In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power su...In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power supply.”Traditional time-series forecasting methods are no longer suitable owing to the complexity and uncertainty associated with generalized loads.From the perspective of image processing,this study proposes a graphical short-term prediction method for generalized loads based on modal decomposition.First,the datasets are normalized and feature-filtered by comparing the results of Xtreme gradient boosting,gradient boosted decision tree,and random forest algorithms.Subsequently,the generalized load data are decomposed into three sets of modalities by modal decomposition,and red,green,and blue(RGB)images are generated using them as the pixel values of the R,G,and B channels.The generated images are diversified,and an optimized DenseNet neural network was used for training and prediction.Finally,the base load,wind power,and photovoltaic power generation data are selected,and the characteristic curves of the generalized load scenarios under different permeabilities of wind power and photovoltaic power generation are obtained using the density-based spatial clustering of applications with noise algorithm.Based on the proposed graphical forecasting method,the feasibility of the generalized load graphical forecasting method is verified by comparing it with the traditional time-series forecasting method.展开更多
Zero-shot learning enables the recognition of new class samples by migrating models learned from semanticfeatures and existing sample features to things that have never been seen before. The problems of consistencyof ...Zero-shot learning enables the recognition of new class samples by migrating models learned from semanticfeatures and existing sample features to things that have never been seen before. The problems of consistencyof different types of features and domain shift problems are two of the critical issues in zero-shot learning. Toaddress both of these issues, this paper proposes a new modeling structure. The traditional approach mappedsemantic features and visual features into the same feature space;based on this, a dual discriminator approachis used in the proposed model. This dual discriminator approach can further enhance the consistency betweensemantic and visual features. At the same time, this approach can also align unseen class semantic features andtraining set samples, providing a portion of information about the unseen classes. In addition, a new feature fusionmethod is proposed in the model. This method is equivalent to adding perturbation to the seen class features,which can reduce the degree to which the classification results in the model are biased towards the seen classes.At the same time, this feature fusion method can provide part of the information of the unseen classes, improvingits classification accuracy in generalized zero-shot learning and reducing domain bias. The proposed method isvalidated and compared with othermethods on four datasets, and fromthe experimental results, it can be seen thatthe method proposed in this paper achieves promising results.展开更多
The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are ...The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID ...This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.展开更多
The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I...The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.展开更多
This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a gen...This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.展开更多
In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set ar...In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.展开更多
Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived ...Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.展开更多
Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses.This paper presents a deep observation on and a comparison between two of those ...Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses.This paper presents a deep observation on and a comparison between two of those methods:the generalized extended-state observer(GESO)and the equivalent input disturbance(EID)from assumptions,system configurations,stability conditions,system design,disturbance-rejection performance,and extensibility.A time-domain index is introduced to assess the disturbance-rejection performance.A detailed observation of disturbance-suppression mechanisms reveals the superiority of the EID approach over the GESO method.A comparison between these two methods shows that assumptions on disturbances are more practical and the adjustment of disturbance-rejection performance is easier for the EID approach than for the GESO method.展开更多
In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various discip...In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.展开更多
The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we ca...The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the heat exchange system, and the nonconservative force system. On this basis, we have further given their generalized Lagrange functions and Hamilton functions. With the Feynman path integration, we have given the generalized Schrodinger equation of nonconservative force system and the heat exchange system.展开更多
False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Ba...False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Based on this, we propose a diffusion least-mean-square algorithm based on the generalized maximum correntropy criterion(GMCC-DLMS)for multi-task networks. The algorithm achieves gratifying estimation results. Even more, compared to the related work,it has better robustness when the number of attacked nodes increases. Moreover, the assumption about the number of attacked nodes is relaxed, which is applicable to multi-task environments. In addition, the performance of the proposed GMCC-DLMS algorithm is analyzed in the mean and mean-square senses. Finally, simulation experiments confirm the performance and effectiveness against FDI attacks of the algorithm.展开更多
Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operat...Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operator Hm,λon l2(Z)with a potential given by v(n)=λVξ(n),whereλ>0 is the coupling and Vξ(n)=1(Vξ(n)=-1)ifξ(n)=a(ξ(n)=b).LetΛ2=2,and for m>2,letΛm=m if m≡0 mod 4;letΛm=m-3 if m≡1 mod 4;letΛm=m-2if m≡2 mod 4;letΛm=m-1 if m≡3 mod 4.We show that the Hausdorff dimension of the spectrumσ(Hm,λ)satisfies that dimHσ(Hm,λ)>logΛm/(log 64m+4).It is interesting to see that dimHσσ(Hm,λ)tends to 1 as m tends to infinity.展开更多
In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property i...In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.展开更多
This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relati...This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.展开更多
We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from ...We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from quantum gravity theories.As an illustration,black hole temperature effects are discussed.It is observed that for specific choices of the moment's kernels,cold black holes may emerge in the theory.展开更多
In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equ...In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equivalent characterizations for invertible Toeplitz operators Tψ,induced by positive bounded symbols φ on F^(2)_(φ).展开更多
This study comprehensively characterizes the boundary values of generalized permeability jail in tight reservoirs through relative-permeability curve analysis,numerical simulation,and economic evaluation.A total numbe...This study comprehensively characterizes the boundary values of generalized permeability jail in tight reservoirs through relative-permeability curve analysis,numerical simulation,and economic evaluation.A total number of 108 relative-permeability curves of rock samples from tight reservoirs were obtained,and the characteristics of relative-permeability curves were analyzed.The irreducible water saturation(Swi)mainly ranges from 20% to 70%,and the residual gas saturation(Sgr)ranges from 5% to 15% for 55% of the samples.The relative-permeability curves are categorized into six types(Category-Ⅰ to Ⅵ)by analyzing the following characteristics:The relative permeability of gas at Swi,the relative permeability of water at Sgr,and the relative permeability corresponding to the isotonic point.The relative permeability curves were normalized to facilitate numerical simulation and evaluate the impact of different types of curves on production performance.The results of simulation show significant difference in production performance for different types of relative-permeability curves:Category-Ⅰ corresponds to the case with best well performance,whereas Categories-Ⅴ and Ⅵ correspond to the cases with least production volume.The results of economic evaluation show a generalized permeability jail for Categories-Ⅳ,Ⅴ,and Ⅵ,and the permeability jail develops when the relative permeability of gas and water is below 0.06.This study further quantifies the range of micro-pore parameters corresponding to the generalized permeability jail for a tight sandstone reservoir.展开更多
Soil strain is the key parameter to control the elasto-plastic deformation and even the failure processes.To overcome the defect that the strain of the model soil is always smaller than that of the prototype in Iai′s...Soil strain is the key parameter to control the elasto-plastic deformation and even the failure processes.To overcome the defect that the strain of the model soil is always smaller than that of the prototype in Iai′s generalized scaling law(GSL),a modified scaling law was proposed based on Iai′s GSL to secure the same dynamic shear strain between the centrifuge model and the prototype by modulating the amplitude and frequency of the input motion at the base.A suite of dynamic centrifuge model tests of dry sand level ground was conducted with the same overall scaling factor(λ=200)under different centrifugal accelerations by using the technique of“modeling of models”to validate the modified GSL.The test results show that the modified GSL could achieve the same dynamic strain in model as that of the prototype,leading to better modeling for geotechnical problems where dynamic strain dominates the response or failure of soils.Finally,the applicability of the proposed scaling law and possible constraints on geometry scaling due to the capability limits of existing centrifuge shaking tables are discussed.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62063016).
文摘In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power supply.”Traditional time-series forecasting methods are no longer suitable owing to the complexity and uncertainty associated with generalized loads.From the perspective of image processing,this study proposes a graphical short-term prediction method for generalized loads based on modal decomposition.First,the datasets are normalized and feature-filtered by comparing the results of Xtreme gradient boosting,gradient boosted decision tree,and random forest algorithms.Subsequently,the generalized load data are decomposed into three sets of modalities by modal decomposition,and red,green,and blue(RGB)images are generated using them as the pixel values of the R,G,and B channels.The generated images are diversified,and an optimized DenseNet neural network was used for training and prediction.Finally,the base load,wind power,and photovoltaic power generation data are selected,and the characteristic curves of the generalized load scenarios under different permeabilities of wind power and photovoltaic power generation are obtained using the density-based spatial clustering of applications with noise algorithm.Based on the proposed graphical forecasting method,the feasibility of the generalized load graphical forecasting method is verified by comparing it with the traditional time-series forecasting method.
