Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control.We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians.Additionally,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of dimensionality.Using existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial costs.We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can achieve.Our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

High-dimension multiparty quantum secret sharing scheme with Einstein-Podolsky-Rosen pairs

In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein-Podolsky-Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity, but also saving storage space. The security analysis is also given.

Pneumatic resistance network analysis and dimension optimization of high pressure electronic pneumatic pressure reducing valve

The structure and working principle of a self-deigned high pressure electronic pneumatic pressure reducing valve (EPPRV) with slide pilot are introduced.The resistance value formulas and the relationship between the resistance and pressure of three typical pneumatic resistances are obtained.Then,the method of static characteristics analysis only considering pneumatic resistances is proposed,the resistance network from gas supply to load is built up,and the mathematical model is derived from the flow rate formulas and flow conservation equations,with the compressibility of high pressure gas and temperature drop during the expansion considered in the model.Finally,the pilot spool displacement of 1.5 mm at an output pressure of 15MPa and the enlarging operating stroke of the pilot spool are taken as optimization targets,and the optimization is carried out based on genetic algorithm and the model mentioned above.The results show that the static characteristics of the EPPRV are significantly improved.The idea of static characteristics analysis and optimization based on pneumatic resistance network is valuable for the design of pneumatic components or system.

Recent advances in statistical methodologies in evaluating program for high-dimensional data

The era of big data brings opportunities and challenges to developing new statistical methods and models to evaluate social programs or economic policies or interventions. This paper provides a comprehensive review on some recent advances in statistical methodologies and models to evaluate programs with high-dimensional data. In particular, four kinds of methods for making valid statistical inferences for treatment effects in high dimensions are addressed. The first one is the so-called doubly robust type estimation, which models the outcome regression and propensity score functions simultaneously. The second one is the covariate balance method to construct the treatment effect estimators. The third one is the sufficient dimension reduction approach for causal inferences. The last one is the machine learning procedure directly or indirectly to make statistical inferences to treatment effect. In such a way, some of these methods and models are closely related to the de-biased Lasso type methods for the regression model with high dimensions in the statistical literature. Finally, some future research topics are also discussed.

Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension

We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann boundary conditions in a smooth bounded domainΩ⊂R^N(N≥3),where 0<ψ(u)≤K(u+1)^a,K1(s+1)^m≤ϕ(s)≤K2(s+1)^m withα,K,K1,K2>0 and m∈R.It is shown that ifα−m<4/N+2,then for any sufficiently smooth initial data,the classical solutions to the system are uniformly-in-time bounded.This extends the known result for the corresponding model with linear diffusion.

Image segmentation algorithm based on high-dimension fuzzy character and restrained clustering network

An image segmentation algorithm of the restrained fuzzy Kohonen clustering network （RFKCN） based on high- dimension fuzzy character is proposed. The algorithm includes two steps. The first step is the fuzzification of pixels in which two redundant images are built by fuzzy mean value and fuzzy median value. The second step is to construct a three-dimensional （3-D） feature vector of redundant images and their original images and cluster the feature vector through RFKCN, to realize image seg- mentation. The proposed algorithm fully takes into account not only gray distribution information of pixels, but also relevant information and fuzzy information among neighboring pixels in constructing 3- D character space. Based on the combination of competitiveness, redundancy and complementary of the information, the proposed algorithm improves the accuracy of clustering. Theoretical anal- yses and experimental results demonstrate that the proposed algorithm has a good segmentation performance.

THE SEMI-DISCREIXTE METHOD FOR SOLVING HIGH-DIMENSION WAVE EQUATION

The article gives a semi-discrete method for solving high-dimension wave equationBy the method, high-dimension wave equation is converted by, means of diseretizationinto I-D wave equation system which is well-posed. The convergence of the semidijcrete method is given. The numerical calculating resulis show that the speed of convergence is high.

