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The UNIFORM C^(0)ESTIMATE AND WEIGHTED ESTIMATE OF GENERALIZED CHRISTOFFEL-MINKOWSKI PROBLEMS
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作者 ZHANG Jin-hu 《数学杂志》 2024年第5期397-405,共9页
In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the... In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2]. 展开更多
关键词 weighted gradient estimate convex solution minkowski type problem
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WEIGHTED WEAK TYPE ESTIMATES INVOLVING SPACES GENERATED BY BLOCKS 被引量:1
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作者 Lu Shanzhen Guido Weiss Beijing Normal University Washington University inst. Louis 《Analysis in Theory and Applications》 1994年第1期58-64,共7页
The problem studied in this paper is how to establish weighted estimates of weak type near L^1 for those operators that are not of weak type(1,1).
关键词 show Math weightED WEAK TYPE estimateS INVOLVING SPACES GENERATED BY BLOCKS
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Weighted Estimates for the Maximal Commutator of Singular Integral Operator on Spaces of Homogeneous Type
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作者 ZHANG HAO 《Communications in Mathematical Research》 CSCD 2010年第1期53-66,共14页
Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associa... Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable. 展开更多
关键词 spaces of homogeneous type weighted estimates singular integral operator COMMUTATOR maximal operator
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A robust triaxial localization method of AE source using refraction path
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作者 Yichao Rui Jie Chen +4 位作者 Jiongkun Chen Jiadong Qiu Zilong Zhou Wenzhong Wang Jinyang Fan 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2024年第4期521-530,共10页
Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE... Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers. 展开更多
关键词 Acoustic emission(AE) Source localization Robust method Refraction paths weight estimations
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Data-Based Filters for Non-Gaussian Dynamic Systems With Unknown Output Noise Covariance
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作者 Elham Javanfar Mehdi Rahmani 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期866-877,共12页
This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise.The challenge of designing a suitable filter in the presence of an unknown cova... This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise.The challenge of designing a suitable filter in the presence of an unknown covariance matrix is addressed by focusing on the output data set of the system.Considering that data generated from a Gaussian distribution exhibit ellipsoidal scattering,we first propose the weighted sum of norms(SON)clustering method that prioritizes nearby points,reduces distant point influence,and lowers computational cost.Then,by introducing the weighted maximum likelihood,we propose a semi-definite program(SDP)to detect outliers and reduce their impacts on each cluster.Detecting these weights paves the way to obtain an appropriate covariance of the output noise.Next,two filtering approaches are presented:a cluster-based robust linear filter using the maximum a posterior(MAP)estimation and a clusterbased robust nonlinear filter assuming that output noise distribution stems from some Gaussian noise resources according to the ellipsoidal clusters.At last,simulation results demonstrate the effectiveness of our proposed filtering approaches. 展开更多
关键词 Data-based filter maximum likelihood estimation unknown covariance weighted maximum likelihood estimation weighted sum-of-norms clustering
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On the rate of complete convergence for weighted sums of NSD random variables and an application 被引量:5
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作者 NADERI Habib AMINI Mohammad BOZORGNIA Abolghasem 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第3期270-280,共11页
In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the ran... In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator. 展开更多
关键词 complete convergence negatively superadditive-dependent random weighted estimate
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Estimating liver weight of adults by body weight and gender 被引量:22
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作者 See Ching Chan Chi Leung Liu +4 位作者 Chung Mau Lo Banny K Lam Evelyn W Lee Yik Wong Sheung Tat Fan 《World Journal of Gastroenterology》 SCIE CAS CSCD 2006年第14期2217-2222,共6页
