A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov...A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.展开更多
Current research on heterogeneous advanced oxidation processes(HAOPs)predominantly emphasizes catalyst iteration and innovation.Significant efforts have been made to regulate the electron structure and optimize the el...Current research on heterogeneous advanced oxidation processes(HAOPs)predominantly emphasizes catalyst iteration and innovation.Significant efforts have been made to regulate the electron structure and optimize the electron distribution,thereby increasing the catalytic activity.However,this focus often overshadows an equally essential aspect of HAOPs:the adsorption effect.Adsorption is a critical initiator for triggering the interaction of oxidants and contaminants with heterogeneous catalysts.The efficacy of these interactions is influenced by a variety of physicochemical properties,including surface chemistry and pore sizes,which determine the affinities between contaminants and material surfaces.This dispar ity in affinity is pivotal because it underpins the selective removal of contaminants,especially in complex waste streams containing diverse contaminants and competing matrices.Consequently,understanding and mastering these interfacial interactions is fundamentally indispensable not only for improving pro cess efficiency but also for enhancing the selectivity of contaminant removal.Herein,we highlight the importance of adsorption-driven interfacial interactions for fundamentally elucidating the catalytic mechanisms of HAOPs.Such interactions dictate the overall performance of the treatment processes by balancing the adsorption,reaction,and desorption rates on the catalyst surfaces.Elucidating the adsorption effect not only shifts the paradigm in understanding HAOPs but also improves their practical ity in water treatment and wastewater decontamination.Overall,we propose that revisiting adsorption driven interfacial interactions holds great promise for optimizing catalytic processes to develop effective HAOP strategies.展开更多
Magnesium and magnesium alloys,serving as crucial lightweight structural materials and hydrogen storage elements,find extensive applications in space technology,aviation,automotive,and magnesium-based hydrogen industr...Magnesium and magnesium alloys,serving as crucial lightweight structural materials and hydrogen storage elements,find extensive applications in space technology,aviation,automotive,and magnesium-based hydrogen industries.The global production of primary magnesium has reached approximately 1.2 million tons per year,with anticipated diversification in future applications and significant market demand.Nevertheless,approximately 80%of the world’s primary magnesium is still manufactured through the Pidgeon process,grappling with formidable issues including high energy consumption,massive carbon emission,significant resource depletion,and environmental pollution.The implementation of the relative vacuum method shows potential in breaking through technological challenges in the Pidgeon process,facilitating clean,low-carbon continuous magnesium smelting.This paper begins by introducing the principles of the relative vacuum method.Subsequently,it elucidates various innovative process routes,including relative vacuum ferrosilicon reduction,aluminum thermal reduction co-production of spinel,and aluminum thermal reduction co-production of calcium aluminate.Finally,and thermodynamic foundations of the relative vacuum,a quantitative analysis of the material,energy flows,carbon emission,and production cost for several new processes is conducted,comparing and analyzing them against the Pidgeon process.The study findings reveal that,with identical raw materials,the relative vacuum silicon thermal reduction process significantly decreases raw material consumption,energy consumption,and carbon dioxide emissions by 15.86%,30.89%,and 26.27%,respectively,compared to the Pidgeon process.The relative vacuum process,using magnesite as the raw material and aluminum as the reducing agent,has the lowest magnesium-to-feed ratio,at only 3.385.Additionally,its energy consumption and carbon dioxide emissions are the lowest,at 1.817 tce/t Mg and 7.782 t CO_(2)/t Mg,respectively.The energy consumption and carbon emissions of the relative vacuum magnesium smelting process co-producing calcium aluminate(12CaO·7Al_(2)O_(3),3CaO·Al_(2)O_(3),and CaO·Al_(2)O_(3))are highly correlated with the consumption of dolomite in the raw materials.When the reduction temperature is around 1473.15 K,the critical volume fraction of magnesium vapor for different processes varies within the range of 5%–40%.Production cost analysis shows that the relative vacuum primary magnesium smelting process has significant economic benefits.This paper offers essential data support and theoretical guidance for achieving energy efficiency,carbon reduction in magnesium smelting,and the industrial adoption of innovative processes.展开更多
Effective vegetation reconstruction plays a vital role in the restoration of desert ecosystems.However,in reconstruction of different vegetation types,the community characteristics,assembly processes,and functions of ...Effective vegetation reconstruction plays a vital role in the restoration of desert ecosystems.However,in reconstruction of different vegetation types,the community characteristics,assembly processes,and functions of different soil microbial taxa under environmental changes are still disputed,which limits the understanding of the sustainability of desert restoration.Hence,we investigated the soil microbial community characteristics and functional attributes of grassland desert(GD),desert steppe(DS),typical steppe(TS),and artificial forest(AF)in the Mu Us Desert,China.Our findings confirmed the geographical conservation of soil microbial composition but highlighted decreased microbial diversity in TS.Meanwhile,the abundance of rare taxa and microbial community stability in TS improved.Heterogeneous and homogeneous selection determined the assembly of rare and abundant bacterial taxa,respectively,with both being significantly influenced by soil moisture.In contrast,fungal communities displayed stochastic processes and exhibited sensitivity to soil nutrient conditions.Furthermore,our investigation revealed a noteworthy augmentation in bacterial metabolic functionality in TS,aligning with improved vegetation restoration and the assemblage of abundant bacterial taxa.However,within nutrient-limited soils(GD,DS,and AF),the assembly dynamics of rare fungal taxa assumed a prominent role in augmenting their metabolic capacity and adaptability to desert ecosystems.These results highlighted the variations in the assembly processes and metabolic functions of soil microorganisms during vegetation reestablishment and provided corresponding theoretical support for anthropogenic revegetation of desert ecosystems.展开更多
