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.

Rapid hologram generation through backward ray tracing and adaptive-resolution wavefront recording plane

An advanced method for rapidly computing holograms of large three-dimensional(3D)objects combines backward ray tracing with adaptive resolution wavefront recording plane(WRP)and adaptive angular spectrum propagation.In the initial phase,a WRP with adjustable resolution and sampling interval based on the object’s size is defined to capture detailed information from large 3D objects.The second phase employs an adaptive angular spectrum method(ASM)to efficiently compute the propagation from the large-sized WRP to the small-sized computer-generated hologram(CGH).The computation process is accelerated using CUDA and OptiX.Optical experiments confirm that the algorithm can generate high-quality holograms with shadow and occlusion effects at a resolution of 1024×1024 in 29 ms.

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.

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.

政治小说的语言策略——以Looking Backward的四个汉译文本为中心

晚清来华传教士将政治小说传入中国,其参与实际政治问题的讨论、强烈的入世精神、变革意识,完全不同于此前抒怀式的中国文学,更是改变了文学向来是"小道"和"消遣"的命运,为文学接下来占领文化领域的制高点,做了重要的铺垫。美国人爱德华·贝拉米(Edward Bellamy)的乌托邦~①小说Looking Backward 2000-1887最早由英国传教士李提摩太(Timothy Richard)以文言译出,在晚清文化政治运动中影响广泛,此后迭经翻译,直至20世纪60年代尚有新译本。各译本选择了不同文体和语言风格,其翻译策略可以见出晚清以来书面语言的变迁、小说在社会改革中扮演的角色以及小说读者群的变化。

二维Master均值方程Backward的形式

如果二维Backward Master平均值方程的转移概率可用参数展开,我们证明了该方程可转化成一系列闭合的线性微分方程组。利用偏微分方程的特征方程组解法,在某种条件下我们求出了均值;将所得结果与线性噪音近似的结果比较,可得扩散系数D_x、D_xy、D_y;最后证明了一般情况下线性噪音近似是不适合的。

Effects of backward path parameters on formability in conventional spinning of aluminum hemispherical parts

During multi-pass conventional spinning, roller paths combined with the forward and the backward pass are usually used to improve the material formability. In order to understand the backward spinning process properly, the backward roller paths of hemispherical parts with aluminum alloy 2024-O are analyzed. Finite element model with parameterized conventional spinning roller paths, which are based on quadratic Bezier curves, is developed to explore the evolution of the stress, strain and thinning during the backward processes. Analysis of the simulation results reveals stress and strain features of backward pass spinning. According to the findings, the application of the backward pass can obviously improve the uniformity of wall thickness. Furthermore, references of the parameters in future backward path design are provided.

EVOLUTION OF DYNAMIC GAMES AND BACKWARD INDUCTION

As an efficient method of solving subgame-perfect Nash equilibrium,the backward induction is analyzed from an evolutionary point of view in this paper,replacing a player with a population and turning a game into a population game,which shows that equilibrium of a perfect information game is the unique evolutionarily stable outcome for dynamic models in the limit.

Forward-backward热方程差分逼近的直接算法

通过利用区域分解技术和并行算法的思想 ,把原问题分解为几个完全独立的子区域上的问题 ,并直接并行求解 ,然后把这些解作适当的线性组合 ,得到原问题的解 .给出了 Forward-

带驻留时间HMM2的Forward-Backward算法

讨论了用状态驻留时间来模型化传统HMM2模型,对传统HMM2的状态转移和输出观测值的Markov假设条件作了改进,在新模型的转移概率和输出观测值的概率中加入驻留时间,并在传统HMM2的基础上定义了新模型的前向-后向变量算法,导出了新模型的前向-后向算法的迭代公式,以及在给定模型λ的条件下,产生观测序列O的概率计算公式.

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

Hot deformation in nanocrystalline Nd-Fe-B backward extruded rings

Radially oriented Nd-Fe-B rings are prepared by backward extrusion of fine grained melt-spun powder. Melt- spun powder with the nominal composition of Nd30.5Febal.Co6.0Ga0.6A10.2B0.9 （wt%） is used as starting material. The effects of process variables, such as deformation temperature （Td）, strain rate （ε） and height reduction （△h%）, on the magnetic properties of the rings are investigated. A scanning electron microscope （SEM） equipped with an energy spectrum device is used to study the metallograph and microfracture of the extruded rings. The Br and （BH）max reach the optimum values at Td =800℃,ε= 0.01 mm/s, and △h% = 70%. It is found by SEM observations that the particle boundaries, which seemingly correspond to the interfaces of the starting melt-spun powders, emerge after the corrosion of metallography specimens. This is helpful for studying the effects of powder-powder interface on the local deformation and deformation homogeneity in the rings. For different spatial positions of the extruded rings, there are characteristic metallographies and microfractures. The upper end of the rings has the least deformation and worst texture, and therefore the worst magnetic properties. The magnetic properties in the radial direction increase slightly along the axis from the bottom to the middle, then steeply decrease at the upper end of the ring. The deformation and the formation-of-texturing processes are discussed. The deformation and the texturing formation of melt-spun Nd-Fe-B alloys probably involve grain boundary sliding and grain rotation, the solution-precipitation process and preferential growth of Nd2Fel4B nanograins along the easy growth a-axis.

