With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavi...With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.展开更多
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this pap...Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.展开更多
The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade tempe...The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade temperature regulation performance.To address these challenges,we propose a composite control scheme combining fuzzy logic and a variable-gain generalized supertwisting algorithm(VG-GSTA).Firstly,a one-dimensional(1D)fuzzy logic controler(FLC)for the pump ensures stable coolant flow,while a two-dimensional(2D)FLC for the fan regulates the stack temperature near the reference value.The VG-GSTA is then introduced to eliminate steady-state errors,offering resistance to disturbances and minimizing control oscillations.The equilibrium optimizer is used to fine-tune VG-GSTA parameters.Co-simulation verifies the effectiveness of our method,demonstrating its advantages in terms of disturbance immunity,overshoot suppression,tracking accuracy and response speed.展开更多
Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_...Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.展开更多
For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observat...For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.展开更多
BACKGROUND Cervical spondylosis(CS)frequently co-occurs with generalized anxiety disorder(GAD),presenting a complex clinical challenge.Managing CS-related pain in patients with GAD is particularly challenging because ...BACKGROUND Cervical spondylosis(CS)frequently co-occurs with generalized anxiety disorder(GAD),presenting a complex clinical challenge.Managing CS-related pain in patients with GAD is particularly challenging because of the bidirectional relationship between pain and anxiety,necessitating integrated treatment strategies.AIM To evaluate the efficacy of electroacupuncture(EA)in treating CS-related pain and anxiety in patients with GAD.METHODS This retrospective cohort study analyzed data from 83 patients with CS-related pain and GAD who received EA treatment over 2-year period.Pain intensity was assessed using the visual analog scale,and anxiety symptoms were measured using the Hamilton Anxiety Rating Scale.Additionally,neuroinflammatory markers,including interleukin-6,tumor necrosis factor-alpha,and high-sensitivity C-reactive protein,were examined.Outcomes were evaluated at baseline,after 4 weeks,and after 8 weeks of treatment.RESULTS EA treatment significantly reduced CS-related pain(mean visual analog scale reduction:3.24±1.18;P<0.001)and improved anxiety symptoms(mean Hamilton Anxiety Rating Scale reduction:7.83±2.65;P<0.001)after 8 weeks of treatment.Neuroinflammatory markers also showed significant reductions,with interleukin-6 and tumor necrosis factor-alpha levels decreasing by 32.7%and 28.5%,respectively(P<0.01).Pain reduction was significantly correlated with improvements in anxiety symptoms(r=0.68;P<0.001)and a decrease in inflammatory markers(r=0.54;P<0.01).CONCLUSION EA demonstrates significant efficacy in reducing CS-related pain in patients with comorbid GAD,along with concurrent improvements in anxiety symptoms and neuroinflammatory profiles.These findings suggest that EA may offer a valuable integrative approach for managing this complex clinical presentation,potentially addressing both pain and anxiety through the modulation of neuroinflammatory pathways.展开更多
We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functi...We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.展开更多
The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequ...The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequently,such models fail to adequately reflect the continuity characteristics of soil deformation.Leveraging the Pasternak foundation-Euler beam model,this study considers the generalized shear force on the beam to account for the influence of soil outside the beam ends on the shear stress.An analytical model for the deformation and internal forces of finite-length beams subjected to arbitrary loads is derived based on the initial parameter method under various conditions.The mechanical model of the elastic foundation beam for advanced umbrella arch under typical tunnel excavation cycles is established,yielding analytical solutions for the longitudinal response of the umbrella arch.The reliability of the analytical model is verified with the existing test data.The improved model addresses anomalies in existing models,such as abnormal upward deformation in the loosened segment and maximum deflection occurring within the soil mass.Additionally,dimensionless characteristic parameters reflecting the relative stiffness between the umbrella arch structure and the foundation soil are proposed.Results indicate that the magnitude of soil characteristic parameters significantly influences the deformation and internal forces of the umbrella arch.Within common ranges of soil values,the maximum deformation and internal forces of the umbrella arch under semi-logarithmic coordinates exhibit nearly linear decay with decreasing soil characteristic parameters.The impact of tunnel excavation height on the stress of unsupported sections of the umbrella arch is minor,but it is more significant for umbrella arch buried within the soil mass.Conversely,the influence of tunnel excavation advance on the umbrella arch is opposite.展开更多
