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Asymptotically Exact a Posteriori Error Estimates for Non-Symmetric Eigenvalue Problems
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作者 Jun ZHANG Jiayu HAN 《Journal of Mathematical Research with Applications》 2025年第3期411-426,共16页
This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ... This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis. 展开更多
关键词 Polynomial Preserving Recovery non-symmetric eigenvalue problem a posteriori error estimates
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Detection of co-phasing error in segmented mirror based on extended Young’s interferometry combined with Vision Transformer
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作者 LIU Yin-ling YAO Chi +3 位作者 OUYANG Shang-tao WAN Yi-rong CHEN Mo LI Bin 《中国光学(中英文)》 北大核心 2026年第1期205-218,共14页
Due to the inability of manufacturing a single monolithic mirror at the 10-meter scales,segmented mirrors have become indispensable tools in modern astronomical research.However,to match the imaging performance of the... Due to the inability of manufacturing a single monolithic mirror at the 10-meter scales,segmented mirrors have become indispensable tools in modern astronomical research.However,to match the imaging performance of the monolithic counterpart,the sub-mirrors must maintain precise co-phasing.Piston error critically degrades segmented mirror imaging quality,necessitating efficient and precise detection.To ad-dress the limitations that the conventional circular-aperture diffraction with two-wavelength algorithm is sus-ceptible to decentration errors,and the traditional convolutional neural networks(CNNs)struggle to capture global features under large-range piston errors due to their restricted local receptive fields,this paper pro-poses a method that integrates extended Young’s interference principles with a Vision Transformer(ViT)to detect piston error.By suppressing decentration error interference through two symmetrically arranged aper-tures and extending the measurement range to±7.95μm via a two-wavelength(589 nm/600 nm)algorithm.This approach exploits ViT’s self-attention mechanism to model global characteristics of interference fringes.Unlike CNNs constrained by local convolutional kernels,the ViT significantly improves sensitivity to inter-ferogram periodicity.The simulation results demonstrate that the proposed method achieves a measurement accuracy of 5 nm(0.0083λ0)across the range of±7.95μm,while maintaining an accuracy exceeding 95%in the presence of Gaussian noise(SNR≥15 dB),Poisson noise(λ≥9 photons/pixel),and sub-mirror gap er-ror(Egap≤0.2)interference.Moreover,the detection speed shows significant improvement compared to the cross-correlation algorithm.This study establishes an accurate,robust framework for segmented mirror error detection,advancing high-precision astronomical observation. 展开更多
关键词 segmented mirror co-phasing piston errors ViT Young’s interference principles
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FeatherGuard:A Data-Driven Lightweight Error Protection Scheme for DNN Inference on Edge Devices
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作者 Dong Hyun Lee Na Kyung Lee Young Seo Lee 《Computers, Materials & Continua》 2026年第2期2000-2016,共17页
There has been an increasing emphasis on performing deep neural network(DNN)inference locally on edge devices due to challenges such as network congestion and security concerns.However,as DRAM process technology conti... There has been an increasing emphasis on performing deep neural network(DNN)inference locally on edge devices due to challenges such as network congestion and security concerns.However,as DRAM process technology continues to scale down,the bit-flip errors in the memory of edge devices become more frequent,thereby leading to substantial DNN inference accuracy loss.Though several techniques have been proposed to alleviate the accuracy loss in edge environments,they require complex computations and additional parity bits for error correction,thus resulting in significant performance and storage overheads.In this paper,we propose FeatherGuard,a data-driven lightweight error protection scheme for DNN inference on edge devices.FeatherGuard selectively protects critical bit positions(that have a significant impact on DNN inference accuracy)against bit-flip errors,by considering various DNN characteristics(e.g.,data format,layer-wise weight distribution,actually stored logical values).Thus,it achieves high error tolerability during DNN inference.Since FeatherGuard reduces the bit-flip errors based on only a few simple arithmetic operations(e.g.,NOT operations)without parity bits,it causes negligible performance overhead and no storage overhead.Our experimental results show that FeatherGuard improves the error tolerability by up to 6667×and 4000×,compared to the conventional systems and the state-of-the-art error protection technique for edge environments,respectively. 展开更多
