Numerical prediction of the incremental melting and solidification process

A mathematical formulation is applied to represent the phenomena in theincremental melting and solidification process (IMSP), and the temperature and electromagneticfields and the depth of steel liquid phase are calculated by a finite difference technique using thecontrol volume method. The result shows that the predicted values are in good agreement with theobservations. In accordance with the calculated values for different kinds of materials anddifferent size of molds, the technological parameter of the IMS process such as the power supply andthe descending speed rate can be determined.

DUAL RANDOM MODEL OF INCREASING ANNUITY

The dual random models about the life insurance and social pension insurance have received considerable attention in the recent articles on actuarial theory and applications. This paper discusses a general kind of increasing annuity based on its force of interest accumulation function as a general random process. The dual random model of the present value of the benefits of the increasing annuity has been set, and their moments have been calculated under certain conditions.

Markov process functionals in finance and insurance

The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.

A NOTE ON SAMPLE PATH PROPERTIES OF l^p-VALUED GAUSSIAN PROCESSES

The a.s. sample path properties for l p valued Gaussian processes with stationary increments under some more general conditions are established.

Incremental QR-based tensor-train decomposition for industrial big data

Industrial big data was usually multi-source, heterogeneous, and deeply intertwined. It had a wide range of data sources, high data dimensions, and strong data correlation. In order to effectively analyze and process streaming industrial big data generated by edge computing, it was very important to provide an effective real-time incremental data method. However, in the process of incremental processing, industrial big data incremental computing faced the challenges of dimensional disaster, repeated calculations, and the explosion of intermediate results. Therefore, in order to solve the above problems effectively, a QR-based tensor-train(TT) decomposition(TTD) method and a QR-based incremental TTD(QRITTD) method were proposed. This algorithm combined the incremental QR-based decomposition algorithm with an approximate singular value decomposition(SVD) algorithm and had good scalability. In addition, the computational complexity, space complexity, and approximation error analysis were analyzed in detail. The effectiveness of the three algorithms of QRITTD, non-incremental TTD(NITTD), and TT rank-1(TTr1) SVD(TTr1 SVD)were verified by comparison. Experimental results show that the SVD QRITTD method has better performance under the premise of ensuring the same tensor size.

Comparison of two reliability models for performance degradation analysis

In order to investigate the general reliability assessment methods based on performance degradation data,two commonly used stochastic process approaches,bilinear process method and random-effect model were studied.Analyzing procedure and effectiveness of these two methodologies were studied and compared.Meanwhile,the two approaches were illustrated through practical applications.The residual plots and the 10th percentile curves of the two methods were presented to demonstrate the comparative results.The randomeffect model yielded more volatile residuals and a lower and unsafe 10th percentile curve.Consequently the bilinear process model can be concluded to derive more reasonable results due to its one-stage estimation property.

A LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENTS

By using the Ito's calculus, a law of the iterated logarithm is established for the processes with independent increments (PⅡ). Let X = {Xt, t ≥ 0} be a PII with Ext=0,V(t)=Ext2<∞and limt∞V(t)=∞ If one of the following conditions is satisfied,(2) Suppose the Levy's measure of X may be written as v(dt,ds) = Ft(dx) dV(t) and there is a σ-finite measure G such tnat ,