AIM: To estimate the standard liver weight for assessing adequacies of graft size in live donor liver transplantation and remnant liver in major hepatectomy for cancer. METHODS: In this study, anthropometric data of... AIM: To estimate the standard liver weight for assessing adequacies of graft size in live donor liver transplantation and remnant liver in major hepatectomy for cancer. METHODS: In this study, anthropometric data of body weight and body height were tested for a correlation with liver weight in 159 live liver donors who underwent donor right hepatectomy including the middle hepatic vein. Liver weights were calculated from the right lobe graft weight obtained at the back table, divided by the proportion of the right lobe on the computed tomography. RESULTS: The subjects, all Chinese, had a mean age of 35.8 ± 10.5 years, and a female to male ratio of 118:41. The mean volume of the right lobe was 710.14 ±131.46 mL and occupied 64.55%±4.47% of the whole liver on computed tomography. Right lobe weighed 598.90±117.39 g and the estimated liver weight was 927.54 ± 168.78 g. When body weight and body height were subjected to multiple stepwise linear regression analysis, body height was found to be insignificant. Females of the same body weight had a slightly lower liver weight. A formula based on body weight and gender was derived: Estimated standard liver weight (g)=218+BW (kg)× 12.3+gender×51 (R^2 = 0.48) (female=0, male= 1). Based on the anthropometric data of these 159 subjects, liver weights were calculated using previously published formulae derived from studies on Caucasian, .lapanese, Korean, and Chinese. All formulae overestimated liver weights compared to this formula. The Japanese formula overestimated the estimated standard liver weight (ESLW) for adults less than 60 kg.CONCLUSION: A formula applicable to Chinese males and females is available. A formula for individual races appears necessary. 展开更多
关键词 estimated standard liver weight Liver tranplantation
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A Telepresence-Guaranteed Control Scheme for Teleoperation Applications of Transferring Weight-Unknown Objects 被引量:1
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作者 Jinfei Hu Zheng Chen +2 位作者 Xin Ma Han Lai Bin Yao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第6期1015-1025,共11页
Currently,most teleoperation work is focusing on scenarios where slave robots interact with unknown environments.However,in some fields such as medical robots or rescue robots,the other typical teleoperation applicati... Currently,most teleoperation work is focusing on scenarios where slave robots interact with unknown environments.However,in some fields such as medical robots or rescue robots,the other typical teleoperation application is precise object transportation.Generally,the object’s weight is unknown yet essential for both accurate control of the slave robot and intuitive perception of the human operator.However,due to high cost and limited installation space,it is unreliable to employ a force sensor to directly measure the weight.Therefore,in this paper,a control scheme free of force sensor is proposed for teleoperation robots to transfer a weight-unknown object accurately.In this scheme,the workspace mapping between master and slave robot is firstly established,based on which,the operator can generate command trajectory on-line by operating the master robot.Then,a slave controller is designed to follow the master command closely and estimate the object’s weight rapidly,accurately and robust to unmodeled uncertainties.Finally,for the sake of telepresence,a master controller is designed to generate force feedback to reproduce the estimated weight of the object.In the end,comparative experiments show that the proposed scheme can achieve better control accuracy and telepresence,with accurate force feedback generated in only 500 ms. 展开更多
关键词 Adaptive robust control TELEOPERATION TELEPRESENCE TRANSPARENCY weight estimation
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The RAMA Ped Card: Does it work for actual weight estimation in child patients at the emergency department 被引量:2
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作者 Thavinee Trainarongsakul Pitsucha Sanguanwit +2 位作者 Supawan Rojcharoenchai Kittisak Sawanyawisuth Yuwares Sittichanbuncha 《World Journal of Emergency Medicine》 CAS 2017年第2期126-130,共5页
