The grain boundary diffusion process(GBDP)has proven to be an effective method for enhancing the coercivity of sintered Nd-Fe-B magnets.However,the limited diffusion depth and thicker shell struc-ture have impeded the...The grain boundary diffusion process(GBDP)has proven to be an effective method for enhancing the coercivity of sintered Nd-Fe-B magnets.However,the limited diffusion depth and thicker shell struc-ture have impeded the further development of magnetic properties.Currently,the primary debates re-garding the mechanism of GBDP with Tb revolve around the dissolution-solidification mechanism and the atomic substitution mechanism.To clarify this mechanism,the microstructure evolution of sintered Nd-Fe-B magnets during the heating process of GBDP has been systematically studied by quenching at different tem peratures.In this study,it was found that the formation of TbFe_(2) phase is related to the dis-solution of _(2)Fe_(14)B grains during GBDP with Tb.The theory of mixing heat and phase separation further confirms that the Nd_(2)Fe_(14)B phase dissolves to form a mixed phase of Nd and TbFe_(2),which then solidifies into the(Nd,Tb)_(2)Fe_(14)B phase.Based on the discovery of the TbFe_(2) phase,the dissolution-solidification mechanism is considered the primary mechanism for GBDP.This is supported by the elemental content of the two typical core-shell structures observed.展开更多
this paper,we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process.As applications,the optimal uniform Berry-Esseen bound and optimal C...this paper,we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process.As applications,the optimal uniform Berry-Esseen bound and optimal Cramer-type moderate deviations of the Ornstein-Uhlenbeck process andα-Brownian bridge can be obtained.The main methods are the change of measure method and asymptotic analysis technique.展开更多
A sintered Nd-Y-Fe-B magnet was designed and manufactured by the multi-main-phase process.Unevenly distributed Y in the magnet decreases the adverse magnetic weakening effect of Y on the coercivity.Grain boundary diff...A sintered Nd-Y-Fe-B magnet was designed and manufactured by the multi-main-phase process.Unevenly distributed Y in the magnet decreases the adverse magnetic weakening effect of Y on the coercivity.Grain boundary diffusion process(GBDP)was conducted to further enhance the coercivity of the Nd-Y-Fe-B magnet.The coercivity increases significantly from 884 to 1741 kA/m after GBDP with Pr_(60)Tb_(10)Cu_(30)alloy.The mechanism of the coercivity enhancement is discussed based on the microstructure analysis.Micromagnetic simulation reveals that when the diffused Tb-rich shell thickness is lower than 12 nm the c-plane shell(perpendicular to the c-axis)is much more effective in enhancing the coercivity than the side plane shell(parallel to the c-axis).But when the Tb-rich shell thickness is above12 nm the side plane shell contributes more to the coercivity enhancement.The results in this work can help to design and manufacture Nd-Fe-B magnets with low cost and high magnetic properties.展开更多
Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion...Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion processes of Gelugpa can not only reveal its historical geographical development but also lay the foundation for anticipating its future development trend.However,existing studies on Gelugpa lack geographical perspective,making it difficult to explore the spatial characteristics.Furthermore,the prevailing macro-perspective overlooks spatiotemporal heterogeneity in diffusion processes.Therefore,taking monastery as the carrier,this study establishes a multi-level diffusion model to reconstruct the diffusion networks of Gelugpa monasteries,as well as a framework to explore the detailed features in the spatial diffusion processes of Gelugpa in Tibetan areas of China based on a geodatabase of Gelugpa monastery.The results show that the multi-level diffusion model has a considerable applicability in the reconstruction of the diffusion networks of Gelugpa monasteries.Gelugpa monasteries in the Three Tibetan Inhabited Areas present disparate spatial diffusion processes with diverse diffusion bases,speeds,stages,as well as diffusion regions and centers.A powerful single-center diffusion-centered Gandan Monastery was rapidly formed in U-Tsang.Kham experienced a slower and more varied spatial diffusion process with multiple diffusion systems far apart from each other.The spatial diffusion process of Amdo was the most complex,with the highest diffusion intensity.Amdo possessed the most influential diffusion centers,with different diffusion shapes and diffusion ranges crossing and overlapping with each other.Multiple natural and human factors may contribute to the formation of Gelugpa monasteries.This study contributes to the understanding of the geography of Gelugpa and provides reference to studies on religion diffusion.展开更多