In November 1984,China launched its first expedition to the Southern Ocean and the Antarctic continent,culminating in the establishment of its first year-round research station—Great Wall Station—on the Antarctic Pe...In November 1984,China launched its first expedition to the Southern Ocean and the Antarctic continent,culminating in the establishment of its first year-round research station—Great Wall Station—on the Antarctic Peninsula in February 1985.Forty years later,in February 2024,China’s fifth research station,Qinling Station,commenced operations on Inexpress-ible Island near Terra Nova Bay.展开更多
Low-valent sulfur oxy-acid salts(LVSOs)represent a category of oxygen-containing salts characterized by their potent reducing capabilities.Notably,sulfite,dithionite,and thiosulfate are prevalent reducing agents that ...Low-valent sulfur oxy-acid salts(LVSOs)represent a category of oxygen-containing salts characterized by their potent reducing capabilities.Notably,sulfite,dithionite,and thiosulfate are prevalent reducing agents that are readily available,cost-effective,and exhibit minimal ecological toxicity.These LVSOs have the ability to generate or promote the generation of strong oxidants or reductants,which makes them widely used in advanced oxidation processes(AOPs)and advanced reduction processes(ARPs).This article provides a comprehensive review of the recent advancements in AOPs and ARPs involving LVSOs,alongside an examination of the fundamental principles governing the generation of active species within these processes.LVSOs fulfill three primary functions in AOPs:Serving as sources of reactive oxygen species(ROS),auxiliary agents,and activators.Particular attention is devoted to elucidating the reaction mechanisms through which LVSOs,in conjunction with metal ions,metal oxides,ultraviolet light(UV),and ozone,produce potent oxidizing agents in both homogeneous and heterogeneous systems.Regarding ARPs,this review delineates the mechanisms by which LVSOs generate strong reducing agents,including hydrated electrons,hydrogen radicals,and sulfite radicals,under UV irradiation,while also exploring the interactions between these reductants and pollutants.The review identifies existing gaps within the current framework and proposes future research avenues to address these challenges.展开更多
Fabric dyeing is a critical production process in the clothing industry and heavily relies on batch processing machines(BPM).In this study,the parallel BPM scheduling problem with machine eligibility in fabric dyeing ...Fabric dyeing is a critical production process in the clothing industry and heavily relies on batch processing machines(BPM).In this study,the parallel BPM scheduling problem with machine eligibility in fabric dyeing is considered,and an adaptive cooperated shuffled frog-leaping algorithm(ACSFLA)is proposed to minimize makespan and total tardiness simultaneously.ACSFLA determines the search times for each memeplex based on its quality,with more searches in high-quality memeplexes.An adaptive cooperated and diversified search mechanism is applied,dynamically adjusting search strategies for each memeplex based on their dominance relationships and quality.During the cooperated search,ACSFLA uses a segmented and dynamic targeted search approach,while in non-cooperated scenarios,the search focuses on local search around superior solutions to improve efficiency.Furthermore,ACSFLA employs adaptive population division and partial population shuffling strategies.Through these strategies,memeplexes with low evolutionary potential are selected for reconstruction in the next generation,while thosewithhighevolutionarypotential are retained to continue their evolution.Toevaluate the performance of ACSFLA,comparative experiments were conducted using ACSFLA,SFLA,ASFLA,MOABC,and NSGA-CC in 90 instances.The computational results reveal that ACSFLA outperforms the other algorithms in 78 of the 90 test cases,highlighting its advantages in solving the parallel BPM scheduling problem with machine eligibility.展开更多
The aging process is an inexorable fact throughout our lives and is considered a major factor in develo ping neurological dysfunctions associated with cognitive,emotional,and motor impairments.Aging-associated neurode...The aging process is an inexorable fact throughout our lives and is considered a major factor in develo ping neurological dysfunctions associated with cognitive,emotional,and motor impairments.Aging-associated neurodegenerative diseases are characterized by the progressive loss of neuronal structure and function.展开更多
The effect of hot band annealing processes—batch annealing and continuous annealing—on the texture evolution and ridging performance of ferritic stainless steel was investigated.The surface and central layers of the...The effect of hot band annealing processes—batch annealing and continuous annealing—on the texture evolution and ridging performance of ferritic stainless steel was investigated.The surface and central layers of the hot band exhibited strong shear and plane deformation textures,respectively.After batch annealing,the texture intensity of the hot-rolled sheet texture significantly decreased,and a weak recrystallization texture appeared,while fully recrystallized grains occurred after continuous annealing.A complete recrystallized{111}texture was obtained after recrystallization annealing.The sheet subjected to continuous annealing exhibited the highest intensity of{111}texture,which was accompanied by a dispersed grain orientation distribution,resulting in the lowest ridging height.展开更多
Light oil and gas reservoirs are abundant in the Ordovician marine carbonate reservoir in Shunbei Oilfield,Tarim Basin.This presents a compelling geological puzzle,as ultra-deep reservoirs undergo intense alteration a...Light oil and gas reservoirs are abundant in the Ordovician marine carbonate reservoir in Shunbei Oilfield,Tarim Basin.This presents a compelling geological puzzle,as ultra-deep reservoirs undergo intense alteration and complex petroleum accumulation processes.A comprehensive suite of geochemical analyses,including molecular components,carbon isotope composition,homogenization temperature of saline inclusions,and burial-thermal history of single wells,was conducted to elucidate the genesis of these ancient reservoirs.Three petroleum filling events have been identified in the study area:Late Caledonian,Hercynian-Indosinian,and Himalayan,through analysis of homogenization temperatures of brine inclusions and burial-thermal histories.Additionally,the oil in the study area has undergone significant alteration processes such as biodegradation,thermal alteration,mixing,evaporative fractionation,and gas invasion.This study particularly emphasizes the influential role of Himalayan gas filling-induced evaporation fractionation and gas invasion in shaping the present petroleum phase distribution.Furthermore,analysis of light hydrocarbon and diamondoid parameters indicates the oil within the study area is at a high maturity stage,with equivalent vitrinite reflectance values ranging from 1.48%to 1.99%.Additionally,the analysis of light hydrocarbons,aromatics,and thiadiamondoids indicates that TSR should occur in reservoirs near the gypsum-salt layers in the Cambrian.The existence of the Cambrian petroleum system in the study area is strongly confirmed when considering the analysis results of natural gas type(oil cracking gas),evaporative fractionation,and gas invasion.Permian local thermal anomalies notably emerge as a significant factor contributing to the destruction of biomarkers in oil.For oil not subject to transient,abnormal thermal events,biomarker reliability extends to at least 190℃.In conclusion,examining the special formation mechanisms and conditions of various secondary processes can offer valuable insights for reconstructing the history of petroleum accumulation in ultradeep reservoirs.This research provides a scientific foundation for advancing our knowledge of petroleum systems and underscores the importance of hydrocarbon geochemistry in unraveling ultra-deep,complex geological phenomena.展开更多
