A note on the backwards uniqueness of the mean curvature flow

In this paper, we show a backwards uniqueness theorem of the mean curvature flow with bounded second fundamental forms in arbitrary codimension.

Critical Conditions for Left-Turn Lane's Stop Line Backwards Setting Under Exclusive Left-Turn Phase

Aiming at the problem that the vehicles always turn left in advance which causes heavy conflicts in the intersection and effected traffic efficiency,the solution of the left-turn lane’s stop line backwards setting was proposed,and the critical conditions on the stop line’s setting were studied.Firstly,we studied the characteristics of trajectories distribution in the release process of turning left in advance vehicles.Based on that,we proposed to move the stop line backwards to solve the problem of turning left in advance.Considering the intersection’s geometric features and the vehicle operation features,the geometric critical condition was given for setting the position of left-turn lane’s stop line.And then the model of left-turn vehicles’queuing length was established based on queuing theory and traffic wave theory.By using queuing length model,the flow restrictions of stop line backwards could be found.Assuming left-turn vehicles’arrival rate is stable in a certain period of time,the minimum green time and the maximum red time of left-turn phase were given after the stop line was set up.According to the changes of the vehicles’turning paths,the shortest yellow setting recommendation was given.Finally,the application of the critical limits used in stop line backwards setting was demonstrated.The research result could provide a theoretical basis for traffic signs and markings’setting and perfect the relevant laws and regulations.

Characteristics Variation of Atmospheric CO_(2)and CH_(4)in Yongxing Island,South China Sea

Using the observation data in Yongxing Island,South China Sea(SCS)from December 2013 to November 2018,the multiple time scales variation of atmospheric CO_(2)and CH_(4)were analyzed to understand their temporal variation characteristics and controlling factors.The regional-averaged background mole fractions of CO_(2)and CH_(4)both show a single-period sinusoidal variation with a lower value at noon and a higher value in the wee hours.In the seasonal scale,they exhibited a significant seasonal difference with higher values in winter and lower values in summer.In the annual scale,CO_(2)and CH_(4)both show an increasing trend,with an annual growth rate of approximately 3.2 ppm and 12 ppb,respectively.The annual growth rate at this site was higher than the global average.The change in atmospheric CO_(2)and CH_(4)in Yongxing Island was probably caused by the higher emission of the surrounding areas and the airflows driven by monsoon.Hopefully,the long-term and high-resolution greenhouse gases(GHGs)dataset will aid relevent researchers and decision-makers in performing more in-depth studies for GHG sources in order to derive effective strategies.

Partially-Observed Maximum Principle for Backward Stochastic Differential Delay Equations

Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is convex.The adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional spaces.Linear backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed rapidly.The corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].

Radioisotope production using lasers:From basic science to applications

The discovery of chirped pulse amplification has led to great improvements in laser technology,enabling energetic laser beams to be compressed to pulse durations of tens of femtoseconds and focused to a few micrometers.Protons with energies of tens of MeV can be accelerated using,for instance,target normal sheath acceleration and focused on secondary targets.Under such conditions,nuclear reactions can occur,with the production of radioisotopes suitable for medical application.The use of high-repetition lasers to produce such isotopes is competitive with conventional methods mostly based on accelerators.In this paper,we study the production of^(67)Cu,^(63)Zn,^(18)F,and^(11)C,which are currently used in positron emission tomography and other applications.At the same time,we study the reactions^(10)B(p,α)^(7)Be and^(70)Zn(p,4n)^(67)Ga to put further constraints on the proton distributions at different angles,as well as the reaction^(11)B(p,α)^(8)Be relevant for energy production.The experiment was performed at the 1 PW laser facility at VegaⅢin Salamanca,Spain.Angular distributions of radioisotopes in the forward(with respect to the laser direction)and backward directions were measured using a high purity germanium detector.Our results are in reasonable agreement with numerical estimates obtained following the approach of Kimura and Bonasera[Nucl.Instrum.Methods Phys.Res.,Sect.A 637,164–170(2011)].

A Novel Accurate Method forMulti-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains

Anovel accuratemethod is proposed to solve a broad variety of linear and nonlinear(1+1)-dimensional and(2+1)-dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity.For(1+1)-dimensional problems,analytical solutions that satisfy the boundary requirements are derived.Such solutions are numerically calculated using the trigonometric basis approximation for(2+1)-dimensional problems.With the aid of these analytical or numerical approximations,the original problems can be converted into the fractional ordinary differential equations,and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients.An efficient backward substitution strategy that was previously provided for a single fractional ordinary differential equation is then used to solve the corresponding systems.The straightforward quasilinearization technique is applied to handle nonlinear issues.Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.