关键词 Edge AI DRAM reliability error protection bit-flip error deep neural networks
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Insights into Student Perceptions of Error Feedback and Improvement Preferences in Online Programming Education
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作者 Li Zhang Tianze Wang +1 位作者 Jing Jiang Yufei Zhou 《计算机教育》 2026年第3期176-189,共14页
Online programming platforms are popular in programming education.However,there has been no research investigating students’real opinions and expectations of the error feedback mechanisms,leaving educators without a ... Online programming platforms are popular in programming education.However,there has been no research investigating students’real opinions and expectations of the error feedback mechanisms,leaving educators without a solid data foundation when attempting to improve the error feedback mechanisms.This paper makes a survey of 834 students across various programming courses and investigates student perceptions of error feedback mechanisms on online programming platforms.It explores the effectiveness of existing feedback,student satisfaction,and preferences for potential improvements,focusing on automatic error localization and program repair mechanisms.Results reveal a significant portion of students are dissatisfied with current feedback due to its limited informativeness.Students also express a clear demand for stronger feedback mechanisms,such as error localization and repair hints.Nevertheless,they prefer feedback that subtly guides them toward solutions,rather than providing direct and explicit answers,valuing the opportunity to enhance their debugging skills.The findings suggest a need for balanced,educational-focused feedback mechanisms that aid learning while promoting independent problem-solving. 展开更多
关键词 error feedback Online programming education Program error localization Automated program repair
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Forecast errors of tropical cyclone track and intensity by the China Meteorological Administration from 2013 to 2022
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作者 Huanmujin Yuan Hong Wang +2 位作者 Yubin Li Kevin K.W.Cheung Zhiqiu Gao 《Atmospheric and Oceanic Science Letters》 2026年第1期72-77,共6页
This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administratio... This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development. 展开更多
关键词 Forecast error Tropical cyclone TRACK INTENSITY
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Total score of the computer vision syndrome questionnaire predicts refractive errors and binocular vision anomalies
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作者 Mosaad Alhassan Tasneem Samman +5 位作者 Hatoun Badukhen Muhamad Alrashed Balsam Alabdulkader Essam Almutleb Tahani Alqahtani Ali Almustanyir 《International Journal of Ophthalmology(English edition)》 2026年第1期90-96,共7页
AIM:To evaluate the efficacy of the total computer vision syndrome questionnaire(CVS-Q)score as a predictive tool for identifying individuals with symptomatic binocular vision anomalies and refractive errors.METHODS:A... AIM:To evaluate the efficacy of the total computer vision syndrome questionnaire(CVS-Q)score as a predictive tool for identifying individuals with symptomatic binocular vision anomalies and refractive errors.METHODS:A total of 141 healthy computer users underwent comprehensive clinical visual function assessments,including evaluations of refractive errors,accommodation(amplitude of accommodation,positive relative accommodation,negative relative accommodation,accommodative accuracy,and accommodative facility),and vergence(phoria,positive and negative fusional vergence,near point of convergence,and vergence facility).Total CVS-Q scores were recorded to explore potential associations between symptom scores and the aforementioned clinical visual function parameters.RESULTS:The cohort included 54 males(38.3%)with a mean age of 23.9±0.58y and 87 age-matched females(61.7%)with a mean age of 23.9±0.53y.The multiple regression model was statistically significant[R²=0.60,F=13.28,degrees of freedom(DF=17122,P<0.001].This indicates that 60%of the variance in total CVS-Q scores(reflecting reported symptoms)could be explained by four clinical measurements:amplitude of accommodation,positive relative accommodation,exophoria at distance and near,and positive fusional vergence at near.CONCLUSION:The total CVS-Q score is a valid and reliable tool for predicting the presence of various nonstrabismic binocular vision anomalies and refractive errors in symptomatic computer users. 展开更多
关键词 computer vision syndrome refractive errors ACCOMMODATION VERGENCE binocular vision SYMPTOMS
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Error Correction Method of Ultra-short-term Prediction Based on Load Peak-valley Characteristics for Wind Farm Cluster