Accurately identifying building distribution from remote sensing images with complex background information is challenging.The emergence of diffusion models has prompted the innovative idea of employing the reverse de...Accurately identifying building distribution from remote sensing images with complex background information is challenging.The emergence of diffusion models has prompted the innovative idea of employing the reverse denoising process to distill building distribution from these complex backgrounds.Building on this concept,we propose a novel framework,building extraction diffusion model(BEDiff),which meticulously refines the extraction of building footprints from remote sensing images in a stepwise fashion.Our approach begins with the design of booster guidance,a mechanism that extracts structural and semantic features from remote sensing images to serve as priors,thereby providing targeted guidance for the diffusion process.Additionally,we introduce a cross-feature fusion module(CFM)that bridges the semantic gap between different types of features,facilitating the integration of the attributes extracted by booster guidance into the diffusion process more effectively.Our proposed BEDiff marks the first application of diffusion models to the task of building extraction.Empirical evidence from extensive experiments on the Beijing building dataset demonstrates the superior performance of BEDiff,affirming its effectiveness and potential for enhancing the accuracy of building extraction in complex urban landscapes.展开更多
In this work,the effect of the Al addition amount in the TbAl coatings on the grain boundary diffusion proces s(GBDP)of Tb were systematically explored.Direct current magnetron sputtering(DCMS)method was utilized in c...In this work,the effect of the Al addition amount in the TbAl coatings on the grain boundary diffusion proces s(GBDP)of Tb were systematically explored.Direct current magnetron sputtering(DCMS)method was utilized in co-sputtering manner to synthesize the TbAl coatings with certain Tb consumption and various Al addition amount.Results show that the moderate Al addition amount significantly improves the wettability of grain boundary(GB)phases,thereby acquiring more continuous and uniform Tb-rich shells and GB phases between matrix phases,as well as deeper diffusion depth and denser microstructure.The largest increase amplitude of intrinsic coercivity(Hcj)is improved by 78.4%in TbAIdiffused magnet compared to the pure Tb-diffused magnet,while the remanence(Br)is expected to show an overall decreasing tendency accompanied with a slight increase in the decreasing process.However,when the Al addition amount is excessive,magnetic dilution effect is enhanced,and the Tbrich shells and GB phases between matrix phases become fuzzy and even invisible,which in turn deteriorates the magnetic properties of diffused magnets.展开更多
A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differen...A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved展开更多
Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample pat...Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.展开更多
The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This met...The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the diffusion process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with exponential rate for the Markov process. Under this condition, we define an estimator of the density based on kernel function and study his properties (almost sure convergence and asymptotic normality). After, using the estimator of the density, we construct the minimum Hellinger distance estimator of the parameters of the diffusion process and establish the almost sure convergence and the asymptotic normality of this estimator. To illustrate the properties of the estimator of the parameters, we apply the method to two examples of multidimensional diffusion processes.展开更多
In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and driv...In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.展开更多
We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts ...We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation.This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.展开更多
The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.
