This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four...This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four compartments:susceptible,latently infected,breaking-out,and antivirus-capable systems.By employing the CF derivative—which uses a nonsingular exponential kernel—the framework effectively captures memory-dependent and nonlocal characteristics intrinsic to cyber systems,aspects inadequately represented by traditional integer-order models.Under Lipschitz continuity and boundedness assumptions,the existence and uniqueness of solutions are rigorously established via fixed-point theory.We develop a tailored two-step Adams-Bashforth numerical scheme for the CF framework and prove its second-order accuracy.Extensive numerical simulations across various fractional orders reveal that memory effects significantly influence virus transmission and control dynamics;smaller fractional orders produce more pronounced memory effects,delaying both infection spread and antivirus activation.Further theoretical analysis,including Hyers-Ulam stability and sensitivity assessments,reinforces the model’s robustness and identifies key parameters governing virus dynamics.The study also extends the framework to incorporate stochastic effects through a stochastic CF formulation.These results underscore fractional-order modeling as a powerful analytical tool for developing robust and effective cybersecurity strategies.展开更多
As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Int...As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.展开更多
This paper investigates the following mixed local and nonlocal elliptic problem fea-turing concave-convex nonlinearities and a discontinuous right-hand side:{L(u)=H(u−μ)|u|^(p−2)u+λ|u|^(q−2)u,x∈Ω,u≥0,x∈Ω,u=0,x...This paper investigates the following mixed local and nonlocal elliptic problem fea-turing concave-convex nonlinearities and a discontinuous right-hand side:{L(u)=H(u−μ)|u|^(p−2)u+λ|u|^(q−2)u,x∈Ω,u≥0,x∈Ω,u=0,x∈R^(N)\Ω,where Ω ⊂R^(N)(N>2)is a bounded domain,μ≥0 and λ>0 are real parameters,H denotes the Heaviside function(H(t)=0 for t<0,H(t)=1 for t>0),and the mixed local and nolocal operator is defined as L(u)=−Δu+(−Δ)^(s)u with(−Δ)^(s) being the restricted fractional Laplace(0<s<1).The exponents satisfy 1<q<2<p.By employing a novel non-smooth variational principle,we establish the existence of an M-solution for this problem and identify a range for the exponent p.展开更多
In the image fusion field,fusing infrared images(IRIs)and visible images(VIs)excelled is a key area.The differences between IRIs and VIs make it challenging to fuse both types into a high-quality image.Accordingly,eff...In the image fusion field,fusing infrared images(IRIs)and visible images(VIs)excelled is a key area.The differences between IRIs and VIs make it challenging to fuse both types into a high-quality image.Accordingly,efficiently combining the advantages of both images while overcoming their shortcomings is necessary.To handle this challenge,we developed an end-to-end IRI andVI fusionmethod based on frequency decomposition and enhancement.By applying concepts from frequency domain analysis,we used the layering mechanism to better capture the salient thermal targets from the IRIs and the rich textural information from the VIs,respectively,significantly boosting the image fusion quality and effectiveness.In addition,the backbone network combined Restormer Blocks and Dense Blocks;Restormer blocks utilize global attention to extract shallow features.Meanwhile,Dense Blocks ensure the integration between shallow and deep features,thereby avoiding the loss of shallow attributes.Extensive experiments on TNO and MSRS datasets demonstrated that the suggested method achieved state-of-the-art(SOTA)performance in various metrics:Entropy(EN),Mutual Information(MI),Standard Deviation(SD),The Structural Similarity Index Measure(SSIM),Fusion quality(Qabf),MI of the pixel(FMI_(pixel)),and modified Visual Information Fidelity(VIF_(m)).展开更多
Quantile regression(QR)has become an important tool to measure dependence of response variable's quantiles on a number of predictors for heterogeneous data,especially heavy-tailed data and outliers.However,it is q...Quantile regression(QR)has become an important tool to measure dependence of response variable's quantiles on a number of predictors for heterogeneous data,especially heavy-tailed data and outliers.However,it is quite challenging to make statistical inference on distributed high-dimensional QR with missing data due to the distributed nature,sparsity and missingness of data and nondifferentiable quantile loss function.To overcome the challenge,this paper develops a communicationefficient method to select variables and estimate parameters by utilizing a smooth function to approximate the non-differentiable quantile loss function and incorporating the idea of the inverse probability weighting and the penalty function.The proposed approach has three merits.First,it is both computationally and communicationally efficient because only the first-and second-order information of the approximate objective function are communicated at each iteration.Second,the proposed estimators possess the oracle property after a limited number of iterations without constraint on the number of machines.Third,the proposed method simultaneously selects variables and estimates parameters within a distributed framework,ensuring robustness to the specified response probability or propensity score function of the missing data mechanism.Simulation studies and a real example are used to illustrate the effectiveness of the proposed methodologies.展开更多