Backward stochastic Volterra integral equations——a brief survey

In this paper, we present a brief survey on the updated theory of backward stochas-tic Volterra integral equations （BSVIEs, for short）. BSVIEs are a natural generalization of backward stochastic diff erential equations （BSDEs, for short）. Some interesting motivations of studying BSVIEs are recalled. With proper solution concepts, it is possible to establish the corresponding well-posedness for BSVIEs. We also survey various comparison theorems for solutions to BSVIEs.

Rheological behavior,microstructure and hardness of A356 aluminum alloy in semisolid state using backward extrusion process

The influence of temperature on the flow behavior and rheological characteristics of an A356 alloy in the semi-solid state was investigated using backward extrusion process.Experiments were performed at 5 temperatures and 4 different wall thicknesses.Viscosities were determined using the force-displacement graphs obtained form back extrusion tests.As observed experimentally,at a constant temperature,the increase of shear rate results in the decrease of alloy viscosity exponentially.Raising the temperature increases the liquid fraction hence reduces the semi-solid alloy viscosity.Metallographic and image analyses show that,because of low forming speed,liquid has time to escape from solid phase forward the sample wall.This condition is the main reason for the segregation phenomenon seen in the base and walls.Vickers hardness test on samples reveals that the hardness increases with the decrease of temperature and wall thickness.

Improved Car-Following Model Considering Modified Backward Optimal Velocity and Velocity Difference with Backward-Looking Effect

In this paper, a new traffic flow model called the forward-backward velocity difference (FBVD) model based on the full velocity difference model is proposed to investigate the backward-looking effect by applying a modified backward optimal velocity using generalized backward maximum speed. The FBVD model belongs to the family of microscopic models that consider spatiotemporally continuous formulations. Neutral stability conditions of the discrete car-following model are derived using the linear stability theory. The stability analysis results prove that the modified backward optimal velocity has a significant positive effect in stabilizing the traffic flow. Through nonlinear analysis, a kink-antikink solution is derived from the modified Korteweg-de Vries equation of the FBVD model to explain traffic congestion of the model. The validity of this theoretical model is checked using numerical results, according to which traffic jams were found to have been significantly diminished by the introduction of the modified backward optimal velocity.

A Backward Stable Hyperbolic QR Factorization Method for Solving Indefinite Least Squares Problem

We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.

A novel multi-pin rectangular waveguide slow-wave structure based backward wave amplifier at 340 GHz

A backward wave amplifier（BWA） in a terahertz regime with a novel slow-wave structure（SWS） composed of multi parallel grating pins inside a rectangular waveguide is analyzed. The multi-pin rectangular waveguide SWS possesses good performance and is compatible with micro-fabrication technologies. The dispersion and interaction impedance of the multipin SWS are presented. The stopbands of the modes cling together in a Brillouim zone. The SWS has a high interaction impedance that is suitable for the interaction of multi cylindrical beams. The design, which is based on three parallel pins supporting the wave–beam interaction with four cylindrical beams, is verified by three-dimensional particle-in-cell simulations. A BWA with the central frequency at 340 GHz is demonstrated, and the output power is more than 100 mW.A tuning frequency range of 15 GHz（333–348 GHz） is obtained with a gain of more than 20 dB.

Effect of circumferential strain rate on dynamic recrystallization and texture of Mg-13Gd-4Y-2Zn-0.5Zr alloy during rotary backward extrusion

Gleeble-3500 thermal simulator was applied to realize the rotary backward extrusion forming of Mg-13Gd-4Y-2Zn-0.5Zr(wt%)alloy at different circumferential strain rate from 0.009 s^(-1)to 0.027 s^(-1)at 400℃and the dynamic recrystallization mechanism and texture evolution were studied.The results show that the grain size of the alloy was obviously refined after rotary backward extrusion.As the circumferenlial strain rate increased,the dynamic recrystallization fraction gradually increased causing the grain size decreased and the distribution of microstructure became more uniform.At the same time,the texture of{0001},{10-10},{11-20}was weakened and the grain orientation distribution became more random.With the increase of circumferential strain rate,the discontinuous dynamic recrystallization mechanism became dominant,which promoted the weakening of texture and grain refinement of the alloy.