Prediction of corrosion rate for friction stir processed WE43 alloy by combining PSO-based virtual sample generation and machine learning

The corrosion rate is a crucial factor that impacts the longevity of materials in different applications.After undergoing friction stir processing(FSP),the refined grain structure leads to a notable decrease in corrosion rate.However,a better understanding of the correlation between the FSP process parameters and the corrosion rate is still lacking.The current study used machine learning to establish the relationship between the corrosion rate and FSP process parameters(rotational speed,traverse speed,and shoulder diameter)for WE43 alloy.The Taguchi L27 design of experiments was used for the experimental analysis.In addition,synthetic data was generated using particle swarm optimization for virtual sample generation(VSG).The application of VSG has led to an increase in the prediction accuracy of machine learning models.A sensitivity analysis was performed using Shapley Additive Explanations to determine the key factors affecting the corrosion rate.The shoulder diameter had a significant impact in comparison to the traverse speed.A graphical user interface(GUI)has been created to predict the corrosion rate using the identified factors.This study focuses on the WE43 alloy,but its findings can also be used to predict the corrosion rate of other magnesium alloys.

On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.

Hyper-exponential jump-diffusion model under the barrier dividend strategy

In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.

Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate

In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.

THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.

Optimal Control for Insurers with a Jump-diffusion Risk Process

In this paper, the optimal XL-reinsurance of an insurer with jump-diffusion risk process is studied. With the assumptions that the risk process is a compound Possion process perturbed by a standard Brownian motion and the reinsurance premium is calculated according to the variance principle, the implicit expression of the priority and corresponding value function when the utility function is exponential are obtained. At last, the value function is argued, the properties of the priority about parameters are discussed and numerical results of the priority for various claim-size distributions are shown.

On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

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.

Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals

The classical Poisson risk model in ruin theory assumed that the interarrival times between two successive claims are mutually independent, and the claim sizes and claim intervals are also mutually independent. In this paper, we modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent. Using the properties of conditional expectation, we establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability.

Monitoring damage evolution of steel strand using acoustic emission technique and rate process theory

Utilizing the acoustic emission(AE) technique, an experimental investigation into the damage evolution for steel strand under axial tension was described. The damage evolution model for steel stand relating the damage evolution to acoustic emission parameters was proposed by incorporating the AE rate process theory. The AE monitoring results indicate that damages occur in both elastic and plastic phases of steel strand. In elastic phase, AE signals are mainly sent out from the micro damage due to the surface friction among the wires of steel strand, while in plastic phase, AE signals emitted from the plastic deformation of wires. In addition, the AE cumulative parameters curves closely resemble the loading curve. The AE cumulative parameters curves can well describe the damage evolution process including the damage occurrence and damage development for steel strands. It is concluded that the AE technique is an effective and useful nondestructive technique for evaluating the damage characteristics of steel strand.

Effect of unequal injection rates and different hopping rates on asymmetric exclusion processes with junction

In this paper, the effects of unequal injection rates and different hopping rates on the asymmetric simple exclusion process （ASEP） with a 2-input 1-output junction are studied by using a simple mean-field approach and extensive computer simulations. The steady-state particle currents, the density profiles, and the phase diagrams are obtained. It is shown that with unequal injection rates and different hopping rates, the phase diagram structure is qualitatively changed. The theoretical calculations are in good agreement with Monte Carlo simulations.

ENTROPY PRODUCTION RATE OF THE MINIMAL DIFFUSION PROCESS

The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.

VISUAL OBSERBATION OF HCFC141b GAS HYDRATE FORMATION/DECOMPOSITION PROCESS OUTSIDE OF A TUBE

In order to design a kind of heat exchanger suitable to the indirect-touched gas hydrate cool storage vessel, a visual observation of HCFC141b gas hydrate formation/decomposition process was presented through a self-designed small-scale visualization apparatus of gas hydrate cool storage. Based on the shooted photos and recorded temperatures, the formation/decomposition process of HCFC141b are described, some characteristics are concluded, and some suggestions of designing heat exchanger are indicated according to the specific characteristics of HCFC141b gas hydrate formation/decomposition process.

CENTRAL LIMIT THEOREM AND CONVERGENCE RATES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT

We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.

Analysis of the factors affecting the fuel rate in the COREX process and improvement measures

Increasing production capacity and operating rate, reducing fuel rates and costs of hot metal （HM） are the urgent tasks for the COREX process. In this study ,the various factors on the fuel consumption of COREX are researched from the theoretical analysis based on the calculations of material balances and heat balances. Combined with the production performances and practices of COREX-2000 （ Saldanha, India） and COREX-3000 （ Baosteel ）, the technical measures of reducing the fuel rate are analyzed and the way forward of technical innovation is addressed and discussed with the standpoint of the COREX process improvement.

Local inhomogeneity in totally asymmetric simple exclusion processes with different hopping rates

Local inhomogeneity in totally asymmetric simple exclusion processes （TASEPs） with different hopping rates was studied. Many biological and chemical phenomena can be described by these non-equilibrium processes. A simple approximate theory and extensive Monte Carlo computer simulations were used to calculate the steady-state phase diagrams and bulk densities. It is found that the phase diagram for local inhomogeneity in TASEP with different hopping rates p is qualitatively similar to homogeneous models. Interestingly, there is a saturation point pair （a＊, fl＊） for the system, which is decided by parameters p and q. There are three stationary phases in the system, when parameter p is fixed （i.e., p=0.8）, with the increase of the parameter q, the region of LD/LD and HD/HD phase increases and the HD/LD is the only phase which the region shrinks. The analytical results are in good agreement with simulations.

Effect of bubble morphology and behavior on power consumption in non-Newtonian fluids’aeration process

Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.

A Decomposition of the Ruin Probability for Risk Process with Vasicek Interest Rate

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.

Study on the Retention Rate of Green Tea Catechins Components and Tea Polyphenol by Different Processing Technology

The aim of this research was to explore the effect of fixation,rolling,and drying processing technology on the retention rate of green tea catechins components and tea polyphenol.Different fixation processes(rotary drumfiring,microwave,steam-blasting),rolling process(weight of rolling,gently press rolling and traditional rolling),drying process(stove drying,roasting dehydration,baked fried drying) were adopted.The effect of different tea processing technology on the retention rate of catechins component and tea polyphenol was analyzed.It showed that the microwave fixation process,gently press rolling process,baked fried dry process were beneficial to keep high levels of EGCG,C,EGC,EC,ECG.

Models of the Short Interest Rate in Discrete Processes

The modeling of the term structure of interest rates is one of primary topics for researches in financial economics. Here we consider models of the short interest rate in discrete processes. Our methodology of analysis follows the framework of discrete stochastic calculus.

The Effect of Hydraulic Retention Times and Loading Rates on the Removal of Pollutants from Fish Processing Wastewater by Anaerobic Process

Anaerobic treatment model treats fish processing wastewater to be necessary for a small and medium factory that is very popular in Vietnam and other countries.Several techniques have been proposed.However,they are quite expensive and hard to operate,especially in remote areas.In this study,the hydraulic retention times(HRT)including 3,5,and 7 hours with a various organic loading rate of 1.5 to 6.5 kg COD/m3/day were investigated.Biomass concentration as mix-liquor volatile suspended solid(MLVSS)in the model is at 6,000 to 9,000 mg/L.On the basis of the result the optimal HRT with a 4.0 kg COD/m3/day organic loading rate was 8 hours which BOD5,COD removal efficiency were 92.18,87.36 percent respectively.By the end of the optimal hydraulic retention times,the total methane gas volume as a by-product was collected with 2.6 liters.