The proposed algorithm utilizes the Newton-Raph... This research proposes an improved Puma optimization algorithm(IPuma)as a novel dynamic recon-figuration tool for a photovoltaic(PV)array linked in total-cross-tied(TCT).The proposed algorithm utilizes the Newton-Raphson search rule(NRSR)to boost the exploration process,especially in search spaces with more local regions,and boost the exploitation with adaptive parameters alternating with random parameters in the original Puma.The effectiveness of the introduced IPuma is confirmed through comprehensive evaluations on the CEC’20 benchmark problems.It shows superior performance compared to both established and modern metaheuristic algorithms in terms of effectively navigating the search space and achieving convergence towards near-optimal regions.The findings indicated that the IPuma algorithm demonstrates considerable statistical promise and surpasses the performance of competing algorithms.In addition,the proposed IPuma is utilized to reconfigure a 9×9 PV array that operates under different shade patterns,such as lower triangular(LT),long wide(LW),and short wide(SW).In addition to other programmed approaches,such as the Whale optimization algorithm(WOA),grey wolf optimizer(GWO),Harris Hawks optimization(HHO),particle swarm optimization(PSO),gravitational search algorithm(GSA),biogeography-based optimization(BBO),sine cosine algorithm(SCA),equilibrium optimizer(EO),and original Puma,the indicated method is contrasted to the traditional configurations of TCT and Sudoku.In addition,the metrics of mismatch power loss,maximum efficiency improvement,efficiency improvement ratio,and peak-to-mean ratio are calculated to assess the effectiveness of the indicated approach.The proposed IPuma improved the generated power by 36.72%,28.03%,and 40.97%for SW,LW,and LT,respectively,outperforming the TCT configuration.In addition,it achieved the best maximum efficiency improvement among the algorithms considered,with 26.86%,21.89%,and 29.07%for the examined patterns.The results highlight the superiority and competence of the proposed approach in both convergence rates and stability,as well as applicability to dynamically reconfigure the PV system and enhance its harvested energy. 展开更多
关键词 Photovoltaic partial shade RECONFIGURATION improved puma METAHEURISTIC
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Investigating the Dynamic Behavior of Bubbles in Oil During Partial Discharge
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作者 Hongbin Wu Hongshun Liu +7 位作者 Yifan Wang Pengfei Lu Luyao Liu Hanliang Lin Dongxin He Qingmin Li Qingquan Li Weijiang Chen 《CSEE Journal of Power and Energy Systems》 2026年第1期547-556,共10页
The partial discharge occurring in the weak part of the insulation of a converter transformer results in the formation of a large number of bubbles in the insulating oil.The migration,deformation,and other dynamic beh... The partial discharge occurring in the weak part of the insulation of a converter transformer results in the formation of a large number of bubbles in the insulating oil.The migration,deformation,and other dynamic behaviors of bubbles in the region of a strong electric field can cause them to easily accumulate into“small bridges”of impurities that can lead to breakdown of the oil gap.The authors of this study experimentally investigate and discuss the mechanisms of migration and deformation of bubbles in oil during partial discharge under composite AC/DC voltage to clarify their dynamic behaviors.The influence of the initial position of the bubbles on their trajectory of migration and velocity as well as the morphological changes occurring in them are analyzed using numerical simulations.The results show that the bubbles move away from the strong electric field due to the action of the dielectrophoretic force.The interface of the bubbles is longitudinally stretched under the action of the electrostrictive force and the vertical component of the drag force and gradually recovers to assume a spherical shape under the influence of surface tension and the horizontal component of the drag force. 展开更多
关键词 BUBBLE converter transformer dynamic behavior partial discharge
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树与圈的笛卡尔积的(sum-)Balaban指标
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作者 因草吉 邓波 周丽娟 《南开大学学报(自然科学版)》 北大核心 2026年第1期63-72,共10页
研究了图的Balaban指标和sum-Balaban指标的计算,获得了树与圈的笛卡尔积的Balanban指标和sum-Balaban指标的计算表达式,并且建立了相应的上界和下界,同时构造了达到对应上界和下界的图.