In this paper,we study the geometric ergodicity of continuous time Markov pro-cesses in general state space.For the geometric ergodic continuous time Markov processes,the condition π(f^(p))<∞,p>1 is added.Usin...In this paper,we study the geometric ergodicity of continuous time Markov pro-cesses in general state space.For the geometric ergodic continuous time Markov processes,the condition π(f^(p))<∞,p>1 is added.Using the coupling method,we obtain the existence of a full absorbing set on which continuous time Markov processes are f-geometric ergodic.展开更多
Models that predict a forest stand’s evolution are essential for developing plans for sustainable management.A simple mathematical framework was developed that con-siders the individual tree and stand basal area unde...Models that predict a forest stand’s evolution are essential for developing plans for sustainable management.A simple mathematical framework was developed that con-siders the individual tree and stand basal area under random resource competition and is based on two assumptions:(1)a sigmoid-type stochastic process governs tree and stand basal area dynamics of living and dying trees,and(2)the total area that a tree may potentially occupy determines the number of trees per hectare.The most effective method to satisfy these requirements is formalizing each tree diameter and potentially occupied area using Gompertz-type stochastic differential equations governed by fixed and mixed-effect parameters.Data from permanent experimental plots from long-term Lithuania experiments were used to construct the tree and stand basal area models.The new models were relatively unbiased for live trees of all species,including silver birch(Betula pen-dula Roth)and downy birch(Betula pubescens Ehrh.),[spruce(Picea abies),and pine(Pinus sylvestris)].Less reliable predic-tions were made for the basal area of dying trees.Pines gave the highest accuracy prediction of mean basal area among all live trees.The mean basal area prediction for all dying trees was lower than that for live trees.Among all species,pine also had the best average basal area prediction accuracy for live trees.Newly developed basal area growth and yield models can be recommended despite their complex formulation and implementation challenges,particularly in situations when data is scarce.This is because the newly observed plot provides sufficient information to calibrate random effects.展开更多
Efficient and innovative nano-catalytic oxidation technologies offer a breakthrough in removing emerging contaminants(ECs)from water,surpassing the limitations of traditional methods.Environmental functional materials...Efficient and innovative nano-catalytic oxidation technologies offer a breakthrough in removing emerging contaminants(ECs)from water,surpassing the limitations of traditional methods.Environmental functional materials(EFMs),particularly high-end oxidation systems using eco-friendly nanomaterials,show promise for absorbing and degrading ECs.This literature review presents a comprehensive analysis of diverse traditional restoration techniques-biological,physical,and chemical-assessing their respective applications and limitations in pesticide-contaminated water purification.Through meticulous comparison,we unequivocally advocate for the imperative integration of environmentally benign nanomaterials,notably titanium-based variants,in forthcoming methodologies.Our in-depth exploration scrutinizes the catalytic efficacy,underlying mechanisms,and adaptability of pioneering titanium-based nanomaterials across a spectrum of environmental contexts.Additionally,strategic recommendations are furnished to surmount challenges and propel the frontiers of implementing eco-friendly nanomaterials in practical water treatment scenarios.展开更多
Mantle plumes and surface erosion and sediment deposition affect the modes of continental lithospheric rupturing in extensional tectonic settings,modulating the evolution of rifting margins.However,their relative cont...Mantle plumes and surface erosion and sediment deposition affect the modes of continental lithospheric rupturing in extensional tectonic settings,modulating the evolution of rifting margins.However,their relative contributions to the overall evolution of rifting margins and possible roles in the formation of microcontinent are still elusive.Here,we use coupled geodynamic and surface processes numerical modeling to assess the extent to which surface processes may determine the formation of microcontinent during lithospheric stretching in presence or absence of a mantle plume underneath.Our modeling results indicate that fast extension rates and hillslope(i.e.,diffusion)erosion promote ridge jump events and therefore the formation of microcontinents.On the contrary,efficient fluvial erosion and far-reaching sediment transport(i.e.,stream power erosion)inhibits ridge jump events and the formation of microcontinents.The ridge jump event and overall evolution in our numerical models is consistent with the shift from the Mascarene Ridge to the Carlsberg Ridge that determined the formation of the Seychelles microcontinent.We therefore speculate that hillslope erosion,rather than fluvial erosion,was predominant during the formation of the Seychelles,a possible indication of overall dry local climate conditions.展开更多
On December 18,2023,an M_(s)6.2 earthquake jolted Jishishan County in the Linxia Hui Autonomous Prefecture in Northwest China's Gansu Province,causing substantial casualties and building collapses.The earthquake o...On December 18,2023,an M_(s)6.2 earthquake jolted Jishishan County in the Linxia Hui Autonomous Prefecture in Northwest China's Gansu Province,causing substantial casualties and building collapses.The earthquake occurred in the Qilian Block on the northeastern border of the Qinghai-Tibet Plateau,where faults are highly active and the geological structure is complex.In this study,we utilized methods such as relocation,focal mechanism solutions,and earthquake rupture processes to describe seismogenic faults.The results indicated that the majority of aftershocks occurred at a depth of 12 km.The centroid depth of the main shock and the depth of the maximum rupture point during the rupture process were also 12 km.Various geophysical methods exhibited a high degree of consistency in depth exploration.Aftershocks were distributed mainly to the west and north of the main shock and extended in the NNW direction,primarily through unilateral rupture.The main shock was a reverse thrust event with a small dextral strike-slip component.In this study,more regional data,such as previous GPS observations,field geological observations,and the distributions of the primary stress states in the region,were also incorporated.We inferred that the main shock was triggered by the main fault at the northern margin of the Lajishan Fault and that the movement of the main fault also activated some secondary faults.The compressive forces on both sides of the Lajishan Fault Zone led to the uplift of mountain areas,accompanied by some landslides,leading to this catastrophic earthquake event.In this article,the activity relationships among the 2022 M_(s)6.9 Menyuan earthquake,the 2019 M_(s)5.7 Xiahe earthquake,and the Jishishan earthquake under the action of regional stress are also discussed.This study provides additional evidence and new ideas for exploring the seismogenic process of the Lajishan Fault Zone and has implications for future in-depth research on underground activity in this region.展开更多
