ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

ERRATUM TO： LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2） ：394-408）

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

Parameter Estimation for Complex Ornstein-Uhlenbeck Processes

The drift parameter estimation problem of the complex Ornstein-Uhlenbeck process driven by a complexα-stable motion is considered.Based on discrete observations,an estimator of the unknown drift parameter is constructed by using the least squares method.Moreover,the strong consistency and the asymptotic distribution of the least squares estimator are derived under some assumptions.

LEAST SQUARES TYPE ESTIMATION FOR DISCRETELY OBSERVED NON-ERGODIC GAUSSIAN ORNSTEIN-UHLENBECK PROCESSES

In this article, we consider the drift parameter estimation problem for the nonergodic Ornstein-Uhlenbeck process defined as dXt = OXtdt + dGt, i > 0 with an unknown parameter θ> 0, where G is a Gaussian process. We assume that the process {xt,t≥ 0} is observed at discrete time instants t1=△n,…, tn = n△n, and we construct two least squares type estimators θn and θn for θ on the basis of the discrete observations ,{xti,i= 1,…, n} as →∞. Then, we provide sufficient conditions, based on properties of G, which ensure that θn and θn are strongly consistent and the sequences √n△n(θn-θ) and √n△n(θn-θ) are tight. Our approach offers an elementary proof of [11], which studied the case when G is a fractional Brownian motion with Hurst parameter H∈(1/2, 1). As such, our results extend the recent findings by [11] to the case of general Hurst parameter H∈(0,1). We also apply our approach to study subfractional Ornstein-Uhlenbeck and bifractional Ornstein-Uhlenbeck processes.

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

The purpose of this article is to obtain the quasi-stationary distributions of the δ（δ 〈 2）-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin （2001）. It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a （4 - δ）- dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.

Asymptotic Properties of Estimators for Ornstein-Uhlenbeck Processes with Small Symmetricα-Stable Motions

The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

Multimodal Data-Driven Reinforcement Learning for Operational Decision-Making in Industrial Processes

Dear Editor, This letter proposes a multimodal data-driven reinforcement learning-based method for operational decision-making in industrial processes. Due to the frequent fluctuations of feedstock properties and operating conditions in the industrial processes, existing data-driven methods cannot effectively adjust the operational variables. In addition, multimodal data such as images, audio.

Correlation of Microbiological Stability with Redox Processes in White Wines

In this paper, the authors analyzed the correlation between the microbiological stability of white wines and the content of sulfur dioxide, which influences the main redox processes that take place in the technological stages of the wine. The consecutive, parallel and spontaneous development of several redox processes and their impact on the quality, microbiological and crystalline stability of white wines were examined. The reduction of additive and subtractive technological interventions, of the amounts of adjuvants (sulphurous anhydride) is essential for the production of organic wines.

THE EXTREMES OF DEPENDENT CHI-PROCESSES ATTRACTED BY THE BROWN-RESNICK PROCESS

Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normalized pointwise maxima of those processes are attracted by the Brown-Resnick process.

Modeling and analysis of air combustion and steam regeneration in methanol to olefins processes

Light olefins is the incredibly important materials in chemical industry.Methanol to olefins(MTO),which provides a non-oil route for light olefins production,received considerable attention in the past decades.However,the catalyst deactivation is an inevitable feature in MTO processes,and regeneration,therefore,is one of the key steps in industrial MTO processes.Traditionally the MTO catalyst is regenerated by removing the deposited coke via air combustion,which unavoidably transforms coke into carbon dioxide and reduces the carbon utilization efficiency.Recent study shows that the coke species over MTO catalyst can be regenerated via steam,which can promote the light olefins yield as the deactivated coke species can be essentially transferred to industrially useful synthesis gas,is a promising pathway for further MTO processes development.In this work,we modelled and analyzed these two MTO regeneration methods in terms of carbon utilization efficiency and technology economics.As shown,the steam regeneration could achieve a carbon utilization efficiency of 84.31%,compared to 74.74%for air combustion regeneration.The MTO processes using steam regeneration can essentially achieve the near-zero carbon emission.In addition,light olefins production of the MTO processes using steam regeneration is 12.81%higher than that using air combustion regeneration.In this regard,steam regeneration could be considered as a potential yet promising regeneration method for further MTO processes,showing not only great environmental benefits but also competitive economic performance.