关键词 Balanban指标 sum-Balaban指标 笛卡尔积 距离
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Quality related fault detection based on dynamic-inner convolutional autoencoder and partial least squares and its application to ironmaking process
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作者 Ping Wu Yuxuan Ni +4 位作者 Huaimin Wang Xuguang Hu Zhenquan Wu Jian Jiang Yaowu Hu 《Chinese Journal of Chemical Engineering》 2026年第1期267-276,共10页
Partial least squares (PLS) model maximizes the covariance between process variables and quality variables,making it widely used in quality-related fault detection.However,traditional PLS methods focus primarily on li... Partial least squares (PLS) model maximizes the covariance between process variables and quality variables,making it widely used in quality-related fault detection.However,traditional PLS methods focus primarily on linear processes,leading to poor performance in dynamic nonlinear processes.In this paper,a novel quality-related fault detection method,named DiCAE-PLS,is developed by combining dynamic-inner convolutional autoencoder with PLS.In the proposed DiCAE-PLS method,latent features are first extracted through dynamic-inner convolutional autoencoder (DiCAE) to capture process dynamics and nonlinearity from process variables.Then,a PLS model is established to build the relationship between the extracted latent features and the final product quality.To detect quality-related faults,Hotelling's T^(2) statistic is employed.The developed quality-related fault detection is applied to the widely used industrial benchmark of the Tennessee. 展开更多
关键词 partial least squares Dynamic-inner convolutional autoencoder Quality-related fault detection Neural networks Safety Dynamic modeling
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Data-Driven Predictive Control for Continuous-Time Nonlinear Systems:A Nonzero-Sum Game Approach
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作者 Juan Liu Hao Zhang +1 位作者 Yifan Xie Frank Allgöwer 《IEEE/CAA Journal of Automatica Sinica》 2026年第2期495-497,共3页
Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over p... Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over predictive control input sequences,deriving multiple optimal predictive control input sequences from its solution. 展开更多
关键词 predictive control nonzero sum game observation loss predictive control input sequencesderiving continuous time nonlinear systems optimal predictive control input sequences reinforcement learning
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Partial-EMT in oral squamous cell carcinoma:molecular circuitry and clinical translation
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作者 Chunhua Wang Motoharu Sarubo +1 位作者 Siqi Chen Yasusei Kudo 《International Journal of Oral Science》 2026年第1期18-32,共15页
Oral squamous cell carcinoma(OSCC)is a prevalent malignancy with high morbidity and mortality.Globally,about 400000 people are affected,often with a poor quality of life.Its high mortality is mainly due to its aggress... Oral squamous cell carcinoma(OSCC)is a prevalent malignancy with high morbidity and mortality.Globally,about 400000 people are affected,often with a poor quality of life.Its high mortality is mainly due to its aggressive growth and tendency to spread.Epithelial-mesenchymal transition(EMT)is a central regulatory hub driving tumor cell migration and invasion by enabling changes in cell characteristics.During EMT,epithelial cells gradually take on mesenchymal traits,gaining mobility and spreading mo re easily.Recent multi-omics studies show that many cancer cells exist in a hybrid or partial-EMT state,which lies between the full epithelial and mesenchymal forms.Cells in this state are especially invasive and metastatic,with high plasticity that promotes tumor progression.This review summarizes the role of partial-EMT in OSCC,with a focus on how it alters the tumor microenvironment(TME),promotes invasion and metastasis,and influences cancer stem cells(CSCs).We also highlight the link between partial-EMT and treatment resistance in OSCC.Based on these insights,we discuss therapeutic strategies targeting partial-EMT to improve outcomes.Targeting partial-EMT may offer promising strategies to enhance treatment effectiveness and improve patient survival and quality of life. 展开更多
关键词 cancer stem cells partial Epithelial mesenchymal transition oral squamous cell carcinoma emtepithelial cells invasion metastasis treatment resistance therapeutic strategies oral squamous cell carcinoma oscc
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Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence 被引量:4
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作者 TAN Zhong-quan PENG Zuo-xiang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期319-326,共8页
Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ(n) =EX1Xn+1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level (x/√2 l... Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ(n) =EX1Xn+1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level (x/√2 log n+√2 log n-log(4π log n)/2√log n) √1-τ(n) + X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on (0,1]. 展开更多
关键词 stationary Gaussian sequence exceedances point process partial sum.
