A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

A New Method to Estimate Nonlinear Diffusions Based on Discretely Observed Data

The paper proposes a new method to estimate nonlinear diffusions based on discretely observed data, and gives some properties of the corresponding parameters estimation.

Necessary Conditions for Optimal Control of Diffusions with Hard Terminal State Restrictions

Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time. The necessary conditions are stated in terms of weak variations. Two versions of necessary conditions are given, one version involving solutions of variational equations, the other one involving first order adjoint equations.

On the Dynamics of Controlled Diffusions

Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable forms of stochastic action associated with the controlled diffusions are introduced in the general framework of stochastic control theory.By discretizing the stochastic action,the dynamical equations for the controlled diffusions of the given systems are derived in terms of generalized coordinates.These equations,together with the continuity equation,describe exactly the probability approach of the diffusion motion.

Adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co(200): A first-principles density-functional study

First-principles calculations based on density functional theory are used to investigate the adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co （200）. The preferred site for the carbon atom on the surface is the hollow site, and the preferred site in the subsurface is the octahedral site. There is charge transfer from the surface to the adsorbed carbon atom, and for the most favorable adsorbed structure the charge transfer is largest. Moreover, the energy barriers for the diffusions of carbon atoms on the surface and from the surface into the subsurface and then back to the surface are calculated in detail. The results indicate that the energy barrier for the diffusion of carbon atoms on the surface is comparable to that from the subsurface to the surface. The results imply that both the direct surface nucleation and the surface segregation from Co bulk can be observed in the chemical vapor deposition growth of graphene on Co （200） substrate, which can gain a new insight into the growth mechanism of graphene.

PERSISTENCE OF TWO-SPECIES AYALA COMPETITIVE MODEL WITH DIFFERENT DIFFUSIONS

In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.

Practical stability and instability of regime-switching diffusions

This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Moreover, examples are supplied for demonstration purposes.

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.

Estimation in Interacting Diffusions: Continuous and Discrete Sampling

Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, observations are taken on a fixed time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the dimension of the sieve. For the approximate maximum likelihood estimator, discrete observations are taken in a time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the number of observation time points.

The Voice of Physics in Finance:A Glance on the Theoretical Application of Heat Equation to Stock Price Diffusions

Stock price volatility is considered the main matter of concern within the investment grounds.However,the diffusivity of these prices should as well be considered.As such,proper modelling should be done for investors to stay healthy-informed.This paper suggest to model stock price diffusions using the heat equation from physics.We hypothetically state that,our model captures and model the diffusion bubbles of stock prices with a better precision of reality.We compared our model with the standard geometric Brownian motion model which is the wide commonly used stochastic differential equation in asset valuation.Interestingly,the models proved to agree as evidenced by a bijective relation between the volatility coefficients of the Brownian motion model and the diffusion coefficients of our heat diffusion model as well as the corresponding drift components.Consequently,a short proof for the martingale of our model is done which happen to hold.

Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.

基于AIGC技术的民族服饰设计研究——以畲族为例

民族服饰的当代创新需要在创作过程中寻求民族传统与现代审美的最佳平衡点,生成式人工智能(AIGC)技术的出现为民族服饰的当代设计应用提供了新的路径和方法。文章通过分析目前人工智能技术在民族服饰生成过程中遇到的问题,提出基于专属资源库模型训练的方法并以畲族服饰为例进行实验。实验表明,通过对畲族资源库中的服饰样本进行品类归纳和图像标注进行专属模型的训练,可以使被训练的模型理解、学习到资源库样本中畲族服饰的特征,进而使生成的内容具有畲族服饰风格的图像。通过这一实验,展示了人工智能技术给民族服饰创新设计带来的全新思路和方法,旨在建立一条民族服饰设计与AIGC技术相结合的创新实践路径,通过AIGC技术能促进民族服饰设计的创新性发展和创造性转化。

Talagrand's T_2-transportation Inequality w.r.t.a Uniform Metric for Diffusions

Using the method of Girsanov transformation, we establish the Talagrand’s T 2-inequality for diffusion on the path space C([0,N],? d ) with respect to a uniform metric, with the constant independent of N. This improves the known results for the L 2-metric.

Effectiveness of radiative heat flux in MHD flow of Jeffrey-nanofluid subject to Brownian and thermophoresis diffusions

Our interest here in this investigation is to explore the thermophoresis and Brownian motion characteristics in flow induced by stretched surface.Electrically conducted Jeffrey material formulates the flow equation.Linear forms of stretching and free stream velocities are imposed.Nonlinear radiation and convective heating processes describe the phenomenon of heat transfer.Passive controls of nanoparticles are considered on the boundary.The compatible transformations produce the strong nonlinear differential systems.The problems are computed analytically utilizing HAM.Converge nee domain is detennined and major results are concluded for different parameters involved.Heat transfer rate and drag force are also explained for various physical variables.Our analysis reveals that heat transfer rate augments via larger radiation parameter and Biot number.Moreover larger Brownian motion and thermophoresis parameters have opposite characteristics on concentration field.