文摘Zero-shot learning enables the recognition of new class samples by migrating models learned from semanticfeatures and existing sample features to things that have never been seen before. The problems of consistencyof different types of features and domain shift problems are two of the critical issues in zero-shot learning. Toaddress both of these issues, this paper proposes a new modeling structure. The traditional approach mappedsemantic features and visual features into the same feature space;based on this, a dual discriminator approachis used in the proposed model. This dual discriminator approach can further enhance the consistency betweensemantic and visual features. At the same time, this approach can also align unseen class semantic features andtraining set samples, providing a portion of information about the unseen classes. In addition, a new feature fusionmethod is proposed in the model. This method is equivalent to adding perturbation to the seen class features,which can reduce the degree to which the classification results in the model are biased towards the seen classes.At the same time, this feature fusion method can provide part of the information of the unseen classes, improvingits classification accuracy in generalized zero-shot learning and reducing domain bias. The proposed method isvalidated and compared with othermethods on four datasets, and fromthe experimental results, it can be seen thatthe method proposed in this paper achieves promising results.
文摘The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金supported in part by the NSF of China under Grant 62322106,62071131the Guangdong Basic and Applied Basic Research Foundation under Grant 2022B1515020086+2 种基金the International Collaborative Research Program of Guangdong Science and Technology Department under Grant 2022A0505050070in part by the Open Research Fund of the State Key Laboratory of Integrated Services Networks under Grant ISN22-23the National Research Foundation,Singapore University of Technology Design under its Future Communications Research&Development Programme“Advanced Error Control Coding for 6G URLLC and mMTC”Grant No.FCP-NTU-RG-2022-020.
文摘This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.
基金Supported by National Nature Science Foundation in China(12101564,11971425,11801508)Nature Science Foundation of Zhejiang province(LY22A010013)Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
文摘The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.
基金Project supported by the National Research Foundation of Korea(Nos.NRF-2020R1C1C1011970 and NRF-2018R1A5A7023490)。
文摘This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.
文摘In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA17010105)National Key Research and Development Program(Grant No.2018YFC1507104)+2 种基金Science and Technology Development Plan Project of Jilin Province(20180201035SF)Flexible Talents Introducing Project of Xinjiang(2019)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(EarthLab)。
文摘Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.
基金This work was supported in part by the JSPS(Japan Society for the Promotion of Science)KAKENHI(20H04566,22H03998)the National Natural Science Foundation of China(61873348)+1 种基金the Natural Science Foundation of Hubei Province,China(2020CFA031)Wuhan Applied Foundational Frontier Project(2020010601012175).
文摘Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses.This paper presents a deep observation on and a comparison between two of those methods:the generalized extended-state observer(GESO)and the equivalent input disturbance(EID)from assumptions,system configurations,stability conditions,system design,disturbance-rejection performance,and extensibility.A time-domain index is introduced to assess the disturbance-rejection performance.A detailed observation of disturbance-suppression mechanisms reveals the superiority of the EID approach over the GESO method.A comparison between these two methods shows that assumptions on disturbances are more practical and the adjustment of disturbance-rejection performance is easier for the EID approach than for the GESO method.
文摘In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
文摘The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the heat exchange system, and the nonconservative force system. On this basis, we have further given their generalized Lagrange functions and Hamilton functions. With the Feynman path integration, we have given the generalized Schrodinger equation of nonconservative force system and the heat exchange system.
文摘False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Based on this, we propose a diffusion least-mean-square algorithm based on the generalized maximum correntropy criterion(GMCC-DLMS)for multi-task networks. The algorithm achieves gratifying estimation results. Even more, compared to the related work,it has better robustness when the number of attacked nodes increases. Moreover, the assumption about the number of attacked nodes is relaxed, which is applicable to multi-task environments. In addition, the performance of the proposed GMCC-DLMS algorithm is analyzed in the mean and mean-square senses. Finally, simulation experiments confirm the performance and effectiveness against FDI attacks of the algorithm.