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Almost sure central limit theory for products of sums of partial sums 被引量:7
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作者 WU Qun-ying 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第2期169-180,共12页
Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a... Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp(lnβk),0≤β〈1.And in a sense,our results have reached the optimal form. 展开更多
关键词 almost sure central limit theorem WEIGHT product of sums of partial sums.
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ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES 被引量:3
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作者 甘师信 陈平炎 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期283-290,共8页
Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n|^k∑i=1 Xni| is inv... Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n|^k∑i=1 Xni| is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2]. 展开更多
关键词 NA random variable maximum partial sum complete convergence convergence in probability
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SELF-NORMALIZED CENTRAL LIMIT THEOREM AND ESTIMATION OF VARIANCE OF PARTIAL SUMS FOR NEGATIVE DEPENDENT RANDOM VARIABLES 被引量:1
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作者 Zhang Lixin\ Shi StrongwayDept.of Math.,Zhejiang Univ.,Xixi Campus,Hangzhou 310028,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第3期326-334,共9页
Let {X n,n≥1} be a stationary LNQD or NA sequence satisfying EX 1=μ,EX 2 1<∞ and (Var S n)/n→σ 2 as n→∞.In this paper a class of self-normalized central limit theorems and estimators of Var S n are ... Let {X n,n≥1} be a stationary LNQD or NA sequence satisfying EX 1=μ,EX 2 1<∞ and (Var S n)/n→σ 2 as n→∞.In this paper a class of self-normalized central limit theorems and estimators of Var S n are studied.The weak and strong consistency of the estimators of Var S n are presented. 展开更多
关键词 estimation negative dependence CONSISTENCY variance of partial sums.
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Moments of the maximum of normed partial sums of ρ^--mixing random variables 被引量:1
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作者 LIU Xiang-dong LIU Jin-xia 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第3期355-360,共6页
Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 |Sn/n^1/r|^p(0 〈 r... Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 |Sn/n^1/r|^p(0 〈 r 〈 2,p 〉 0) are given,which are the same as that in the independent case. 展开更多
关键词 moment of supremum of normed partial sum ρ^--mixing random variable
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2010—2023年北京市西城区猩红热流行病学特征及CUSUM模型的预警分析
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作者 秦迪 魏孝侃 +5 位作者 马春娜 管秀刚 陈瑜 孙景異 肖征 初艳慧 《预防医学情报杂志》 2025年第6期746-752,共7页
目的 分析2010—2023年北京市西城区猩红热的流行特征,并结合累积和(CUSUM)模型进行预警分析,为制定有针对性的防控措施提供科学依据。方法 应用描述性流行病学方法对2010—2023年北京市西城区猩红热病例进行分析,使用SPSS 25.0软件进... 目的 分析2010—2023年北京市西城区猩红热的流行特征,并结合累积和(CUSUM)模型进行预警分析,为制定有针对性的防控措施提供科学依据。方法 应用描述性流行病学方法对2010—2023年北京市西城区猩红热病例进行分析,使用SPSS 25.0软件进行数据整理分析,率的比较采用χ^(2)检验,R 4.3.3软件绘制发病率分布热图,应用CUSUM模型探测猩红热流行的起始时间,检验水准α=0.05。结果 2010—2023年,北京市西城区共报告猩红热病例3 328例,年均发病率为18.84/10万,不同年份发病率差异有统计学意义(χ^(2)=1 450.543,P<0.001;χ_(趋势)^(2)=238.637,P<0.001)。2011年报告病例数及发病率最高(504例,40.54/10万);2014年和2017—2018年分别出现2次反弹,发病率分别为30.62/10万、32.09/10万和33.03/10万;2020—2022年为低发年,年均发病率为1.85/10万,较2010—2019年下降了92.35%。猩红热发病具有显著的季节性,4至6月和11月至次年1月为发病高峰期,2020—2023年流行高峰并不明显,流行起始时间最早为每年的第11周和第39周,不同月份发病率差异有统计学意义(χ^(2)=1 260.787,P<0.001)。男性年均发病率高于女性(χ^(2)=228.578,P<0.001)。3~9岁发病人数最多,3岁~组和6岁~组发病率较高,不同年龄组发病率差异有统计学意义(χ^(2)=37 869.544,P<0.001)。病例以学生(70.43%)和幼托儿童(27.46%)为主。年均报告病例数和年均发病率最高的3个街道分别为展览路、新街口和德胜街道,月均发病率最高的为展览路街道5月发病率,各地区发病率差异有统计学意义(χ^(2)=315.562,P<0.001)。结论 2010—2023年北京市西城区猩红热发病率整体呈波动下降趋势,流行的起始时间在每年的3月和10月,3~9岁年龄组的小学生及幼托儿童为主要发病人群。流行前期应做好预测预警,加强对小学及托幼机构等重点场所和重点区域的监测与报告,严格落实各项防控措施,防止疫情出现反弹。 展开更多
