Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These ...Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.展开更多
The Rural Minimum Living Standard Guarantee(Rural Dibao)is an important unconditional cash transfer program to alleviate poverty in rural China.Despite the importance of children’s nutrition in breaking poverty cycle...The Rural Minimum Living Standard Guarantee(Rural Dibao)is an important unconditional cash transfer program to alleviate poverty in rural China.Despite the importance of children’s nutrition in breaking poverty cycles,little is known about the impact of Rural Dibao on child nutrition outcomes.Using China Family Panel Studies(CFPS),this paper examines the effects of Rural Dibao on child nutrition outcomes and investigates potential pathways and heterogeneous effects.We exploit propensity score matching and difference-in-differences techniques to evaluate the effects of the Rural Dibao program on child nutrition outcomes.Our results suggest that Rural Dibao significantly impacts the nutrition outcomes of children up to 15 years of age.Specifically,our results suggest that Rural Dibao improves child height-to-age z-scores by 1.05 standard deviations and lowers the probability of stunting by 11.9 percentage points.Additional analyses suggest that increased protein intake is the main pathway through which Rural Dibao participation contributes to better nutrition outcomes.We also find that the effect of the program is more pronounced among girls,children who are non-left-behind or live with highly educated mothers,and those from low-income families and poor areas.Our findings suggest that Rural Dibao participation helps improve child nutrition outcomes through improving diet quality.展开更多
Minimum temperatures have remarkable impacts on tree growth at high-elevation sites on the Tibetan Plateau,but the shortage of long-term and high-resolution paleoclimate records inhibits understanding of recent minimu...Minimum temperatures have remarkable impacts on tree growth at high-elevation sites on the Tibetan Plateau,but the shortage of long-term and high-resolution paleoclimate records inhibits understanding of recent minimum temperature anomalies.In this study,a warm season(April–September)reconstruction is presented for the past 467 years(1550–2016)based on Sabina tibetica ring-width chronology on the Lianbaoyeze Mountain of the central eastern Tibetan Plateau.Eight warm periods and eight cold periods were identified.Long-term minimum temperature variations revealed a high degree of coherence with nearby reconstructions.Spatial correlations between our reconstruction and global sea surface temperatures suggest that warm season minimum temperature anomalies in the central eastern Tibetan Plateau were strongly influenced by large-scale ocean atmospheric circulations,such as the El Ni?o-Southern Oscillation and the Atlantic Multidecadal Oscillation.展开更多
In this paper,we optimize the spectrum efficiency(SE)of uplink massive multiple-input multiple-output(MIMO)system with imperfect channel state information(CSI)over Rayleigh fading channel.The SE optimization problem i...In this paper,we optimize the spectrum efficiency(SE)of uplink massive multiple-input multiple-output(MIMO)system with imperfect channel state information(CSI)over Rayleigh fading channel.The SE optimization problem is formulated under the constraints of maximum power and minimum rate of each user.Then,we develop a near-optimal power allocation(PA)scheme by using the successive convex approximation(SCA)method,Lagrange multiplier method,and block coordinate descent(BCD)method,and it can obtain almost the same SE as the benchmark scheme with lower complexity.Since this scheme needs three-layer iteration,a suboptimal PA scheme is developed to further reduce the complexity,where the characteristic of massive MIMO(i.e.,numerous receive antennas)is utilized for convex reformulation,and the rate constraint is converted to linear constraints.This suboptimal scheme only needs single-layer iteration,thus has lower complexity than the near-optimal scheme.Finally,we joint design the pilot power and data power to further improve the performance,and propose an two-stage algorithm to obtain joint PA.Simulation results verify the effectiveness of the proposed schemes,and superior SE performance is achieved.展开更多
Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum a...Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.展开更多
This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynami...This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.展开更多
This paper investigates the anomaly-resistant decentralized state estimation(SE) problem for a class of wide-area power systems which are divided into several non-overlapping areas connected through transmission lines...This paper investigates the anomaly-resistant decentralized state estimation(SE) problem for a class of wide-area power systems which are divided into several non-overlapping areas connected through transmission lines. Two classes of measurements(i.e., local measurements and edge measurements) are obtained, respectively, from the individual area and the transmission lines. A decentralized state estimator, whose performance is resistant against measurement with anomalies, is designed based on the minimum error entropy with fiducial points(MEEF) criterion. Specifically, 1) An augmented model, which incorporates the local prediction and local measurement, is developed by resorting to the unscented transformation approach and the statistical linearization approach;2) Using the augmented model, an MEEF-based cost function is designed that reflects the local prediction errors of the state and the measurement;and 3) The local estimate is first obtained by minimizing the MEEF-based cost function through a fixed-point iteration and then updated by using the edge measuring information. Finally, simulation experiments with three scenarios are carried out on the IEEE 14-bus system to illustrate the validity of the proposed anomaly-resistant decentralized SE scheme.展开更多