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作者 Mao Yang Yunfeng Guo 《CSEE Journal of Power and Energy Systems》 2026年第1期258-270,共13页
In recent years,the global installed capacity of wind power has grown rapidly,making the enhancement of wind power prediction accuracy crucial for facilitating the integration and consumption of renewable energy.Curre... In recent years,the global installed capacity of wind power has grown rapidly,making the enhancement of wind power prediction accuracy crucial for facilitating the integration and consumption of renewable energy.Current research on ultra-short-term wind power prediction often overlooks load characteristics,resulting in an inability to adequately address grid connection requirements and load dispatching demands across different time periods.To address this limitation,this study proposes a novel approach to ultra-short-term wind power prediction error correction that incorporates load peak-valley characteristics.The methodology involves three key steps:first,deriving interannual prediction error characteristics from ultra-short-term prediction results of wind farm clusters;second,establishing error correction intervals for load peak and valley periods,calculating corresponding correction coefficients,and analyzing the impact of varying correction radii on the final results;third,validating the proposed method through empirical analysis of wind farm clusters in three northeastern provinces.The results demonstrate that this approach not only improves wind power prediction accuracy but also significantly reduces the occurrence of harmful error days,thereby better meeting the operational requirements of power system dispatch. 展开更多
关键词 Correction interval correction radius error correction load peak-valley characteristics
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Bias Calibration under Constrained Communication Using Modified Kalman Filter:Algorithm Design and Application to Gyroscope Parameter Error Calibration
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作者 Qi Li Yifan Wang +2 位作者 Yuxi Liu Xingjing She Yixuan Wu 《Computer Modeling in Engineering & Sciences》 2026年第1期680-697,共18页
In data communication,limited communication resources often lead to measurement bias,which adversely affects subsequent system estimation if not effectively handled.This paper proposes a novel bias calibration algorit... In data communication,limited communication resources often lead to measurement bias,which adversely affects subsequent system estimation if not effectively handled.This paper proposes a novel bias calibration algorithm under communication constraints to achieve accurate system states of the interested system.An output-based event-triggered scheme is first employed to alleviate transmission burden.Accounting for the limited-communication-induced measurement bias,a novel bias calibration algorithm following the Kalman filtering line is developed to restrain the effect of the measurement bias on system estimation,thereby achieving accurate system state estimates.Subsequently,the Field Programmable Gate Array(FPGA)implementation of the proposed algorithm is also realized with the hope of providing fast bias calibration in practical scenarios.A simulation about a numerical example and a practical example(for gyroscope’s angular velocity bias calibration)on MATLAB is provided to demonstrate the feasibility and effectiveness of the proposed algorithm. 展开更多
关键词 Bias calibration state estimation limited communication event-Triggered scheme
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Rateless Polar Codes with Unequal Error Protection Property
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作者 Cui Chen Xiang Wei +1 位作者 Ma Siwei Guo Qing 《China Communications》 2026年第1期10-23,共14页
Mobile communications are reaching out to every aspect of our daily life,necessitating highefficiency data transmission and support for diverse data types and communication scenarios.Polar codes have emerged as a prom... Mobile communications are reaching out to every aspect of our daily life,necessitating highefficiency data transmission and support for diverse data types and communication scenarios.Polar codes have emerged as a promising solution due to their outstanding error-correction performance and low complexity.Unequal error protection(UEP)involves nonuniform error safeguarding for distinct data segments,achieving a fine balance between error resilience and resource allocation,which ultimately enhancing system performance and efficiency.In this paper,we propose a novel class of UEP rateless polar codes.The codes are designed based on matrix extension of polar codes,and elegant mapping and duplication operations are designed to achieve UEP property while preserving the overall performance of conventional polar codes.Superior UEP performance is attained without significant modifications to conventional polar codes,making it straightforward for compatibility with existing polar codes.A theoretical analysis is conducted on the block error rate and throughput efficiency performance.To the best of our knowledge,this work provides the first theoretical performance analysis of UEP rateless polar codes.Simulation results show that the proposed codes significantly outperform existing polar coding schemes in both block error rate and throughput efficiency. 展开更多