In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy di...In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.展开更多
Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglo...Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.展开更多
Background Polycystic ovarian syndrome(PCOS),a common endocrine disorder in reproductive-aged women,has substantial physical and psychological impacts.While the physical manifestations of PCOS are well established,the...Background Polycystic ovarian syndrome(PCOS),a common endocrine disorder in reproductive-aged women,has substantial physical and psychological impacts.While the physical manifestations of PCOS are well established,the psychological burden,especially anxiety,is understudied in Saudi Arabia.This study aimed to assess the prevalence of generalized anxiety disorder among females with PCOS compared to those without PCOS,and to identify the clinical and sociodemographic factors associated with anxiety in the Jazan region of Saudi Arabia.Methods A cross-sectional study was conducted between January and March 2023 using an Arabic self-administered online questionnaire distributed via social media platforms.The study recruited 410 reproductive-age females(≥18 years)from the Jazan region using convenience sampling.The questionnaire encompassed socio-demographic characteristics,economic indicators,medical history,PCOS symptoms,and the validated Generalized Anxiety Disorder-7(GAD-7)assessment tool.Results The prevalence of PCOS in the study population was 22.44%.Women with PCOS showed significantly higher anxiety levels compared to controls without PCOS(32.61%vs.22.33%).Biochemical hyperandrogenism was the strongest predictor of anxiety(OR=4.179).Menstrual irregularities demonstrated a dose-dependent relationship with anxiety risk,wherein participants with 2–3 months and≥3 months of amenorrhea had 2.5-and 3.3-times higher odds of anxiety compared to those with regular cycles(OR=2.451 and 3.314).Other PCOS-related dermatological manifestations were also associated with increased anxiety,including hirsutism(OR=1.745),alopecia(OR=2.285)and acne(OR=1.723).Marital status was a significant factor,with divorced/widowed females having 4.4-fold higher anxiety odds compared to single females(OR=4.371).Conclusion PCOS presents a significant psychological burden in Saudi women,with anxiety prevalence higher than the general population.The robust associations between PCOS manifestations and anxiety emphasize the need for integrated healthcare approaches that address both endocrine and mental health aspects.Routine psychological screening and support services should be incorporated into PCOS management protocols.展开更多
BACKGROUND Patients with chronic obstructive pulmonary disease(COPD)frequently experience exacerbations requiring multiple hospitalizations over prolonged disease courses,which predispose them to generalized anxiety d...BACKGROUND Patients with chronic obstructive pulmonary disease(COPD)frequently experience exacerbations requiring multiple hospitalizations over prolonged disease courses,which predispose them to generalized anxiety disorder(GAD).This comorbidity exacerbates breathing difficulties,activity limitations,and social isolation.While previous studies predominantly employed the GAD 7-item scale for screening,this approach is somewhat subjective.The current literature on predictive models for GAD risk in patients with COPD is limited.AIM To construct and validate a GAD risk prediction model to aid healthcare professionals in preventing the onset of GAD.METHODS This retrospective analysis encompassed patients with COPD treated at our institution from July 2021 to February 2024.The patients were categorized into a modeling(MO)group and a validation(VA)group in a 7:3 ratio on the basis of the occurrence of GAD.Univariate and multivariate logistic regression analyses were utilized to construct the risk prediction model,which was visualized using forest plots.The model’s performance was evaluated using Hosmer-Lemeshow(H-L)goodness-of-fit test and receiver operating characteristic(ROC)curve analysis.RESULTS A total of 271 subjects were included,with 190 in the MO group and 81 in the VA group.GAD was identified in 67 patients with COPD,resulting in a prevalence rate of 24.72%(67/271),with 49 cases(18.08%)in the MO group and 18 cases(22.22%)in the VA group.Significant differences were observed between patients with and without GAD in terms of educational level,average household income,smoking history,smoking index,number of exacerbations in the past year,cardiovascular comorbidities,disease knowledge,and personality traits(P<0.05).Multivariate logistic regression analysis revealed that lower education levels,household income<3000 China yuan,smoking history,smoking index≥400 cigarettes/year,≥two exacerbations in the past year,cardiovascular comorbidities,complete lack of disease information,and introverted personality were significant risk factors for GAD in the MO group(P<0.05).ROC analysis indicated that the area under the curve for predicting GAD in the MO and VA groups was 0.978 and 0.960.The H-L test yieldedχ^(2) values of 6.511 and 5.179,with P=0.275 and 0.274.Calibration curves demonstrated good agreement between predicted and actual GAD occurrence risks.CONCLUSION The developed predictive model includes eight independent risk factors:Educational level,household income,smoking history,smoking index,number of exacerbations in the past year,presence of cardiovascular comorbidities,level of disease knowledge,and personality traits.This model effectively predicts the onset of GAD in patients with COPD,enabling early identification of high-risk individuals and providing a basis for early preventive interventions by nursing staff.展开更多