With the development of global urbanization,the utilization of underground space is more critical and attractive for civil purposes.Various shapes of shield tunnels have been gradually proposed to cope with different ...With the development of global urbanization,the utilization of underground space is more critical and attractive for civil purposes.Various shapes of shield tunnels have been gradually proposed to cope with different geological conditions and service purposes of underground structures.Generally,reducing the burial depth of shield tunnel is conducive to construction and cost saving.However,extremely small overburden depth cannot provide sufficient uplift resistance to maintain the stability and serviceability of the tunnel.To this end,this paper firstly reviewed the status of deriving the minimum sand over-burden depth of circular shield tunnel using mechanical equilibrium(ME)method.It revealed that the estimated depth is rather conservative.Then,the uplift resistance mechanism of both circular and rectangular tunnels was deduced theoretically and verified with the model tests.The theoretical uplift resistance is consistent with the experimental values,indicating the feasibility of the proposed equations.Furthermore,the determination of the minimum soil overburden depth of rectangular shield tunnel under various working conditions was presented through integrated ME method,which can provide more reasonable estimations of suggested tunnel burial depth for practical construction.Additionally,optimizations were made for calculating the uplift resistance,and the soil thickness providing uplift resistance is suggested to be adjusted according to the testing results.The results can provide reference for the design and construction of various shapes of shield tunnels in urban underground space exploitation.展开更多
Nanofluid minimum quantity lubrication(NMQL)is a green processing technology.Cottonseed oil is suitable as base oil because of excellent lubrication performance,low freezing temperature,and high yield.Al_(2)O_(3)nanop...Nanofluid minimum quantity lubrication(NMQL)is a green processing technology.Cottonseed oil is suitable as base oil because of excellent lubrication performance,low freezing temperature,and high yield.Al_(2)O_(3)nanoparticles improve not only the heat transfer capacity but also the lubrication performance.The physical and chemical proper-ties of nanofluid change when Al_(2)O_(3)nanoparticles are added.However,the effects of the concentration of nanofluid on lubrication performance remain unknown.Furthermore,the mechanisms of interaction between Al_(2)O_(3)nanoparti-cles and cottonseed oil are unclear.In this research,nanofluid is prepared by adding different mass concentrations of Al_(2)O_(3)nanoparticles(0,0.2%,0.5%,1%,1.5%,and 2%wt)to cottonseed oil during minimum quantity lubrication(MQL)milling 45 steel.The tribological properties of nanofluid with different concentrations at the tool/workpiece interface are studied through macro-evaluation parameters(milling force,specific energy)and micro-evaluation parameters(surface roughness,micro morphology,contact angle).The result show that the specific energy is at the minimum(114 J/mm^(3)),and the roughness value is the lowest(1.63μm)when the concentration is 0.5 wt%.The surfaces of the chip and workpiece are the smoothest,and the contact angle is the lowest,indicating that the tribological proper-ties are the best under 0.5 wt%.This research investigates the intercoupling mechanisms of Al_(2)O_(3)nanoparticles and cottonseed base oil,and acquires the optimal Al_(2)O_(3)nanofluid concentration to receive satisfactory tribological properties.展开更多
Graphene has superhigh thermal conductivity up to 5000 W/(m·K),extremely thin thickness,superhigh mechanical strength and nano-lamellar structure with low interlayer shear strength,making it possess great potenti...Graphene has superhigh thermal conductivity up to 5000 W/(m·K),extremely thin thickness,superhigh mechanical strength and nano-lamellar structure with low interlayer shear strength,making it possess great potential in mini-mum quantity lubrication(MQL)grinding.Meanwhile,ionic liquids(ILs)have higher thermal conductivity and better thermal stability than vegetable oils,which are frequently used as MQL grinding fluids.And ILs have extremely low vapor pressure,thereby avoiding film boiling in grinding.These excellent properties make ILs also have immense potential in MQL grinding.However,the grinding performance of graphene and ionic liquid mixed fluid under nano-fluid minimum quantity lubrication(NMQL),and its tribological mechanism on abrasive grain/workpiece grinding interface,are still unclear.This research firstly evaluates the grinding performance of graphene and ionic liquid mixed nanofluids(graphene/IL nanofluids)under NMQL experimentally.The evaluation shows that graphene/IL nanofluids can further strengthen both the cooling and lubricating performances compared with MQL grinding using ILs only.The specific grinding energy and grinding force ratio can be reduced by over 40%at grinding depth of 10μm.Work-piece machined surface roughness can be decreased by over 10%,and grinding temperature can be lowered over 50℃at grinding depth of 30μm.Aiming at the unclear tribological mechanism of graphene/IL nanofluids,molecular dynamics simulations for abrasive grain/workpiece grinding interface are performed to explore the formation mechanism of physical adsorption film.The simulations show that the grinding interface is in a boundary lubrication state.IL molecules absorb in groove-like fractures on grain wear flat face to form boundary lubrication film,and graphene nanosheets can enter into the grinding interface to further decrease the contact area between abrasive grain and workpiece.Compared with MQL grinding,the average tangential grinding force of graphene/IL nanofluids can decrease up to 10.8%.The interlayer shear effect and low interlayer shear strength of graphene nanosheets are the principal causes of enhanced lubricating performance on the grinding interface.EDS and XPS analyses are further carried out to explore the formation mechanism of chemical reaction film.The analyses show that IL base fluid happens chemical reactions with workpiece material,producing FeF_(2),CrF_(3),and BN.The fresh machined surface of workpiece is oxidized by air,producing NiO,Cr_(2)O_(3) and Fe_(2)O_(3).The chemical reaction film is constituted by fluorides,nitrides and oxides together.The combined action of physical adsorption film and chemical reaction film make graphene/IL nano-fluids obtain excellent grinding performance.展开更多