Background Pain sensitivity is critical for preventing non-suicidal self-injury(NSSI)behaviours;however,individuals engaging in such behaviours often exhibit decreased pain sensitivity,which may undermine this natural...Background Pain sensitivity is critical for preventing non-suicidal self-injury(NSSI)behaviours;however,individuals engaging in such behaviours often exhibit decreased pain sensitivity,which may undermine this natural safeguard.The dorsolateral prefrontal cortex(DLPFC)is a key region involved in pain regulation,and recent approaches using transcranial direct current stimulation(tDCS)to target the DLPFC have shown potential for modulating pain processing and restoring normal pain perception for individuals engaging in NSSI behaviours.Aims This study aimed to explore the immediate and short-term effects of a single session of tDCS on pain sensitivity in individuals with NSSI,as well as its secondary effects on mood and NSSI-related factors.Methods In this randomised,double-blind,parallel,sham-controlled clinical trial,participants with a history of NSSI were randomly assigned to receive either active or sham tDCS.The intervention consisted of a single 20 min tDCS session targeting the left DLPFC.The primary outcome was pain sensitivity,measured by the pressure pain threshold(PPT)and heat pain score(HPS).Secondary and additional outcomes included NSSI urges,NSSI resistance,self-efficacy in resisting NSSI,mood-related variables and exploratory cognitive-affective processes such as rumination,self-criticism and self-perceived pain sensitivity,assessed at baseline,immediately post-intervention,and at 24 hours,1 week and 2 weeks follow-ups.Results For the primary outcomes,no significant differences between groups were observed for pain sensitivity(PPT,padj=0.812;HPS,padj=0.608).However,an exploratory sensitivity analysis treating each trial as an individual observation revealed a significant effect on HPS(padj=0.036).For the secondary and additional outcomes,although there were initial improvements in joyful feelings and reductions in negative affect at 2 weeks post-intervention,these effects did not remain significant after multiple comparison corrections.Notably,reductions in rumination were statistically significant at both 1-week and 2-week follow-ups(1 week,p_(adj)=0.040;2 weeks,p_(adj)=0.042).There were no significant effects on NSSI urges,NSSI resistance,self-efficacy in resisting NSSI or self-criticism.Conclusions A single session of tDCS over the left DLPFC did not produce significant changes in pain sensitivity in individuals with NSSI.A sensitivity analysis indicated an effect on heat pain sensitivity,possibly reflecting changes in brain activity,warranting confirmation through neuroimaging.These findings suggest that tDCS warrants further investigation for its potential to influence pain-related cognitive-affective processes in individuals with NSSI.展开更多
Acetone-butanol-ethanol(ABE)fermentation is a primary strategy for producing bio-based n-butanol from abundant renewable biomass.In the typical ABE production chain,distillation is an essential unit for high purity AB...Acetone-butanol-ethanol(ABE)fermentation is a primary strategy for producing bio-based n-butanol from abundant renewable biomass.In the typical ABE production chain,distillation is an essential unit for high purity ABE productions,but has long been criticized by the energy-inefficient processes due to the extremely low solvents concentration received in the upstream fermentation system.Over the past decades,efforts have been dedicated to developing eco-efficient ABE distillation processes aimed at reducing both energy costs and capital investments.In this review,a comprehensive overview on ABE distillation systems is provided from physico-chemical properties in feed and thermodynamics to the process constructions and applications.The recent trends in distillation sequence construction that fitting with the rapid developed upstream in situ product recovery(ISPR)systems are emphasized.Furthermore,towards developing a more efficient ABE distillation system,the review takes a broad overview of the intensification strategies for ABE distillation.Along with systematic introduction of the key examples,the future directions for ABE distillation techniques development are also discussed towards a sustainable and low-carbon emission biorefineries.展开更多
This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a f...This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.展开更多
A numerical simulation was performed using the Thompson microphysics scheme to preliminarily investigate the features of the microphysical processes involved in the record-breaking rainfall event that occurred in Hena...A numerical simulation was performed using the Thompson microphysics scheme to preliminarily investigate the features of the microphysical processes involved in the record-breaking rainfall event that occurred in Henan Province,China,on 20 July 2021.The simulation results showed that a strong meso-𝛾-scale vortical updraft was concurrent with the torrential rainfall.The main finding is that this event was characterized by typical midlatitude warm-rain processes.The simulation with the Thompson microphysics scheme further indicated that highly efficient collision-coalescence of cloud water to rainwater resulted in a considerably active rain droplet growth,leading to this record-breaking rainfall event.展开更多
The massless dark photon~γ can only interact with the Standard Model(SM)sector via higherdimensional operators.In this letter,we investigate its production associated with the ordinary photonγfrom the lepton flavor ...The massless dark photon~γ can only interact with the Standard Model(SM)sector via higherdimensional operators.In this letter,we investigate its production associated with the ordinary photonγfrom the lepton flavor violation(LFV)process l_(i)→l_(j)γγ and di-production from the LFV process l_(i)→l_(j)γγ induced by dipole operators.Comparing the obtained numerical results with the corresponding experimental measurements,we obtain the constraints on the effective couplings of γ with the SM charged leptons.The upper limit of the effective coupling|DLμe|2+|DRμe|2coming from the process μ→e~γγis looser than the processμ→eγ by about one order of magnitude.展开更多
文摘A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.