BACKGROUND Postpartum women are at an increased risk of generalized anxiety disorder(GAD),which can negatively affect both mental health and physical recovery.Pelvic floor dysfunction,common in this population,can exa...BACKGROUND Postpartum women are at an increased risk of generalized anxiety disorder(GAD),which can negatively affect both mental health and physical recovery.Pelvic floor dysfunction,common in this population,can exacerbate psychological distress.Although pelvic floor rehabilitation is effective in physical recovery,its potential to improve psychological outcomes,especially in women with GAD,remains underexplored.AIM To evaluate the effectiveness of an individualized pelvic floor rehabilitation program in improving anxiety,pelvic floor function,and quality of life in postpartum women with GAD.METHODS A retrospective study was performed to analyze 80 postpartum women with GAD who completed a 12-week individualized pelvic floor rehabilitation program(January 2020-December 2024),combining supervised pelvic floor muscle training and psychological support.Primary outcomes were changes in GAD-7 and Hamilton anxiety rating scale(HAM-A)scores and pelvic floor function measured by surface electromyography(sEMG).Secondary outcomes included World Health Organization quality of life-BREF,pelvic floor symptom severity,and impact on daily activities(pelvic floor impact questionnaire).Assessments were conducted at baseline and 6 and 12 weeks during the intervention period.RESULTS Significant improvements were observed in anxiety measures,with mean GAD-7 scores decreasing from 14.8±3.2 at baseline to 8.2±2.9 at week 12(P<0.001)and HAM-A scores decreasing from 22.6±4.5 to 12.4±3.8(P<0.001).Pelvic floor function showed substantial enhancement,with sEMG amplitude increasing from 22.4±5.6μV to 35.9±6.8μV(P<0.001).Quality of life improved across all domains,with the most significant improvements in psychological(28.5%increase)and physical health(25.8%increase).Program adherence was 91.5%for the supervised sessions,and no serious adverse events were reported.CONCLUSION Individualized pelvic floor rehabilitation training effectively improves both psychological and functional outcomes in postpartum women with GAD.The high adherence and significant outcomes make this integrated approach feasible and effective.展开更多
Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for conse...Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences,we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences.We show that this ratio is solely dependent on the order of the grid,providing a concise and splendid identity.展开更多
The growth of Sakhalin fir(Abies sachalinen-sis)seedlings,an important forest tree species in northern Hokkaido,Japan,is significantly affected by competition from surrounding vegetation,especially evergreen dwarf bam...The growth of Sakhalin fir(Abies sachalinen-sis)seedlings,an important forest tree species in northern Hokkaido,Japan,is significantly affected by competition from surrounding vegetation,especially evergreen dwarf bamboo.In this study,we investigated the height and root collar diameter(RCD)growth of Sakhalin fir seedlings under various degrees of cover by deciduous vegetation and evergreen dwarf bamboo.Generalized additive models were used to quantify the effects of canopy cover and forest floor cover on the relative growth rates of these two parameters.The canopy cover of Sakhalin fir seedlings had a nonlin-ear negative effect on both the height growth of seedlings in the subsequent year and the RCD growth in the current year,given the general growth pattern in this species,where height growth ceases in early summer and RCD growth con-tinues until autumn.Height growth declined sharply after the canopy cover rate exceeded 50%,while RCD growth declined rapidly between 0 and 50%canopy cover rate.The forest floor cover had a greater negative impact on RCD growth than on height growth.These results suggested that Sakhalin fir seedlings respond to vegetative competition by prioritizing height growth for light acquisition at the expense of diameter growth and possibly root growth for below-ground competition.The cover of evergreen dwarf bamboo reduced the height growth of fir seedlings significantly more than the cover of deciduous vegetation.This difference is likely due to the timing of light availability.When competing with deciduous vegetation,Sakhalin fir seedlings exposed to light during the post-snow melt and early spring before the development of the deciduous vegetation canopy can photosynthesize more effectively,leading to greater height growth.The results of this study highlighted the importance of vegetation control considering the type of vegetation for successful Sakhalin fir reforestation.Adjusting the intensity and timing of weeding based on the presence and abundance of dwarf bamboo and other competing vegetation could potentially reduce weeding costs and increase biodiversity in reforested areas.展开更多
