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Serum proteins differentially expressed in gestational diabetes mellitus assessed using isobaric tag for relative and absolute quantitation proteomics 被引量:3
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作者 Wei-Li Cao Cui-Ping Yu Ling-Li Zhang 《World Journal of Clinical Cases》 SCIE 2024年第8期1395-1405,共11页
BACKGROUND As a well-known fact to the public,gestational diabetes mellitus(GDM)could bring serious risks for both pregnant women and infants.During this important investigation into the linkage between GDM patients a... BACKGROUND As a well-known fact to the public,gestational diabetes mellitus(GDM)could bring serious risks for both pregnant women and infants.During this important investigation into the linkage between GDM patients and their altered expression in the serum,proteomics techniques were deployed to detect the differentially expressed proteins(DEPs)of in the serum of GDM patients to further explore its pathogenesis,and find out possible biomarkers to forecast GDM occurrence.METHODS Subjects were divided into GDM and normal control groups according to the IADPSG diagnostic criteria.Serum samples were randomly selected from four cases in each group at 24-28 wk of gestation,and the blood samples were identified by applying iTRAQ technology combined with liquid chromatography-tandem mass spectrometry.Key proteins and signaling pathways associated with GDM were identified by bioinformatics analysis,and the expression of key proteins in serum from 12 wk to 16 wk of gestation was further verified using enzyme-linked immunosorbent assay (ELISA).RESULTS Forty-seven proteins were significantly differentially expressed by analyzing the serum samples between the GDMgravidas as well as the healthy ones. Among them, 31 proteins were found to be upregulated notably and the rest16 proteins were downregulated remarkably. Bioinformatic data report revealed abnormal expression of proteinsassociated with lipid metabolism, coagulation cascade activation, complement system and inflammatory responsein the GDM group. ELISA results showed that the contents of RBP4, as well as ANGPTL8, increased in the serumof GDM gravidas compared with the healthy ones, and this change was found to initiate from 12 wk to 16 wk ofgestation.CONCLUSION GDM symptoms may involve abnormalities in lipid metabolism, coagulation cascade activation, complementsystem and inflammatory response. RBP4 and ANGPTL8 are expected to be early predictors of GDM. 展开更多
关键词 Gestational diabetes mellitus Liquid chromatography-tandem mass spectrometry Isobaric tag for relative and absolute quantitation PROTEOMICS BIOMARKER
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Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables
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作者 MENG Bing WU Qunying 《应用概率统计》 CSCD 北大核心 2024年第5期710-724,共15页
In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distri... In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them. 展开更多
关键词 ANA random variables complete convergence complete moment convergence weighted sums
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Valence Bands Convergence in p-Type CoSb_(3) through Electronegative Fluorine Filling
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作者 黄写格 李家良 +5 位作者 马浩钦 李昌隆 刘天乐 段波 翟鹏程 李国栋 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第7期87-94,共8页
Band convergence is considered to be a strategy with clear benefits for thermoelectric performance,generally favoring the co-optimization of conductivity and Seebeck coefficients,and the conventional means include ele... Band convergence is considered to be a strategy with clear benefits for thermoelectric performance,generally favoring the co-optimization of conductivity and Seebeck coefficients,and the conventional means include elemental filling to regulate the band.However,the influence of the most electronegative fluorine on the CoSb_(3) band remains unclear.We carry out density-functional-theory calculations and show that the valence band maximum gradually shifts downward with the increase of fluorine filling,lastly the valence band maximum converges to the highly degenerated secondary valence bands in fluorine-filled skutterudites. 展开更多
关键词 VALENCE convergence BANDS
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Call for Papers——Feature Topic Vol.22,No.3,2025 Special Issue of China Communications:Convergence of 6G empowered Edge Intelligence and Generative AI:Theories,Algorithms,and Applications
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《China Communications》 SCIE CSCD 2024年第1期F0003-F0003,共1页
Generative artificial intelligence(AI),as an emerging paradigm in content generation,has demonstrated its great potentials in creating high-fidelity data including images,texts,and videos.Nowadays wireless networks an... Generative artificial intelligence(AI),as an emerging paradigm in content generation,has demonstrated its great potentials in creating high-fidelity data including images,texts,and videos.Nowadays wireless networks and applications have been rapidly evolving from achieving“connected things”to embracing“connected intelligence”.Generative AI has been recognized as a fundamentally innovative technology to drive the advancement of intelligent wireless communications and networks. 展开更多
