Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems

This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward-forward systems of equations of mean field games. We present local well-posedness, global existence and some regularity results for these equations.

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.

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].

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.

Blocking backward reaction on hydrogen evolution cocatalyst in a photosystem Ⅱ hybrid Z-scheme water splitting system

Photocatalytic Z-scheme water splitting is considered as a promising approach to produce solar hydrogen.However,the forward hydrogen production reaction is often impeded by backward reactions.In the present study,in a photosystem Ⅱ-integrated hybrid Z-scheme water splitting system,the backward hydrogen oxidation reaction was significantly suppressed by loading a PtCrOx cocatalyst on a ZrO2/TaON photocatalyst.Due to the weak chemisorption and activation of molecular hydrogen on PtCrOx,where Pt is stabilized in the oxidized forms,Pt^Ⅱ and Pt^Ⅳ,hydrogen oxidation is inhibited.However,it is remarkably well-catalyzed by the metallic Pt cocatalyst,thereby rapidly consuming the produced hydrogen.This work describes an approach to inhibit the backward reaction in the photosystem Ⅱ-integrated hybrid Z-scheme water splitting system using Fe(CN)6^3-/Fe(CN)6^4-redox couple as an electron shuttle.

A GENERALIZED QUASI MINIMAL BACKWARD ERROR (GQMBACK) ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS

Orthogonal projection methods have been widely used to solve linear systems. Little attention has been given to oblique projection methods, but the class of oblique projection methods is particularly attractive for large nonsymmetric systems. The purpose of this paper is to consider a criterion for judging whether a given appro ximation is acceptable and present an algorithm which computes an approximate solution to the linear systems Ax=b such that the normwise backward error meets some optimality condition.

The Maximum Principle for Fully Coupled Forward-backward Stochastic Control System

The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.

Calaulation of Time-Optimal Control Law for Double Integrator System with Complex Constraints: Endpoint Backward Method

An endpoint backward method is proposed to calculate the time-optimal control law of double integrator system. First, the time intervals between the switch points and the endpoints are calculated. Then, the positions of switch points are decided according to the motion equation, and the switch line is formed. Theoretical analysis shows that this method can be used to solve the double integrator system with functional constraint target set and deal with the second order oscillation system.

ON OPTIMAL BACKWARD PERTURBATION ANALYSIS FOR THE LINEAR SYSTEM WITH BLOCK CYCLIC COEFFICIENT MATRIX

Based on the block style spectral decomposition,this paper deals with the optimal backward perturbation analysis for the linear system with block cyclic coefficient matrix.

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.

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.

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. .

Influences of electric-hydraulic chattering on backward extrusion process of 6061 aluminum alloy

The possibility of the electric-hydraulic chattering technology and its application in the cold extrusion were presented.The conventional and electric-hydraulic chattering assisted backward extrusion processes were performed on 6061 aluminum alloy billets at room temperature.The experimental results showed that 5.65% reduction in the extrusion load was attained if the die and ejector were vibrated at a frequency of 100 Hz and amplitude of 0.013 mm in the longitudinal direction.The friction coefficient at the billet and tool system interface determined from the finite element analysis（FEA） decreased from 0.2 without chattering to 0.1 with application of electric-hydraulic chattering.The higher values of instantaneous velocity and direction change of material flow were achieved during the chattering assisted backward extrusion process.The strain distribution of the chattering assisted backward extrusion billet revealed lower maximum strain and smoother strain distribution in comparison with that produced by the conventional extrusion method.

Inhomogeneity of density and mechanical properties of A357 aluminum alloy backward extruded in semi-solid state

The inhomogeneity of density and mechanical properties of A357 aluminum alloy in the semi-solid state were investigated.Numerical simulation and backward extrusion were adopted to study the preparation of cup shells.The results show that the relative density of the wall is the lowest in samples,and that of the base is the highest.With increasing the billet height,more time is needed for relative density of the corner to reach the maximum value,and the relative densities in every region improve evidently with increasing the pressure.The tensile stress was simulated to be the largest at the corner,and the hot tearings were forecasted to mainly appear at the corner too.By employing proper billet height and pressure,the extruded samples consisted of fine and uniform microstructures,and can obtain excellent mechanical properties and Brinell hardness.

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)].