A compact X-band backward traveling-wave accelerating structure

Very high-energy electrons(VHEEs)are potential candidates for FLASH radiotherapy for deep-seated tumors.We proposed a compact VHEE facility based on an X-band high-gradient high-power technique.In this study,we investigated and realized the first X-band backward traveling-wave(BTW)accelerating structure as the buncher for a VHEE facility.A method for calculating the parameters of single cell from the field distribution was introduced to simplify the design of the BTW structure.Time-domain circuit equations were applied to calculate the transient beam parameters of the buncher in the unsteady state.A prototype of the BTW structure with a thermionic cathode-diode electron gun was designed,fabricated,and tested at high power at the Tsinghua X-band high-power test stand.The structure successfully operated with 5-MW microwave pulses from the pulse compressor and outputted electron bunches with an energy of 8 MeV and a pulsed current of 108 mA.

Dielectric Resonator Magnetoelectric Dipole Arrays with Low Cross Polarization,Backward Radiation,and Mutual Coupling for MIMO Base Station Applications

Dielectric resonator magnetoelectric dipole(DRMED)arrays with enhanced isolation,reduced cross-polarization,and backward radiation are proposed for base station(BS)applications.The proposed antenna comprises an elevated dielectric resonator antenna(DRA)on a small metal plate above a sizeable common ground plane.The DRA is designed in its T Eδ11 mode,acting like a magnetic dipole.The surface current excited by the differential probes flowing on the small ground plane is equivalent to an electric dipole.Since these two equivalent dipoles are orthogonal,they have the magnetoelectric dipole characteristics with reduced backward radiation.Meanwhile,the small ground planes can be treated as decoupling structures to provide a neutralization path to cancel the original coupling path.A linearly-polarized 4-element prototype array was verified experimentally in previous work.Here,a dual-polarized DRMED antenna is presented to construct a 2-element and 4×4 array for BS applications.To investigate its MIMO performance,sophisticated multi-cell scenario simulations are carried out.By using the proposed dualpolarized DRMED array,the cellular system capacityis improved by 118.6%compared to a conventional DRA array.This significant MIMO system improvement is mainly due to the reduced backward radiation and,therefore,reduced inter-cell interferences.Measurements align well with the simulations.

A COMPUTATIONAL STUDY ON BACKWARDS WI MMING HYDRODYNAMICS IN THE EELANGUILLA ANGUILLA

Eels can perform both forward and backward undulatory swimming but few studies are seen on how eels propel themselves backward. A computational study on the unsteady hydrodynamicsoof the backward swimming in the eel anguilla anguilla is carried out and presented. A two-dimensional geometric model of the European eel body in its middle horizontal section is appropriately approximated by a NACA0005 airfoil. Kinematic data of the backward and forward swimming eel used in the computational modeling are based on the experimental results of the European eel. Present study provided the different flow field characteristics of three typical cases in the backward swimming, and confirmed the guess of Wu： When the eel swims steadily, the vortex centers of the reversed von Kármán vortex street are aligned approximately. An extensive comparison between the backward and forward swimming further reveals that the controllable parameters, such as frequency, amplitude and wavelength of the traveling wave, have a similar influence on the propulsion performance as in forward swimming. But it is shown that the backward swimming does not be a ＂reversed＂ forward swimming one. The backward swimming does show significant discrepancy in the propulsion performance： utilization of a constant-amplitude wave profile enables larger force generation for maneuverability but with much lower propulsive efficiency instead of the linear-increasing amplitude wave profile in the forward swimming. The actual swimming modes eels choose is the best choice associated with their propulsive requirement, as well as their physiological and ecological adaptation.

Extreme Cold Events in North America and Eurasia in November-December 2022: A Potential Vorticity Gradient Perspective

From 17 November to 27 December 2022, extremely cold snowstorms frequently swept across North America and Eurasia. Diagnostic analysis reveals that these extreme cold events were closely related to the establishment of blocking circulations. Alaska Blocking(AB) and subsequent Ural Blocking(UB) episodes are linked to the phase transition of the North Atlantic Oscillation(NAO) and represent the main atmospheric regimes in the Northern Hemisphere. The downstream dispersion and propagation of Rossby wave packets from Alaska to East Asia provide a large-scale connection between AB and UB episodes. Based on the nonlinear multi-scale interaction(NMI) model, we found that the meridional potential vorticity gradient(PVy) in November and December of 2022 was anomalously weak in the mid-high latitudes from North America to Eurasia and provided a favorable background for the prolonged maintenance of UB and AB events and the generation of associated severe extreme snowstorms. However, the difference in the UB in terms of its persistence,location, and strength between November and December is related to the positive(negative) NAO in November(December). During the La Ni?a winter of 2022, the UB and AB events are related to the downward propagation of stratospheric anomalies, in addition to contributions by La Ni?a and low Arctic sea ice concentrations as they pertain to reducing PVyin mid-latitudes.