基金supported by the National Key Research and Development Program of China(2022YFC3205300)the National Natural Science Foundation of China(22176124).
文摘Current research on heterogeneous advanced oxidation processes(HAOPs)predominantly emphasizes catalyst iteration and innovation.Significant efforts have been made to regulate the electron structure and optimize the electron distribution,thereby increasing the catalytic activity.However,this focus often overshadows an equally essential aspect of HAOPs:the adsorption effect.Adsorption is a critical initiator for triggering the interaction of oxidants and contaminants with heterogeneous catalysts.The efficacy of these interactions is influenced by a variety of physicochemical properties,including surface chemistry and pore sizes,which determine the affinities between contaminants and material surfaces.This dispar ity in affinity is pivotal because it underpins the selective removal of contaminants,especially in complex waste streams containing diverse contaminants and competing matrices.Consequently,understanding and mastering these interfacial interactions is fundamentally indispensable not only for improving pro cess efficiency but also for enhancing the selectivity of contaminant removal.Herein,we highlight the importance of adsorption-driven interfacial interactions for fundamentally elucidating the catalytic mechanisms of HAOPs.Such interactions dictate the overall performance of the treatment processes by balancing the adsorption,reaction,and desorption rates on the catalyst surfaces.Elucidating the adsorption effect not only shifts the paradigm in understanding HAOPs but also improves their practical ity in water treatment and wastewater decontamination.Overall,we propose that revisiting adsorption driven interfacial interactions holds great promise for optimizing catalytic processes to develop effective HAOP strategies.
基金supported by the China Postdoctoral Science Foundation(No.2023T160088)the Youth Fund of the National Natural Science Foundation of China(No.52304324).
文摘Magnesium and magnesium alloys,serving as crucial lightweight structural materials and hydrogen storage elements,find extensive applications in space technology,aviation,automotive,and magnesium-based hydrogen industries.The global production of primary magnesium has reached approximately 1.2 million tons per year,with anticipated diversification in future applications and significant market demand.Nevertheless,approximately 80%of the world’s primary magnesium is still manufactured through the Pidgeon process,grappling with formidable issues including high energy consumption,massive carbon emission,significant resource depletion,and environmental pollution.The implementation of the relative vacuum method shows potential in breaking through technological challenges in the Pidgeon process,facilitating clean,low-carbon continuous magnesium smelting.This paper begins by introducing the principles of the relative vacuum method.Subsequently,it elucidates various innovative process routes,including relative vacuum ferrosilicon reduction,aluminum thermal reduction co-production of spinel,and aluminum thermal reduction co-production of calcium aluminate.Finally,and thermodynamic foundations of the relative vacuum,a quantitative analysis of the material,energy flows,carbon emission,and production cost for several new processes is conducted,comparing and analyzing them against the Pidgeon process.The study findings reveal that,with identical raw materials,the relative vacuum silicon thermal reduction process significantly decreases raw material consumption,energy consumption,and carbon dioxide emissions by 15.86%,30.89%,and 26.27%,respectively,compared to the Pidgeon process.The relative vacuum process,using magnesite as the raw material and aluminum as the reducing agent,has the lowest magnesium-to-feed ratio,at only 3.385.Additionally,its energy consumption and carbon dioxide emissions are the lowest,at 1.817 tce/t Mg and 7.782 t CO_(2)/t Mg,respectively.The energy consumption and carbon emissions of the relative vacuum magnesium smelting process co-producing calcium aluminate(12CaO·7Al_(2)O_(3),3CaO·Al_(2)O_(3),and CaO·Al_(2)O_(3))are highly correlated with the consumption of dolomite in the raw materials.When the reduction temperature is around 1473.15 K,the critical volume fraction of magnesium vapor for different processes varies within the range of 5%–40%.Production cost analysis shows that the relative vacuum primary magnesium smelting process has significant economic benefits.This paper offers essential data support and theoretical guidance for achieving energy efficiency,carbon reduction in magnesium smelting,and the industrial adoption of innovative processes.
基金supported by the National Natural Science Foundation of China(No.42007428)the National Forage Industry Technology System Program of China(No.CARS34)+1 种基金the Key Research and Development Program of Shaanxi,China(No.2022SF-285)Shaanxi Province Forestry Science and Technology Innovation Program,China(No.SXLK2022-02-14)。
文摘Effective vegetation reconstruction plays a vital role in the restoration of desert ecosystems.However,in reconstruction of different vegetation types,the community characteristics,assembly processes,and functions of different soil microbial taxa under environmental changes are still disputed,which limits the understanding of the sustainability of desert restoration.Hence,we investigated the soil microbial community characteristics and functional attributes of grassland desert(GD),desert steppe(DS),typical steppe(TS),and artificial forest(AF)in the Mu Us Desert,China.Our findings confirmed the geographical conservation of soil microbial composition but highlighted decreased microbial diversity in TS.Meanwhile,the abundance of rare taxa and microbial community stability in TS improved.Heterogeneous and homogeneous selection determined the assembly of rare and abundant bacterial taxa,respectively,with both being significantly influenced by soil moisture.In contrast,fungal communities displayed stochastic processes and exhibited sensitivity to soil nutrient conditions.Furthermore,our investigation revealed a noteworthy augmentation in bacterial metabolic functionality in TS,aligning with improved vegetation restoration and the assemblage of abundant bacterial taxa.However,within nutrient-limited soils(GD,DS,and AF),the assembly dynamics of rare fungal taxa assumed a prominent role in augmenting their metabolic capacity and adaptability to desert ecosystems.These results highlighted the variations in the assembly processes and metabolic functions of soil microorganisms during vegetation reestablishment and provided corresponding theoretical support for anthropogenic revegetation of desert ecosystems.
文摘In November 1984,China launched its first expedition to the Southern Ocean and the Antarctic continent,culminating in the establishment of its first year-round research station—Great Wall Station—on the Antarctic Peninsula in February 1985.Forty years later,in February 2024,China’s fifth research station,Qinling Station,commenced operations on Inexpress-ible Island near Terra Nova Bay.