基金supported by the National Natural ScienceFoundation of China(11871098)。
文摘Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operator Hm,λon l2(Z)with a potential given by v(n)=λVξ(n),whereλ>0 is the coupling and Vξ(n)=1(Vξ(n)=-1)ifξ(n)=a(ξ(n)=b).LetΛ2=2,and for m>2,letΛm=m if m≡0 mod 4;letΛm=m-3 if m≡1 mod 4;letΛm=m-2if m≡2 mod 4;letΛm=m-1 if m≡3 mod 4.We show that the Hausdorff dimension of the spectrumσ(Hm,λ)satisfies that dimHσ(Hm,λ)>logΛm/(log 64m+4).It is interesting to see that dimHσσ(Hm,λ)tends to 1 as m tends to infinity.
基金supported by National Natural Science Foundation of China(12071018)Fundamental Research Funds for the Central Universitiessupported by the National Research Foundation of Korea(NRF)funded by the Korea government(MIST)(2020R1F1A1A01051370)。
文摘In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.
文摘This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.
文摘We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from quantum gravity theories.As an illustration,black hole temperature effects are discussed.It is observed that for specific choices of the moment's kernels,cold black holes may emerge in the theory.
基金supported by the NNSF of China(12071155)supported by the NNSF of China(11871170)+1 种基金the open project of Key Laboratory,school of Mathematical Sciences,Chongqing Normal University(CSSXKFKTM202002)supported by the Innovation Research for the Postgraduates of Guangzhou University(2020GDJC-D08)。
文摘In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equivalent characterizations for invertible Toeplitz operators Tψ,induced by positive bounded symbols φ on F^(2)_(φ).
基金the financial support from the National Natural Science Foundation of China(No.51774255 and 52174037).
文摘This study comprehensively characterizes the boundary values of generalized permeability jail in tight reservoirs through relative-permeability curve analysis,numerical simulation,and economic evaluation.A total number of 108 relative-permeability curves of rock samples from tight reservoirs were obtained,and the characteristics of relative-permeability curves were analyzed.The irreducible water saturation(Swi)mainly ranges from 20% to 70%,and the residual gas saturation(Sgr)ranges from 5% to 15% for 55% of the samples.The relative-permeability curves are categorized into six types(Category-Ⅰ to Ⅵ)by analyzing the following characteristics:The relative permeability of gas at Swi,the relative permeability of water at Sgr,and the relative permeability corresponding to the isotonic point.The relative permeability curves were normalized to facilitate numerical simulation and evaluate the impact of different types of curves on production performance.The results of simulation show significant difference in production performance for different types of relative-permeability curves:Category-Ⅰ corresponds to the case with best well performance,whereas Categories-Ⅴ and Ⅵ correspond to the cases with least production volume.The results of economic evaluation show a generalized permeability jail for Categories-Ⅳ,Ⅴ,and Ⅵ,and the permeability jail develops when the relative permeability of gas and water is below 0.06.This study further quantifies the range of micro-pore parameters corresponding to the generalized permeability jail for a tight sandstone reservoir.
基金National Natural Science Foundation of China under Grant Nos.51988101,51978613 and 52278374the Chinese Program of Introducing Talents of Discipline to University(the 111 Project,B18047)。
文摘Soil strain is the key parameter to control the elasto-plastic deformation and even the failure processes.To overcome the defect that the strain of the model soil is always smaller than that of the prototype in Iai′s generalized scaling law(GSL),a modified scaling law was proposed based on Iai′s GSL to secure the same dynamic shear strain between the centrifuge model and the prototype by modulating the amplitude and frequency of the input motion at the base.A suite of dynamic centrifuge model tests of dry sand level ground was conducted with the same overall scaling factor(λ=200)under different centrifugal accelerations by using the technique of“modeling of models”to validate the modified GSL.The test results show that the modified GSL could achieve the same dynamic strain in model as that of the prototype,leading to better modeling for geotechnical problems where dynamic strain dominates the response or failure of soils.Finally,the applicability of the proposed scaling law and possible constraints on geometry scaling due to the capability limits of existing centrifuge shaking tables are discussed.