Literature review is an important component in any scientific research. In ecological and agricultural sciences, many studies have been conducted over years. With accumulation of scientific studies and published paper...Literature review is an important component in any scientific research. In ecological and agricultural sciences, many studies have been conducted over years. With accumulation of scientific studies and published papers, it is critical to summarize and evaluate these previous research findings. Different literature review methods have been applied, including traditional qualitative literature review, quantitative meta-analysis, and more recently, mega-analysis, or meta-meta-analysis. Here we briefly describe these different approaches and draw attention to the recent development of data synthesis. Several case studies were used to illustrate the application of these methods in the ecological and agricultural sciences.展开更多
Solar activity plays an important role in influencing space weather,making it important to understand numerous aspects of spatial and temporal variations in the Sun's radiative output.High-performance deep learnin...Solar activity plays an important role in influencing space weather,making it important to understand numerous aspects of spatial and temporal variations in the Sun's radiative output.High-performance deep learning models and long-term observational records of sunspot relative numbers are essential for solar cycle forecasting.Using the multivariate time series of monthly sunspot relative numbers provided by the National Astronomical Observatory of Japan and two Informer-based models,we forecast the amplitude and timing of solar cycles 25 and 26.The main results are as follows:(1)The maximum amplitude of solar cycle 25 is higher than the previous solar cycle 24 and the following solar cycle 26,suggesting that the long-term oscillatory variation of sunspot magnetic fields is related to the roughly centennial Gleissberg cyclicity.(2)Solar cycles 25 and 26 exhibit a pronounced Gnevyshev gap,which might be caused by two non-coincident peaks resulting from solar magnetic flux transported by meridional circulation and mid-latitude diffusion in the convection zone.(3)Hemispheric prediction of sunspot activity reveals a significant northsouth asynchrony,with activity level of the Sun being more intense in the southern hemisphere.These results are consistent with expectations derived from precursor methods and dynamo theories,and further provide evidence for internal changes in solar magnetic field during the decay of the Modern Maximum.展开更多
Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physic...Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physical law asserts that the nonlinear change of continuous variable Y is proportional to the nonlinear change in continuous variable X. Mathematically, this is expressed as dα{Y, Yu, Yb} = −Kdβ{X, Xu, Xb}, with Yu, Yb, Xu, and Xb representing the upper and baseline asymptotes of Y and X. Y is the continuous cumulative numbers of the elementary y and X is the continuous cumulative numbers of elementary x. K is the proportionality constant or equally is the rate constant.展开更多
Accurate prediction of wastewater treatment plants(WWTPs) influent quality can provide valuable decision-making support to facilitate operations and management.However,since existing methods overlook the data noise ge...Accurate prediction of wastewater treatment plants(WWTPs) influent quality can provide valuable decision-making support to facilitate operations and management.However,since existing methods overlook the data noise generated from harsh operations and instruments,while the local feature pattern and long-term dependency in the wastewater quality time series,the prediction performance can be degraded.In this paper,a discrete wavelet transform and convolutional enhanced Transformer(DWT-Ce Transformer) method is developed to predict the influent quality in WWTPs.Specifically,we perform multi-scale analysis on time series of wastewater quality using discrete wavelet transform,effectively removing noise while preserving key data characteristics.Further,a tightly coupled convolutional-enhanced Transformer model is devised where convolutional neural network is used to extract local features,and then these local features are combined with Transformer's self-attention mechanism,so that the model can not only capture long-term dependencies,but also retain the sensitivity to local context.In this study,we conduct comprehensive experiments based on the actual data from a WWTP in Shaanxi Province and the simulated data generated by BSM2.The experimental results show that,compared to baseline models,DWT-Ce Transformer can significantly improve the prediction performance of influent COD and NH_(3)-N.Specifically,MSE,MAE,and RMSE improve by 78.7%,79.5%,and 53.8% for COD,and 79.4%,70.2%,and 54.5% for NH_(3)-N.On simulated data,our method shows strong improvements under various weather conditions,especially in dry weather,with MSE,MAE,and RMSE for COD improving by 68.9%,48.0%,and 44.3%,and for NH_(3)-N by 78.4%,54.8%,and 53.2%.展开更多