基金supported by Natural Science Foundation of China(Nos.52070133,42107073,42477075)Natural Science Foundation of Sichuan Province(No.2024NSFSC0130)+2 种基金the Sichuan Science and Technology Program(No.2024NSFTD0014)Key Laboratory of Jiangxi Province for Persistent Pollutants Prevention Control and Resource Reuse(No.2023SSY02061)Key R&D Program of Heilongjiang Province(No.2023ZX02C01)。
文摘Low-valent sulfur oxy-acid salts(LVSOs)represent a category of oxygen-containing salts characterized by their potent reducing capabilities.Notably,sulfite,dithionite,and thiosulfate are prevalent reducing agents that are readily available,cost-effective,and exhibit minimal ecological toxicity.These LVSOs have the ability to generate or promote the generation of strong oxidants or reductants,which makes them widely used in advanced oxidation processes(AOPs)and advanced reduction processes(ARPs).This article provides a comprehensive review of the recent advancements in AOPs and ARPs involving LVSOs,alongside an examination of the fundamental principles governing the generation of active species within these processes.LVSOs fulfill three primary functions in AOPs:Serving as sources of reactive oxygen species(ROS),auxiliary agents,and activators.Particular attention is devoted to elucidating the reaction mechanisms through which LVSOs,in conjunction with metal ions,metal oxides,ultraviolet light(UV),and ozone,produce potent oxidizing agents in both homogeneous and heterogeneous systems.Regarding ARPs,this review delineates the mechanisms by which LVSOs generate strong reducing agents,including hydrated electrons,hydrogen radicals,and sulfite radicals,under UV irradiation,while also exploring the interactions between these reductants and pollutants.The review identifies existing gaps within the current framework and proposes future research avenues to address these challenges.
文摘Fabric dyeing is a critical production process in the clothing industry and heavily relies on batch processing machines(BPM).In this study,the parallel BPM scheduling problem with machine eligibility in fabric dyeing is considered,and an adaptive cooperated shuffled frog-leaping algorithm(ACSFLA)is proposed to minimize makespan and total tardiness simultaneously.ACSFLA determines the search times for each memeplex based on its quality,with more searches in high-quality memeplexes.An adaptive cooperated and diversified search mechanism is applied,dynamically adjusting search strategies for each memeplex based on their dominance relationships and quality.During the cooperated search,ACSFLA uses a segmented and dynamic targeted search approach,while in non-cooperated scenarios,the search focuses on local search around superior solutions to improve efficiency.Furthermore,ACSFLA employs adaptive population division and partial population shuffling strategies.Through these strategies,memeplexes with low evolutionary potential are selected for reconstruction in the next generation,while thosewithhighevolutionarypotential are retained to continue their evolution.Toevaluate the performance of ACSFLA,comparative experiments were conducted using ACSFLA,SFLA,ASFLA,MOABC,and NSGA-CC in 90 instances.The computational results reveal that ACSFLA outperforms the other algorithms in 78 of the 90 test cases,highlighting its advantages in solving the parallel BPM scheduling problem with machine eligibility.
文摘The aging process is an inexorable fact throughout our lives and is considered a major factor in develo ping neurological dysfunctions associated with cognitive,emotional,and motor impairments.Aging-associated neurodegenerative diseases are characterized by the progressive loss of neuronal structure and function.
文摘The effect of hot band annealing processes—batch annealing and continuous annealing—on the texture evolution and ridging performance of ferritic stainless steel was investigated.The surface and central layers of the hot band exhibited strong shear and plane deformation textures,respectively.After batch annealing,the texture intensity of the hot-rolled sheet texture significantly decreased,and a weak recrystallization texture appeared,while fully recrystallized grains occurred after continuous annealing.A complete recrystallized{111}texture was obtained after recrystallization annealing.The sheet subjected to continuous annealing exhibited the highest intensity of{111}texture,which was accompanied by a dispersed grain orientation distribution,resulting in the lowest ridging height.
基金funded by the National Natural Science Foundations of China(Grant No.42173054)。
文摘Light oil and gas reservoirs are abundant in the Ordovician marine carbonate reservoir in Shunbei Oilfield,Tarim Basin.This presents a compelling geological puzzle,as ultra-deep reservoirs undergo intense alteration and complex petroleum accumulation processes.A comprehensive suite of geochemical analyses,including molecular components,carbon isotope composition,homogenization temperature of saline inclusions,and burial-thermal history of single wells,was conducted to elucidate the genesis of these ancient reservoirs.Three petroleum filling events have been identified in the study area:Late Caledonian,Hercynian-Indosinian,and Himalayan,through analysis of homogenization temperatures of brine inclusions and burial-thermal histories.Additionally,the oil in the study area has undergone significant alteration processes such as biodegradation,thermal alteration,mixing,evaporative fractionation,and gas invasion.This study particularly emphasizes the influential role of Himalayan gas filling-induced evaporation fractionation and gas invasion in shaping the present petroleum phase distribution.Furthermore,analysis of light hydrocarbon and diamondoid parameters indicates the oil within the study area is at a high maturity stage,with equivalent vitrinite reflectance values ranging from 1.48%to 1.99%.Additionally,the analysis of light hydrocarbons,aromatics,and thiadiamondoids indicates that TSR should occur in reservoirs near the gypsum-salt layers in the Cambrian.The existence of the Cambrian petroleum system in the study area is strongly confirmed when considering the analysis results of natural gas type(oil cracking gas),evaporative fractionation,and gas invasion.Permian local thermal anomalies notably emerge as a significant factor contributing to the destruction of biomarkers in oil.For oil not subject to transient,abnormal thermal events,biomarker reliability extends to at least 190℃.In conclusion,examining the special formation mechanisms and conditions of various secondary processes can offer valuable insights for reconstructing the history of petroleum accumulation in ultradeep reservoirs.This research provides a scientific foundation for advancing our knowledge of petroleum systems and underscores the importance of hydrocarbon geochemistry in unraveling ultra-deep,complex geological phenomena.