Stochastic quantization and ergodic theorem for density of diffusions

For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.

Recent Advances in Fibrous Materials for Hydroelectricity Generation

Depleting fossil energy sources and conventional polluting power generation pose a threat to sustainable development.Hydroelectricity generation from ubiquitous and spontaneous phase transitions between liquid and gaseous water has been considered a promising strategy for mitigating the energy crisis.Fibrous materials with unique flexibility,processability,multifunctionality,and practicability have been widely applied for fibrous materials-based hydroelectricity generation(FHG).In this review,the power generation mechanisms,design principles,and electricity enhancement factors of FHG are first introduced.Then,the fabrication strategies and characteristics of varied constructions including 1D fiber,1D yarn,2D fabric,2D membrane,3D fibrous framework,and 3D fibrous gel are demonstrated.Afterward,the advanced functions of FHG during water harvesting,proton dissociation,ion separation,and charge accumulation processes are analyzed in detail.Moreover,the potential applications including power supply,energy storage,electrical sensor,and information expression are also discussed.Finally,some existing challenges are considered and prospects for future development are sincerely proposed.

Defect Engineering:Can it Mitigate Strong Coulomb Effect of Mg^(2+)in Cathode Materials for Rechargeable Magnesium Batteries?

Rechargeable magnesium batteries(RMBs)have been considered a promising“post lithium-ion battery”system to meet the rapidly increasing demand of the emerging electric vehicle and grid energy storage market.However,the sluggish diffusion kinetics of bivalent Mg^(2+)in the host material,related to the strong Coulomb effect between Mg^(2+)and host anion lattices,hinders their further development toward practical applications.Defect engineering,regarded as an effective strategy to break through the slow migration puzzle,has been validated in various cathode materials for RMBs.In this review,we first thoroughly understand the intrinsic mechanism of Mg^(2+)diffusion in cathode materials,from which the key factors affecting ion diffusion are further presented.Then,the positive effects of purposely introduced defects,including vacancy and doping,and the corresponding strategies for introducing various defects are discussed.The applications of defect engineering in cathode materials for RMBs with advanced electrochemical properties are also summarized.Finally,the existing challenges and future perspectives of defect engineering in cathode materials for the overall high-performance RMBs are described.

Influence of Al,Cu and Mn additions on diffusion behaviors in CoCrFeNi high-entropy alloys

The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of interdiffusion coefficients(HitDIC)software at 1273−1373 K.The results show that the addition of Al,Cu,and Mn to CoCrFeNi high-entropy alloys promotes the diffusion of Co,Cr,and Fe atoms.The comparison of tracer diffusion coefficients indicates that there is no sluggish diffusion in tracer diffusion on the thermodynamic temperature scale for the present Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys.The linear relationship between diffusion entropy and activation energy reveals that the diffusion process of atoms is unaffected by an increase in the number of components as long as the crystal structure remains unchanged.

EFFECTS OF TRANSVERSE OSCILLATIONS ON NATURAL CONVECTIVE FLOW INDUCED BY COMBINED THERMAL AND MASS DIFFUSIONS IN POROUS MEDIA

This paper studies the unsteady heat and mass natural convection in a highly porous medium bounded by an infinite vertical porous wall. The unsteady source of the problem arises from the transverse oscillations in suction velocity of fluids, The analytical results for the problem are obtained based on the method of small parameter, and show that the natural circulation in the porous medium is affected by this kind of oscillation.

Pyrimidine derivative as eco-friendly corrosion inhibitor for nickel−aluminum bronze in seawater

A pyrimidine derivative,6-phenyl-2-thiouracil(PT),was synthesized for developing a corrosion inhibitor(CI)applied in the protection of the nickel−aluminum bronze(NAB)in seawater.The anti-corrosion effect of PT was evaluated by the mass loss experiment,electrochemical tests and surface analysis.The results show that PT exhibits excellent inhibition performance and the maximum inhibition efficiency of PT reaches 99.6%.The interaction mechanism was investigated through X-ray photoelectron spectroscopy(XPS)and molecule dynamics simulation based on the density functional theory(DFT).The S-Cu,Al-N and Cu-N bonds are formed by the chemical interactions,leading to the adsorption of PT on the NAB surface.The diffusion of corrosive species is hindered considerably by the protective PT film with composition of(PT-Cu)_(ads)and(PT-Al)_(ads)on the PT/NAB interface.The degree of suppression is increased with the addition of more PT molecules.