关键词 matrix extension polar codes rateless coding unequal error protection
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Error Analysis of Geomagnetic Field Reconstruction Model Using Negative Learning for Seismic Anomaly Detection
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作者 Nur Syaiful Afrizal KhairulAdibYusof +5 位作者 Lokman Hakim Muhamad Nurul Shazana Abdul Hamid Mardina Abdullah Mohd Amiruddin Abd Rahman Syamsiah Mashohor Masashi Hayakawa 《Computers, Materials & Continua》 2026年第2期1338-1353,共16页
Detecting geomagnetic anomalies preceding earthquakes is a challenging yet promising area of research that has gained increasing attention in recent years.This study introduces a novel reconstruction-based modeling ap... Detecting geomagnetic anomalies preceding earthquakes is a challenging yet promising area of research that has gained increasing attention in recent years.This study introduces a novel reconstruction-based modeling approach enhanced by negative learning,employing a Bidirectional Long Short-Term Memory(BiLSTM)network explicitly trained to accurately reconstruct non-seismic geomagnetic signals while intentionally amplifying reconstruction errors for seismic signals.By penalizing the model for accurately reconstructing seismic anomalies,the negative learning approach effectively magnifies the differences between normal and anomalous data.This strategic differentiation enhances the sensitivity of the BiLSTM network,enabling improved detection of subtle geomagnetic anomalies that may serve as earthquake precursors.Experimental validation clearly demonstrated statistically significant higher reconstruction errors for seismic signals compared to non-seismic signals,confirmed through the Mann-Whitney U test with a p-value of 0.0035 for Root Mean Square Error(RMSE).These results provide compelling evidence of the enhanced anomaly detection capability achieved through negative learning.Unlike traditional classification-based methods,negative learning explicitly encourages sensitivity to subtle precursor signals embedded within complex geomagnetic data,establishing a robust basis for further development of reliable earthquake prediction methods. 展开更多
关键词 error analysis geomagnetic field BiLSTM model negative learning earthquake precursor
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Research on ultraprecision turning and profile-error compensation technology for multi-axis linkage
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作者 Xipeng Guo Jiabin Yuan +1 位作者 Wei Shi Shaohui Yin 《Nanotechnology and Precision Engineering》 2026年第1期60-69,共10页
In an ultraprecision turning process for small-diameter optical aspheric workpieces,tool-profile errors induce mid-frequency errors in the workpiece profile,limiting further improvements in precision.In this study,an ... In an ultraprecision turning process for small-diameter optical aspheric workpieces,tool-profile errors induce mid-frequency errors in the workpiece profile,limiting further improvements in precision.In this study,an XZB three-axis linkage ultraprecision machining method is proposed,and the effects of tool-center errors are analyzed.To address residual errors in Z-direction profile-error compensation,a workpiece normal-profile-error compensation method is proposed.After XZB three-axis linkage turning and compensation,the workpiece profile error(PV)reaches 0.086μm,surpassing the precision of XZ two-axis machining,and mid-frequency errors are reduced.Compared with Z-direction profile-error compensation,which results in a profile error of 0.092μm,normal-profile-error compensation reduces PV to 0.047μm,considerably improving aspheric accuracy.Experimental results demonstrate that XZB three-axis linkage machining significantly improves the aspheric workpiece profile,enhancing both its accuracy and surface quality.This method reduces mid-frequency errors,and the subsequent application of normal-profile-error compensation further refines the profile,achieving higher overall accuracy. 展开更多
关键词 Aspheric workpiece Ultraprecision turning XZB three-axis linkage Normal error compensation
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Retaining local chemical effects:An error cancellation strategy for calculating standard gas-phase enthalpy of formation