基金Supported by the Natural Science Foundation of Hubei Province(2021CFB275)National Natural Science Foundation of China(12301667).
文摘In this paper,we study the geometric ergodicity of continuous time Markov pro-cesses in general state space.For the geometric ergodic continuous time Markov processes,the condition π(f^(p))<∞,p>1 is added.Using the coupling method,we obtain the existence of a full absorbing set on which continuous time Markov processes are f-geometric ergodic.
基金supported by the Horizon Europe Framework Programme(HORIZON),call Teaming for Excellence(HORIZONWIDERA-2022-ACCESS-01-two-stage)-Creation of the Centre of Excellence in Smart Forestry“Forest 4.0”No.101059985″This research was cofunded by FOREST 4.0-“Ekscelencijos centras tvariai miško bioekonomikai vystyti”(Nr.10-042-P-0002).
文摘Models that predict a forest stand’s evolution are essential for developing plans for sustainable management.A simple mathematical framework was developed that con-siders the individual tree and stand basal area under random resource competition and is based on two assumptions:(1)a sigmoid-type stochastic process governs tree and stand basal area dynamics of living and dying trees,and(2)the total area that a tree may potentially occupy determines the number of trees per hectare.The most effective method to satisfy these requirements is formalizing each tree diameter and potentially occupied area using Gompertz-type stochastic differential equations governed by fixed and mixed-effect parameters.Data from permanent experimental plots from long-term Lithuania experiments were used to construct the tree and stand basal area models.The new models were relatively unbiased for live trees of all species,including silver birch(Betula pen-dula Roth)and downy birch(Betula pubescens Ehrh.),[spruce(Picea abies),and pine(Pinus sylvestris)].Less reliable predic-tions were made for the basal area of dying trees.Pines gave the highest accuracy prediction of mean basal area among all live trees.The mean basal area prediction for all dying trees was lower than that for live trees.Among all species,pine also had the best average basal area prediction accuracy for live trees.Newly developed basal area growth and yield models can be recommended despite their complex formulation and implementation challenges,particularly in situations when data is scarce.This is because the newly observed plot provides sufficient information to calibrate random effects.
基金supported by the Research Platform Open Fund Project of Zhejiang Industry and Trade Vocation College(No.Kf202203)the Scientific Research Project of CCCC First Harbor Engineering Company Ltd.(No.2022-7-2)+3 种基金the National Natural Science Foundation of China(No.22406142)the Fellowship of China National Postdoctoral Program for Innovative Talents(No.BX20230262)the Fellowship of China Postdoctoral Science Foundation(No.2023M732636)the Shanghai Post-doctoral Excellence Program(No.2023755).
文摘Efficient and innovative nano-catalytic oxidation technologies offer a breakthrough in removing emerging contaminants(ECs)from water,surpassing the limitations of traditional methods.Environmental functional materials(EFMs),particularly high-end oxidation systems using eco-friendly nanomaterials,show promise for absorbing and degrading ECs.This literature review presents a comprehensive analysis of diverse traditional restoration techniques-biological,physical,and chemical-assessing their respective applications and limitations in pesticide-contaminated water purification.Through meticulous comparison,we unequivocally advocate for the imperative integration of environmentally benign nanomaterials,notably titanium-based variants,in forthcoming methodologies.Our in-depth exploration scrutinizes the catalytic efficacy,underlying mechanisms,and adaptability of pioneering titanium-based nanomaterials across a spectrum of environmental contexts.Additionally,strategic recommendations are furnished to surmount challenges and propel the frontiers of implementing eco-friendly nanomaterials in practical water treatment scenarios.
基金financially supported by the National Science Foundation of China(No.41920104010)the China Postdoctoral Science Foundation(No.2024M762767)+3 种基金the Fundamental Research Funds for the Central University,CHD(No.300102264104)by the Postdoctoral Fellowship Program of CPSF(No.GZC20241444)supported by Fondazione Cariplo and Fondazione CDP(No.2022-1546_001)by the Italian Ministry of Education,MUR(Project Dipartimenti di Eccellenza,TECLA,Department of Earth and Environmental Sciences,University of Milano-Bicocca)。
文摘Mantle plumes and surface erosion and sediment deposition affect the modes of continental lithospheric rupturing in extensional tectonic settings,modulating the evolution of rifting margins.However,their relative contributions to the overall evolution of rifting margins and possible roles in the formation of microcontinent are still elusive.Here,we use coupled geodynamic and surface processes numerical modeling to assess the extent to which surface processes may determine the formation of microcontinent during lithospheric stretching in presence or absence of a mantle plume underneath.Our modeling results indicate that fast extension rates and hillslope(i.e.,diffusion)erosion promote ridge jump events and therefore the formation of microcontinents.On the contrary,efficient fluvial erosion and far-reaching sediment transport(i.e.,stream power erosion)inhibits ridge jump events and the formation of microcontinents.The ridge jump event and overall evolution in our numerical models is consistent with the shift from the Mascarene Ridge to the Carlsberg Ridge that determined the formation of the Seychelles microcontinent.We therefore speculate that hillslope erosion,rather than fluvial erosion,was predominant during the formation of the Seychelles,a possible indication of overall dry local climate conditions.
基金funded by the National Natural Science Foundation of China(Grant No.42304072)。
文摘On December 18,2023,an M_(s)6.2 earthquake jolted Jishishan County in the Linxia Hui Autonomous Prefecture in Northwest China's Gansu Province,causing substantial casualties and building collapses.The earthquake occurred in the Qilian Block on the northeastern border of the Qinghai-Tibet Plateau,where faults are highly active and the geological structure is complex.In this study,we utilized methods such as relocation,focal mechanism solutions,and earthquake rupture processes to describe seismogenic faults.The results indicated that the majority of aftershocks occurred at a depth of 12 km.The centroid depth of the main shock and the depth of the maximum rupture point during the rupture process were also 12 km.Various geophysical methods exhibited a high degree of consistency in depth exploration.Aftershocks were distributed mainly to the west and north of the main shock and extended in the NNW direction,primarily through unilateral rupture.The main shock was a reverse thrust event with a small dextral strike-slip component.In this study,more regional data,such as previous GPS observations,field geological observations,and the distributions of the primary stress states in the region,were also incorporated.We inferred that the main shock was triggered by the main fault at the northern margin of the Lajishan Fault and that the movement of the main fault also activated some secondary faults.The compressive forces on both sides of the Lajishan Fault Zone led to the uplift of mountain areas,accompanied by some landslides,leading to this catastrophic earthquake event.In this article,the activity relationships among the 2022 M_(s)6.9 Menyuan earthquake,the 2019 M_(s)5.7 Xiahe earthquake,and the Jishishan earthquake under the action of regional stress are also discussed.This study provides additional evidence and new ideas for exploring the seismogenic process of the Lajishan Fault Zone and has implications for future in-depth research on underground activity in this region.