The dinoflagellate Prorocentrum minimum is known to affect the normal physiological function of Exopalaemon carinicauda by inducing oxidative stress,apoptosis,and cellular injury.To study the effects of P.minimum on t...The dinoflagellate Prorocentrum minimum is known to affect the normal physiological function of Exopalaemon carinicauda by inducing oxidative stress,apoptosis,and cellular injury.To study the effects of P.minimum on the immune defense system of shrimp,E.carinicauda were exposed to 5×10^(3)cells mL^(-1)and 5×10^(4)cells mL^(-1)of P.minimum for 336 h in treatment groups,while E.carinicauda cultured in filtered seawater was employed as control.The total hemocyte counts(THC),hemocyanin concentration(HEM),and the activity of alkaline phosphatase(AKP)in hemolymph serum,as well as expressions of six immunity-related genes in hemocytes,hepatopancreases and gills were determined.The exposure of P.minimum significantly reduced the THC,HEM concentration and AKP activity in hemolymph serum.Immunity-related genes expressed differently in hemocytes,hepatopancreases and gills.Compared with the control group,the expressions of Crustin and pro PO in hemocytes were significantly up-regulated in the treatment groups,while the up-regulated expressions of LGBP,Lysozyme and Serpin were only found in the group exposed to 5×10^(4)cells mL^(-1)of P.minimum.In the gills of E.carinicauda exposed to P.minimum,the down-regulation of ALF,proPO and Serpin,up-regulation of LGBP and Lysozyme,as well as unaffected Crustin were observed.In hepatopancreases,the up-regulated expressions of LGBP,Crustin,Lysozyme,Serpin and proPO(only in 5×10^(3)cells mL^(-1)of P.minimum group)were found in the treatment groups.After exposure to P.minimum for 336 h,shrimps were injected with Vibrio parahaemolyticus and WSSV.The results showed that the mortality rates of shrimp in the treatment groups were significantly increased with a dose-dependent effect,which suggests that exposure to P.minimum may reduce the immunity of E.carinicauda.The research indicates that hemocytes and hepatopancreases play important roles in protecting the shrimp immune response to harmful algae,while the protection effect of hemolymph serum and gills may be suppressed.Since the exposure to P.minimum depressed the immunity of E.carinicauda,further studies are needed to confirm whether the presence of the algae will affect the susceptibility of shrimp to pathogens.展开更多
Four extreme ultraviolet(EUV)solar radiation proxies(Magnesium II core-to-wing ratio(MgII),Lymanαflux(Fα),10.7-cm solar radio flux(F10.7),and sunspot number(Rz))were analyzed during the last four consecutive solar a...Four extreme ultraviolet(EUV)solar radiation proxies(Magnesium II core-to-wing ratio(MgII),Lymanαflux(Fα),10.7-cm solar radio flux(F10.7),and sunspot number(Rz))were analyzed during the last four consecutive solar activity minima to investigate how they differ during minimum periods and how well they represent solar EUV radiation.Their variability within each minimum and between minima was compared by considering monthly means.A comparison was also made of their role in filtering the effect of solar activity from the critical frequency of the ionospheric F2 layer,foF2,which at mid to low latitudes depends mainly on EUV solar radiation.The last two solar cycles showed unusually low EUV radiation levels according to the four proxies.Regarding the connection between the EUV“true”variation and that of solar proxies,according to the foF2 filtering analysis,MgII and Fαbehaved in a more stable and suitable way,whereas Rz and F10.7 could be overestimating EUV levels during the last two minima,implying they would both underestimate the inter-minima difference of EUV when compared with the first two minima.展开更多
This paper concerns minimum-energy leader-following formation design and analysis problems of distributed multiagent systems(DMASs)subjected to randomly switching topologies and aperiodic communication pauses.The crit...This paper concerns minimum-energy leader-following formation design and analysis problems of distributed multiagent systems(DMASs)subjected to randomly switching topologies and aperiodic communication pauses.The critical feature of this paper is that the energy consumption during the formation control process is restricted by the minimum-energy constraint in the sense of the linear matrix inequality.Firstly,the leader-following formation control protocol is proposed based on the relative state information of neighboring agents,where the total energy consumption is considered.Then,minimum-energy leader-following formation design and analysis criteria are presented in the form of the linear matrix inequality,which can be checked by the generalized eigenvalue method.Especially,the value of the minimum-energy constraint is determined.An illustrative simulation is provided to show the effectiveness of the main results.展开更多
Workers who conduct regular facility inspections in radioactive environments will inevitably be affected by radiation.Therefore,it is important to optimize the inspection path to ensure that workers are exposed to the...Workers who conduct regular facility inspections in radioactive environments will inevitably be affected by radiation.Therefore,it is important to optimize the inspection path to ensure that workers are exposed to the least amount of radiation.This study proposes a discrete Rao-combined artificial bee colony(ABC)algorithm for planning inspection paths with minimum exposure doses in radioactive environments with obstacles.In this algorithm,retaining the framework of the traditional ABC algorithm,we applied the directional solution update rules of Rao algorithms at the employed bee stage and onlooker bee stage to increase the exploitation ability of the algorithm and implement discretion using the swap operator and swap sequence.To increase the randomness of solution generation,the chaos algorithm was used at the initialization stage.The K-opt operation technique was introduced at the scout bee stage to increase the exploration ability of the algorithm.For path planning in an environment with complex structural obstacles,an obstacle detour technique using a recursive algorithm was applied.To evaluate the performance of the proposed algorithm,we performed experimental simulations in three hypothetical environments and compared the results with those of improved particle swarm optimization,chaos particle swarm optimization,improved ant colony optimization,and discrete Rao’s algorithms.The experimental results show the high performance of the proposed discrete Rao-combined ABC algorithm and its obstacle detour capability.展开更多