Multi-Perspective Data Fusion Framework Based on Hierarchical BERT: Provide Visual Predictions of Business Processes

Predictive Business Process Monitoring(PBPM)is a significant research area in Business Process Management(BPM)aimed at accurately forecasting future behavioral events.At present,deep learning methods are widely cited in PBPM research,but no method has been effective in fusing data information into the control flow for multi-perspective process prediction.Therefore,this paper proposes a process prediction method based on the hierarchical BERT and multi-perspective data fusion.Firstly,the first layer BERT network learns the correlations between different category attribute data.Then,the attribute data is integrated into a weighted event-level feature vector and input into the second layer BERT network to learn the impact and priority relationship of each event on future predicted events.Next,the multi-head attention mechanism within the framework is visualized for analysis,helping to understand the decision-making logic of the framework and providing visual predictions.Finally,experimental results show that the predictive accuracy of the framework surpasses the current state-of-the-art research methods and significantly enhances the predictive performance of BPM.

Local Torrential Rainfall Event within a Mei-Yu Season Mesoscale Convective System:Importance of Back-Building Processes

An extreme rainfall event occurred over Hangzhou,China,during the afternoon hours on 24 June 2013.This event occurred under suitable synoptic conditions and the maximum 4-h cumulative rainfall amount was over 150 mm.This rainfall event had two major rainbands.One was caused by a quasi-stationary convective line,and the other by a backbuilding convective line related to the interaction of the outflow boundary from the first rainband and an existing low-level mesoscale convergence line associated with a mei-yu frontal system.The rainfall event lasted 4 h,while the back-building process occurred in 2 h when the extreme rainfall center formed.So far,few studies have examined the back-building processes in the mei-yu season that are caused by the interaction of a mesoscale convergence line and a convective cold pool.The two rainbands are successfully reproduced by the Weather Research and Forecasting(WRF)model with fourlevel,two-way interactive nesting.In the model,new cells repeatedly occur at the west side of older cells,and the backbuilding process occurs in an environment with large CAPE,a low LFC,and plenty of water vapor.Outflows from older cells enhance the low-level convergence that forces new cells.High precipitation efficiency of the back-building training cells leads to accumulated precipitation of over 150 mm.Sensitivity experiments without evaporation of rainwater show that the convective cold pool plays an important role in the organization of the back-building process in the current extreme precipitation case.

Comparison of a Spectral Bin and Two Multi-Moment Bulk Microphysics Schemes for Supercell Simulation:Investigation into Key Processes Responsible for Hydrometeor Distributions and Precipitation

There are more uncertainties with ice hydrometeor representations and related processes than liquid hydrometeors within microphysics parameterization(MP)schemes because of their complicated geometries and physical properties.Idealized supercell simulations are produced using the WRF model coupled with“full”Hebrew University spectral bin MP(HU-SBM),and NSSL and Thompson bulk MP(BMP)schemes.HU-SBM downdrafts are typically weaker than those of the NSSL and Thompson simulations,accompanied by less rain evaporation.HU-SBM produces more cloud ice(plates),graupel,and hail than the BMPs,yet precipitates less at the surface.The limiting mass bins(and subsequently,particle size)of rimed ice in HU-SBM and slower rimed ice fall speeds lead to smaller melting-level net rimed ice fluxes than those of the BMPs.Aggregation from plates in HU-SBM,together with snow–graupel collisions,leads to a greater snow contribution to rain than those of the BMPs.Replacing HU-SBM’s fall speeds using the formulations of the BMPs after aggregating the discrete bin values to mass mixing ratios and total number concentrations increases net rain and rimed ice fluxes.Still,they are smaller in magnitude than bulk rain,NSSL hail,and Thompson graupel net fluxes near the surface.Conversely,the melting-layer net rimed ice fluxes are reduced when the fall speeds for the NSSL and Thompson simulations are calculated using HU-SBM fall speed formulations after discretizing the bulk particle size distributions(PSDs)into spectral bins.The results highlight precipitation sensitivity to storm dynamics,fall speed,hydrometeor evolution governed by process rates,and MP PSD design.

Solid-state impedance spectroscopy studies of dielectric properties and relaxation processes in Na_(2)O–V_(2)O_(5)–Nb_(2)O_(5)–P_(2)O_(5) glass

Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary mixed glass former(MGF)system 35Na_(2)O–10V_(2)O_(5)–(55-x)P_(2)O_(5)–xNb_(2)O_(5)(x=0–40,mol%).The dielectric parameters,including the dielectric strength and dielectric loss,are determined from the frequency and temperature-dependent complex permittivity data,revealing a significant dependence on the Nb2O5 content.The transition from a predominantly phosphate glass network(x<10,region I)to a mixed niobate–phosphate glass net-work(10≤x≤20,region II)leads to an increase in the dielectric parameters,which correlates with the observed trend in the direct-cur-rent(DC)conductivity.In the predominantly niobate network(x≥25,region III),the highly polarizable nature of Nb5+ions leads to a fur-ther increase in the dielectric permittivity and dielectric strength.This is particularly evident in Nb-40 glass-ceramic,which contains Na_(13)Nb_(35)O_(94) crystalline phase with a tungsten bronze structure and exhibits the highest dielectric permittivity of 61.81 and the lowest loss factor of 0.032 at 303 K and 10 kHz.The relaxation studies,analyzed through modulus formalism and complex impedance data,show that DC conductivity and relaxation processes are governed by the same mechanism,attributed to ionic conductivity.In contrast to glasses with a single peak in frequency dependence of imaginary part of electrical modulus,M″(ω),Nb-40 glass-ceramic exhibits two distinct contributions with similar relaxation times.The high-frequency peak indicates bulk ionic conductivity,while the additional low-fre-quency peak is associated with the grain boundary effect,confirmed by the electrical equivalent circuit(EEC)modelling.The scaling characteristics of permittivity and conductivity spectra,along with the electrical modulus,validate time-temperature superposition and demonstrate a strong correlation with composition and modification of the glass structure upon Nb_(2)O_(5) incorporation.

Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Levy processes with periodic mean

VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asymptotic distribution.Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Levy process,they can be regarded both as a Levy generalization of fractional Brownian motion and a fractional generalization of Levy process.

On the Key Dynamical Processes Supporting the 21.7 Zhengzhou Record-breaking Hourly Rainfall in China

An extremely heavy rainfall event occurred in Zhengzhou,China,on 20 July 2021 and produced an hourly rainfall rate of 201.9 mm,which broke the station record for China's Mainland.Based on radar observations and a convection-permitting simulation using the WRF-ARW model,this paper investigates the multiscale processes,especially those at the mesoscale,that support the extreme observed hourly rainfall.Results show that the extreme rainfall occurred in an environment characteristic of warm-sector heavy rainfall,with abundant warm moist air transported from the ocean by an abnormally northward-displaced western Pacific subtropical high and Typhoon In-Fa(2021).However,rather than through back building and echo training of convective cells often found in warm-sector heavy rainfall events,this extreme hourly rainfall event was caused by a single,quasi-stationary storm in Zhengzhou.Scale separation analysis reveals that the extreme-rainproducing storm was supported and maintained by the dynamic lifting of low-level converging flows from the north,south,and east of the storm.The low-level northerly flow originated from a mesoscale barrier jet on the eastern slope of the Taihang Mountain due to terrain blocking of large-scale easterly flows,which reached an overall balance with the southerly winds in association with a low-level meso-β-scale vortex located to the west of Zhengzhou.The large-scale easterly inflows that fed the deep convection via transport of thermodynamically unstable air into the storm prevented the eastward propagation of the weak,shallow cold pool.As a result,the convective storm was nearly stationary over Zhengzhou,resulting in record-breaking hourly precipitation.

Effect of cooking processes on tilapia aroma and potential umami perception

Tilapia is a freshwater fish group with a sustainable prospect but suffers off-notes appearing during cooking processes.To promote pleasant odorants by thermal cooking processes,tilapia fillets were cooked in different ways(roasting,microwave-heating,boiling and steaming).Their aroma profiles were analysed with special focus on off-notes and umami-enhancing odorants by principal component analysis,and correlated with the heating time,colour,moisture and water activity by partial least squares regression analysis.Results showed that the“green”and“earthy”off-notes were highly correlated with the boiling process(excess of water,short heating time),while most of the umami-enhancing odorants had a high association with the roasting process(low water content,long heating time,better Maillard reaction).This study indicated that roasting is the most adapted cooking process promoting Maillard-derived aromas,umami-enhancing aromas and meanwhile,reducing off-notes.This research helps in understanding the off-note generation in tilapia and promoting desirable umami-enhancing odorants.

Finite Element Simulation of Radial Tire Building and Shaping Processes Using an Elasto-Viscoplastic Model

The comprehensive tire building and shaping processes are investigated through the finite element method(FEM)in this article.The mechanical properties of the uncured rubber from different tire components are investigated through cyclic loading-unloading experiments under different strain rates.Based on the experiments,an elastoviscoplastic constitutive model is adopted to describe themechanical behaviors of the uncured rubber.The distinct mechanical properties,including the stress level,hysteresis and residual strain,of the uncured rubber can all be well characterized.The whole tire building process(including component winding,rubber bladder inflation,component stitching and carcass band folding-back)and the shaping process are simulated using this constitutive model.The simulated green tire profile is in good agreement with the actual profile obtained through 3D scanning.The deformation and stress of the rubber components and the cord reinforcements during production can be obtained fromthe FE simulation,which is helpful for judging the rationality of the tire construction design.Finally,the influence of the parameter“drum width”is investigated,and the simulated result is found to be consistent with the experimental observations,which verifies the effectiveness of the simulation.The established simulation strategy provides some guiding significance for the improvement of tire design parameters and the elimination of tire production defects.