In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entro...In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry Emery condition.展开更多
The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chose...The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained.展开更多
The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the on...The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.展开更多
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov...A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.展开更多
High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher reso...High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement,there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model(DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement,but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.展开更多
In this study, a two-step heating process is introduced for transient liquid phase ( TLP) diffusion bonding fo r sound joints with T91 heat resistant steels. At first, a short-time higher temperature heating ...In this study, a two-step heating process is introduced for transient liquid phase ( TLP) diffusion bonding fo r sound joints with T91 heat resistant steels. At first, a short-time higher temperature heating step is addressed to melt the interlayer, followed by the second step to complete isothermal solidification at a low temperature. The most critical feature of our new method is producing a non-planar interface at the T9/ heat resistant steels joint. We propose a transitional liquid phase bonding of T91 heat resistant steels by this approach. Since joint microstructures have been studied, we tested the tensile strength to assess joint mechanical property. The result indicates that the solidified bond may contain a primary solid-solution, similar composition to the parent metal and free from precipitates. Joint tensile strength of the joint is not lower than parent materials. Joint bend's strengths are enhanced due to the higher metal-to-metal junction producing a non-planar bond lines. Nevertheless, the traditional transient liquid phase diffusion bonding produces planar ones. Bonding parameters of new process are 1 260 °C for 0. 5 min and 1 230 °C fo r 4 min.展开更多
The grain boundary diffusion process(GBDP)of Tb can improve the coercivity of sintered Nd-Fe-B magnets.In this study,the effect of AI on the diffusion of Tb in the GBDP was investigated.The content of diffused Tb-Al w...The grain boundary diffusion process(GBDP)of Tb can improve the coercivity of sintered Nd-Fe-B magnets.In this study,the effect of AI on the diffusion of Tb in the GBDP was investigated.The content of diffused Tb-Al was precisely controlled by adjusting the magnetron sputtering process.The Tb equivalent of Al was also studied.Results show that AI promotes the diffusion of Tb deeper into the magnet,reducing the thickness of the shell in the core-shell structure.This study is helpful for further developing the process,reducing the consumption of heavy rare earth elements(Tb),and improving the coercivity of sintered Nd-Fe-B magnets.展开更多
Grain boundary diffusion process(GBDP)was first proposed for sintered Nd-Fe-B magnets to achieve the high utilization efficiency of heavy rare earth elements.Recent success of fabricating high performance nanocomposit...Grain boundary diffusion process(GBDP)was first proposed for sintered Nd-Fe-B magnets to achieve the high utilization efficiency of heavy rare earth elements.Recent success of fabricating high performance nanocomposite magnets by GBDP indicates that this method also exerts huge applicable potential on hot-deformed Nd-Fe-B magnets.In this review,the development and magnetic property enhancement mechanisms of different diffusion methods proposed on hot-deformed magnets were thoroughly elucidated.Moreover,the improve room for further property enhancement and the accompanying problems of GBDP on hot-deformed magnets are also discussed in this article.展开更多
基金supported by the National Key Research and Development Program of China(2022YFB3505503)the National Natural Science Foundation of China(52201230)+2 种基金the Key R&D Program of Shandong Province(2022CXGC020307)the China Postdoctoral Science Foundation(2022M71204)the Beijing NOVA Program(Z211100002121092).
文摘The grain boundary diffusion process(GBDP)has proven to be an effective method for enhancing the coercivity of sintered Nd-Fe-B magnets.However,the limited diffusion depth and thicker shell struc-ture have impeded the further development of magnetic properties.Currently,the primary debates re-garding the mechanism of GBDP with Tb revolve around the dissolution-solidification mechanism and the atomic substitution mechanism.To clarify this mechanism,the microstructure evolution of sintered Nd-Fe-B magnets during the heating process of GBDP has been systematically studied by quenching at different tem peratures.In this study,it was found that the formation of TbFe_(2) phase is related to the dis-solution of _(2)Fe_(14)B grains during GBDP with Tb.The theory of mixing heat and phase separation further confirms that the Nd_(2)Fe_(14)B phase dissolves to form a mixed phase of Nd and TbFe_(2),which then solidifies into the(Nd,Tb)_(2)Fe_(14)B phase.Based on the discovery of the TbFe_(2) phase,the dissolution-solidification mechanism is considered the primary mechanism for GBDP.This is supported by the elemental content of the two typical core-shell structures observed.
基金supported by the NSFC(12101358,12471095)the Natural Science Foundation of Hubei Province in China(2024AFC020)the Fundamental Research Funds for the Central Universities,South-Central MinZu University(CZY23010)。
文摘this paper,we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process.As applications,the optimal uniform Berry-Esseen bound and optimal Cramer-type moderate deviations of the Ornstein-Uhlenbeck process andα-Brownian bridge can be obtained.The main methods are the change of measure method and asymptotic analysis technique.
基金Project supported by the National Natural Science Foundation of China(51901087)China Postdoctoral Science Foundation(2021M701504)。
文摘A sintered Nd-Y-Fe-B magnet was designed and manufactured by the multi-main-phase process.Unevenly distributed Y in the magnet decreases the adverse magnetic weakening effect of Y on the coercivity.Grain boundary diffusion process(GBDP)was conducted to further enhance the coercivity of the Nd-Y-Fe-B magnet.The coercivity increases significantly from 884 to 1741 kA/m after GBDP with Pr_(60)Tb_(10)Cu_(30)alloy.The mechanism of the coercivity enhancement is discussed based on the microstructure analysis.Micromagnetic simulation reveals that when the diffused Tb-rich shell thickness is lower than 12 nm the c-plane shell(perpendicular to the c-axis)is much more effective in enhancing the coercivity than the side plane shell(parallel to the c-axis).But when the Tb-rich shell thickness is above12 nm the side plane shell contributes more to the coercivity enhancement.The results in this work can help to design and manufacture Nd-Fe-B magnets with low cost and high magnetic properties.
