CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS

The author discusses necessary and sufficient conditions of the complete con- vergence for sums of B-valued independent but not necessarily identically distributed r.v.'s in Banach space of type p, and obtains characterization of Banach space of type p in terms of the complete convergence. A series of classical results on iid real valued r.v.'s are ex- tended. As application authors give the analogous results for randomly indexed sums.

Complete Conyergence and Strong Laws of Large Numbers-for Weighted Sums of Sequences of Independent B-Valued Random Elements

In this paper, we obtain theorems of complete convergence and strong laws of large numbers for weighted sums of sequences of independent random elements in a Banach space of type p （1 ≤ p ≤ 2）. The results improve and extend the corresponding results on real random variables obtained by [1] and [2].

SOME DISCUSSION ON THE CONDITIONS OF COMPLETE CONVERGENCE FOR SUMS OF B-VALUED RANDOM ELEMENTS

In this paper, we discuss the conditions of complete convergence for partial sums and randomly indexed partial sums of independent but not necessarily identically distributed random elements in type p space, and obtain the characterization of Banach space of type p. Yu. H.’s some results(1989) on the case of real value are extended.

EQUIVALENCE OF COMPLETE CONVERGENCEAND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS

Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker.

L^r Convergence for B-valued Random Elements

The paper investigates Lp convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition that the Banach space is of Rademacher type p, 1 〈 p 〈 2. The paper also discusses Lτ convergence and Lτ bound for random elements without any geometric restriction condition on the Banach space.

Random vibration analysis of FGM plates subjected to moving load using a refined stochastic finite element method

The article introduces a finite element procedure using the bilinear quadrilateral element or four-node rectangular element(namely Q4 element) based on a refined first-order shear deformation theory(rFSDT) and Monte Carlo simulation(MCS), so-called refined stochastic finite element method to investigate the random vibration of functionally graded material(FGM) plates subjected to the moving load.The advantage of the proposed method is to use r-FSDT to improve the accuracy of classical FSDT, satisfy the stress-free condition at the plate boundaries, and combine with MCS to analyze the vibration of the FGM plate when the parameter inputs are random quantities following a normal distribution. The obtained results show that the distribution characteristics of the vibration response of the FGM plate depend on the standard deviation of the input parameters and the velocity of the moving load.Furthermore, the numerical results in this study are expected to contribute to improving the understanding of FGM plates subjected to moving loads with uncertain input parameters.

Detection and characterization of regulatory elements using probabilistic conditional random field and hidden Markov models

By altering the electrostatic charge of histones or providing binding sites to protein recognition molecules, Chromatin marks have been proposed to regulate gene expression, a property that has motivated researchers to link these marks to cis-regulatory elements. With the help of next generation sequencing technologies, we can now correlate one specific chromatin mark with regulatory elements (e.g. enhancers or promoters) and also build tools, such as hidden Markov models, to gain insight into mark combinations. However, hidden Markov models have limitation for their character of generative models and assume that a current observation depends only on a current hidden state in the chain. Here, we employed two graphical probabilistic models, namely the linear conditional random field model and multivariate hidden Markov model, to mark gene regions with different states based on recurrent and spatially coherent character of these eight marks. Both models revealed chromatin states that may correspond to enhancers and promoters, transcribed regions, transcriptional elongation, and low-signal regions. We also found that the linear conditional random field model was more effective than the hidden Markov model in recognizing regulatory elements, such as promoter-, enhancer-, and transcriptional elongation-associated regions, which gives us a better choice.

Rock-soil slope stability analysis by two-phase random media and finite elements

To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.

DISTRIBUTION OF RANDOM ELEMENTS SUBJECTED TO A FLEXIBLE BOUNDARY CONDITION

The probability distribution function of n random elements subjected to the flexible boundary condition is derived. The probability density is a descending curve and converges to a delta function as n tends to infinity. The distribution of the minimum value is discussed in context of ordered statistics.

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements

In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.