Repeated wet swelling and dry shrinkage of soil leads to the gradual occurrence of cracks and the formation of a complex fracture network.In order to study the development characteristics and quantitative analysis of ...Repeated wet swelling and dry shrinkage of soil leads to the gradual occurrence of cracks and the formation of a complex fracture network.In order to study the development characteristics and quantitative analysis of cracks in root-soil complex in different growth periods under dry-wet cycles,the alfalfa root-loess complex was in-vestigated during different growth periods under different dry-wet cycles,and a dry-wet cycle experiment was conducted.The crack rate,relative area,average width,total length,and the cracks fractal dimension in the root-soil complex were extracted;the crack development characteristics of plain soil were analyzed under the PG-DwC(dry-wet cycle caused by plant water management during plant growth period),as well as the crack development characteristics of root-soil complex under PG-DWC and EC-DWC(the dry-wet cycles caused by extreme natural conditions such as continuous rain);the effects of plant roots and dry-wet cycles on soil cracks were discussed.The results showed that the average crack width,crack rate,relative crack area,and total crack length of the alfalfa root-loess complex were higher than those of the plain soil during PG-DWC.The result indicated that compared with plain soil during PG-DWC,the presence of plant roots in alfalfa root-soil complex in the same growth period promoted the cracks development to some extent.The alfalfa root-soil complex crack parameters during different growth periods were relatively stable during PG-DWC(O dry-wet cycle).During EC-DWC(1,3,and 5 dry-wet cycles),the alfalfa root-loess complex crack parameters increased with the number of dry-wet cycles during different growth periods.Unlike PG-DWC,the EC-DWC accelerated crack development,and the degree of crack development increased with the number of dry-wet cycles.The existence of plant roots promoted crack development and expansion in the root-soil complex to a certain extent,and the dry-wet cycle certainly promoted crack development and expansion in the root-soil complex.This result contradicts the im-provement in the root-soil complex's macro-mechanical properties during plant growth,due to differences in the mechanical properties of roots and soil.The research results will provide reference for the root soil complex crack development law and the design of slope protection by vegetation.展开更多
In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attra...In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attractor in C_(Hg) is equal to the global attractor in C_(Vg).展开更多
In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown...In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.展开更多
Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-inje...Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-injective and Cartan-Eilenberg FP_(n)-flat complexes.As applications,we obtain that any complex admits Cartan-Eilenberg FP_(n)-injective(resp.,Cartan-Eilenberg FP_(n)-flat)cover and preenvelope and we characterize left n-coherent rings using these two classes of complexes.展开更多
This paper investigates the adhesive nanocontact behavior of an elastic halfplane indented by a rigid cylindrical indenter,incorporating the simultaneous effects of surface elasticity,couple stresses,and adhesion.The ...This paper investigates the adhesive nanocontact behavior of an elastic halfplane indented by a rigid cylindrical indenter,incorporating the simultaneous effects of surface elasticity,couple stresses,and adhesion.The free surface of the half-plane is modeled by the Steigmann-Ogden surface elasticity theory,while the bulk material behavior is described by the classical couple-stress elasticity theory.The adhesion at the contact interface is characterized by the Maugis-Dugdale(MD)adhesive contact model.Building on the fundamental nonclassical Flamant solution,the governing equations and boundary conditions of the nanocontact problem are reformulated into a system of triple integral equations.These equations are solved numerically by the Gauss-Chebyshev quadratures in combination with an iterative algorithm.The validation against the existing literature confirms the accuracy and robustness of the proposed solution methodology.Comprehensive parametric studies are performed to elucidate the critical roles of surface elasticity and couple stresses in adhesive nanocontact.The numerical results provide insights into the complex interactions among surface,couple-stress,and adhesive effects.Specifically,the interplay between the surface and adhesive effects is predominantly competitive,while the interaction between the couple stresses and adhesion exhibits an intricate nature.The findings highlight the necessity of simultaneously considering surface elasticity,couple stresses,and adhesion in nanoindentation analyses to achieve accurate predictions of material responses.展开更多
In this paper,the author obtains complete convergence for the maximum partial sums of m-widely orthant dependent(m-WOD)random variables sequences under some general conditions.The results extend the complete convergen...In this paper,the author obtains complete convergence for the maximum partial sums of m-widely orthant dependent(m-WOD)random variables sequences under some general conditions.The results extend the complete convergence for m-WOD random variables to a much more general type complete convergence.As the sequences of m-WOD random variables represent a very broad class of dependent sequences,the results improve and generalize the corresponding ones in the literature.展开更多