Possible source and migration pathway for early-summer immigrants of the oriental armyworm, Mythimna separata, arriving in northern Japan

The first generation of the oriental armyworm, Mythimna separata(Walker), arrives every year in northern Japan in mainly late May to early June. Analyses of weather maps suggested that this moth’s immigration source could be eastern China, but the accuracy of those analyses was very limited due to the lack of a current standard trajectory analysis. The management of migratory insect pests such as M. separata benefits from the identification of the migration source(s)and pathway(s) of the pests. The present study provides a trajectory analysis for M. separata. Backward trajectories from trap sites in northern Japan were calculated with the HYSPLIT System developed by the U.S. National Oceanic and Atmospheric Administration, taking the flight speed of M. separata and the limitation of low ambient temperature at flight height into account. The ending times of the moth’s short and long trajectories were set at dusk on the day before and two days before the possible arrival date, respectively. The results suggested two types of possible migration pathway: a multi-step pathway from Northeast China, the Korean Peninsula, and eastern Russia, which are destination areas of the first-generation’s migration, and a direct pathway from seasonal main emigration areas in eastern China such as Jiangsu and Shandong provinces. These findings contribute to our understanding of the migration ecology of M. separata and can be used for the development of methods to predict the migration of this insect.

GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.

Transition from backward to sideward stimulated Raman scattering with broadband lasers in plasmas

Broadband lasers have been proposed as future drivers of inertial confined fusion(ICF)to enhance the laser-target coupling efficiency via the mitigation of various parametric instabilities.The physical mechanisms involved have been explored recently,but are not yet fully understood.Here,stimulated Raman scattering(SRS)as one of the key parametric instabilities is investigated theoretically and numerically for a broadband laser propagating in homogeneous plasma in multidimensional geometry.The linear SRS growth rate is derived as a function of scattering angles for two monochromatic laser beams with a fixed frequency differenceδω.Ifδω/ω_(0)∼1%,withω0 the laser frequency,these two laser beams may be decoupled in stimulating backward SRS while remaining coupled for sideward SRS at the laser intensities typical for ICF.Consequently,side-scattering may dominate over backward SRS for two-color laser light.This finding of SRS transition from backward to sideward SRS is then generalized for a broadband laser with a few-percent bandwidth.Particle-in-cell simulations demonstrate that with increasing laser bandwidth,the sideward SRS gradually becomes dominant over the backward SRS.Since sideward SRS is very efficient in producing harmful hot electrons,attention needs to be paid on this effect if ultra-broadband lasers are considered as next-generation ICF drivers.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

ANTICIPATED BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND APPLICATIONS TO DYNAMIC RISK MEASURES

In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.

Glass-compatible and self-powered temperature alarm system by temperature-responsive organic manganese halides via backward energy transfer process

A pioneering glass-compatible transparent temperature alarm system self-powered by luminescent solar concentrators(LSCs) is reported.Single green-emitted organic manganese halides(OMHs) of PEA_(2)MnBr_(2)I_(2),which has a unique temperature-dependent backward energy transfer process from selftrapped state to^(4)T_(1)energy level of Mn,is used for triggering the temperature alarm.The LSC with redemitted CsPbI_(3)perovskite-polymer composite films on the glass substrate is used for power supply.The spectrally separated nature between the green-emitted OMHs for temperature alarm and red-emitted CsPbI3in LSC for power supply allows for probing the signal light of temperature-responsive OMHs without the interference of LSCs,making it possible to calibrate the temperature visually just by a self-powered brightness detection circuit with LED indicators.Taking advantage of LSC without hot spot effects plaguing the solar cells,as-prepared temperature alarm system can operate well on both sunny and cloudy day.

