The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, v...The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, von Hann, and Börnstein were used to quantify the global (spherical) and spheroidal mean near-surface temperature of the terrestrial atmosphere. Only the datasets of Dove and Forbes published in the 1850s provided global averages below 〈T〉=14°C, mainly due to the poor coverage of the Southern Hemisphere by observations during that time. The global averages derived from the distributions of normal temperatures published between 1877 and 1913 ranged from 〈T〉=14.0°C (Batchelder) to 〈T〉=15.1°C (Ferrel). The differences between the global and the spheroidal mean near-surface air temperature are marginal. To examine the uncertainty due to interannual variability and different years considered in the historic zonal mean temperature distributions, the historical normal temperatures were perturbed within ±2σ to obtain ensembles of 50 realizations for each dataset. Numerical integrations of the perturbed distributions indicate uncertainties in the global averages in the range of ±0.3°C to ±0.6°C and depended on the number of available normal temperatures. Compared to our results, the global mean temperature of 〈T〉=15.0°C published by von Hann in 1897 and von Bezold in 1901 and 1906 is notably too high, while 〈T〉=14.4°C published by von Hann in 1908 seems to be more adequate within the range of uncertainty. The HadCRUT4 record provided 〈T〉≌?13.7°C for 1851-1880 and 〈T〉=13.6°C for 1881-1910. The Berkeley record provided 〈T〉=13.6°C and 〈T〉≌?13.5°C for these periods, respectively. The NASA GISS record yielded 〈T〉=13.6°C for 1881-1910 as well. These results are notably lower than those based on the historic zonal means. For 1991-2018, the HadCRUT4, Berkeley, and NASA GISS records provided 〈T〉=14.4°C, 〈T〉=14.5°C, and 〈T〉=14.5°C, respectively. The comparison of the 1991-2018 globally averaged near-surface temperature with those derived from distributions of zonal temperature averages for numerous parallels of latitude suggests no change for the past 100 years.展开更多
We continue our study Half-Wormholes and Ensemble Averages about the half-wormhole proposal.By generalizing the original proposal of the half-wormhole,we propose a new way to detect half-wormholes.The crucial idea is ...We continue our study Half-Wormholes and Ensemble Averages about the half-wormhole proposal.By generalizing the original proposal of the half-wormhole,we propose a new way to detect half-wormholes.The crucial idea is to decompose the observables into self-averaged sectors and non-self-averaged sectors.We find the contributions from different sectors have interesting statistics in the semi-classical limit.In particular,dominant sectors tend to condense and the condensation explains the emergence of half-wormholes and we expect that the appearance of condensation is a signal of possible bulk description.We also initiate the study of multi-linked half-wormholes using our approach.展开更多
Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes .On the other hand, because of the inertia ...Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes .On the other hand, because of the inertia of the measurement apparatus, measured sampled values obtained in practice may not be the precise value of the signal X(t) at time tk (k∈Z), but only local averages of X(t) near tk. In this paper, it is presented that a wide (or weak ) sense stationary stochastic process can be approximated by generalized sampling series with local average samples.展开更多
We study a well-known problem concerning a random variable uniformly distributed between two independent random variables. Two different extensions, randomly weighted average on independent random variables and random...We study a well-known problem concerning a random variable uniformly distributed between two independent random variables. Two different extensions, randomly weighted average on independent random variables and randomly weighted average on order statistics, have been introduced for this problem. For the second method, two-sided power random variables have been defined. By using classic method and power technical method, we study some properties for these random variables.展开更多
There is an increasing trend to apply GNSS continuous observation of short baselines to the monitoring of engineering works, such as bridges and dams, for their structural analysis and safety control. In the case of l...There is an increasing trend to apply GNSS continuous observation of short baselines to the monitoring of engineering works, such as bridges and dams, for their structural analysis and safety control. In the case of large dams, one important application of the GNSS continuous observation is thc establishment of early warning systems that demand accurate, frequently updated information and where the analysis of the baseline time series, in order to separate signal from noise is mandatory. The paper presents a study on the performance of linear filters of the asymmetric moving average type to smooth baseline time series. The transfer function of the filter is adopted as a smoothing criterion to choose an adequate order for the moving average, in face of the spectral density function of the baseline time series. Onc series of measurements of a short test baseline （325 m）, materialized in the campus of the National Laboratory for Civil Engineering, is used as an example of the proposed strategy.展开更多