关键词 猩红热 A组链球菌 流行病学特征 累积和模型
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Ultrasound-Guided Transmuscular Quadratus Lumbar Block Reduces Opioid Consumption after Laparoscopic Partial Nephrectomy 被引量:13
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作者 Xulei Cui Xu Li +6 位作者 Minna Li Yuelun Zhang Yi Xie Weigang Yan Yushi Zhang Zhigang Ji Yuguang Huang 《Chinese Medical Sciences Journal》 CAS CSCD 2020年第4期289-296,共8页
Objectives Transmuscular quadratus lumborum block(TQLB)may provide postoperative analgesia in patients undergoing intraperitoneal surgeries.The purpose of this study was to examine the potential efficacy of TQLB among... Objectives Transmuscular quadratus lumborum block(TQLB)may provide postoperative analgesia in patients undergoing intraperitoneal surgeries.The purpose of this study was to examine the potential efficacy of TQLB among patients undergoing retroperitoneal procedures,such as the laparoscopic partial nephrectomy(LPN).Methods This prospective,randomized,controlled study was conducted from August 2017 to November 2018 at Peking Union Medical College Hospital(Beijing,China).Patients who were scheduled for a LPN,aged 18・70 years old with an ASA physical status score of I-II were randomly assigned to receive either TQLB with 0.6 ml/kg of 0.5%ropivacaine plus general anesthesia(TQLB group)or general anesthesia alone(control group).Patient-controlled intravenous analgesia with morphine was initiated immediately upon surgery completion.The primary outcome was the cumulative consumption of morphine within 8 h after surgery.The secondary outcome included postoperative consump廿ons of morphine at other time points,pain score at rest and during activity,postoperative nausa and vomitting(PONV),and recovery related parameters.Results Totally 30 patients per group were recruited in the study.The 8 h consumption of morphine was lower in theTQLB group than in the control group(median,0.023 mg/kg vs.0.068 mg/kg,U=207.5,P<0.001).No significant differences were observed in postoperative pain scores between the two groups.Patients in the TQLB group had fewer episodes of PONV(20%vs.47%,χ2=4.&P=0.028)in the first 24 h after surgery and higher scores for quality of recovery(mean,13&6 vs.131.9,t=-2.164,P=0.035)120 h after surgery than the controls.Conclusions TQLB resulted in an opioid-sparing effect during the early postoperative period following LPN,as well as a lower incidence of PONV and improved quality of recovery. 展开更多
关键词 quadratus lumbar block OPIOIDS postoperative analgesia partial nephrectomy
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On Moments of the Maximum of Normed Partial Sums of ρ^--mixing Random Variables 被引量:1
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作者 谭成 吴群英 何燕梅 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第4期499-504,共6页
In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The resul... In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables. 展开更多
关键词 moments of supermun of normed partial sums ρ^--mixing random variables ρ^--mixing random variables negatively associated random variables
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Physicochemical, Biochemical and Instrumental Attributes and Consumer Acceptability of Dry-Fermented Sausages Elaborated with Combined Partial Substitutions of Sodium Chloride and Pork Backfat 被引量:1
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作者 Hassan Safa Philippe Gatellier +5 位作者 Jean-Louis Berdagué Nathalie Kondjoyan Frédéric Mercier Stéphane Portanguen Raphaël Favier Pierre-Sylvain Mirade 《Food and Nutrition Sciences》 2016年第14期1297-1314,共18页