The attitude tracking control problem is addressed for hypersonic vehicles under actuator faults that may cause an uncertain time-varying control gain matrix.An adaptive compensation scheme is developed to ensure syst...The attitude tracking control problem is addressed for hypersonic vehicles under actuator faults that may cause an uncertain time-varying control gain matrix.An adaptive compensation scheme is developed to ensure system stability and asymptotic tracking properties,including a kinematic control signal and a dynamic control signal.To deal with the uncertainties of the control gain matrix,a new positive definite one is constructed.The minimum eigenvalue of such a new control gain matrix is estimated.Simulation results of application to an X-33 vehicle model verify the effectiveness of the proposed minimum eigenvalue based adaptive fault compensation scheme.展开更多
In the field of ultrafast magnetism,i.e.,subpicosecond or femtosecond time scales,the dynamics of magnetization can be described by the inertial Landau-Lifhitz-Gilbert equation.In terms of this equation,the intrinsic ...In the field of ultrafast magnetism,i.e.,subpicosecond or femtosecond time scales,the dynamics of magnetization can be described by the inertial Landau-Lifhitz-Gilbert equation.In terms of this equation,the intrinsic characteristics are investigated in detail for the theoretical limit of the magnetization reversal field.We can find that there is a critical value for the inertia parameterτ_(c),which is affected by the damping and anisotropy parameter of the system.When the inertial parameter factorτ<τ_(c),the limit value of the magnetization reversal field under the ultrafast magnetic mechanism is smaller than that of the fast magnetic mechanism.Whenτ>τ_(c),the limit value of the magnetization reversal field will be larger than the limit value under the fast magnetic mechanism.Moreover,it is important to point out that the limit value of the magnetization reversal field under the ultrafast magnetic mechanism decreases with the increasing inertial factor,asτ<τ_(c)/2,which increases with inertial factorτasτ>τ_(c)/2.Finally,with the joint action of damping and anisotropy,compared with fast magnetism,we find that the limit value of the magnetization reversal field has rich variation characteristics,i.e.,there is not only a linear and proportional relationship,but also an inverse relationship,which is very significant for the study of ultrafast magnetism.展开更多
For the anti-interference/denoise purpose,it usually requires minimizing the sidelobe level(SLL)of a wide-beam pattern with a desired low nulling level(NL)in the nulling region.To realize such an objective,the shaped-...For the anti-interference/denoise purpose,it usually requires minimizing the sidelobe level(SLL)of a wide-beam pattern with a desired low nulling level(NL)in the nulling region.To realize such an objective,the shaped-beam pattern synthesis(SBPS)is the most commonly used approach.However,since the SBPS problem focuses on synthesizing a predetermined beam shape,the minimum SLL via this approach cannot ensure to obtain the maximum power gain.Conversely,it cannot obtain the lowest SLL with a certain power gain requirement.Based on such consideration,this paper tries to further minimize SLL of a wide-beam pattern with a desired low NL nulling region,by solving the power gain pattern synthesis(PGPS)problem.The PGPS problem selects the array excitation by directly optimizing the power gain.Hence,it has the potential to reduce SLL,when achieving the equal mainlobe power gain constraint via SBPS.An iterative algorithm which converts the primal optimization problem into convex sub-problems is proposed,resulting in an effective problem-solving scheme.Numerical simulations demonstrate the proposed algorithm can obtain about 10-dB lower SLL than the existing algorithms.展开更多
Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in p...Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in patients with depression,this paper proposes a depression analysis method based on brain function network(BFN).To avoid the volume conductor effect,BFN was constructed based on phase lag index(PLI).Then the indicators closely related to depression were selected from weighted BFN based on small-worldness(SW)characteristics and binarization BFN based on the minimum spanning tree(MST).Differences analysis between groups and correlation analysis between these indicators and diagnostic indicators were performed in turn.The resting state electroencephalogram(EEG)data of 24 patients with depression and 29 healthy controls(HC)was used to verify our proposed method.The results showed that compared with HC,the information processing of BFN in patients with depression decreased,and BFN showed a trend of randomization.展开更多
In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The est...In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.展开更多
Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attracti...Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. U20A2097,42075087, 91837310)the National Key Research and Development Program of China (Grant No. 2021YFC3000902)。
文摘Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.
基金The authors are grateful for support from the National Social Science Fund of China(21AJL015).