In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville ...In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville fractional integral operators. Moreover, the results are interpreted in alternative form.展开更多
Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M...Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.展开更多
In compartment fires (houses, buildings, underground, warehouse, etc.), smokes are a major dan- ger during firemen intervention. Most of the time, they are at high temperature (>800?C) and they flow everywhere thro...In compartment fires (houses, buildings, underground, warehouse, etc.), smokes are a major dan- ger during firemen intervention. Most of the time, they are at high temperature (>800?C) and they flow everywhere through many kinds of ducts, which leads to the propagation of the combustion by the creation other fires in places which may be far away from the initial fire. In this paper, we present a new approach of the problem, which allows to better follow the fire behavior and especially to detect the dangers that may appear and endanger firefighters. This approach consists in a mathematical analysis based on the comparison of moving averages centered in the past, calculated on the temperature recordings of the smokes. As a consequence, this method may allow to improve decision support in real time and therefore to improve the security and the efficiency of firefighters in their operations against that kind of fires.展开更多
We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p（R）which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averag...Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p（R）which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averages are obtained for functions f∈BpΩwith the decay condition f（t）≤A/t^δ,t≠0,where A and δare positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above.展开更多
This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities fo...This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages.Thus,now we are interested in analyze the capabilities of the new algorithm when working with functions belonging to the subspace L1\L2 and that,consequently,are piecewise smooth and can present jump discontinuities.The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones.We will present the new algorithm for the approximation case and we will analyze its accuracy.Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions.The numerical results confirm the theoretical proofs presented.展开更多
Small datasets are often challenging due to their limited sample size.This research introduces a novel solution to these problems:average linkage virtual sample generation(ALVSG).ALVSG leverages the underlying data st...Small datasets are often challenging due to their limited sample size.This research introduces a novel solution to these problems:average linkage virtual sample generation(ALVSG).ALVSG leverages the underlying data structure to create virtual samples,which can be used to augment the original dataset.The ALVSG process consists of two steps.First,an average-linkage clustering technique is applied to the dataset to create a dendrogram.The dendrogram represents the hierarchical structure of the dataset,with each merging operation regarded as a linkage.Next,the linkages are combined into an average-based dataset,which serves as a new representation of the dataset.The second step in the ALVSG process involves generating virtual samples using the average-based dataset.The research project generates a set of 100 virtual samples by uniformly distributing them within the provided boundary.These virtual samples are then added to the original dataset,creating a more extensive dataset with improved generalization performance.The efficacy of the ALVSG approach is validated through resampling experiments and t-tests conducted on two small real-world datasets.The experiments are conducted on three forecasting models:the support vector machine for regression(SVR),the deep learning model(DL),and XGBoost.The results show that the ALVSG approach outperforms the baseline methods in terms of mean square error(MSE),root mean square error(RMSE),and mean absolute error(MAE).展开更多
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
In sediment transport on a mobile erodible bed,near-bed particles tend to preferentially locate under specific flow regions and form an uneven bedform.These moving and mobile particles can significantly modulate turbu...In sediment transport on a mobile erodible bed,near-bed particles tend to preferentially locate under specific flow regions and form an uneven bedform.These moving and mobile particles can significantly modulate turbulence at various scales,from inertial large-scale motions to small viscous motions.This study analyzes the particle-resolved direct numerical simulation data of particle-laden two-phase flow with multilayers of particles in turbulent flows over static and mobile beds.The double-average method is adopted for energy transfer analysis.The result shows that the alternative streaky bedform in the spanwise directions correlates with the streak structures in the near-wall turbulence in the mobile bed case.The energy redistribution and exchange,as well as the dissipation,are analyzed in detail,and an energy transfer diagram is given in the last to summarize the energy transfer processes.In both the static and mobile bed cases,flow energy is introduced into the system via the work performed by volume forces acting on the mean flow.The viscous dissipations in the double mean and form-induced fields are more pronounced in the static bed case,and the work done by the fluid-particle interfacial stress in the double mean and turbulent fields is more pronounced in the mobile bed case.The prominent energy contribution in the form-induced field is the production by the form-induced stress on the mean strain in the mobile bed case.In addition,sediment transport involving a limited number of mobile particles is insufficient to capture the energy transfer processes that occur over the troughs and may intertwine the energy transfer processes over the mobile particles and the fixed particle bed.展开更多