Research on Preparation and Electrochemical Performance of the High Compacted Density Ni-Co-Mn Ternary Cathode Materials

The high compacted density LiNi0.5-xCo0.2Mn0.3MgxO2 cathode material for lithium-ion batteries was synthesized by high temperature solid-state method, taking the Mg element as a doping element and the spherical Ni0.5Co0.2Mn0.3 (OH)2, Li2CO3 as raw materials. The effects of calcination temperature on the structure and properties of the products were investigated. The structure and morphology of cathode materials powder were analyzed by X-ray diffraction spectroscopy (XRD) and scanning electronmicroscopy (SEM). The electrochemical properties of the cathode materials were studied by charge-discharge test and cyclic properties test. The results show that LiNi0.4985Co0.2Mn0.3 Mg0.0015O2 cathode material prepared at calcination temperature 930°C has a good layered structure, and the compacted density of the electrode sheet is above 3.68 g/cm3. The discharge capacity retention rate is more than 97.5% after 100 cycles at a charge-discharge rate of 1C, displaying a good cyclic performance.

Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series

Analysis of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using embedded solid concentration time series collected from a 76 mm internal diameter and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s air velocity and 50 to 550 kg/m2s solids flux of spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3. Data were analyzed using prepared FORTRAN 2008 code to get correlation integral followed by determination of correlation dimensions with respect to the hyperspherical radius and their profiles, plots of which were studied. It was found that correlation dimension profiles at the centre have single peak with higher values than the wall region profiles. Towards the wall, these profiles have double or multiple peaks showing bifractal or multifractal flow behaviors. As the velocity increases the wall region profiles become random and irregular. Further it was found that, as the height increases the correlation dimension profiles shift towards higher hyperspherical radius at the centre and towards lower hyperspherical radius in the wall region at r/R = 0.81. The established method of mapping correlation dimension profiles in this study forms a suitable tool for analysis of high-flux riser dynamics compared to other analyses approaches. However, further analysis is recommended to other gas-solid CFB riser of different dimensions operated at high-flux conditions using the established method.

Carbide refinement in M42 high speed steel by rare earth metals and spheroidizing treatment

The influence of rare earth metals and heat treatment on the microstructure and performance of M42 steel has been investigated by means of an optical microscope OM scanning electron microscope SEM energy dispersive spectroscopy EDS transmission electron microscope TEM electron back-scatter diffraction EBSD and X-ray diffraction XRD . The results show that M2 C is the prevailing type of eutectic carbides in M42 steel. After modification with rare earth metals M2 C eutectic carbides change from the ordered lamellar structure into a circular structure.Despite different morphologies the two carbides present the same characteristics of microstructure and growth orientation.Compared with lamellar carbides M2 C carbides with the circular structure are much easier to decompose and spheroidize after heating which remarkably refines the carbide dimensions.The refined carbides improve the supersaturation of alloying elements in martensite and increase the hardness of M42 steel by 1.5 HRC.

Effects of initial particle gradation and rock content on crushing behaviors of weathered phyllite fills——A case of eastern Ankang section of Shiyan—Tianshui highway,China

The objective of this paper is to investigate the effects of initial particle gradation and rock content on the crushing behavior(i.e.grain size before and after crushing) of weathered phyllite fills.Compaction tests were conducted on weathered phyllite fills with rock contents of 35%,45%,55%,65% and 75%(by weight).First,the particle size distributions(PSDs) were observed before and after compaction,and then the particle breakage of weathered phyllite fills was analyzed by fractal dimension.Relative fractal dimension was proposed to evaluate the effects of initial rock content and initial gradation on the particle breakage.It was found that the fractal dimension method can well characterize the crushing behaviors of the weathered phyllite fills.The finer the fills were,the more they were compacted.That is,after the first compaction,the relative fractal dimension of the weathered phyllite fills increased as the rock content increased,reaching the values of 0.013,0.016,0.024,0.037 and 0.08,respectively.After the second compaction,these relative fractal dimension values,dominated by the initial particle gradation,became 0.059,0.072,0.052,0.095 and 0.118,respectively.In conclusion,the weathered phyllite fills with 55% rock content exhibited the least breakage and were most suitable for filling the subgrade.Findings in this paper will provide significant guidance for the construction of weathered phyllite filling subgrade in future projects.