文摘The Rural Minimum Living Standard Guarantee(Rural Dibao)is an important unconditional cash transfer program to alleviate poverty in rural China.Despite the importance of children’s nutrition in breaking poverty cycles,little is known about the impact of Rural Dibao on child nutrition outcomes.Using China Family Panel Studies(CFPS),this paper examines the effects of Rural Dibao on child nutrition outcomes and investigates potential pathways and heterogeneous effects.We exploit propensity score matching and difference-in-differences techniques to evaluate the effects of the Rural Dibao program on child nutrition outcomes.Our results suggest that Rural Dibao significantly impacts the nutrition outcomes of children up to 15 years of age.Specifically,our results suggest that Rural Dibao improves child height-to-age z-scores by 1.05 standard deviations and lowers the probability of stunting by 11.9 percentage points.Additional analyses suggest that increased protein intake is the main pathway through which Rural Dibao participation contributes to better nutrition outcomes.We also find that the effect of the program is more pronounced among girls,children who are non-left-behind or live with highly educated mothers,and those from low-income families and poor areas.Our findings suggest that Rural Dibao participation helps improve child nutrition outcomes through improving diet quality.
基金funded by the National Key Research and Development Program of China(No.2018YFA0605601)Hong Kong Research Grants Council(No.106220169)+1 种基金the National Natural Science Foundation of China(No.42105155,41671042,and 42077417)the National Geographic Society(No.EC-95776R-22)。
文摘Minimum temperatures have remarkable impacts on tree growth at high-elevation sites on the Tibetan Plateau,but the shortage of long-term and high-resolution paleoclimate records inhibits understanding of recent minimum temperature anomalies.In this study,a warm season(April–September)reconstruction is presented for the past 467 years(1550–2016)based on Sabina tibetica ring-width chronology on the Lianbaoyeze Mountain of the central eastern Tibetan Plateau.Eight warm periods and eight cold periods were identified.Long-term minimum temperature variations revealed a high degree of coherence with nearby reconstructions.Spatial correlations between our reconstruction and global sea surface temperatures suggest that warm season minimum temperature anomalies in the central eastern Tibetan Plateau were strongly influenced by large-scale ocean atmospheric circulations,such as the El Ni?o-Southern Oscillation and the Atlantic Multidecadal Oscillation.
基金supported by the Fundamental Research Funds for the Central Universities of NUAA(No.kfjj20200414)Natural Science Foundation of Jiangsu Province in China(No.BK20181289).
文摘In this paper,we optimize the spectrum efficiency(SE)of uplink massive multiple-input multiple-output(MIMO)system with imperfect channel state information(CSI)over Rayleigh fading channel.The SE optimization problem is formulated under the constraints of maximum power and minimum rate of each user.Then,we develop a near-optimal power allocation(PA)scheme by using the successive convex approximation(SCA)method,Lagrange multiplier method,and block coordinate descent(BCD)method,and it can obtain almost the same SE as the benchmark scheme with lower complexity.Since this scheme needs three-layer iteration,a suboptimal PA scheme is developed to further reduce the complexity,where the characteristic of massive MIMO(i.e.,numerous receive antennas)is utilized for convex reformulation,and the rate constraint is converted to linear constraints.This suboptimal scheme only needs single-layer iteration,thus has lower complexity than the near-optimal scheme.Finally,we joint design the pilot power and data power to further improve the performance,and propose an two-stage algorithm to obtain joint PA.Simulation results verify the effectiveness of the proposed schemes,and superior SE performance is achieved.
基金Project supported by the National Natural Science Foundation of China(Grant No.62101600)the Science Foundation of China University of Petroleum,Beijing(Grant No.2462021YJRC008)the State Key Laboratory of Cryptology(Grant No.MMKFKT202109).
文摘Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.
基金supported in part by the National Natural Science Foundation of China(51939001,61976033,62273072)the Natural Science Foundation of Sichuan Province (2022NSFSC0903)。
文摘This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.
基金supported in part by the National Natural Science Foundation of China(61933007, U21A2019, 62273005, 62273088, 62303301)the Program of Shanghai Academic/Technology Research Leader of China (20XD1420100)+2 种基金the Hainan Province Science and Technology Special Fund of China(ZDYF2022SHFZ105)the Natural Science Foundation of Anhui Province of China (2108085MA07)the Alexander von Humboldt Foundation of Germany。
文摘This paper investigates the anomaly-resistant decentralized state estimation(SE) problem for a class of wide-area power systems which are divided into several non-overlapping areas connected through transmission lines. Two classes of measurements(i.e., local measurements and edge measurements) are obtained, respectively, from the individual area and the transmission lines. A decentralized state estimator, whose performance is resistant against measurement with anomalies, is designed based on the minimum error entropy with fiducial points(MEEF) criterion. Specifically, 1) An augmented model, which incorporates the local prediction and local measurement, is developed by resorting to the unscented transformation approach and the statistical linearization approach;2) Using the augmented model, an MEEF-based cost function is designed that reflects the local prediction errors of the state and the measurement;and 3) The local estimate is first obtained by minimizing the MEEF-based cost function through a fixed-point iteration and then updated by using the edge measuring information. Finally, simulation experiments with three scenarios are carried out on the IEEE 14-bus system to illustrate the validity of the proposed anomaly-resistant decentralized SE scheme.
基金support from National Major Scientific Instruments Development Project of China(Grant No.5202780029)Program of Distinguished Young Scholars,Natural Science Foundation of Chongqing,China(Grant No.cstc2020jcyjjq0087)Research on resilience prevention,control and adaptation strategy of flood disaster in megacities under changing environment(Grant No.2021-ZD-CQ-2).