This paper investigates the distributed continuoustime aggregative optimization problem for second-order multiagent systems,where the local cost function is not only related to its own decision variables,but also to t...This paper investigates the distributed continuoustime aggregative optimization problem for second-order multiagent systems,where the local cost function is not only related to its own decision variables,but also to the aggregation of the decision variables of all the agents.By using the gradient descent method,the distributed average tracking(DAT)technique and the time-base generator(TBG)technique,a distributed continuous-time aggregative optimization algorithm is proposed.Subsequently,the optimality of the system's equilibrium point is analyzed,and the convergence of the closed-loop system is proved using the Lyapunov stability theory.Finally,the effectiveness of the proposed algorithm is validated through case studies on multirobot systems and power generation systems.展开更多
1.Introduction.Since the Industrial Revolution,the partial pressure of atmospheric carbon dioxide(pCO_(2))has increased markedly,rising from approximately 280 ppm(1 ppm=1μL/L)to about 420 ppm.This escalation has inte...1.Introduction.Since the Industrial Revolution,the partial pressure of atmospheric carbon dioxide(pCO_(2))has increased markedly,rising from approximately 280 ppm(1 ppm=1μL/L)to about 420 ppm.This escalation has intensified global warming,with 2024 the hottest year on record since 1850.The global mean temperature now stands 1.46℃ above the pre-industrial average(1850-1900),a value already approaching the 1.5℃ threshold set by the Paris Agreement(NOAA,2025).展开更多
Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolu...Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolution sums of the type Σ|h|≤H |ΣX<n≤2XAf (1,…, 1, n+h)λ(n)|^2. We succeed in obtaining a saving of an arbitrary power of the logarithm, provided that X^8/33+ε≤H≤X^1-ε.展开更多
Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power sta...Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.展开更多
文摘The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, von Hann, and Börnstein were used to quantify the global (spherical) and spheroidal mean near-surface temperature of the terrestrial atmosphere. Only the datasets of Dove and Forbes published in the 1850s provided global averages below 〈T〉=14°C, mainly due to the poor coverage of the Southern Hemisphere by observations during that time. The global averages derived from the distributions of normal temperatures published between 1877 and 1913 ranged from 〈T〉=14.0°C (Batchelder) to 〈T〉=15.1°C (Ferrel). The differences between the global and the spheroidal mean near-surface air temperature are marginal. To examine the uncertainty due to interannual variability and different years considered in the historic zonal mean temperature distributions, the historical normal temperatures were perturbed within ±2σ to obtain ensembles of 50 realizations for each dataset. Numerical integrations of the perturbed distributions indicate uncertainties in the global averages in the range of ±0.3°C to ±0.6°C and depended on the number of available normal temperatures. Compared to our results, the global mean temperature of 〈T〉=15.0°C published by von Hann in 1897 and von Bezold in 1901 and 1906 is notably too high, while 〈T〉=14.4°C published by von Hann in 1908 seems to be more adequate within the range of uncertainty. The HadCRUT4 record provided 〈T〉≌?13.7°C for 1851-1880 and 〈T〉=13.6°C for 1881-1910. The Berkeley record provided 〈T〉=13.6°C and 〈T〉≌?13.5°C for these periods, respectively. The NASA GISS record yielded 〈T〉=13.6°C for 1881-1910 as well. These results are notably lower than those based on the historic zonal means. For 1991-2018, the HadCRUT4, Berkeley, and NASA GISS records provided 〈T〉=14.4°C, 〈T〉=14.5°C, and 〈T〉=14.5°C, respectively. The comparison of the 1991-2018 globally averaged near-surface temperature with those derived from distributions of zonal temperature averages for numerous parallels of latitude suggests no change for the past 100 years.
基金supported by the National Youth Fund No.12105289funds from the UCAS program of special research associates+2 种基金supported by the Fundamental Research Funds for the Central Universitiesfunds from the University of Chinese Academy of Science(UCAS)NSFC NO.12175237。
文摘We continue our study Half-Wormholes and Ensemble Averages about the half-wormhole proposal.By generalizing the original proposal of the half-wormhole,we propose a new way to detect half-wormholes.The crucial idea is to decompose the observables into self-averaged sectors and non-self-averaged sectors.We find the contributions from different sectors have interesting statistics in the semi-classical limit.In particular,dominant sectors tend to condense and the condensation explains the emergence of half-wormholes and we expect that the appearance of condensation is a signal of possible bulk description.We also initiate the study of multi-linked half-wormholes using our approach.