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(Grant No.18YJAZH140).
文摘Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion processes of Gelugpa can not only reveal its historical geographical development but also lay the foundation for anticipating its future development trend.However,existing studies on Gelugpa lack geographical perspective,making it difficult to explore the spatial characteristics.Furthermore,the prevailing macro-perspective overlooks spatiotemporal heterogeneity in diffusion processes.Therefore,taking monastery as the carrier,this study establishes a multi-level diffusion model to reconstruct the diffusion networks of Gelugpa monasteries,as well as a framework to explore the detailed features in the spatial diffusion processes of Gelugpa in Tibetan areas of China based on a geodatabase of Gelugpa monastery.The results show that the multi-level diffusion model has a considerable applicability in the reconstruction of the diffusion networks of Gelugpa monasteries.Gelugpa monasteries in the Three Tibetan Inhabited Areas present disparate spatial diffusion processes with diverse diffusion bases,speeds,stages,as well as diffusion regions and centers.A powerful single-center diffusion-centered Gandan Monastery was rapidly formed in U-Tsang.Kham experienced a slower and more varied spatial diffusion process with multiple diffusion systems far apart from each other.The spatial diffusion process of Amdo was the most complex,with the highest diffusion intensity.Amdo possessed the most influential diffusion centers,with different diffusion shapes and diffusion ranges crossing and overlapping with each other.Multiple natural and human factors may contribute to the formation of Gelugpa monasteries.This study contributes to the understanding of the geography of Gelugpa and provides reference to studies on religion diffusion.
基金supported by the National Natural Science Foundation of China(Nos.61906168,62202429 and 62272267)the Zhejiang Provincial Natural Science Foundation of China(No.LY23F020023)the Construction of Hubei Provincial Key Laboratory for Intelligent Visual Monitoring of Hydropower Projects(No.2022SDSJ01)。
文摘Accurately identifying building distribution from remote sensing images with complex background information is challenging.The emergence of diffusion models has prompted the innovative idea of employing the reverse denoising process to distill building distribution from these complex backgrounds.Building on this concept,we propose a novel framework,building extraction diffusion model(BEDiff),which meticulously refines the extraction of building footprints from remote sensing images in a stepwise fashion.Our approach begins with the design of booster guidance,a mechanism that extracts structural and semantic features from remote sensing images to serve as priors,thereby providing targeted guidance for the diffusion process.Additionally,we introduce a cross-feature fusion module(CFM)that bridges the semantic gap between different types of features,facilitating the integration of the attributes extracted by booster guidance into the diffusion process more effectively.Our proposed BEDiff marks the first application of diffusion models to the task of building extraction.Empirical evidence from extensive experiments on the Beijing building dataset demonstrates the superior performance of BEDiff,affirming its effectiveness and potential for enhancing the accuracy of building extraction in complex urban landscapes.
基金Project supported by National Key Research and Development Program of China(2021YFB3500100)National Natural Science Foundation of China(52301068)。
文摘In this work,the effect of the Al addition amount in the TbAl coatings on the grain boundary diffusion proces s(GBDP)of Tb were systematically explored.Direct current magnetron sputtering(DCMS)method was utilized in co-sputtering manner to synthesize the TbAl coatings with certain Tb consumption and various Al addition amount.Results show that the moderate Al addition amount significantly improves the wettability of grain boundary(GB)phases,thereby acquiring more continuous and uniform Tb-rich shells and GB phases between matrix phases,as well as deeper diffusion depth and denser microstructure.The largest increase amplitude of intrinsic coercivity(Hcj)is improved by 78.4%in TbAIdiffused magnet compared to the pure Tb-diffused magnet,while the remanence(Br)is expected to show an overall decreasing tendency accompanied with a slight increase in the decreasing process.However,when the Al addition amount is excessive,magnetic dilution effect is enhanced,and the Tbrich shells and GB phases between matrix phases become fuzzy and even invisible,which in turn deteriorates the magnetic properties of diffused magnets.