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作者 Rui Liu Chaoyang Zhang +2 位作者 Linyuan Wang Zhiyu Huang Jian Liu 《Defence Technology(防务技术)》 2026年第1期172-179,共8页
Conventional error cancellation approaches separate molecules into smaller fragments and sum the errors of all fragments to counteract the overall computational error of the parent molecules.However,these approaches m... Conventional error cancellation approaches separate molecules into smaller fragments and sum the errors of all fragments to counteract the overall computational error of the parent molecules.However,these approaches may be ineffective for systems with strong localized chemical effects,as fragmenting specific substructures into simpler chemical bonds can introduce additional errors instead of mitigating them.To address this issue,we propose the Substructure-Preserved Connection-Based Hierarchy(SCBH),a method that automatically identifies and freezes substructures with significant local chemical effects prior to molecular fragmentation.The SCBH is validated by the gas-phase enthalpy of formation calculation of CHNO molecules.Therein,based on the atomization scheme,the reference and test values are derived at the levels of Gaussian-4(G4)and M062X/6-31+G(2df,p),respectively.Compared to commonly used approaches,SCBH reduces the average computational error by half and requires only15%of the computational cost of G4 to achieve comparable accuracy.Since different types of local effect structures have differentiated influences on gas-phase enthalpy of formation,substituents with strong electronic effects should be retained preferentially.SCBH can be readily extended to diverse classes of organic compounds.Its workflow and source code allow flexible customization of molecular moieties,including azide,carboxyl,trinitromethyl,phenyl,and others.This strategy facilitates accurate,rapid,and automated computations and corrections,making it well-suited for high-throughput molecular screening and dataset construction for gas-phase enthalpy of formation. 展开更多
关键词 Gas-phase enthalpy of formation error cancellation Quantum chemical High throughput
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Noisy data-driven identification for errors-in-variables MISO Hammerstein nonlinear models
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作者 Jie Hou Haoran Wang +1 位作者 Penghua Li Hao Su 《Control Theory and Technology》 2026年第1期111-126,共16页
In this paper,we consider a multiple-input single-output(MISO)Hammerstein system whose inputs and output are disturbed by unknown Gaussian white measurement noises.The parameter estimation of such a system is a typica... In this paper,we consider a multiple-input single-output(MISO)Hammerstein system whose inputs and output are disturbed by unknown Gaussian white measurement noises.The parameter estimation of such a system is a typical errors-in-variables(EIV)nonlinear system identification problem.This paper proposes a bias-correction least squares(BCLS)identification methods to compute a consistent estimate of EIV MISO Hammerstein systems from noisy data.To obtain the unbiased parameter estimates of EIV MISO Hammerstein system,the analytical expression of estimated bias for the standard least squares(LS)algorithm is derived first,which is a function about the variances of noises.And then a recursive algorithm is proposed to estimate the unknown term of noises variances from noisy data.Finally,based on bias estimation scheme,the bias caused by the correlation between the input–output signals exciting the true system and the corresponding measurement noise,resulting in unbiased parameter estimates of the EIV MISO Hammerstein system.The performance of the proposed method is demonstrated through a simulation example and a chemical continuously stirred tank reactor(CSTR)system. 展开更多
关键词 Biased-corrected least squares errorS-IN-VARIABLES MISO Hammerstein models Parameter estimation System identification
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Pogorelov type estimates for a class of complex Hessian quotient type equations
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作者 XU Wenzhao CHEN Chuanqiang 《纯粹数学与应用数学》 2026年第1期156-169,共14页
For the complex nonlinear elliptic partial differential equations,it is not easy to prove the Pogorelov type estimates.In this paper,we study a class of complex Hessian quotient type equations in convex cone Γ_(k),wh... For the complex nonlinear elliptic partial differential equations,it is not easy to prove the Pogorelov type estimates.In this paper,we study a class of complex Hessian quotient type equations in convex cone Γ_(k),which is of mixed Hessian type.For the Γ_(k)-admissible solutions,we establish the corresponding Pogorelov estimates with 0≤l<k<n and Pogorelov type estimates with l+1<k=n and l≥0.These extend the previous related results on the real Hessian quotient type equations. 展开更多
关键词 COMPLEX HESSIAN QUOTIENT TYPE EQUATIONS Pogorelov TYPE estimates Γ_(k)-admissible solutions