基金supported by National Natural Science Foundation of China(82471564)YT is supported by National Natural Science Foundation of China(32322035,32171078).
文摘Background Pain sensitivity is critical for preventing non-suicidal self-injury(NSSI)behaviours;however,individuals engaging in such behaviours often exhibit decreased pain sensitivity,which may undermine this natural safeguard.The dorsolateral prefrontal cortex(DLPFC)is a key region involved in pain regulation,and recent approaches using transcranial direct current stimulation(tDCS)to target the DLPFC have shown potential for modulating pain processing and restoring normal pain perception for individuals engaging in NSSI behaviours.Aims This study aimed to explore the immediate and short-term effects of a single session of tDCS on pain sensitivity in individuals with NSSI,as well as its secondary effects on mood and NSSI-related factors.Methods In this randomised,double-blind,parallel,sham-controlled clinical trial,participants with a history of NSSI were randomly assigned to receive either active or sham tDCS.The intervention consisted of a single 20 min tDCS session targeting the left DLPFC.The primary outcome was pain sensitivity,measured by the pressure pain threshold(PPT)and heat pain score(HPS).Secondary and additional outcomes included NSSI urges,NSSI resistance,self-efficacy in resisting NSSI,mood-related variables and exploratory cognitive-affective processes such as rumination,self-criticism and self-perceived pain sensitivity,assessed at baseline,immediately post-intervention,and at 24 hours,1 week and 2 weeks follow-ups.Results For the primary outcomes,no significant differences between groups were observed for pain sensitivity(PPT,padj=0.812;HPS,padj=0.608).However,an exploratory sensitivity analysis treating each trial as an individual observation revealed a significant effect on HPS(padj=0.036).For the secondary and additional outcomes,although there were initial improvements in joyful feelings and reductions in negative affect at 2 weeks post-intervention,these effects did not remain significant after multiple comparison corrections.Notably,reductions in rumination were statistically significant at both 1-week and 2-week follow-ups(1 week,p_(adj)=0.040;2 weeks,p_(adj)=0.042).There were no significant effects on NSSI urges,NSSI resistance,self-efficacy in resisting NSSI or self-criticism.Conclusions A single session of tDCS over the left DLPFC did not produce significant changes in pain sensitivity in individuals with NSSI.A sensitivity analysis indicated an effect on heat pain sensitivity,possibly reflecting changes in brain activity,warranting confirmation through neuroimaging.These findings suggest that tDCS warrants further investigation for its potential to influence pain-related cognitive-affective processes in individuals with NSSI.
基金funded by the National Natural Science Foundation of China(22078018)the Natural Science Foundation of Beijing(2222016).
文摘Acetone-butanol-ethanol(ABE)fermentation is a primary strategy for producing bio-based n-butanol from abundant renewable biomass.In the typical ABE production chain,distillation is an essential unit for high purity ABE productions,but has long been criticized by the energy-inefficient processes due to the extremely low solvents concentration received in the upstream fermentation system.Over the past decades,efforts have been dedicated to developing eco-efficient ABE distillation processes aimed at reducing both energy costs and capital investments.In this review,a comprehensive overview on ABE distillation systems is provided from physico-chemical properties in feed and thermodynamics to the process constructions and applications.The recent trends in distillation sequence construction that fitting with the rapid developed upstream in situ product recovery(ISPR)systems are emphasized.Furthermore,towards developing a more efficient ABE distillation system,the review takes a broad overview of the intensification strategies for ABE distillation.Along with systematic introduction of the key examples,the future directions for ABE distillation techniques development are also discussed towards a sustainable and low-carbon emission biorefineries.
基金supported by the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NNSF of China(12371312)+1 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the project cooperation between Guangxi Normal University and Yulin Normal University.
文摘This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.
基金jointly supported by the National Natural Science Foundation of China[grant numbers U2342202 and 42175005]the Qing Lan Project[grant number R2023Q06]。
文摘A numerical simulation was performed using the Thompson microphysics scheme to preliminarily investigate the features of the microphysical processes involved in the record-breaking rainfall event that occurred in Henan Province,China,on 20 July 2021.The simulation results showed that a strong meso-𝛾-scale vortical updraft was concurrent with the torrential rainfall.The main finding is that this event was characterized by typical midlatitude warm-rain processes.The simulation with the Thompson microphysics scheme further indicated that highly efficient collision-coalescence of cloud water to rainwater resulted in a considerably active rain droplet growth,leading to this record-breaking rainfall event.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.11875157,12147214the Doctoral Start-up Fund of Liaoning Normal University under Grant No.2024BSL018the Universitylevel National Research Project Cultivation Program under Grant No.2024170。
文摘The massless dark photon~γ can only interact with the Standard Model(SM)sector via higherdimensional operators.In this letter,we investigate its production associated with the ordinary photonγfrom the lepton flavor violation(LFV)process l_(i)→l_(j)γγ and di-production from the LFV process l_(i)→l_(j)γγ induced by dipole operators.Comparing the obtained numerical results with the corresponding experimental measurements,we obtain the constraints on the effective couplings of γ with the SM charged leptons.The upper limit of the effective coupling|DLμe|2+|DRμe|2coming from the process μ→e~γγis looser than the processμ→eγ by about one order of magnitude.