关键词 CONNECTED convergence networks
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Measurement and Analysis of Vibration Effect of Free-falling Corner Cube Driving Mechanism in Free Fall Absolute Gravimeter
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作者 ZHANG Bing ZHU Xiaoyi +7 位作者 WU Qiong XUE Bing XING Lili WU Yanxiong SU Peng WANG Xiaolei WANG Yuru WANG Chuhan 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2024年第S01期84-86,共3页
The vibration interference of the reference corner cube runs through the free flight process of the free-falling corner cube,which is superimposed on the whole laser interference fringes.Thus,it is necessary to solve ... The vibration interference of the reference corner cube runs through the free flight process of the free-falling corner cube,which is superimposed on the whole laser interference fringes.Thus,it is necessary to solve the interference fringes with the entire fringe to analyze the quantitative influence of vibration on gravity measurements. 展开更多
关键词 laser interference absolute gravimeter gravity measurement vibration influence
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Diagnostic values of questionnaires of Convergence Insufficiency Symptom Survey and College of Optometrists Vision Development Quality of Life in the screening of convergence insufficiency
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作者 Ling Xiong Qian Chen Ye Wu 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2024年第5期904-908,共5页
AIM:To compare and analyse the diagnostic efficacy of the College of Optometrists Vision Development Quality of Life Questionnaire(COVD-QOL)and the Convergence Insufficiency Symptom Survey(CISS)in detecting convergenc... AIM:To compare and analyse the diagnostic efficacy of the College of Optometrists Vision Development Quality of Life Questionnaire(COVD-QOL)and the Convergence Insufficiency Symptom Survey(CISS)in detecting convergence insufficiency and to compare their diagnostic value in clinical applications.METHODS:Using the diagnostic test method,62 adult patients with convergence insufficiency(age:24.74±3.75y)and 62 normal participants(age:23.61±3.13y)who visited the Optometry Clinic of West China Hospital of Sichuan University from April 2021 to January 2023 were included.All subjects completed the CISS and COVD-QOL.Statistical analysis of the sensitivity and specificity of the CISS and COVD-QOL and comparison and joint experimental analysis of their diagnostic efficacy were performed.RESULTS:The sensitivity of the CISS and COVD-QOL for convergence insufficiency was 64.5%and 71.0%,respectively,while the specificity was 96.8%and 67.7%,respectively.Compared to the CISS alone,the combination of the CISS and COVD-QOL demonstrated lower sensitivity and specificity.The areas under the receiver operating characteristic curve of CISS,COVD-QOL and CISS combined with COVD-QOL were 0.806,0.694 and 0.782,respectively.CONCLUSION:Considering the low sensitivity of the CISS and the low specificity of the COVD-QOL,it is recommended to supplement these questionnaires with other screening tests for the detection of convergence insufficiency. 展开更多
关键词 convergence insufficiency symptom survey College of Optometrists Vision Development Quality of Life Questionnaire convergence insufficiency ASTHENOPIA
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GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY
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作者 Gonglin YUAN Xiong ZHAO Jiajia YU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1735-1746,共12页
A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gr... A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments. 展开更多
关键词 cautious BFGS nonconvex problems Lipschitz continuity projection technique global convergence
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A Novel Inverse-Free Neurodynamic Approach for Solving Absolute Value Equations
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作者 Tao Li 《Journal of Applied Mathematics and Physics》 2024年第10期3458-3468,共11页
We propose a novel inverse-free neurodynamic approach (NIFNA) for solving absolute value equations (AVE). The NIFNA guarantees global convergence and notably improves convergence speed by achieving fixed-time converge... We propose a novel inverse-free neurodynamic approach (NIFNA) for solving absolute value equations (AVE). The NIFNA guarantees global convergence and notably improves convergence speed by achieving fixed-time convergence. To validate the theoretical findings, numerical simulations are conducted, demonstrating the effectiveness and efficiency of the proposed NIFNA. 展开更多
关键词 absolute Value Equations Neurodynamic Approach Fixed-Time convergence Numerical Simulations
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Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra
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作者 SUN Rong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期438-447,共10页
In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some ... In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved. 展开更多
关键词 convergence theorems fuzzy concave integral fuzzyσ-algebra
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Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods
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作者 Ming Li Yuhang Liu +1 位作者 Yiyuan Sun Kefeng Liu 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2024年第5期110-120,共11页
The mesoscale eddy(ME)has a significant influence on the convergence effect in deep-sea acoustic propagation.This paper use statistical approaches to express quantitative relationships between the ME conditions and co... The mesoscale eddy(ME)has a significant influence on the convergence effect in deep-sea acoustic propagation.This paper use statistical approaches to express quantitative relationships between the ME conditions and convergence zone(CZ)characteristics.Based on the Gaussian vortex model,we construct various sound propagation scenarios under different eddy conditions,and carry out sound propagation experiments to obtain simulation samples.With a large number of samples,we first adopt the unified regression to set up analytic relationships between eddy conditions and CZ parameters.The sensitivity of eddy indicators to the CZ is quantitatively analyzed.Then,we adopt the machine learning(ML)algorithms to establish prediction models of CZ parameters by exploring the nonlinear relationships between multiple ME indicators and CZ parameters.Through the research,we can express the influence of ME on the CZ quantitatively,and achieve the rapid prediction of CZ parameters in ocean eddies.The prediction accuracy(R)of the CZ distance(mean R:0.9815)is obviously better than that of the CZ width(mean R:0.8728).Among the three ML algorithms,Gradient Boosting Decision Tree has the best prediction ability(root mean square error(RMSE):0.136),followed by Random Forest(RMSE:0.441)and Extreme Learning Machine(RMSE:0.518). 展开更多
关键词 convergence zone mesoscale eddy statistic analysis quantitative prediction machine learning
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On power series statistical convergence and new uniform integrability of double sequences
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作者 Sevda Y■ld■z Kamil Demirci 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期519-532,共14页
In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p... In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings. 展开更多
关键词 power series methods statistical convergence uniform integrability double sequences
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Euler Product Expressions of Absolute Tensor Products of Dirichlet L-Functions
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作者 Hidenori Tanaka Shin-ya Koyama 《Advances in Pure Mathematics》 2024年第6期451-486,共36页
In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se... In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992. 展开更多
关键词 Dirichlet L-Function absolute Tensor Product (Kurokawa Tensor Product) Euler Product
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Multi-modal knowledge graph inference via media convergence and logic rule
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作者 Feng Lin Dongmei Li +5 位作者 Wenbin Zhang Dongsheng Shi Yuanzhou Jiao Qianzhong Chen Yiying Lin Wentao Zhu 《CAAI Transactions on Intelligence Technology》 SCIE EI 2024年第1期211-221,共11页
Media convergence works by processing information from different modalities and applying them to different domains.It is difficult for the conventional knowledge graph to utilise multi-media features because the intro... Media convergence works by processing information from different modalities and applying them to different domains.It is difficult for the conventional knowledge graph to utilise multi-media features because the introduction of a large amount of information from other modalities reduces the effectiveness of representation learning and makes knowledge graph inference less effective.To address the issue,an inference method based on Media Convergence and Rule-guided Joint Inference model(MCRJI)has been pro-posed.The authors not only converge multi-media features of entities but also introduce logic rules to improve the accuracy and interpretability of link prediction.First,a multi-headed self-attention approach is used to obtain the attention of different media features of entities during semantic synthesis.Second,logic rules of different lengths are mined from knowledge graph to learn new entity representations.Finally,knowledge graph inference is performed based on representing entities that converge multi-media features.Numerous experimental results show that MCRJI outperforms other advanced baselines in using multi-media features and knowledge graph inference,demonstrating that MCRJI provides an excellent approach for knowledge graph inference with converged multi-media features. 展开更多
关键词 logic rule media convergence multi-modal knowledge graph inference representation learning
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Spatial Differentiation and Convergence Trend of High-quality Development Level of China’s Tourism Economy
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作者 CAO Shanshan HE Zhaoli +2 位作者 NIU Jinlan WANG Songmao ZHAO Lei 《Chinese Geographical Science》 SCIE CSCD 2024年第2期230-249,共20页