Electronic circular dichroism(ECD)spectrum is an important tool for as-sessing molecular chirality.Tradition-al methods,like linear response time-dependent density functional theory(LR-TDDFT),predict ECD spectra well ...Electronic circular dichroism(ECD)spectrum is an important tool for as-sessing molecular chirality.Tradition-al methods,like linear response time-dependent density functional theory(LR-TDDFT),predict ECD spectra well for small or medium-sized molecules,but struggle with large sys-tems due to high computational costs,making it a significant challenge to ac-curately and efficiently predict the ECD properties of complex systems.Within the framework of the generalized energy-based fragmentation(GEBF)method for localized excited states(ESs)calculation,we propose a combination algorithm for calculating rotatory strengths of ESs in condensed phase systems.This algorithm estimates the rotatory strength of the total system by calculating and combin-ing the transition electric and magnetic dipole moments of subsystems.We have used the GEBF method to calculate the ECD properties of chiral drug molecule derivatives,green fluo-rescent protein,and cyclodextrin derivatives,and compared their results with traditional methods or experimental data.The results show that this method can efficiently and accu-rately predict the ECD spectra of these systems.Thus,the GEBF method for ECD spectra demonstrates great potential in the chiral analysis of complex systems and chiral material design,promising to become a powerful theoretical tool in chiral chemistry.展开更多
The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environmen...The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environment.This study aims to build a prediction model to understand the spatial characteristics and piecewise effects of forest fire drivers.Using monthly grid data from 2006 to 2020,a modeling study analyzed fire occurrences during the September to April fire season in Fujian Province,China.We compared the fitting performance of the logistic regression model(LRM),the generalized additive logistic model(GALM),and the spatial generalized additive logistic model(SGALM).The results indicate that SGALMs had the best fitting results and the highest prediction accuracy.Meteorological factors significantly impacted forest fires in Fujian Province.Areas with high fire incidence were mainly concentrated in the northwest and southeast.SGALMs improved the fitting effect of fire prediction models by considering spatial effects and the flexible fitting ability of nonlinear interpretation.This model provides piecewise interpretations of forest wildfire occurrences,which can be valuable for relevant departments and will assist forest managers in refining prevention measures based on temporal and spatial differences.展开更多
Accurate description of noncova-lent interactions in large systems is challenging due to the require-ment of high-level electron corre-lation methods.The generalized energy-based fragmentation(GEBF)approach,in conjunc...Accurate description of noncova-lent interactions in large systems is challenging due to the require-ment of high-level electron corre-lation methods.The generalized energy-based fragmentation(GEBF)approach,in conjunc-tion with the domain-based local pair natural orbital(DLPNO)method,has been applied to assess the average binding energies(ABEs)of large benzene clus-ters,specifically(C6H6)13,at the coupled cluster singles and doubles with perturbative triples correction[CCSD(T)]level and the complete basis set(CBS)limit.Utilizing GEBF-DLPNO-CCSD(T)/CBS ABEs as benchmarks,various DFT functionals were evaluated.It was found that several functionals with empirical dispersion correction,including M06-2X-D3,B3LYP-D3(BJ),and PBE-D3(BJ),provide accurate descriptions of the ABEs for(C6H6)13 clusters.Additionally,the M06-2X-D3 functional was used to calculate the ABEs and relative stabili-ties of(C6H6)n clusters for n=11,12,13,14,and 15 revealing that the(C6H6)13 cluster ex-hibits the highest relative stability.These findings align with experimental evidence suggest-ing that n=13 is one of the magic numbers for benzene clusters(C6H6)n,with n≤30.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local ac...Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].展开更多
基金Project supported by the Guangdong Basic and Applied Basic Research Foundation of China(No.2023A1515012809)the Natural Science Foundation of Shaanxi Province of China(No.2023-JC-YB-073)the Fundamental Research Funds for the Central Universities of China(No.D5000230066)。
文摘With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.
文摘Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.
基金Supported by the Major Science and Technology Project of Jilin Province(20220301010GX)the International Scientific and Technological Cooperation(20240402071GH).