BACKGROUND: In emergency conditions, the actual weight of infants and young children are essential for treatments. The RAMATHIBODI Pediatric Emergency Drug Card or RAMA Ped Card has also been developed to estimate act... BACKGROUND: In emergency conditions, the actual weight of infants and young children are essential for treatments. The RAMATHIBODI Pediatric Emergency Drug Card or RAMA Ped Card has also been developed to estimate actual weight of the subjects. This study aimed to validate the RAMA Ped Card in correctly identifying the actual weight of infants and young adults.METHODS: This study was a prospective study. We enrolled all consecutive patients under 15 years of age who visited the emergency department(ED). All eligible patients' actual weight and height were measured at the screening point of the ED. The weight of each patient was also measured using the unlabeled RAMA Ped Card. The Cohen's kappa values and agreement percentages were calculated.RESULTS: During the study period, there were 345 eligible patients. The RAMA Ped Card had a 61.16% agreement with the actual weight with a kappa of 0.54(P<0.01), while the agreement with the actual height had a kappa of 0.90 and 91.59% agreement. Sub-group analysis found kappa scores with good range in two categories: in cases of accidents and in the infant group(kappa of 0.68 and 0.65, respectively).CONCLUSION: The RAMA Ped Card had a fair correlation with the actual weight in child patients presenting at the ED. Weight estimation in infant patients and children who presented with accidents were more accurate. 展开更多
关键词 CHILD weight estimation CARD KAPPA
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Weighted Likelihood Estimation Method Based on the Multidimensional Nominal Response Model
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作者 孙珊珊 陶剑 《Northeastern Mathematical Journal》 CSCD 2008年第3期250-256,共7页
The Monte Carlo study evaluates the relative accuracy of Warm's (1989) weighted likelihood estimate (WLE) compared to the maximum likelihood estimate (MLE) using the nominal response model. And the results indi... The Monte Carlo study evaluates the relative accuracy of Warm's (1989) weighted likelihood estimate (WLE) compared to the maximum likelihood estimate (MLE) using the nominal response model. And the results indicate that WLE was more accurate than MLE. 展开更多
关键词 weighted likelihood estimation item response model nominal response model
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An Non-parametrical Approach to Estimate Location Parameters under Simple Order
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作者 孙旭 《Northeastern Mathematical Journal》 CSCD 2005年第2期175-180,共6页
This paper deals with estimating parameters under simple order when samples come from location models. Based on the idea of Hodges and Lehmann estimator (H-L estimator), a new approach to estimate parameters is propos... This paper deals with estimating parameters under simple order when samples come from location models. Based on the idea of Hodges and Lehmann estimator (H-L estimator), a new approach to estimate parameters is proposed, which is difference with the classical L1 isotonic regression and L2 isotonic regression. An algorithm to compute estimators is given. Simulations by the Monte-Carlo method is applied to compare the likelihood functions with respect to L1 estimators and weighted isotonic H-L estimators. 展开更多
关键词 H-L estimator simple partial the ith population isotonic H-L estimator weighted isotonic H-L estimator
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Factors Influencing the Accuracy of Sonographyestimated Fetal Weight:A Retrospective Cohort Study in the Chinese Population
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作者 Fang-Can Sun Hai-Hong Wang +6 位作者 Jing-Jing Zhang Xin-Xian Gu Ting Hu Ming-Yue Wang Yin-Di Zhu You-Guo Cheni Bing Han 《Reproductive and Developmental Medicine》 CAS CSCD 2023年第4期203-209,共7页
Objective:To evaluate the accuracy of sonography-estimated fetal weight(EFW)and to determine the potential factors influencing EFW accuracy in the Chinese population.Methods:Eleven widely used formulae were chosen to ... Objective:To evaluate the accuracy of sonography-estimated fetal weight(EFW)and to determine the potential factors influencing EFW accuracy in the Chinese population.Methods:Eleven widely used formulae were chosen to evaluate the accuracy of EFW in 7016 cases in a retrospective cohort study.Nine potential factors(prenatal body mass index[BMI],gestational age[GA],birth weight[BW],fetal sex,fetal presentation,amniotic fluid volume[AFV],seniority of sonographers,the time interval between ultrasonic measurement and delivery,and diabetes mellitus)were analyzed by binary logistic regression to determine whether they influenced sonography-EFW.Results:All 11 models had high correlation coefficients between EFW and BW(r=0.819–0.843).Model 3 was the most accurate formula for the Chinese population.Compared to fetuses with EFW of 2500–3999g,the accuracy of EFW decreased by 69.10%(P<0.001)for fetuses less than 2500g,and decreased by 54.10%(P<0.001)for fetuses larger than 4000g.The accuracy of EFW in female fetuses decreased by 12.70%compared with male fetuses(P=0.021).Compared to the EFW calculated 1-3 days before delivery,the accuracy of the EFW performed 4–7 days before delivery showed a significant decrease(P=0.014).The accuracy of EFW was influenced by the individual measurement accuracy of the sonographers.Maternal BMI,DM,GA,fetal presentation,and AFV did not influence the accuracy of EFW after adjustment.Conclusion:Model 3 was the most accurate model for the Chinese population.The BW,fetal sex,time interval,and technique of the sonographers had different influences on the accuracy of EFW. 展开更多