文摘With the development of global urbanization,the utilization of underground space is more critical and attractive for civil purposes.Various shapes of shield tunnels have been gradually proposed to cope with different geological conditions and service purposes of underground structures.Generally,reducing the burial depth of shield tunnel is conducive to construction and cost saving.However,extremely small overburden depth cannot provide sufficient uplift resistance to maintain the stability and serviceability of the tunnel.To this end,this paper firstly reviewed the status of deriving the minimum sand over-burden depth of circular shield tunnel using mechanical equilibrium(ME)method.It revealed that the estimated depth is rather conservative.Then,the uplift resistance mechanism of both circular and rectangular tunnels was deduced theoretically and verified with the model tests.The theoretical uplift resistance is consistent with the experimental values,indicating the feasibility of the proposed equations.Furthermore,the determination of the minimum soil overburden depth of rectangular shield tunnel under various working conditions was presented through integrated ME method,which can provide more reasonable estimations of suggested tunnel burial depth for practical construction.Additionally,optimizations were made for calculating the uplift resistance,and the soil thickness providing uplift resistance is suggested to be adjusted according to the testing results.The results can provide reference for the design and construction of various shapes of shield tunnels in urban underground space exploitation.
基金Supported by National Natural Science Foundation of China(Grant Nos.51806112,51975305)PhD Research Startup Foundation of Qingdao University of Technology,China(Grant Nos.JC2022-012,20312008).
文摘Nanofluid minimum quantity lubrication(NMQL)is a green processing technology.Cottonseed oil is suitable as base oil because of excellent lubrication performance,low freezing temperature,and high yield.Al_(2)O_(3)nanoparticles improve not only the heat transfer capacity but also the lubrication performance.The physical and chemical proper-ties of nanofluid change when Al_(2)O_(3)nanoparticles are added.However,the effects of the concentration of nanofluid on lubrication performance remain unknown.Furthermore,the mechanisms of interaction between Al_(2)O_(3)nanoparti-cles and cottonseed oil are unclear.In this research,nanofluid is prepared by adding different mass concentrations of Al_(2)O_(3)nanoparticles(0,0.2%,0.5%,1%,1.5%,and 2%wt)to cottonseed oil during minimum quantity lubrication(MQL)milling 45 steel.The tribological properties of nanofluid with different concentrations at the tool/workpiece interface are studied through macro-evaluation parameters(milling force,specific energy)and micro-evaluation parameters(surface roughness,micro morphology,contact angle).The result show that the specific energy is at the minimum(114 J/mm^(3)),and the roughness value is the lowest(1.63μm)when the concentration is 0.5 wt%.The surfaces of the chip and workpiece are the smoothest,and the contact angle is the lowest,indicating that the tribological proper-ties are the best under 0.5 wt%.This research investigates the intercoupling mechanisms of Al_(2)O_(3)nanoparticles and cottonseed base oil,and acquires the optimal Al_(2)O_(3)nanofluid concentration to receive satisfactory tribological properties.
基金Supported by Shandong Provincial Natural Science Foundation of China(Grant Nos.ZR2022ME208,ZR2020QE181)National Natural Science Foundation of China(Grant Nos.51705272,52005281)+1 种基金China Postdoctoral Science Foundation(Grant No.2018M642628)111 project(Grant No.D21017).
文摘Graphene has superhigh thermal conductivity up to 5000 W/(m·K),extremely thin thickness,superhigh mechanical strength and nano-lamellar structure with low interlayer shear strength,making it possess great potential in mini-mum quantity lubrication(MQL)grinding.Meanwhile,ionic liquids(ILs)have higher thermal conductivity and better thermal stability than vegetable oils,which are frequently used as MQL grinding fluids.And ILs have extremely low vapor pressure,thereby avoiding film boiling in grinding.These excellent properties make ILs also have immense potential in MQL grinding.However,the grinding performance of graphene and ionic liquid mixed fluid under nano-fluid minimum quantity lubrication(NMQL),and its tribological mechanism on abrasive grain/workpiece grinding interface,are still unclear.This research firstly evaluates the grinding performance of graphene and ionic liquid mixed nanofluids(graphene/IL nanofluids)under NMQL experimentally.The evaluation shows that graphene/IL nanofluids can further strengthen both the cooling and lubricating performances compared with MQL grinding using ILs only.The specific grinding energy and grinding force ratio can be reduced by over 40%at grinding depth of 10μm.Work-piece machined surface roughness can be decreased by over 10%,and grinding temperature can be lowered over 50℃at grinding depth of 30μm.Aiming at the unclear tribological mechanism of graphene/IL nanofluids,molecular dynamics simulations for abrasive grain/workpiece grinding interface are performed to explore the formation mechanism of physical adsorption film.The simulations show that the grinding interface is in a boundary lubrication state.IL molecules absorb in groove-like fractures on grain wear flat face to form boundary lubrication film,and graphene nanosheets can enter into the grinding interface to further decrease the contact area between abrasive grain and workpiece.Compared with MQL grinding,the average tangential grinding force of graphene/IL nanofluids can decrease up to 10.8%.The interlayer shear effect and low interlayer shear strength of graphene nanosheets are the principal causes of enhanced lubricating performance on the grinding interface.EDS and XPS analyses are further carried out to explore the formation mechanism of chemical reaction film.The analyses show that IL base fluid happens chemical reactions with workpiece material,producing FeF_(2),CrF_(3),and BN.The fresh machined surface of workpiece is oxidized by air,producing NiO,Cr_(2)O_(3) and Fe_(2)O_(3).The chemical reaction film is constituted by fluorides,nitrides and oxides together.The combined action of physical adsorption film and chemical reaction film make graphene/IL nano-fluids obtain excellent grinding performance.