文摘The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade temperature regulation performance.To address these challenges,we propose a composite control scheme combining fuzzy logic and a variable-gain generalized supertwisting algorithm(VG-GSTA).Firstly,a one-dimensional(1D)fuzzy logic controler(FLC)for the pump ensures stable coolant flow,while a two-dimensional(2D)FLC for the fan regulates the stack temperature near the reference value.The VG-GSTA is then introduced to eliminate steady-state errors,offering resistance to disturbances and minimizing control oscillations.The equilibrium optimizer is used to fine-tune VG-GSTA parameters.Co-simulation verifies the effectiveness of our method,demonstrating its advantages in terms of disturbance immunity,overshoot suppression,tracking accuracy and response speed.
基金supported by the National Key Research and Development Program of China(2023YFA1010200,2020YFA0713100)the National Natural Science Foundation of China(12071453)the Innovation Program for Quantum Science and Technology(2021ZD0302902).
文摘Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.
基金co-supported by the National Natural Science Foundation of China(No.62303246,No.62103204)the China Postdoctoral Science Foundation(No.2023M731788)。
文摘For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.
文摘BACKGROUND Cervical spondylosis(CS)frequently co-occurs with generalized anxiety disorder(GAD),presenting a complex clinical challenge.Managing CS-related pain in patients with GAD is particularly challenging because of the bidirectional relationship between pain and anxiety,necessitating integrated treatment strategies.AIM To evaluate the efficacy of electroacupuncture(EA)in treating CS-related pain and anxiety in patients with GAD.METHODS This retrospective cohort study analyzed data from 83 patients with CS-related pain and GAD who received EA treatment over 2-year period.Pain intensity was assessed using the visual analog scale,and anxiety symptoms were measured using the Hamilton Anxiety Rating Scale.Additionally,neuroinflammatory markers,including interleukin-6,tumor necrosis factor-alpha,and high-sensitivity C-reactive protein,were examined.Outcomes were evaluated at baseline,after 4 weeks,and after 8 weeks of treatment.RESULTS EA treatment significantly reduced CS-related pain(mean visual analog scale reduction:3.24±1.18;P<0.001)and improved anxiety symptoms(mean Hamilton Anxiety Rating Scale reduction:7.83±2.65;P<0.001)after 8 weeks of treatment.Neuroinflammatory markers also showed significant reductions,with interleukin-6 and tumor necrosis factor-alpha levels decreasing by 32.7%and 28.5%,respectively(P<0.01).Pain reduction was significantly correlated with improvements in anxiety symptoms(r=0.68;P<0.001)and a decrease in inflammatory markers(r=0.54;P<0.01).CONCLUSION EA demonstrates significant efficacy in reducing CS-related pain in patients with comorbid GAD,along with concurrent improvements in anxiety symptoms and neuroinflammatory profiles.These findings suggest that EA may offer a valuable integrative approach for managing this complex clinical presentation,potentially addressing both pain and anxiety through the modulation of neuroinflammatory pathways.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12461048 and 12061051)the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2023MS01003)+2 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT23096)the financial support from the Program of China Scholarships Council(Grant No.202306810054)for one year study at the University of Leedsthe support of Professor Ke Wu and Professor Weizhong Zhao at Capital Normal University,China。
文摘We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.
基金Projects(52008403,52378421)supported by the National Natural Science Foundation of ChinaProject(2022-Key-10)supported by the Science and Technology Research and Development Program Project of China Railway Group LimitedProject(202207)supported by the Hunan Provincial Transportation Science and Technology,China。
文摘The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequently,such models fail to adequately reflect the continuity characteristics of soil deformation.Leveraging the Pasternak foundation-Euler beam model,this study considers the generalized shear force on the beam to account for the influence of soil outside the beam ends on the shear stress.An analytical model for the deformation and internal forces of finite-length beams subjected to arbitrary loads is derived based on the initial parameter method under various conditions.The mechanical model of the elastic foundation beam for advanced umbrella arch under typical tunnel excavation cycles is established,yielding analytical solutions for the longitudinal response of the umbrella arch.The reliability of the analytical model is verified with the existing test data.The improved model addresses anomalies in existing models,such as abnormal upward deformation in the loosened segment and maximum deflection occurring within the soil mass.Additionally,dimensionless characteristic parameters reflecting the relative stiffness between the umbrella arch structure and the foundation soil are proposed.Results indicate that the magnitude of soil characteristic parameters significantly influences the deformation and internal forces of the umbrella arch.Within common ranges of soil values,the maximum deformation and internal forces of the umbrella arch under semi-logarithmic coordinates exhibit nearly linear decay with decreasing soil characteristic parameters.The impact of tunnel excavation height on the stress of unsupported sections of the umbrella arch is minor,but it is more significant for umbrella arch buried within the soil mass.Conversely,the influence of tunnel excavation advance on the umbrella arch is opposite.
