Stochastic maximum principle for systems driven by local martingales with spatial parameters

We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter.Assuming the convexity of the control domain,we obtain the stochastic maximum principle as the necessary condition for an optimal control,and we also prove its sufficiency under proper conditions.The stochastic linear quadratic problem in this setting is also discussed.

Design and Experiment of ф-type-knots Knotters on Chinese Small Square Balers

Since the knotters on the Chinese rectangular balers are imported from outside of the country, Chinese knotters with independent intellectual property rights is far away from being closed. In order to harvest a large quantity of straw in a short period on the small-scale lands of China, basic requirements on the knotters are summarized. Mathematical model of the knotter is also determined uniquely. Furthermore, the ^-type-knots knotter equipped on the Chinese square baler to form the ~ type knots is designed. Knotting rate experiments of the qb-type-knots knotter on the test bench and in the wheat/maize straws covered fields are carried out to check the knotting performances of the knotter. The parameters of the formed knots are also tested. The experiments results show that the knotting rate of the qb-type-knots knotter reaches 100.0% on the test bench without straws, while reaches 99.6% in the wheat straws covered field and 100.0% in the maize straws covered field. The average maximum force in the knotting process is 194.7 N in the lab experiment. The length out of the knots formed in lab is 15.9%-20.6% lower than the knots formed in the field experiment. The breaking force of the knots formed in the field is 115.9%-167.2% higher than the knots formed in lab due to the higher preload and interactions with the compacted bales. Highly relevant relationships exist between the breaking force of the formed knots and the maximum force in the forming process of the knots in the lab experiment. The designed knotter breaks out the embarrassing situation of the domestic knotters which don＇t have independent intellectual property rights, and promotes the development of Chinese knotter technology, and the mathematical model is helpful for designing new type of knotters.

Influence of urban spatial and socioeconomic parameters on PM_(2.5) at subdistrict level:A land use regression study in Shenzhen,China

The intraurban distribution of PM_(2.5)concentration is influenced by various spatial,socioeconomic,and meteorological parameters.This study investigated the influence of 37 parameters on monthly average PM_(2.5)concentration at the subdistrict level with Pearson correlation analysis and land-use regression(LUR)using data from a subdistrict-level air pollution monitoring network in Shenzhen,China.Performance of LUR models is evaluated with leave-one-out-cross-validation(LOOCV)and holdout cross-validation(holdout CV).Pearson correlation analysis revealed that Normalized Difference Built-up Index,artificial land fraction,land surface temperature,and point-of-interest(POI)numbers of factories and industrial parks are significantly positively correlated with monthly average PM_(2.5)concentrations,while Normalized Difference Vegetation Index and Green View Factor show significant negative correlations.For the sparse national stations,robust LUR modelling may rely on a priori assumptions in direction of influence during the predictor selection process.The month-bymonth spatial regression shows that RF models for both national stations and all stations show significantly inflated mean values of R^(2)compared with cross-validation results.For MLR models,inflation of both R^(2)and R^(2)CVwas detected when using only national stations and may indicate the restricted ability to predict spatial distribution of PM_(2.5)levels.Inflated within-sample R^(2)also exist in the spatiotemporal LUR models developed with only national stations,although not as significant as spatial LUR models.Our results suggest that a denser subdistrict level air pollutant monitoring network may improve the accuracy and robustness in intraurban spatial/spatiotemporal prediction of PM_(2.5)concentrations.

Complex Pattern Formations by Spatial Varying Parameters

Pattern formations by Gierer-Meinhardt(GM)activator-inhibitor model are considered in this paper.By linear analysis,critical value of bifurcation parameter can be evaluated to ensure Turing instability.Numerical simulations are tested by using second order semi-implicit backward difference methods for time discretization and the meshless Kansa method for spatially discretization.We numerically show the convergence of our algorithm.Pattern transitions in irregular domains are shown.We also provide various parameter settings on some irregular domains for different patterns appeared in nature.To further simulate patterns in reality,we construct different kinds of animal type domains and obtain desired patterns by applying proposed parameter settings.

Sound propagation in ducts with spatially variant parameters

The one-dimensional theory of sound propagation in ducts is generalized and investigated in this paper . It can be assumed that any duct system consists of two kinds of elementary structures : One is the piped structure in which the characteristics , such as the acoustical parameter on the interior surface of the wall , the cross-section area and the aerodynamic parameters of the flow , etc., will vary continuously and slowly with distance along the axis of the duct . The other is the local structure with discontinuity in which the characteristics will change abruptly. The acoustical properties of both structures are analysed in general cases based upon the fundamental equations of aerodynamics , and their transmission matrixes are derived and discussed respectively . Two typical examples are analysed and discussed .

Spatial anisotropy: a method to study anisotropic flow in heavy ion collisions

We introduce a method to study anisotropic flow parameter v n as a collective probe to Quark Gluon Plasma in relativistic heavy ion collisions. The emphasis is put on the use of the Fourier expansion of initial spatial azimuthal distributions of participant nucleons in the overlapped region. The coefficients ε n of Fourier expansion are called the spatial anisotropy parameter for the n-th harmonic. We propose that collective dynamics can be studied by v n /ε n . In this paper, we will discuss in particular the second （n = 2） and the fourth （n = 4） harmonics.

Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter

This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.