This study examined size inequality and size-growth relationships as essential aspects of stand structure in loblolly pine plantations(Pinus taeda L.),particularly focusing on a critical stage with strong competition ...This study examined size inequality and size-growth relationships as essential aspects of stand structure in loblolly pine plantations(Pinus taeda L.),particularly focusing on a critical stage with strong competition from mid-rotation to rotation age and changes due to thinning.Data were from a loblolly pine thinning study of multiple sites in the western Gulf region,USA,which were thinned around age 14.Four treatments were evaluated:three thinning intensities(TIs:residual densities of 740,555,and 370 trees·ha^(-1))and an unthinned control.An operational thinning method was implemented,involving the removal of every fifth row and selective thinning from below to achieve the desired intensity.The Gini index(GI)for diameter at breast height(DBH),height(H),and volume was computed annually for the first five years since thinning and at year seven,while growth dominance(GD)of these traits was calculated by growth interval.The control exhibited increasing trends over the year in GIs and greater inequality in DBH compared to height(GI=0.10 vs.0.04),and thinning reduced both GIs.Competition for DBH growth in the control was weakly asymmetric(GD=0.06),and thinning decreased GD,fostering weaker asymmetric competitive environments.The control displayed reverse asymmetric competition for height(GD=-0.10),and thinning strengthened reverse dominance.The thinning effects on reducing GIs and GD increased with TI.The observed patterns of competition appear to stem from adaptive resource allocation strategies rather than being influenced by neighboring tree sizes.The tree volume(VOLT)-based GI and GD might overestimate size inequality for DBH or height,and misinterpret GD for height.Stand volume growth in the control is linearly related to GD,being negative for DBH and positive for height,indicating GD offers valuable insights into stand growth dynamics.Thinning did not change the relationships but slowed the rates of change.The decline in stand growth associated with reduced DBH GD by thinning suggests that GD itself may not be the primary causal factor behind growth changes by thinning.展开更多
In this paper,we consider the Hopf lemma of the following mixed local and nonlocal weighted semilinear elliptic equations{-div(|x|^(-2α)■u)+(-△)_(α)^(s)u=0,x∈U,u(x^(^))=-u(x),x∈H,u(x)=0,x∈R^(N)\U,where H belong...In this paper,we consider the Hopf lemma of the following mixed local and nonlocal weighted semilinear elliptic equations{-div(|x|^(-2α)■u)+(-△)_(α)^(s)u=0,x∈U,u(x^(^))=-u(x),x∈H,u(x)=0,x∈R^(N)\U,where H belong to R^(N)with 0∈H is an open and affine half space,U belong to H is an open and bounded set,s∈(0,1),α∈[0,N-2s/2),(-△)_(α)^(s)is weighted fractional Laplacian with a weighted function.展开更多
With the unprecedented prevalence of Industrial Internet of Things(IIoT)and 5G technology,various applications supported by industrial communication systems have generated exponentially increased processing tasks,whic...With the unprecedented prevalence of Industrial Internet of Things(IIoT)and 5G technology,various applications supported by industrial communication systems have generated exponentially increased processing tasks,which makes task assignment inefficient due to insufficient workers.In this paper,an Intelligent and Trustworthy task assignment method based on Trust and Social relations(ITTS)is proposed for scenarios with many tasks and few workers.Specifically,ITTS first makes initial assignments based on trust and social influences,thereby transforming the complex large-scale industrial task assignment of the platform into the small-scale task assignment for each worker.Then,an intelligent Q-decision mechanism based on workers'social relation is proposed,which adopts the first-exploration-then-utilization principle to allocate tasks.Only when a worker cannot cope with the assigned tasks,it initiates dynamic worker recruitment,thus effectively solving the worker shortage problem as well as the cold start issue.More importantly,we consider trust and security issues,and evaluate the trust and social circles of workers by accumulating task feedback,to provide the platform a reference for worker recruitment,thereby creating a high-quality worker pool.Finally,extensive simulations demonstrate ITTS outperforms two benchmark methods by increasing task completion rates by 56.49%-61.53%and profit by 42.34%-47.19%.展开更多
The probability of phase formation was predicted using k-nearest neighbor algorithm(KNN)and artificial neural network algorithm(ANN).Additionally,the composition ranges of Ti,Cu,Ni,and Hf in 40 unknown amorphous alloy...The probability of phase formation was predicted using k-nearest neighbor algorithm(KNN)and artificial neural network algorithm(ANN).Additionally,the composition ranges of Ti,Cu,Ni,and Hf in 40 unknown amorphous alloy composites(AACs)were predicted using ANN.The predicted alloys were then experimentally verified through X-ray diffraction(XRD)and high-resolution transmission electron microscopy(HRTEM).The prediction accuracies of the ANN for AM and IM phases are 93.12%and 85.16%,respectively,while the prediction accuracies of KNN for AM and IM phases are 93%and 84%,respectively.It is observed that when the contents of Ti,Cu,Ni,and Hf fall within the ranges of 32.7−34.5 at.%,16.4−17.3 at.%,30.9−32.7 at.%,and 17.3−18.3 at.%,respectively,it is more likely to form AACs.Based on the results of XRD and HRTEM,the Ti_(34)Cu17Ni_(31.36)Hf_(17.64)and Ti_(36)Cu_(18)Ni_(29.44)Hf_(16.56)alloys are identified as good AACs,which are in closely consistent with the predicted amorphous alloy compositions.展开更多
This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity a...This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.展开更多
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2601).