Evaluation of corneal backward light scattering in type 2 diabetes mellitus

AIM:To compare the corneal backward light scattering values in type 2 diabetes mellitus(DM)patients with those of age and sex-matched healthy controls.METHODS:The study included 30 patients(30 eyes)with type 2 DM and 30 control subjects(30 eyes).Duration of diabetes,most recent hemoglobin A1c levels,along with the status of diabetic retinopathy,and existing medical treatment of all subjects were recorded.All subjects underwent a complete ophthalmologic examination.In addition,backward light scattering(densitometry)was measured to assess changes in corneal transparency using tomography(Pentacam HR).RESULTS:The type 2 DM patients included 12 males and 18 females and control subjects included 16 males and 14 females.The age was 50.40±7.80y(range:40-68y)of the diabetic group and 49.30±9.50y(rang:40-73y)of control group.The diabetic group demonstrated significantly higher mean densitometry values of the anterior(6-10 mm)zone(P=0.047),the total anterior layer(P=0.036)and the total cornea(P=0.043)than control group.The corneal densitometry of the diabetic eyes demonstrated no significant correlation with hemoglobin A1c levels and DM duration.CONCLUSION:Diabetic group has higher densitometry in anterior corneal(6-10 mm)zone,total anterior cornea,and total cornea and with no correlation with hemoglobin A1c levels and DM duration.

Moisture Transport and Associated Background Circulation for the Regional Extreme Precipitation Events over South China in Recent 40 Years

Based on the hourly precipitation data at 176 observational stations over south China and the hourly ERA5reanalysis data during the 40-yr period of 1981-2020, we analyzed the universal characteristics of moisture transport and their associated background circulations for four types of regional extreme precipitation events(REPEs) over south China. Main findings are shown as follow.(i) The wind that transported moisture for the REPEs over south China featured a notable diurnal variation, which was consistent with the variations of the precipitation.(ii) Four types of REPEs could be determined, among which the southwest type(SWT) and the southeast type(SET) accounted for ~92%and ~5.7%, respectively, ranking the first and second, respectively.(iii) Trajectory analyses showed that the air particles of the SWT-REPEs had the largest specific humidity and experienced the most intense ascending motion, and therefore their precipitation was the strongest among the four types.(iv) South China was dominated by notable moisture flux convergence for the four types of REPEs, but their moisture transport was controlled by different flow paths.(v)Composite analyses indicated that the background circulation of the four types of REPEs showed different features,particularly for the intensity, location and coverage of a western Pacific subtropical high. For the SWT-REPEs, their moisture transport was mainly driven by a lower-tropospheric strong southwesterly wind band in the low-latitude regions. Air particles for this type of REPEs mainly passed over the Indochina Peninsula and South China Sea. For the SET-REPEs, their moisture transport was mainly steered by a strong low-tropospheric southeasterly wind northeast of a transversal trough. Air particles mainly passed over the South China Sea for this type of REPEs.

Backward Support Computation Method for Positive and Negative Frequent Itemset Mining

Association rules mining is a major data mining field that leads to discovery of associations and correlations among items in today’s big data environment. The conventional association rule mining focuses mainly on positive itemsets generated from frequently occurring itemsets (PFIS). However, there has been a significant study focused on infrequent itemsets with utilization of negative association rules to mine interesting frequent itemsets (NFIS) from transactions. In this work, we propose an efficient backward calculating negative frequent itemset algorithm namely EBC-NFIS for computing backward supports that can extract both positive and negative frequent itemsets synchronously from dataset. EBC-NFIS algorithm is based on popular e-NFIS algorithm that computes supports of negative itemsets from the supports of positive itemsets. The proposed algorithm makes use of previously computed supports from memory to minimize the computation time. In addition, association rules, i.e. positive and negative association rules (PNARs) are generated from discovered frequent itemsets using EBC-NFIS algorithm. The efficiency of the proposed algorithm is verified by several experiments and comparing results with e-NFIS algorithm. The experimental results confirm that the proposed algorithm successfully discovers NFIS and PNARs and runs significantly faster than conventional e-NFIS algorithm.

Microstructure Distribution Characteristics of High-Strength Aluminum Alloy Thin-Walled Tubes during Multi-Passes Hot Power Backward Spinning Process

The microstructure of the thin-walled tubes with high-strength aluminum alloy determines their final forming quality and performance. This type of tube can be manufactured by multi-pass hot power backward spinning process as it can eliminate casting defects, refine microstructure and improve the plasticity of the tube. To analyze the microstructure distribution characteristics of the tube during the spinning process, a 3D coupled thermo-mechanical FE model coupled with the microstructure evolution model of the process was established under the ABAQUS environment. The microstructure evolution characteristics and laws of the tube for the whole spinning process were analyzed. The results show that the dynamic recrystallization is mainly produced in the spinning deformation zone and root area of the tube. In the first pass, the dynamic recrystallization phenomenon is not obvious in the tube. With the pass increasing, the trend of dynamic recrystallization volume percentage gradually increases and extends from the outer surface of the tube to the inner surface. The fine-grained area shows the states of concentration, dispersion, and re-concentration as the pass number increases. .