基金funded by Researchers Supporting Project number(RSPD2025R969),King Saud University,Riyadh,Saudi Arabia.
文摘In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.
基金supported by the National Natural Science Foundation of China(Grant No.12272248)the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX23_3296).
文摘Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.
文摘Background Polycystic ovarian syndrome(PCOS),a common endocrine disorder in reproductive-aged women,has substantial physical and psychological impacts.While the physical manifestations of PCOS are well established,the psychological burden,especially anxiety,is understudied in Saudi Arabia.This study aimed to assess the prevalence of generalized anxiety disorder among females with PCOS compared to those without PCOS,and to identify the clinical and sociodemographic factors associated with anxiety in the Jazan region of Saudi Arabia.Methods A cross-sectional study was conducted between January and March 2023 using an Arabic self-administered online questionnaire distributed via social media platforms.The study recruited 410 reproductive-age females(≥18 years)from the Jazan region using convenience sampling.The questionnaire encompassed socio-demographic characteristics,economic indicators,medical history,PCOS symptoms,and the validated Generalized Anxiety Disorder-7(GAD-7)assessment tool.Results The prevalence of PCOS in the study population was 22.44%.Women with PCOS showed significantly higher anxiety levels compared to controls without PCOS(32.61%vs.22.33%).Biochemical hyperandrogenism was the strongest predictor of anxiety(OR=4.179).Menstrual irregularities demonstrated a dose-dependent relationship with anxiety risk,wherein participants with 2–3 months and≥3 months of amenorrhea had 2.5-and 3.3-times higher odds of anxiety compared to those with regular cycles(OR=2.451 and 3.314).Other PCOS-related dermatological manifestations were also associated with increased anxiety,including hirsutism(OR=1.745),alopecia(OR=2.285)and acne(OR=1.723).Marital status was a significant factor,with divorced/widowed females having 4.4-fold higher anxiety odds compared to single females(OR=4.371).Conclusion PCOS presents a significant psychological burden in Saudi women,with anxiety prevalence higher than the general population.The robust associations between PCOS manifestations and anxiety emphasize the need for integrated healthcare approaches that address both endocrine and mental health aspects.Routine psychological screening and support services should be incorporated into PCOS management protocols.
基金Supported by the Henan Provincial Health Commission,No.232102310145.
文摘BACKGROUND Patients with chronic obstructive pulmonary disease(COPD)frequently experience exacerbations requiring multiple hospitalizations over prolonged disease courses,which predispose them to generalized anxiety disorder(GAD).This comorbidity exacerbates breathing difficulties,activity limitations,and social isolation.While previous studies predominantly employed the GAD 7-item scale for screening,this approach is somewhat subjective.The current literature on predictive models for GAD risk in patients with COPD is limited.AIM To construct and validate a GAD risk prediction model to aid healthcare professionals in preventing the onset of GAD.METHODS This retrospective analysis encompassed patients with COPD treated at our institution from July 2021 to February 2024.The patients were categorized into a modeling(MO)group and a validation(VA)group in a 7:3 ratio on the basis of the occurrence of GAD.Univariate and multivariate logistic regression analyses were utilized to construct the risk prediction model,which was visualized using forest plots.The model’s performance was evaluated using Hosmer-Lemeshow(H-L)goodness-of-fit test and receiver operating characteristic(ROC)curve analysis.RESULTS A total of 271 subjects were included,with 190 in the MO group and 81 in the VA group.GAD was identified in 67 patients with COPD,resulting in a prevalence rate of 24.72%(67/271),with 49 cases(18.08%)in the MO group and 18 cases(22.22%)in the VA group.Significant differences were observed between patients with and without GAD in terms of educational level,average household income,smoking history,smoking index,number of exacerbations in the past year,cardiovascular comorbidities,disease knowledge,and personality traits(P<0.05).Multivariate logistic regression analysis revealed that lower education levels,household income<3000 China yuan,smoking history,smoking index≥400 cigarettes/year,≥two exacerbations in the past year,cardiovascular comorbidities,complete lack of disease information,and introverted personality were significant risk factors for GAD in the MO group(P<0.05).ROC analysis indicated that the area under the curve for predicting GAD in the MO and VA groups was 0.978 and 0.960.The H-L test yieldedχ^(2) values of 6.511 and 5.179,with P=0.275 and 0.274.Calibration curves demonstrated good agreement between predicted and actual GAD occurrence risks.CONCLUSION The developed predictive model includes eight independent risk factors:Educational level,household income,smoking history,smoking index,number of exacerbations in the past year,presence of cardiovascular comorbidities,level of disease knowledge,and personality traits.This model effectively predicts the onset of GAD in patients with COPD,enabling early identification of high-risk individuals and providing a basis for early preventive interventions by nursing staff.