文摘This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four compartments:susceptible,latently infected,breaking-out,and antivirus-capable systems.By employing the CF derivative—which uses a nonsingular exponential kernel—the framework effectively captures memory-dependent and nonlocal characteristics intrinsic to cyber systems,aspects inadequately represented by traditional integer-order models.Under Lipschitz continuity and boundedness assumptions,the existence and uniqueness of solutions are rigorously established via fixed-point theory.We develop a tailored two-step Adams-Bashforth numerical scheme for the CF framework and prove its second-order accuracy.Extensive numerical simulations across various fractional orders reveal that memory effects significantly influence virus transmission and control dynamics;smaller fractional orders produce more pronounced memory effects,delaying both infection spread and antivirus activation.Further theoretical analysis,including Hyers-Ulam stability and sensitivity assessments,reinforces the model’s robustness and identifies key parameters governing virus dynamics.The study also extends the framework to incorporate stochastic effects through a stochastic CF formulation.These results underscore fractional-order modeling as a powerful analytical tool for developing robust and effective cybersecurity strategies.
文摘As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.
基金Supported by the National Natural Science Foundation of China(Grant No.12361026)the Discipline Construction Fund Project of Northwest Minzu University.
文摘This paper investigates the following mixed local and nonlocal elliptic problem fea-turing concave-convex nonlinearities and a discontinuous right-hand side:{L(u)=H(u−μ)|u|^(p−2)u+λ|u|^(q−2)u,x∈Ω,u≥0,x∈Ω,u=0,x∈R^(N)\Ω,where Ω ⊂R^(N)(N>2)is a bounded domain,μ≥0 and λ>0 are real parameters,H denotes the Heaviside function(H(t)=0 for t<0,H(t)=1 for t>0),and the mixed local and nolocal operator is defined as L(u)=−Δu+(−Δ)^(s)u with(−Δ)^(s) being the restricted fractional Laplace(0<s<1).The exponents satisfy 1<q<2<p.By employing a novel non-smooth variational principle,we establish the existence of an M-solution for this problem and identify a range for the exponent p.
基金funded by Anhui Province University Key Science and Technology Project(2024AH053415)Anhui Province University Major Science and Technology Project(2024AH040229)+3 种基金Talent Research Initiation Fund Project of Tongling University(2024tlxyrc019)Tongling University School-Level Scientific Research Project(2024tlxyptZD07)TheUniversity Synergy Innovation Programof Anhui Province(GXXT-2023-050)Tongling City Science and Technology Major Special Project(Unveiling and Commanding Model)(200401JB004).
文摘In the image fusion field,fusing infrared images(IRIs)and visible images(VIs)excelled is a key area.The differences between IRIs and VIs make it challenging to fuse both types into a high-quality image.Accordingly,efficiently combining the advantages of both images while overcoming their shortcomings is necessary.To handle this challenge,we developed an end-to-end IRI andVI fusionmethod based on frequency decomposition and enhancement.By applying concepts from frequency domain analysis,we used the layering mechanism to better capture the salient thermal targets from the IRIs and the rich textural information from the VIs,respectively,significantly boosting the image fusion quality and effectiveness.In addition,the backbone network combined Restormer Blocks and Dense Blocks;Restormer blocks utilize global attention to extract shallow features.Meanwhile,Dense Blocks ensure the integration between shallow and deep features,thereby avoiding the loss of shallow attributes.Extensive experiments on TNO and MSRS datasets demonstrated that the suggested method achieved state-of-the-art(SOTA)performance in various metrics:Entropy(EN),Mutual Information(MI),Standard Deviation(SD),The Structural Similarity Index Measure(SSIM),Fusion quality(Qabf),MI of the pixel(FMI_(pixel)),and modified Visual Information Fidelity(VIF_(m)).
基金supported by the National Key R&D Program of China under Grant No.2022YFA1003701the Open Research Fund of Yunnan Key Laboratory of Statistical Modeling and Data Analysis,Yunnan University under Grant No.SMDAYB2023004。
文摘Quantile regression(QR)has become an important tool to measure dependence of response variable's quantiles on a number of predictors for heterogeneous data,especially heavy-tailed data and outliers.However,it is quite challenging to make statistical inference on distributed high-dimensional QR with missing data due to the distributed nature,sparsity and missingness of data and nondifferentiable quantile loss function.To overcome the challenge,this paper develops a communicationefficient method to select variables and estimate parameters by utilizing a smooth function to approximate the non-differentiable quantile loss function and incorporating the idea of the inverse probability weighting and the penalty function.The proposed approach has three merits.First,it is both computationally and communicationally efficient because only the first-and second-order information of the approximate objective function are communicated at each iteration.Second,the proposed estimators possess the oracle property after a limited number of iterations without constraint on the number of machines.Third,the proposed method simultaneously selects variables and estimates parameters within a distributed framework,ensuring robustness to the specified response probability or propensity score function of the missing data mechanism.Simulation studies and a real example are used to illustrate the effectiveness of the proposed methodologies.