基金National Natural Science Foundation of China (No60572113,No10501026) and Liuhui Center for Applied Mathematics
文摘Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes .On the other hand, because of the inertia of the measurement apparatus, measured sampled values obtained in practice may not be the precise value of the signal X(t) at time tk (k∈Z), but only local averages of X(t) near tk. In this paper, it is presented that a wide (or weak ) sense stationary stochastic process can be approximated by generalized sampling series with local average samples.
文摘We study a well-known problem concerning a random variable uniformly distributed between two independent random variables. Two different extensions, randomly weighted average on independent random variables and randomly weighted average on order statistics, have been introduced for this problem. For the second method, two-sided power random variables have been defined. By using classic method and power technical method, we study some properties for these random variables.
文摘There is an increasing trend to apply GNSS continuous observation of short baselines to the monitoring of engineering works, such as bridges and dams, for their structural analysis and safety control. In the case of large dams, one important application of the GNSS continuous observation is thc establishment of early warning systems that demand accurate, frequently updated information and where the analysis of the baseline time series, in order to separate signal from noise is mandatory. The paper presents a study on the performance of linear filters of the asymmetric moving average type to smooth baseline time series. The transfer function of the filter is adopted as a smoothing criterion to choose an adequate order for the moving average, in face of the spectral density function of the baseline time series. Onc series of measurements of a short test baseline （325 m）, materialized in the campus of the National Laboratory for Civil Engineering, is used as an example of the proposed strategy.
文摘In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville fractional integral operators. Moreover, the results are interpreted in alternative form.
基金supported by the National Natural Science Foundation of China (11071190)
文摘Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.
文摘In compartment fires (houses, buildings, underground, warehouse, etc.), smokes are a major dan- ger during firemen intervention. Most of the time, they are at high temperature (>800?C) and they flow everywhere through many kinds of ducts, which leads to the propagation of the combustion by the creation other fires in places which may be far away from the initial fire. In this paper, we present a new approach of the problem, which allows to better follow the fire behavior and especially to detect the dangers that may appear and endanger firefighters. This approach consists in a mathematical analysis based on the comparison of moving averages centered in the past, calculated on the temperature recordings of the smokes. As a consequence, this method may allow to improve decision support in real time and therefore to improve the security and the efficiency of firefighters in their operations against that kind of fires.
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
基金Supported by the National Natural Science Foundation of China(Nos.61379014 and 11271199)
文摘Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p（R）which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averages are obtained for functions f∈BpΩwith the decay condition f（t）≤A/t^δ,t≠0,where A and δare positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above.
基金The first and second authors have been supported through project 20928/PI/18(Proyecto financiado por la Comunidad Autonoma de la Region de Murcia a traves de la convocatoria de Ayudas a proyectos para el desarrollo de investigacion cientffica y tecnica por grupos competitivos,incluida en el Programa Regional de Fomento de la Investigacion Cientffica y Tecnica(Plan de Actuacion 2018)de la Fundacion Seneca-Agencia de Ciencia y Tecnologia de la Region de Murcia)by the national research project MTM2015-64382-P(MINECO/FEDER)The third author has been supported through the National Science Foundation grant DMS-1719410.
文摘This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages.Thus,now we are interested in analyze the capabilities of the new algorithm when working with functions belonging to the subspace L1\L2 and that,consequently,are piecewise smooth and can present jump discontinuities.The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones.We will present the new algorithm for the approximation case and we will analyze its accuracy.Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions.The numerical results confirm the theoretical proofs presented.
基金funding support from the National Science and Technology Council(NSTC),under Grant No.114-2410-H-011-026-MY3.