基金2022 Annual Medical Science Research Project Plan of Hebei Province,No.20221111.
文摘BACKGROUND Postpartum women are at an increased risk of generalized anxiety disorder(GAD),which can negatively affect both mental health and physical recovery.Pelvic floor dysfunction,common in this population,can exacerbate psychological distress.Although pelvic floor rehabilitation is effective in physical recovery,its potential to improve psychological outcomes,especially in women with GAD,remains underexplored.AIM To evaluate the effectiveness of an individualized pelvic floor rehabilitation program in improving anxiety,pelvic floor function,and quality of life in postpartum women with GAD.METHODS A retrospective study was performed to analyze 80 postpartum women with GAD who completed a 12-week individualized pelvic floor rehabilitation program(January 2020-December 2024),combining supervised pelvic floor muscle training and psychological support.Primary outcomes were changes in GAD-7 and Hamilton anxiety rating scale(HAM-A)scores and pelvic floor function measured by surface electromyography(sEMG).Secondary outcomes included World Health Organization quality of life-BREF,pelvic floor symptom severity,and impact on daily activities(pelvic floor impact questionnaire).Assessments were conducted at baseline and 6 and 12 weeks during the intervention period.RESULTS Significant improvements were observed in anxiety measures,with mean GAD-7 scores decreasing from 14.8±3.2 at baseline to 8.2±2.9 at week 12(P<0.001)and HAM-A scores decreasing from 22.6±4.5 to 12.4±3.8(P<0.001).Pelvic floor function showed substantial enhancement,with sEMG amplitude increasing from 22.4±5.6μV to 35.9±6.8μV(P<0.001).Quality of life improved across all domains,with the most significant improvements in psychological(28.5%increase)and physical health(25.8%increase).Program adherence was 91.5%for the supervised sessions,and no serious adverse events were reported.CONCLUSION Individualized pelvic floor rehabilitation training effectively improves both psychological and functional outcomes in postpartum women with GAD.The high adherence and significant outcomes make this integrated approach feasible and effective.
基金Supported by the National Natural Science Foundation of China(Grant No.12471298)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.23JSQ031)the Shaanxi Province College Student Innovation and Entrepreneurship Training Program(Grant Nos.S202210699481 and S202310699324X).
文摘Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences,we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences.We show that this ratio is solely dependent on the order of the grid,providing a concise and splendid identity.
基金supported by the Ministry of Agriculture,Forestry,and Fisheries of Japan (25093 C)JSPS KAKENHI (JP23H02262)
文摘The growth of Sakhalin fir(Abies sachalinen-sis)seedlings,an important forest tree species in northern Hokkaido,Japan,is significantly affected by competition from surrounding vegetation,especially evergreen dwarf bamboo.In this study,we investigated the height and root collar diameter(RCD)growth of Sakhalin fir seedlings under various degrees of cover by deciduous vegetation and evergreen dwarf bamboo.Generalized additive models were used to quantify the effects of canopy cover and forest floor cover on the relative growth rates of these two parameters.The canopy cover of Sakhalin fir seedlings had a nonlin-ear negative effect on both the height growth of seedlings in the subsequent year and the RCD growth in the current year,given the general growth pattern in this species,where height growth ceases in early summer and RCD growth con-tinues until autumn.Height growth declined sharply after the canopy cover rate exceeded 50%,while RCD growth declined rapidly between 0 and 50%canopy cover rate.The forest floor cover had a greater negative impact on RCD growth than on height growth.These results suggested that Sakhalin fir seedlings respond to vegetative competition by prioritizing height growth for light acquisition at the expense of diameter growth and possibly root growth for below-ground competition.The cover of evergreen dwarf bamboo reduced the height growth of fir seedlings significantly more than the cover of deciduous vegetation.This difference is likely due to the timing of light availability.When competing with deciduous vegetation,Sakhalin fir seedlings exposed to light during the post-snow melt and early spring before the development of the deciduous vegetation canopy can photosynthesize more effectively,leading to greater height growth.The results of this study highlighted the importance of vegetation control considering the type of vegetation for successful Sakhalin fir reforestation.Adjusting the intensity and timing of weeding based on the presence and abundance of dwarf bamboo and other competing vegetation could potentially reduce weeding costs and increase biodiversity in reforested areas.