文摘Literature review is an important component in any scientific research. In ecological and agricultural sciences, many studies have been conducted over years. With accumulation of scientific studies and published papers, it is critical to summarize and evaluate these previous research findings. Different literature review methods have been applied, including traditional qualitative literature review, quantitative meta-analysis, and more recently, mega-analysis, or meta-meta-analysis. Here we briefly describe these different approaches and draw attention to the recent development of data synthesis. Several case studies were used to illustrate the application of these methods in the ecological and agricultural sciences.
基金supported by the National Nature Science Foundation of China(12463009)the Yunnan Fundamental Research Projects(202301AV070007,202401AU070026)+2 种基金the"Yunnan Revitalization Talent Support Program"Innovation Team Project(202405AS350012)the Scientific Research Foundation Project of Yunnan Education Department(2023J0624,2024Y469)the GHfund A(202407016295)。
文摘Solar activity plays an important role in influencing space weather,making it important to understand numerous aspects of spatial and temporal variations in the Sun's radiative output.High-performance deep learning models and long-term observational records of sunspot relative numbers are essential for solar cycle forecasting.Using the multivariate time series of monthly sunspot relative numbers provided by the National Astronomical Observatory of Japan and two Informer-based models,we forecast the amplitude and timing of solar cycles 25 and 26.The main results are as follows:(1)The maximum amplitude of solar cycle 25 is higher than the previous solar cycle 24 and the following solar cycle 26,suggesting that the long-term oscillatory variation of sunspot magnetic fields is related to the roughly centennial Gleissberg cyclicity.(2)Solar cycles 25 and 26 exhibit a pronounced Gnevyshev gap,which might be caused by two non-coincident peaks resulting from solar magnetic flux transported by meridional circulation and mid-latitude diffusion in the convection zone.(3)Hemispheric prediction of sunspot activity reveals a significant northsouth asynchrony,with activity level of the Sun being more intense in the southern hemisphere.These results are consistent with expectations derived from precursor methods and dynamo theories,and further provide evidence for internal changes in solar magnetic field during the decay of the Modern Maximum.
文摘Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physical law asserts that the nonlinear change of continuous variable Y is proportional to the nonlinear change in continuous variable X. Mathematically, this is expressed as dα{Y, Yu, Yb} = −Kdβ{X, Xu, Xb}, with Yu, Yb, Xu, and Xb representing the upper and baseline asymptotes of Y and X. Y is the continuous cumulative numbers of the elementary y and X is the continuous cumulative numbers of elementary x. K is the proportionality constant or equally is the rate constant.
基金funded by the Natural Science Basic Research Program of Shaanxi (2024JCYBMS576)the National Natural Science Foundation of China (62366053)。
文摘Accurate prediction of wastewater treatment plants(WWTPs) influent quality can provide valuable decision-making support to facilitate operations and management.However,since existing methods overlook the data noise generated from harsh operations and instruments,while the local feature pattern and long-term dependency in the wastewater quality time series,the prediction performance can be degraded.In this paper,a discrete wavelet transform and convolutional enhanced Transformer(DWT-Ce Transformer) method is developed to predict the influent quality in WWTPs.Specifically,we perform multi-scale analysis on time series of wastewater quality using discrete wavelet transform,effectively removing noise while preserving key data characteristics.Further,a tightly coupled convolutional-enhanced Transformer model is devised where convolutional neural network is used to extract local features,and then these local features are combined with Transformer's self-attention mechanism,so that the model can not only capture long-term dependencies,but also retain the sensitivity to local context.In this study,we conduct comprehensive experiments based on the actual data from a WWTP in Shaanxi Province and the simulated data generated by BSM2.The experimental results show that,compared to baseline models,DWT-Ce Transformer can significantly improve the prediction performance of influent COD and NH_(3)-N.Specifically,MSE,MAE,and RMSE improve by 78.7%,79.5%,and 53.8% for COD,and 79.4%,70.2%,and 54.5% for NH_(3)-N.On simulated data,our method shows strong improvements under various weather conditions,especially in dry weather,with MSE,MAE,and RMSE for COD improving by 68.9%,48.0%,and 44.3%,and for NH_(3)-N by 78.4%,54.8%,and 53.2%.
基金the Key Research and Development Project of Ningxia Hui Autonomous Region(No.2023BEG02072)for their financial support.