This paper aims to interpret the connotation of high-quality development of tourism economy(HQTE)from the perspective of the new development concepts of innovation,coordination,green,openness and sharing,and then to e... This paper aims to interpret the connotation of high-quality development of tourism economy(HQTE)from the perspective of the new development concepts of innovation,coordination,green,openness and sharing,and then to evaluate the spatial differenti-ation of China’s HQTE based on provincial panel data from 2009 to 2018.Specifically,we employ the spatial convergence model to ex-plore the absolute and conditionalβconvergence trends of HQTE in the whole country and the eastern,central and western regions of China.Our empirical results reveal that:1)within the decade,from 2009 to 2018,regions of China with the highest HQTE index is its eastern region followed by the central region and then the western region,but the fastest growing one is the western region of China fol-lowed by the central region and then the eastern region.2)Whether or not the spatial effect is included,there are absolute and condition-alβconvergence in HQTE in the whole country and aforementioned three regions.3)The degree of government attention as well as the level of economic development and location accessibility are the positive driving factors for the convergence of HQTE in the whole country and the three regions.The degree of marketization and human capital have not passed the significance test either in the whole country or in the three regions.The above conclusions could deepen the understanding of the regional imbalance and spatial conver-gence characteristics of HQTE,clarify the primary development objects,and accomplish the goal of China’s HQTE. 展开更多
关键词 new development concepts high-quality development of tourism economy(HQTE) spatial convergence China
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Exploring the Dynamics of Industrial Convergence Among RCEP Member Countries: An Empirical Study
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作者 Zheng Yuanfang 《Contemporary Social Sciences》 2024年第5期26-50,共25页
The evolving dynamics of industrial convergence among the member countries of the Regional Comprehensive Economic Partnership(RCEP)framework have emerged as a significant subject that merits in-depth consideration and... The evolving dynamics of industrial convergence among the member countries of the Regional Comprehensive Economic Partnership(RCEP)framework have emerged as a significant subject that merits in-depth consideration and analysis.This study initially employs multi-regional input-output(MRIO)data and the social network analysis(SNA)method to delineate the levels and variation trends of this industrial convergence across the RCEP member countries.It then delves into the positive effects of this convergence phenomenon on the trade and investment fields of the member countries.The research findings indicate:(a)In 2006 and 2015,before the implementation of the RCEP,the RCEP member countries displayed a relatively close industrial convergence.The convergence levels exhibited a general upward trend on both the supply and the demand sides,but there were significant disparities in the levels of industrial convergence among the member countries.Furthermore,while the convergence in the three economic sectors showed an increasing trend,the development was uneven across the board.(b)Since the implementation of the RCEP,the trade ties among the member countries within the region have strengthened significantly,and the interplay between the countries’industrial and supply chains has been characterized by high-quality collaboration and demonstrated remarkable resilience.In addition,the convergence in the investment fields of the RCEP member countries and their respective industries has unleashed a wave of positive synergies.These findings offer valuable insights that can serve as a robust foundation for formulating effective policies to advance the growth and prosperity of the RCEP region. 展开更多
关键词 RCEP international industrial convergence input-output table social network analysis method
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Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
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作者 Wes Whiting Bao Wang Jack Xin 《Communications on Applied Mathematics and Computation》 EI 2024年第2期1175-1188,共14页
We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a ... We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks. 展开更多
关键词 Hyperbolic neural network Riemannian gradient descent Riemannian Adam(RAdam) Training convergence
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Convergence over AI Governance Amid Differences
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作者 THORSTEN JELINEK 《China Today》 2024年第4期58-61,共4页
As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensurin... As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensuring safety,and promoting fairness”? 展开更多
关键词 FAIRNESS convergence LAW
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Selective Technology Importation and the Convergence in the Late Qing Dynasty: Evidence from Wired Telegraph
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作者 Jiao Yinyi Cai Meng 《China Economist》 2024年第5期117-136,共20页