Analysis of density and mechanical properties of high velocity compacted iron powder

A new method for producing higher density PM parts, high velocity compaction （HVC）, was presented in the paper. Using water atomized pure iron powder without lubricant admixed as the staring material, ring samples were compacted by the technique. Scanning electron microscopy （SEM） and a computer controlled universal testing machine were used to investigate the morphologies and the mechanical properties of samples, respectively. The relationships among the impact velocity, the green density, the sintered density, the bending strength and the tensile strength were discussed, The results show that with increasing impact velocity, the green density and the bending strength increase gradually, so the sintered density does. In addition, the tensile strength of sintered material is improved continuously with the sintered density enhancing. In the study, the sintered density of 7.545 g/cm^3 and the tensile strength of 190 MPa are achieved at the optimal impact velocity of 9.8 m/s.

Design,fabrication,and cold test of an S-band high-gradient accelerating structure for compact proton therapy facility

An S-band high-gradient accelerating structure is designed for a proton therapy linear accelerator(linac)to accommodate the new development of compact,singleroom facilities and ultra-high dose rate(FLASH)radiotherapy.To optimize the design,an efficient optimization scheme is applied to improve the simulation efficiency.An S-band accelerating structure with 2856 MHz is designed with a low beta of 0.38,which is a difficult structure to achieve for a linac accelerating proton particles from 70 to 250 MeV,as a high gradient up to 50 MV/m is required.A special design involving a dual-feed coupler eliminates the dipole field effect.This paper presents all the details pertaining to the design,fabrication,and cold test results of the S-band high-gradient accelerating structure.

Polycrystalline cubic boron nitride prepared with cubic-hexagonal boron nitride under high pressure and high temperature

Polycrystalline cubic boron nitride(Pc BN)compacts,using the mixture of submicron cubic boron nitride(c BN)powder and hexagonal BN(h BN)powder as starting materials,were sintered at pressures of 6.5–10.0 GPa and temperature of1750℃without additives.In this paper,the sintering behavior and mechanical properties of samples were investigated.The XRD patterns of samples reveal that single cubic phase was observed when the sintering pressure exceeded 7.5 GPa and h BN contents ranged from 20 vol.%to 24 vol.%,which is ascribed to like-internal pressure generated at grain-to-grain contact under high pressure.Transmission electron microscopy(TEM)analysis shows that after high pressure and high temperature(HPHT)treatments,the submicron c BN grains abounded with high-density nanotwins and stacking faults,and this contributed to the outstanding mechanical properties of Pc BN.The pure bulk Pc BN that was obtained at 7.7 GPa/1750℃possessed the outstanding properties,including a high Vickers hardness(~61.5 GPa),thermal stability(~1290℃in air),and high density(~3.46 g/cm^(3)).

High-Sensitivity Ozone Sensing Using 280 nm Deep Ultraviolet Light-Emitting Diode for Detection of Natural Hazard Ozone

Recently ozone is one of natural hazards which comes from cars, industry using ozone for sterilization of organic and inorganic materials and for water purification. So, ozone sensing becomes very important, and convenient and accurate ozone sensor is required. A new high sensitivity ozone sensing system using an deep ultra-violet light emitting diode (DUV-LED) operated at the wavelength of 280 nm has been successfully constructed. The fabrication of diode operated at 280 nm is much easier than that of DUV-LED operated at Hg lamp wavelength of 254 nm. The system is compact and possible to sense the ozone concentration less than 0.1 ppm with an accuracy of 0.5% easily with low power DUV-LED of around 200 micro Watts operated at 280 nm without any data processing circuit.