基金financially supported by the earmarked fund for National Key R&D Program of China(No.2019YFD0900403)the Modern Agro-Industry Technology Research System(No.CARS-48)+2 种基金the Program of Shandong Leading Talent(No.LNJY2015002)the Central Public-Interest Scientific Institution Basal Research Fund of CAFS(No.2020TD46)the Scientific Research Start-Up Funding of Shandong Agricultural University(No.72188)。
文摘The dinoflagellate Prorocentrum minimum is known to affect the normal physiological function of Exopalaemon carinicauda by inducing oxidative stress,apoptosis,and cellular injury.To study the effects of P.minimum on the immune defense system of shrimp,E.carinicauda were exposed to 5×10^(3)cells mL^(-1)and 5×10^(4)cells mL^(-1)of P.minimum for 336 h in treatment groups,while E.carinicauda cultured in filtered seawater was employed as control.The total hemocyte counts(THC),hemocyanin concentration(HEM),and the activity of alkaline phosphatase(AKP)in hemolymph serum,as well as expressions of six immunity-related genes in hemocytes,hepatopancreases and gills were determined.The exposure of P.minimum significantly reduced the THC,HEM concentration and AKP activity in hemolymph serum.Immunity-related genes expressed differently in hemocytes,hepatopancreases and gills.Compared with the control group,the expressions of Crustin and pro PO in hemocytes were significantly up-regulated in the treatment groups,while the up-regulated expressions of LGBP,Lysozyme and Serpin were only found in the group exposed to 5×10^(4)cells mL^(-1)of P.minimum.In the gills of E.carinicauda exposed to P.minimum,the down-regulation of ALF,proPO and Serpin,up-regulation of LGBP and Lysozyme,as well as unaffected Crustin were observed.In hepatopancreases,the up-regulated expressions of LGBP,Crustin,Lysozyme,Serpin and proPO(only in 5×10^(3)cells mL^(-1)of P.minimum group)were found in the treatment groups.After exposure to P.minimum for 336 h,shrimps were injected with Vibrio parahaemolyticus and WSSV.The results showed that the mortality rates of shrimp in the treatment groups were significantly increased with a dose-dependent effect,which suggests that exposure to P.minimum may reduce the immunity of E.carinicauda.The research indicates that hemocytes and hepatopancreases play important roles in protecting the shrimp immune response to harmful algae,while the protection effect of hemolymph serum and gills may be suppressed.Since the exposure to P.minimum depressed the immunity of E.carinicauda,further studies are needed to confirm whether the presence of the algae will affect the susceptibility of shrimp to pathogens.
基金Research Project Numbers PIUNT E642 and PIP 2957supported by National Science Foundation Grant Number AGS-2152365
文摘Four extreme ultraviolet(EUV)solar radiation proxies(Magnesium II core-to-wing ratio(MgII),Lymanαflux(Fα),10.7-cm solar radio flux(F10.7),and sunspot number(Rz))were analyzed during the last four consecutive solar activity minima to investigate how they differ during minimum periods and how well they represent solar EUV radiation.Their variability within each minimum and between minima was compared by considering monthly means.A comparison was also made of their role in filtering the effect of solar activity from the critical frequency of the ionospheric F2 layer,foF2,which at mid to low latitudes depends mainly on EUV solar radiation.The last two solar cycles showed unusually low EUV radiation levels according to the four proxies.Regarding the connection between the EUV“true”variation and that of solar proxies,according to the foF2 filtering analysis,MgII and Fαbehaved in a more stable and suitable way,whereas Rz and F10.7 could be overestimating EUV levels during the last two minima,implying they would both underestimate the inter-minima difference of EUV when compared with the first two minima.
基金the National Natural Science Foundation of China(62176263,62103434,62003363)the Science Foundation for Distinguished Youth of Shaanxi Province(2021JC-35)+2 种基金the Youth Talent Promotion Program of Shaanxi Provincial Association for Science and Technology(20220123)the Natural Science Basic Research Program of Shaanxi Province(2022KJXX-99)the National Defense Basic Research Program of Technology and Industry for National Defense(JCKY2021912B001).
文摘This paper concerns minimum-energy leader-following formation design and analysis problems of distributed multiagent systems(DMASs)subjected to randomly switching topologies and aperiodic communication pauses.The critical feature of this paper is that the energy consumption during the formation control process is restricted by the minimum-energy constraint in the sense of the linear matrix inequality.Firstly,the leader-following formation control protocol is proposed based on the relative state information of neighboring agents,where the total energy consumption is considered.Then,minimum-energy leader-following formation design and analysis criteria are presented in the form of the linear matrix inequality,which can be checked by the generalized eigenvalue method.Especially,the value of the minimum-energy constraint is determined.An illustrative simulation is provided to show the effectiveness of the main results.