Using the adoption and expansion of wired telegraph in China during the late 19^(th) century,this paper investigates the effect of cost reductions for knowledge exchange on China’s industrial growth before the outbre... Using the adoption and expansion of wired telegraph in China during the late 19^(th) century,this paper investigates the effect of cost reductions for knowledge exchange on China’s industrial growth before the outbreak of the War of Resistance Against Japanese Aggression(1931-1945),thus testing Baldwin’s theory of“the Great Convergence”in which developing countries are empowered by information and communication technologies.Based on panel data of 1858-1937,we found that wired telegraph access had a significantly positive effect,as well as a long-term growth effect,on the entry of industrial enterprises.Our mechanism analysis indicates that wired telegraph access accelerated early-stage industrialization in localities by encouraging market integration,human capital accumulation,and auxiliary commercial organizations.Only a few countries firmly asserted their telegraph sovereignty and set up their own workforce educational system during telegraph adoption.This explains why the Great Convergence arising from technology importation only occurred in a small number of countries.Our findings contribute to understanding the source of China’s modern industrial progress,as well as why global inequities remain. 展开更多
关键词 wired telegraph entry of industrial enterprises the Great convergence human capital
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Tunnel, Infrastructure Convergences/Monitoring and Engineering Role
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作者 Sali Bedaj 《Engineering(科研)》 2024年第5期134-147,共14页
Worldwide we see that the construction industry is expanding, requiring new directions, new perspectives that can help reduce time, cost, and make transportation easy, safe, and affordable. For decades now, most of th... Worldwide we see that the construction industry is expanding, requiring new directions, new perspectives that can help reduce time, cost, and make transportation easy, safe, and affordable. For decades now, most of the large cities have completed their surface infrastructure. It has become urgent to address their issues for overpopulated cities where nowadays all infrastructure is overwhelmed, these issues must be addressed, solved and have vision to build underground infrastructure. Developed countries are focused on expanding their infrastructure for road systems, subway network, railway, storm, and sanitary systems. The emergency for underground infrastructure development requires more large-scale projects to be built and it is becoming more crucial building tunnels/underground structures for the future than ever before. Engineering focus, scientific searches are looking to develop their ideas for designing and delivering project underground, but government, agencies and engineers are concerned about the safety, durability, functionality, and the lifetime of this structures planned to be functional for decades. To address all this concerns this study provides information of how to identify the risk on tunnels and underground structures by capturing data from the beginning phases of construction, to analyze, evaluate and produce bulletins and engineering reports through convergences and monitoring. Convergences are the key factor on development of infrastructure underground as it is the only way to explore and analyze the rock mass disturbance during excavation. Convergences and monitoring in infrastructure are the safety coefficient for building underground, preventing accidents, and assessing real risks associated with tunnel/mine works and ensuring progress of the construction in underground structures. This study delves into the engineering role of convergence monitoring, during construction activities on project excavated using New Austrian Tunnelling method and Sequential Excavation Method. The primary objective of convergence monitoring is to gather critical information on ground movements and disturbances, thereby enhancing safety measures during tunnel construction. The monitoring process serves as an early warning system offering evidence of the real risks associated with underground infrastructure, bringing results and engineering data to be used for the design as key coefficient for structural design, type of material, type and strength of the concrete, rebars, concrete mix design. By using the convergence and monitoring system on underground infrastructure this study represents information that can contribute to risk assessment, structural analysis, and the lifetime of a project. 展开更多
关键词 TUNNEL INFRASTRUCTURE convergence/Monitoring Underground Monitoring
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Convergence Phenomenon with Fourier Series of tg(x2)and Alike
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作者 Alfred Wünsche 《Advances in Pure Mathematics》 2024年第7期556-595,共40页
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali... The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. . 展开更多
关键词 Gibbs Phenomenon Generalized Functions Weak convergence Chebyshev Polynomials of First and Second Kind Even and Odd Generating Functions for Chebyshev Polynomials POLYLOGARITHMS Completeness Relations
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