关键词 ACCURACY estimated fetal weight ULTRASONOGRAPHY Fetal sex Birth weight
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Robust Estimators for Poisson Regression
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作者 Idriss Abdelmajid Idriss Weihu Cheng 《Open Journal of Statistics》 2023年第1期112-118,共7页
The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation st... The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators. 展开更多
关键词 Poisson Regression Model Maximum Likelihood Estimator Robust Estimation Contaminated Model weighted Maximum Likelihood Estimator
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Weighted Probability Density Estimator with Updated Bandwidths
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作者 WU Yi YU Wei +1 位作者 WANG Xuejun PRAKASA RAO B L S 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2024年第2期886-906,共21页
In this paper,the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursiv... In this paper,the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursive or non-recursive.Some statistical results including weak consistency,strong consistency,rate of strong consistency,and asymptotic normality are established under some mild conditions.Moreover,the random weighted estimator is also investigated.Some numerical simulations and a real data analysis are presented to study the numerical performances of the estimators. 展开更多
关键词 Asymptotic normality CONSISTENCY numerical simulation probability density real data analysis updated bandwidths weighted estimator
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2.5D induced polarization forward modeling using the adaptive finite-element method
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作者 叶益信 李予国 +1 位作者 邓居智 李泽林 《Applied Geophysics》 SCIE CSCD 2014年第4期500-507,511,共9页
The conventional finite-element(FE) method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such... The conventional finite-element(FE) method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization(IP). In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4 % and 1.2 % for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models. 展开更多
关键词 Induced polarization(IP) dual error estimate weighting unstructured mesh ADAPTIVE finite-element(FE)
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Dynamic Case Retrieval Method With Subjective Preferences and Objective Information for Emergency Decision Making 被引量:8
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作者 Jing Zheng Yingming Wang Shengqun Chen 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第3期749-757,共9页
Case-based reasoning(CBR) is one of the best methods for generating an effective solution in an emergency. In recent years, some methods for generating emergency alternatives have been included in practical CBR applic... Case-based reasoning(CBR) is one of the best methods for generating an effective solution in an emergency. In recent years, some methods for generating emergency alternatives have been included in practical CBR applications, but there have been no in-depth studies of these processes. In this study,we propose a new method for dynamic case retrieval with subjective preferences and objective information, which considers the personal preferences of the decision makers and changes in the attributes of the emergency as the situation develops. First,we present a formula for calculating the case similarity and changing trends in the case considered, where similar cases are obtained. Next, we describe a method for measuring the overall assessment value with respect to similar historical cases, which is obtained by aggregating the case similarity, the utility case similarity, the first response time, and the implementation effect.The subjective preferences and objective information are also integrated in the decision-making process. Finally, we present a case study based on the emergency response to a fire in a highrise building, which illustrates the applicability and feasibility of the proposed method. 展开更多
关键词 Case-based reasoning(CBR) dynamic case retrieval pairwise comparison matrix preference relation weight estimation
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Weighted L^p-estimates for Stokes flow in R_+~n with applications to the non-stationary Navier-Stokes flow 被引量:4
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作者 HE Cheng1 & WANG LiZhen21Division of Mathematics, Department of Mathematical and Physical Sciences, National Natural Science Foundation of China, Beijing 100085, China 2Department of Mathematics and Center for Nonlinear Studies, Northwest University, Xi’an 710069, China 《Science China Mathematics》 SCIE 2011年第3期573-586,共14页