文摘Workers who conduct regular facility inspections in radioactive environments will inevitably be affected by radiation.Therefore,it is important to optimize the inspection path to ensure that workers are exposed to the least amount of radiation.This study proposes a discrete Rao-combined artificial bee colony(ABC)algorithm for planning inspection paths with minimum exposure doses in radioactive environments with obstacles.In this algorithm,retaining the framework of the traditional ABC algorithm,we applied the directional solution update rules of Rao algorithms at the employed bee stage and onlooker bee stage to increase the exploitation ability of the algorithm and implement discretion using the swap operator and swap sequence.To increase the randomness of solution generation,the chaos algorithm was used at the initialization stage.The K-opt operation technique was introduced at the scout bee stage to increase the exploration ability of the algorithm.For path planning in an environment with complex structural obstacles,an obstacle detour technique using a recursive algorithm was applied.To evaluate the performance of the proposed algorithm,we performed experimental simulations in three hypothetical environments and compared the results with those of improved particle swarm optimization,chaos particle swarm optimization,improved ant colony optimization,and discrete Rao’s algorithms.The experimental results show the high performance of the proposed discrete Rao-combined ABC algorithm and its obstacle detour capability.
基金supported by the National Natural Science Foundation of China(62020106003,62273177,62233009)the Natural Science Foundation of Jiangsu Province of China(BK20222012,BK20211566)+1 种基金the Programme of Introducing Talents of Discipline to Universities of China(B20007)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(MCMS-I-0121G03).
文摘The attitude tracking control problem is addressed for hypersonic vehicles under actuator faults that may cause an uncertain time-varying control gain matrix.An adaptive compensation scheme is developed to ensure system stability and asymptotic tracking properties,including a kinematic control signal and a dynamic control signal.To deal with the uncertainties of the control gain matrix,a new positive definite one is constructed.The minimum eigenvalue of such a new control gain matrix is estimated.Simulation results of application to an X-33 vehicle model verify the effectiveness of the proposed minimum eigenvalue based adaptive fault compensation scheme.
基金Project supported by the National Natural Science Foundation of China (Grant No.61774001)the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices,Shanxi University,China (Grant No.KF202203)+1 种基金the NSF of Changsha City (Grant No.kq2208008)the NSF of Hunan Province (Grant No.2023JJ30116)。
文摘In the field of ultrafast magnetism,i.e.,subpicosecond or femtosecond time scales,the dynamics of magnetization can be described by the inertial Landau-Lifhitz-Gilbert equation.In terms of this equation,the intrinsic characteristics are investigated in detail for the theoretical limit of the magnetization reversal field.We can find that there is a critical value for the inertia parameterτ_(c),which is affected by the damping and anisotropy parameter of the system.When the inertial parameter factorτ<τ_(c),the limit value of the magnetization reversal field under the ultrafast magnetic mechanism is smaller than that of the fast magnetic mechanism.Whenτ>τ_(c),the limit value of the magnetization reversal field will be larger than the limit value under the fast magnetic mechanism.Moreover,it is important to point out that the limit value of the magnetization reversal field under the ultrafast magnetic mechanism decreases with the increasing inertial factor,asτ<τ_(c)/2,which increases with inertial factorτasτ>τ_(c)/2.Finally,with the joint action of damping and anisotropy,compared with fast magnetism,we find that the limit value of the magnetization reversal field has rich variation characteristics,i.e.,there is not only a linear and proportional relationship,but also an inverse relationship,which is very significant for the study of ultrafast magnetism.
基金supported by the Natural Science Foundation of Sichuan Province under Grant No.2022NSFSC0564the National Natural Science Foundation of China under Grants No.U20B2043 and No.62001095.
文摘For the anti-interference/denoise purpose,it usually requires minimizing the sidelobe level(SLL)of a wide-beam pattern with a desired low nulling level(NL)in the nulling region.To realize such an objective,the shaped-beam pattern synthesis(SBPS)is the most commonly used approach.However,since the SBPS problem focuses on synthesizing a predetermined beam shape,the minimum SLL via this approach cannot ensure to obtain the maximum power gain.Conversely,it cannot obtain the lowest SLL with a certain power gain requirement.Based on such consideration,this paper tries to further minimize SLL of a wide-beam pattern with a desired low NL nulling region,by solving the power gain pattern synthesis(PGPS)problem.The PGPS problem selects the array excitation by directly optimizing the power gain.Hence,it has the potential to reduce SLL,when achieving the equal mainlobe power gain constraint via SBPS.An iterative algorithm which converts the primal optimization problem into convex sub-problems is proposed,resulting in an effective problem-solving scheme.Numerical simulations demonstrate the proposed algorithm can obtain about 10-dB lower SLL than the existing algorithms.
基金supported by the National Natural Science Foundation of China(Nos.61962034,61862058)Longyuan Youth Innovation and Entrepreneurship Talent(Individual)Project and Tianyou Youth Talent Lift Program of Lanzhou Jiaotong Univesity。
文摘Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in patients with depression,this paper proposes a depression analysis method based on brain function network(BFN).To avoid the volume conductor effect,BFN was constructed based on phase lag index(PLI).Then the indicators closely related to depression were selected from weighted BFN based on small-worldness(SW)characteristics and binarization BFN based on the minimum spanning tree(MST).Differences analysis between groups and correlation analysis between these indicators and diagnostic indicators were performed in turn.The resting state electroencephalogram(EEG)data of 24 patients with depression and 29 healthy controls(HC)was used to verify our proposed method.The results showed that compared with HC,the information processing of BFN in patients with depression decreased,and BFN showed a trend of randomization.
文摘In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.
文摘Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.