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Acute liver failure caused by amino acid or organic acid related inborn errors of metabolism
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作者 Ying Zhou Chi Chen Xin Yang 《Hepatobiliary & Pancreatic Diseases International》 2026年第1期112-114,共3页
Inborn errors of metabolism(IEMs)are a large group of disorders resulting from deficient activities in several metabolic pathways due to the dysfunction of a distinct enzyme associated with a biochemical pathway[1,2].... Inborn errors of metabolism(IEMs)are a large group of disorders resulting from deficient activities in several metabolic pathways due to the dysfunction of a distinct enzyme associated with a biochemical pathway[1,2].Toxic intermediates will be produced due to the dysfunction of biochemical pathways.The liver is responsible for many essential metabolic processes,therefore it becomes one of the most severely affected organ by metabolic diseases[3].Early onset of liver disorders in IEMs includes jaundice,hepatomegaly,splenomegaly,ascites,hepatic encephalopathy,and liver failure[4].In infants and young children under 3 years old with acute liver failure(ALF),IEMs account for 18.9%-43%[5]. 展开更多
关键词 biochemical pathway toxic intermediates metabolic diseases early acute liver failure inborn errors metabolism iems organic acid dysfunction distinct enzyme metabolic processestherefore metabolic pathways
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Perioperative management of pediatric patients with inborn errors of metabolism during liver transplantation
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作者 Susan Paulin Akila Rajakumar +2 位作者 Jagadeesh Menon Naresh Shanmugam Mohamed Rela 《World Journal of Transplantation》 2026年第1期91-102,共12页
Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progre... Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progression and provide symptomatic improvement in patients with IEM.Each metabolic disorder is unique,with the missing enzyme or transporter protein causing substrate deficiency or toxic byproduct production.Knowledge about the distribution of deficient enzymes,the percentage of enzymes replaced by LT,and the extent of extrahepatic involvement helps anticipate and manage complications in the perioperative period.Most patients have multisystem involvement and can be on complex dietary regimens.Metabolic decompensation can be triggered due to the stress response to surgery,fasting and other unanticipated complications perioperatively.Thus,a multidisciplinary team’s input including those from metabolic specialists is essential to develop disease and patient-specific strategies for the perioperative management of these patients during LT.In this review,we outline the classification of IEM,indications for LT along with potential benefits,basic metabolic defects and their implications,details of extrahepatic involvement and perioperative management strategies for LT in children with some of the commonly presenting IEM,to assist anesthesiologists handling this cohort of patients. 展开更多
关键词 Inborn errors of metabolism Anaesthesia for paediatric liver transplantation Metabolic crisis Hyperammonemia in paediatric liver transplantation Perioperative care in metabolic liver diseases
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Error estimates of H^1-Galerkin mixed finite element method for Schrdinger equation 被引量:28
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作者 LIU Yang LI Hong WANG Jin-feng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第1期83-89,共7页
An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t... An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition. 展开更多
关键词 H1-Galerkin mixed finite element method Schrdinger equation LBB condition optimal error estimates
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A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation 被引量:5
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作者 Ningning Yan Zhaojie Zhou 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第3期297-320,共24页
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc... In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results. 展开更多
关键词 Constrained optimal control problem convection dominated diffusion equation stream-line diffusion finite element method a priori error estimate a posteriori error estimate.
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Error Estimates for Mixed Finite Element Methods for Sobolev Equation 被引量:24
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作者 姜子文 陈焕祯 《Northeastern Mathematical Journal》 CSCD 2001年第3期301-304,共4页
The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space ... The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2). 展开更多
关键词 error estimate mixed finite element Sobolev equation
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