ON MULTI-DIMENSIONAL SONIC-SUBSONIC FLOW

In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional （n ≥ 2） Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy Hloc^-1（Ω） compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional （n ≥ 2） Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension （n ≥ 3）.

A Highly Compact Third-Order Silicon Elliptical Micro-Ring Add-Drop Filter with a Large Free Spectral Range

We demonstrate a highly compact third-order elliptical micro-ring add-drop filter based on a silicon-on-insulator wafer. The elliptical micro-ring resonator has a major radius of 6μm （minor radius of 4.112μm） and a large free spectral range of 18 nm. Experimental results show a box-like channel dropping response, which has a 3 dB bandwidth of -2.7nm, high out-of-band signal rejection of around 40dB and a very low drop loss （〈0.5dB）. Simulation agrees well with the experiments. The footprint of the whole chip is only 0.0003mm2.

Neutron Diffraction of Large-Volume Samples at High Pressure Using Compact Opposed-Anvil Cells

Neutron diffraction techniques of large-volume samples at high pressure using compact opposed-anvil cells are developed at a reactor neutron source, China＇s Mianyang research reactor. We achieve a high-pressure condition of in situ neutron diffraction by means of a newly designed large-volume opposed-anvil cell. This pressure calibration is based on resistance measurements of bismuth and the neutron diffraction of iron. Pressure calibration experiments are performed at room temperature for a new cell using the tungsten carbide anvils with a tapered angle of 30°, Φ4.5 mm culet diameter and the metal-nonmetal composite gasket with a thickness of 2 mm. Transitions in Bi（Ⅰ–Ⅱ 2.55 GPa, Ⅱ–V 7.7 GPa） are observed at 100 and 300 kN, respectively, by resistance measurements.The pressure measurement results of neutron diffraction are consistent with resistance measurements of bismuth.As a result, pressures up to about 7.7 GPa can routinely and stably be achieved using this apparatus, with the sample volume of 9 mm^3.

A novel approach to predict green density by high-velocity compaction based on the materials informatics method

High-velocity compaction is an advanced compaction technique to obtain high-density compacts at a compaction velocity of ≤10 m/s. It was applied to various metallic powders and was verified to achieve a density greater than 7.5 g/cm^3 for the Fe-based powders. The ability to rapidly and accurately predict the green density of compacts is important, especially as an alternative to costly and time-consuming materials design by trial and error. In this paper, we propose a machine-learning approach based on materials informatics to predict the green density of compacts using relevant material descriptors, including chemical composition, powder properties, and compaction energy. We investigated four models using an experimental dataset for appropriate model selection and found the multilayer perceptron model worked well, providing distinguished prediction performance, with a high correlation coefficient and low error values. Applying this model, we predicted the green density of nine materials on the basis of specific processing parameters. The predicted green density agreed very well with the experimental results for each material, with an inaccuracy less than 2%. The prediction accuracy of the developed method was thus confirmed by comparison with experimental results.

The Frost-resisting Durability of High Strength Self-Compacting Pervious Concrete in Deicing Salt Environment

A high strength self-compacting pervious concrete(SCPC) with top-bottom interconnected pores was prepared in this paper. The frost-resisting durability of such SCPC in different deicing salt concentrations(0%, 3%, 5%, 10%, and 20%) was investigated. The mass-loss rate, relative dynamic modulus of elasticity, compressive strength, flexural strength and hydraulic conductivity of SCPC after 300 freeze-thaw cycles were measured to evaluate the frost-resisting durability. In addition, the microstructures of SCPC near the top-bottom interconnected pores after 300 freeze-thaw cycles were observed by SEM. The results show that the high strength SCPC possesses much better frost-resisting durability than traditional pervious concrete(TPC) after 300 freeze-thaw cycles, which can be used in heavy loading roads. The most serious freeze-thaw damage emerges in the SCPC immersed in the 3% of Na Cl solution, while there is no obvious damage in 20% of Na Cl solution. Furthermore, it can be deduced that the high strength SCPC can be used for 100 years in a cold environment.