文摘A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved
基金supported by National Natural Science Foundation of China(11371321)Zhejiang Provincial Natural Science Foundation of China(Y6100663)the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statis-tics of Zhejiang Gongshang University)
文摘Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.
文摘The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the diffusion process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with exponential rate for the Markov process. Under this condition, we define an estimator of the density based on kernel function and study his properties (almost sure convergence and asymptotic normality). After, using the estimator of the density, we construct the minimum Hellinger distance estimator of the parameters of the diffusion process and establish the almost sure convergence and the asymptotic normality of this estimator. To illustrate the properties of the estimator of the parameters, we apply the method to two examples of multidimensional diffusion processes.
文摘In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.
基金Supported in part by the Kavli Institute for Theoretical Physics Chinathe National Science Foundation of China under Grant No.11174025Z.L.acknowledges support from the National Science Foundation(U.S.A.)under Grant No.DMR-1206971
文摘We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation.This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.
基金Supported by the National Natural Science Foundation of China(201130486) and a Grant from the Ministry of Education of China
文摘The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.
基金Supported by the National Natural Science Foundation of China (11001208)the Fundamental Research Funds for the Central Universities
文摘In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry Emery condition.
基金National Natural Science Foundations of China (No. 11071076,No. 11126124)
文摘The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained.
文摘The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.
文摘A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.
基金supported by the National Natural Science Foundation of China (NSFC): Grant number 42274147。
文摘High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement,there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model(DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement,but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.
基金supported by the Natural Science Foundation of Henan Province(Grant No.152107000047)
文摘In this study, a two-step heating process is introduced for transient liquid phase ( TLP) diffusion bonding fo r sound joints with T91 heat resistant steels. At first, a short-time higher temperature heating step is addressed to melt the interlayer, followed by the second step to complete isothermal solidification at a low temperature. The most critical feature of our new method is producing a non-planar interface at the T9/ heat resistant steels joint. We propose a transitional liquid phase bonding of T91 heat resistant steels by this approach. Since joint microstructures have been studied, we tested the tensile strength to assess joint mechanical property. The result indicates that the solidified bond may contain a primary solid-solution, similar composition to the parent metal and free from precipitates. Joint tensile strength of the joint is not lower than parent materials. Joint bend's strengths are enhanced due to the higher metal-to-metal junction producing a non-planar bond lines. Nevertheless, the traditional transient liquid phase diffusion bonding produces planar ones. Bonding parameters of new process are 1 260 °C for 0. 5 min and 1 230 °C fo r 4 min.
基金supported by the National Key R&D Program of China(2021YFB3502902)Ningbo Major Special Projects of Science and Technology Innovation 2025 Plan(2020Z045)Key Research and Development Program of Zhejiang Province(2020C05013)。
文摘The grain boundary diffusion process(GBDP)of Tb can improve the coercivity of sintered Nd-Fe-B magnets.In this study,the effect of AI on the diffusion of Tb in the GBDP was investigated.The content of diffused Tb-Al was precisely controlled by adjusting the magnetron sputtering process.The Tb equivalent of Al was also studied.Results show that AI promotes the diffusion of Tb deeper into the magnet,reducing the thickness of the shell in the core-shell structure.This study is helpful for further developing the process,reducing the consumption of heavy rare earth elements(Tb),and improving the coercivity of sintered Nd-Fe-B magnets.
基金Project supported by the Pioneer and Leading Goose R&D Program of Zhejiang(2020C01190)the Science and Technology Innovation 2025Major Project of Ningbo(2020Z064)+1 种基金the Zhejiang Province Postdoctoral Science Foundation(ZJ2021080)the Inner Mongolia Major Technology Project(2021ZD0035)。
文摘Grain boundary diffusion process(GBDP)was first proposed for sintered Nd-Fe-B magnets to achieve the high utilization efficiency of heavy rare earth elements.Recent success of fabricating high performance nanocomposite magnets by GBDP indicates that this method also exerts huge applicable potential on hot-deformed Nd-Fe-B magnets.In this review,the development and magnetic property enhancement mechanisms of different diffusion methods proposed on hot-deformed magnets were thoroughly elucidated.Moreover,the improve room for further property enhancement and the accompanying problems of GBDP on hot-deformed magnets are also discussed in this article.