文摘Repeated wet swelling and dry shrinkage of soil leads to the gradual occurrence of cracks and the formation of a complex fracture network.In order to study the development characteristics and quantitative analysis of cracks in root-soil complex in different growth periods under dry-wet cycles,the alfalfa root-loess complex was in-vestigated during different growth periods under different dry-wet cycles,and a dry-wet cycle experiment was conducted.The crack rate,relative area,average width,total length,and the cracks fractal dimension in the root-soil complex were extracted;the crack development characteristics of plain soil were analyzed under the PG-DwC(dry-wet cycle caused by plant water management during plant growth period),as well as the crack development characteristics of root-soil complex under PG-DWC and EC-DWC(the dry-wet cycles caused by extreme natural conditions such as continuous rain);the effects of plant roots and dry-wet cycles on soil cracks were discussed.The results showed that the average crack width,crack rate,relative crack area,and total crack length of the alfalfa root-loess complex were higher than those of the plain soil during PG-DWC.The result indicated that compared with plain soil during PG-DWC,the presence of plant roots in alfalfa root-soil complex in the same growth period promoted the cracks development to some extent.The alfalfa root-soil complex crack parameters during different growth periods were relatively stable during PG-DWC(O dry-wet cycle).During EC-DWC(1,3,and 5 dry-wet cycles),the alfalfa root-loess complex crack parameters increased with the number of dry-wet cycles during different growth periods.Unlike PG-DWC,the EC-DWC accelerated crack development,and the degree of crack development increased with the number of dry-wet cycles.The existence of plant roots promoted crack development and expansion in the root-soil complex to a certain extent,and the dry-wet cycle certainly promoted crack development and expansion in the root-soil complex.This result contradicts the im-provement in the root-soil complex's macro-mechanical properties during plant growth,due to differences in the mechanical properties of roots and soil.The research results will provide reference for the root soil complex crack development law and the design of slope protection by vegetation.
基金Supported by the National Natural Science Foundation of China(11971378)Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSY050)Shaanxi Innovative Training Program for College Students(S202410719114)。
文摘In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attractor in C_(Hg) is equal to the global attractor in C_(Vg).
基金Supported by the National Natural Science Foundation of China(12061061)Young Talents Team Project of Gansu Province(2025QNTD49)+1 种基金Lanshan Talents Project of Northwest Minzu University(Xbmulsrc202412)Longyuan Young Talents of Gansu Province。
文摘In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.
基金Supported by the National Natural Science Foundation of China(Grant No.12061061)the Science and Technology Project of Gansu Province(Grant No.22JR5RA153).
文摘Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-injective and Cartan-Eilenberg FP_(n)-flat complexes.As applications,we obtain that any complex admits Cartan-Eilenberg FP_(n)-injective(resp.,Cartan-Eilenberg FP_(n)-flat)cover and preenvelope and we characterize left n-coherent rings using these two classes of complexes.
基金Project supported by the National Natural Science Foundation of China(No.12072072)。
文摘This paper investigates the adhesive nanocontact behavior of an elastic halfplane indented by a rigid cylindrical indenter,incorporating the simultaneous effects of surface elasticity,couple stresses,and adhesion.The free surface of the half-plane is modeled by the Steigmann-Ogden surface elasticity theory,while the bulk material behavior is described by the classical couple-stress elasticity theory.The adhesion at the contact interface is characterized by the Maugis-Dugdale(MD)adhesive contact model.Building on the fundamental nonclassical Flamant solution,the governing equations and boundary conditions of the nanocontact problem are reformulated into a system of triple integral equations.These equations are solved numerically by the Gauss-Chebyshev quadratures in combination with an iterative algorithm.The validation against the existing literature confirms the accuracy and robustness of the proposed solution methodology.Comprehensive parametric studies are performed to elucidate the critical roles of surface elasticity and couple stresses in adhesive nanocontact.The numerical results provide insights into the complex interactions among surface,couple-stress,and adhesive effects.Specifically,the interplay between the surface and adhesive effects is predominantly competitive,while the interaction between the couple stresses and adhesion exhibits an intricate nature.The findings highlight the necessity of simultaneously considering surface elasticity,couple stresses,and adhesion in nanoindentation analyses to achieve accurate predictions of material responses.
基金Supported by the Academic Funding Projects for Top Talents in Universities of Anhui Province(gxbjZD2022067)Talent Planning Project of Tongling University(2022tlxyrc32)the Key Grant Project for Academic Leaders of Tongling University(2020tlxyxs31)。
文摘In this paper,the author obtains complete convergence for the maximum partial sums of m-widely orthant dependent(m-WOD)random variables sequences under some general conditions.The results extend the complete convergence for m-WOD random variables to a much more general type complete convergence.As the sequences of m-WOD random variables represent a very broad class of dependent sequences,the results improve and generalize the corresponding ones in the literature.
基金supported by the McIntire-Stennis program and ETPPRP.