文摘Small datasets are often challenging due to their limited sample size.This research introduces a novel solution to these problems:average linkage virtual sample generation(ALVSG).ALVSG leverages the underlying data structure to create virtual samples,which can be used to augment the original dataset.The ALVSG process consists of two steps.First,an average-linkage clustering technique is applied to the dataset to create a dendrogram.The dendrogram represents the hierarchical structure of the dataset,with each merging operation regarded as a linkage.Next,the linkages are combined into an average-based dataset,which serves as a new representation of the dataset.The second step in the ALVSG process involves generating virtual samples using the average-based dataset.The research project generates a set of 100 virtual samples by uniformly distributing them within the provided boundary.These virtual samples are then added to the original dataset,creating a more extensive dataset with improved generalization performance.The efficacy of the ALVSG approach is validated through resampling experiments and t-tests conducted on two small real-world datasets.The experiments are conducted on three forecasting models:the support vector machine for regression(SVR),the deep learning model(DL),and XGBoost.The results show that the ALVSG approach outperforms the baseline methods in terms of mean square error(MSE),root mean square error(RMSE),and mean absolute error(MAE).
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
基金supported by the National Natural Science Foundation of China(Grant Nos.12388101 and 12472221)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2024-oy10).
文摘In sediment transport on a mobile erodible bed,near-bed particles tend to preferentially locate under specific flow regions and form an uneven bedform.These moving and mobile particles can significantly modulate turbulence at various scales,from inertial large-scale motions to small viscous motions.This study analyzes the particle-resolved direct numerical simulation data of particle-laden two-phase flow with multilayers of particles in turbulent flows over static and mobile beds.The double-average method is adopted for energy transfer analysis.The result shows that the alternative streaky bedform in the spanwise directions correlates with the streak structures in the near-wall turbulence in the mobile bed case.The energy redistribution and exchange,as well as the dissipation,are analyzed in detail,and an energy transfer diagram is given in the last to summarize the energy transfer processes.In both the static and mobile bed cases,flow energy is introduced into the system via the work performed by volume forces acting on the mean flow.The viscous dissipations in the double mean and form-induced fields are more pronounced in the static bed case,and the work done by the fluid-particle interfacial stress in the double mean and turbulent fields is more pronounced in the mobile bed case.The prominent energy contribution in the form-induced field is the production by the form-induced stress on the mean strain in the mobile bed case.In addition,sediment transport involving a limited number of mobile particles is insufficient to capture the energy transfer processes that occur over the troughs and may intertwine the energy transfer processes over the mobile particles and the fixed particle bed.
基金supported by the National Key Research and Development Program of China(2025YFE0213100)the National Natural Science Foundation of China(62422315,62573348)+1 种基金the Natural Science Basic Research Program of Shaanxi(2025JC-YBMS-667)the“Shuang Yi Liu”Construction Foundation(25GH02010366)。
文摘This paper investigates the distributed continuoustime aggregative optimization problem for second-order multiagent systems,where the local cost function is not only related to its own decision variables,but also to the aggregation of the decision variables of all the agents.By using the gradient descent method,the distributed average tracking(DAT)technique and the time-base generator(TBG)technique,a distributed continuous-time aggregative optimization algorithm is proposed.Subsequently,the optimality of the system's equilibrium point is analyzed,and the convergence of the closed-loop system is proved using the Lyapunov stability theory.Finally,the effectiveness of the proposed algorithm is validated through case studies on multirobot systems and power generation systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.42425305,42293290,and 42172216).
文摘1.Introduction.Since the Industrial Revolution,the partial pressure of atmospheric carbon dioxide(pCO_(2))has increased markedly,rising from approximately 280 ppm(1 ppm=1μL/L)to about 420 ppm.This escalation has intensified global warming,with 2024 the hottest year on record since 1850.The global mean temperature now stands 1.46℃ above the pre-industrial average(1850-1900),a value already approaching the 1.5℃ threshold set by the Paris Agreement(NOAA,2025).
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
文摘Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolution sums of the type Σ|h|≤H |ΣX<n≤2XAf (1,…, 1, n+h)λ(n)|^2. We succeed in obtaining a saving of an arbitrary power of the logarithm, provided that X^8/33+ε≤H≤X^1-ε.
基金supported in part by the National Natural Science Foundation of China under Grant No.61473066in part by the Natural Science Foundation of Hebei Province under Grant No.F2021501020+2 种基金in part by the S&T Program of Qinhuangdao under Grant No.202401A195in part by the Science Research Project of Hebei Education Department under Grant No.QN2025008in part by the Innovation Capability Improvement Plan Project of Hebei Province under Grant No.22567637H
文摘Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.