We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space Rn+ (n 2). Three kinds of the weighted Lp-Lr estimates are established for th... We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space Rn+ (n 2). Three kinds of the weighted Lp-Lr estimates are established for the Stokes semigroup generated by the Stokes operator in the half-space R+n (n 2). As an application of the weighted estimates of the Stokes semigroup, a class of local and global strong solutions in weighted Lp (R+n) are constructed, following the approach given by Kato. 展开更多
关键词 Navier-Stokes flow Stokes flow weighted estimate
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Non-invasive evaluation of lower urinary tract symptoms(LUTS)in men 被引量:6
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作者 Reshma Mangat Henry S.S.Ho Tricia L.C.Kuo 《Asian Journal of Urology》 2018年第1期42-47,共6页
Lower urinary tract symptoms(LUTS)are common in males over the age of 40 years old and are likely to increase with an aging population.Currently urodynamic studies are the gold standard to determine the aetiology of v... Lower urinary tract symptoms(LUTS)are common in males over the age of 40 years old and are likely to increase with an aging population.Currently urodynamic studies are the gold standard to determine the aetiology of voiding dysfunction and LUTS.However,due to its invasive nature,a great number of non-invasive ultrasound based investigations have been developed to assess patients with symptomatic LUTS.The clinical application of noninvasive tests could potentially stratify patients who would require more invasive investigations and allow more precise patient directed treatment.A PubMed literature review was performed and we will discuss the non-invasive investigations that have been developed thus far,focusing on bladder wall and detrusor wall thickness(BWT&DWT),ultrasound estimated bladder weight(UEBW)and intravesical prostatic protrusion(IPP). 展开更多
关键词 Bladder outlet obstruction Benign prostatic enlargement Intravesical prostatic protrusion Lower urinary tract symptoms Bladder wall thickness Ultrasound estimated bladder weight Near infrared spectroscopy
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Robust LS-SVM regression for ore grade estimation in a seafloor hydrothermal sulphide deposit 被引量:2
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作者 ZHANG Xunan SONG Shiji +1 位作者 LI Jiabiao WU Cheng 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2013年第8期16-25,共10页
Due to the geological complexities of ore body formation and limited borehole sampling, this paper propos- es a robust weighted least square support vector machine (LS-SVM) regression model to solve the ore grade es... Due to the geological complexities of ore body formation and limited borehole sampling, this paper propos- es a robust weighted least square support vector machine (LS-SVM) regression model to solve the ore grade estimation for a seafloor hydrothermal sulphide deposit in Solwara 1, which consists of a large proportion of incomplete samples without ore types and grade values. The standard LS-SVM classification model is applied to identify the ore type for each incomplete sample. Then, a weighted K-nearest neighbor (WKNN) algorithm is proposed to interpolate the missing values. Prior to modeling, the particle swarm optimiza- tion (PSO) algorithm is used to obtain an appropriate splitting for the training and test data sets so as to eliminate the large discrepancies caused by random division. Coupled simulated annealing (CSA) and grid search using 10-fold cross validation techniques are adopted to determine the optimal tuning parameter- s in the LS-SVM models. The effectiveness of the proposed model by comparing with other well-known techniques such as inverse distance weight (IDW), ordinary kriging (OK), and back propagation (BP) neural network is demonstrated. The experimental results show that the robust weighted LS-SVM outperforms the other methods, and has strong predictive and generalization ability. 展开更多
关键词 weighted LS-SVIVl.grade estimation incomplete samples data division
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SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS 被引量:1
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作者 刘颖博 Ingo WITT 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期125-150,共26页
For the 2-D quasilinear wave equation (δt2-△x)u+2∑i,j=0gij(δu)δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consid... For the 2-D quasilinear wave equation (δt2-△x)u+2∑i,j=0gij(δu)δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation (δt2-△x)u+2∑i,j=0gij(δu)δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction. 展开更多
关键词 global existence null condition weighted energy estimate continuous induction
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