文摘This study examined size inequality and size-growth relationships as essential aspects of stand structure in loblolly pine plantations(Pinus taeda L.),particularly focusing on a critical stage with strong competition from mid-rotation to rotation age and changes due to thinning.Data were from a loblolly pine thinning study of multiple sites in the western Gulf region,USA,which were thinned around age 14.Four treatments were evaluated:three thinning intensities(TIs:residual densities of 740,555,and 370 trees·ha^(-1))and an unthinned control.An operational thinning method was implemented,involving the removal of every fifth row and selective thinning from below to achieve the desired intensity.The Gini index(GI)for diameter at breast height(DBH),height(H),and volume was computed annually for the first five years since thinning and at year seven,while growth dominance(GD)of these traits was calculated by growth interval.The control exhibited increasing trends over the year in GIs and greater inequality in DBH compared to height(GI=0.10 vs.0.04),and thinning reduced both GIs.Competition for DBH growth in the control was weakly asymmetric(GD=0.06),and thinning decreased GD,fostering weaker asymmetric competitive environments.The control displayed reverse asymmetric competition for height(GD=-0.10),and thinning strengthened reverse dominance.The thinning effects on reducing GIs and GD increased with TI.The observed patterns of competition appear to stem from adaptive resource allocation strategies rather than being influenced by neighboring tree sizes.The tree volume(VOLT)-based GI and GD might overestimate size inequality for DBH or height,and misinterpret GD for height.Stand volume growth in the control is linearly related to GD,being negative for DBH and positive for height,indicating GD offers valuable insights into stand growth dynamics.Thinning did not change the relationships but slowed the rates of change.The decline in stand growth associated with reduced DBH GD by thinning suggests that GD itself may not be the primary causal factor behind growth changes by thinning.
基金Supported by the National Natural Science Foundation of China(Grant No.12361026)Fundamental Research Funds for the Central Universities(Grant No.31920240069)Innovation Team Project of Northwest Minzu University.
文摘In this paper,we consider the Hopf lemma of the following mixed local and nonlocal weighted semilinear elliptic equations{-div(|x|^(-2α)■u)+(-△)_(α)^(s)u=0,x∈U,u(x^(^))=-u(x),x∈H,u(x)=0,x∈R^(N)\U,where H belong to R^(N)with 0∈H is an open and affine half space,U belong to H is an open and bounded set,s∈(0,1),α∈[0,N-2s/2),(-△)_(α)^(s)is weighted fractional Laplacian with a weighted function.
基金supported by the National Natural Science Foundation of China under Grant No.62072475 and No.62302062in part by the Hunan Provincial Natural Science Foundation of China under Grant Number 2023JJ40081。
文摘With the unprecedented prevalence of Industrial Internet of Things(IIoT)and 5G technology,various applications supported by industrial communication systems have generated exponentially increased processing tasks,which makes task assignment inefficient due to insufficient workers.In this paper,an Intelligent and Trustworthy task assignment method based on Trust and Social relations(ITTS)is proposed for scenarios with many tasks and few workers.Specifically,ITTS first makes initial assignments based on trust and social influences,thereby transforming the complex large-scale industrial task assignment of the platform into the small-scale task assignment for each worker.Then,an intelligent Q-decision mechanism based on workers'social relation is proposed,which adopts the first-exploration-then-utilization principle to allocate tasks.Only when a worker cannot cope with the assigned tasks,it initiates dynamic worker recruitment,thus effectively solving the worker shortage problem as well as the cold start issue.More importantly,we consider trust and security issues,and evaluate the trust and social circles of workers by accumulating task feedback,to provide the platform a reference for worker recruitment,thereby creating a high-quality worker pool.Finally,extensive simulations demonstrate ITTS outperforms two benchmark methods by increasing task completion rates by 56.49%-61.53%and profit by 42.34%-47.19%.
基金supported by the National Natural Science Foundation of China(No.51601019)the Guangdong Basic and Applied Basic Research Foundation,China(No.2022A1515010233)+1 种基金the Key Project of Shaanxi Province of Qinchuangyuan“Scientist and Engineer”Team Construction,China(No.2023KXJ-123)the Natural Science Foundation of Shaanxi Province,China(No.2024JC-YBMS-014).
文摘The probability of phase formation was predicted using k-nearest neighbor algorithm(KNN)and artificial neural network algorithm(ANN).Additionally,the composition ranges of Ti,Cu,Ni,and Hf in 40 unknown amorphous alloy composites(AACs)were predicted using ANN.The predicted alloys were then experimentally verified through X-ray diffraction(XRD)and high-resolution transmission electron microscopy(HRTEM).The prediction accuracies of the ANN for AM and IM phases are 93.12%and 85.16%,respectively,while the prediction accuracies of KNN for AM and IM phases are 93%and 84%,respectively.It is observed that when the contents of Ti,Cu,Ni,and Hf fall within the ranges of 32.7−34.5 at.%,16.4−17.3 at.%,30.9−32.7 at.%,and 17.3−18.3 at.%,respectively,it is more likely to form AACs.Based on the results of XRD and HRTEM,the Ti_(34)Cu17Ni_(31.36)Hf_(17.64)and Ti_(36)Cu_(18)Ni_(29.44)Hf_(16.56)alloys are identified as good AACs,which are in closely consistent with the predicted amorphous alloy compositions.
基金the Researchers Supporting Project number(RSPD2025R997),King Saud University,Riyadh,Saudi Arabia.
文摘This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.