We performed 6 fabrications of dry-fermented sausages to investigate, at laboratory scale, the effects of combined partial substitutions of sodium chloride by potassium chloride and pork backfat by sunflower oil on ke... We performed 6 fabrications of dry-fermented sausages to investigate, at laboratory scale, the effects of combined partial substitutions of sodium chloride by potassium chloride and pork backfat by sunflower oil on key physical-chemical and biochemical parameters, instrumental colour and texture measurements, and the consumer acceptability of the end-products. Regarding the physical-chemical parameters, statistical analysis of results showed that final product weight loss was impacted by fat content and use of sunflower oil;final mean water activity value was only affected by salt level;and animal fat content impacted pH values, only at the end of drying. Regarding the biochemical parameters investigated, we statistically found a marked impact of partial substitution of NaCl by KCl on the proteolysis evolution, of fat level and sodium content on the end-product lipolysis, and finally, a significant effect of animal fat level and incorporation of sunflower oil on both protein and lipid oxidations. However, the new product formulations combining salt and fat substitutions lead to globally acceptable water loss and water activity values and similar rates of proteolysis, lipolysis and lipid oxidation, but less protein oxidation. From a practical point of view, the results clearly showed that sodium and animal fat contents in dryfermented sausages can be drastically reduced with no too marked adverse effect on colour, final textural properties or consumer acceptability. On the basis of these laboratory results, new healthier dry-fermented products can be manufactured by an industrial company in the near future. 展开更多
关键词 Dry-Fermented Sausage Combined partial Substitutions KCL Sunflower Oil Oxidation
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On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences
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作者 Gan Shi-xin 1, Qiu De-hua 2 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China 2. Department of Mathematics, Hengyang Teacher’s College, Hengyang 421008, Hunan, China 《Wuhan University Journal of Natural Sciences》 CAS 2002年第2期133-136,共4页
Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are ob... Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained. 展开更多
关键词 p-smoothable Banach space weighted partial sum martingale difference sequence strong law of large numbers
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Partial sums of generalized harmonic starlike univalent functions generated by a (p,q)−Ruscheweyh-type harmonic differential operator
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作者 Om P Ahuja Asena Cetinkaya Raj Kumar 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第4期584-595,共12页
Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruschewey... Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in D.We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class.Using this coefficient condition,we then examine ratios of partial sums of f in H.In all cases the results are sharp.In addition,the results so obtained generalize the related works of some authors,and many other new results are obtained. 展开更多
关键词 (p q)-calculus (p q)-derivative operator Q-CALCULUS q-derivative operator (p q)-Ruscheweyhtype harmonic differential operator partial sums coefficient estimate
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