基金supported by the National Natural Science Foundation of China(No.22273038 and No.22033004).
文摘Electronic circular dichroism(ECD)spectrum is an important tool for as-sessing molecular chirality.Tradition-al methods,like linear response time-dependent density functional theory(LR-TDDFT),predict ECD spectra well for small or medium-sized molecules,but struggle with large sys-tems due to high computational costs,making it a significant challenge to ac-curately and efficiently predict the ECD properties of complex systems.Within the framework of the generalized energy-based fragmentation(GEBF)method for localized excited states(ESs)calculation,we propose a combination algorithm for calculating rotatory strengths of ESs in condensed phase systems.This algorithm estimates the rotatory strength of the total system by calculating and combin-ing the transition electric and magnetic dipole moments of subsystems.We have used the GEBF method to calculate the ECD properties of chiral drug molecule derivatives,green fluo-rescent protein,and cyclodextrin derivatives,and compared their results with traditional methods or experimental data.The results show that this method can efficiently and accu-rately predict the ECD spectra of these systems.Thus,the GEBF method for ECD spectra demonstrates great potential in the chiral analysis of complex systems and chiral material design,promising to become a powerful theoretical tool in chiral chemistry.
基金supported by the Fujian Provincial Science and Technology Program“University-Industry Cooperation Project”(2024Y4015)National Key R&D Plan of Strategic International Scientific and Technological Innovation Cooperation Project(2018YFE0207800).
文摘The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environment.This study aims to build a prediction model to understand the spatial characteristics and piecewise effects of forest fire drivers.Using monthly grid data from 2006 to 2020,a modeling study analyzed fire occurrences during the September to April fire season in Fujian Province,China.We compared the fitting performance of the logistic regression model(LRM),the generalized additive logistic model(GALM),and the spatial generalized additive logistic model(SGALM).The results indicate that SGALMs had the best fitting results and the highest prediction accuracy.Meteorological factors significantly impacted forest fires in Fujian Province.Areas with high fire incidence were mainly concentrated in the northwest and southeast.SGALMs improved the fitting effect of fire prediction models by considering spatial effects and the flexible fitting ability of nonlinear interpretation.This model provides piecewise interpretations of forest wildfire occurrences,which can be valuable for relevant departments and will assist forest managers in refining prevention measures based on temporal and spatial differences.
基金supported by the National Key R&D Program of China(No.2023YFB3712504)the National Natural Science Foundation of China(Nos.22273038,22073043,and 22033004)。
文摘Accurate description of noncova-lent interactions in large systems is challenging due to the require-ment of high-level electron corre-lation methods.The generalized energy-based fragmentation(GEBF)approach,in conjunc-tion with the domain-based local pair natural orbital(DLPNO)method,has been applied to assess the average binding energies(ABEs)of large benzene clus-ters,specifically(C6H6)13,at the coupled cluster singles and doubles with perturbative triples correction[CCSD(T)]level and the complete basis set(CBS)limit.Utilizing GEBF-DLPNO-CCSD(T)/CBS ABEs as benchmarks,various DFT functionals were evaluated.It was found that several functionals with empirical dispersion correction,including M06-2X-D3,B3LYP-D3(BJ),and PBE-D3(BJ),provide accurate descriptions of the ABEs for(C6H6)13 clusters.Additionally,the M06-2X-D3 functional was used to calculate the ABEs and relative stabili-ties of(C6H6)n clusters for n=11,12,13,14,and 15 revealing that the(C6H6)13 cluster ex-hibits the highest relative stability.These findings align with experimental evidence suggest-ing that n=13 is one of the magic numbers for benzene clusters(C6H6)n,with n≤30.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
基金Supported by Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].