Numerical investigations on mechanical characteristics and failure mechanism of outwash deposits based on random meso-structures using discrete element method

Outwash deposit is a unique type of geological materials, and its features such as heterogeneity, discontinuity and nonlinearity determine the complexity of mechanical characteristics and failure mechanism. In this work, random meso-structure of outwash deposits was constructed by the technique of computer random simulation based on characteristics of its meso-structure in the statistical sense and some simplifications, and a series of large direct shear tests on numerical samples of outwash deposits with stone contents of 15%, 30%, 45% and 60% were conducted using the discrete element method to further investigate its mechanical characteristics and failure mechanism under external load. The results show that the deformation characteristics and shear strength of outwash deposits are to some extent improved with the increase of stone content, and the shear stress–shear displacement curves of outwash deposits show great differences at the post-peak stage due to the random spatial distribution and content of stones. From the mesoscopic view, normal directions of contacts between "soil" and "stone" particles undergo apparent deflection as the shear displacement continues during the shearing process, accompanying redistribution of the magnitude of contact forces during the shearing process. For outwash deposits, the shear zone formed after shear failure is an irregular stripe due to the movements of stones near the shear zone, and it expands gradually with the increase of stone content. In addition, there is an approximately linear relation between the mean increment of internal friction angle and the stone content lying between 30% and 60%, and a concave nonlinear relation between the mean increment of cohesion and stone content, which are in good agreement with the existing research results.

Neumann stochastic finite element method for calculating temperature field of frozen soil based on random field theory

To study the effect of uncertain factors on the temperature field of frozen soil, we propose a method to calculate the spatial average variance from just the point variance based on the local average theory of random fields. We model the heat transfer coefficient and specific heat capacity as spatially random fields instead of traditional random variables. An analysis for calculating the random temperature field of seasonal frozen soil is suggested by the Neumann stochastic finite element method, and here we provide the computational formulae of mathematical expectation, variance and variable coefficient. As shown in the calculation flow chart, the stochastic finite element calculation program for solving the random temperature field, as compiled by Matrix Laboratory （MATLAB） sottware, can directly output the statistical results of the temperature field of frozen soil. An example is presented to demonstrate the random effects from random field parameters, and the feasibility of the proposed approach is proven by compar- ing these results with the results derived when the random parameters are only modeled as random variables. The results show that the Neumann stochastic finite element method can efficiently solve the problem of random temperature fields of frozen soil based on random field theory, and it can reduce the variability of calculation results when the random parameters are modeled as spatial- ly random fields.

Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling

An optimized device structure for reducing the RESET current of phase-change random access memory （PCRAM） with blade-type like （BTL） phase change layer is proposed. The electrical thermal analysis of the BTL cell and the blade heater contactor structure by three-dimensional finite element modeling are compared with each other during RESET operation. The simulation results show that the programming region of the phase change layer in the BTL cell is much smaller, and thermal electrical distributions of the BTL cell are more concentrated on the TiN/GST interface. The results indicate that the BTL cell has the superiorities of increasing the heating efficiency, decreasing the power consumption and reducing the RESET current from 0.67mA to 0.32mA. Therefore, the BTL cell will be appropriate for high performance PCRAM device with lower power consumption and lower RESET current.

Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods

A long slope consisting of spatially random soils is a common geographical feature. This paper examined the necessity of three-dimensional(3 D) analysis when dealing with slope with full randomness in soil properties. Although 3 D random finite element analysis can well reflect the spatial variability of soil properties, it is often time-consuming for probabilistic stability analysis. For this reason, we also examined the least advantageous(or most pessimistic) cross-section of the studied slope. The concept of"most pessimistic" refers to the minimal cross-sectional average of undrained shear strength. The selection of the most pessimistic section is achievable by simulating the undrained shear strength as a 3 D random field. Random finite element analysis results suggest that two-dimensional(2 D) plane strain analysis based the most pessimistic cross-section generally provides a more conservative result than the corresponding full 3 D analysis. The level of conservativeness is around 15% on average. This result may have engineering implications for slope design where computationally tractable 2 D analyses based on the procedure proposed in this study could ensure conservative results.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD FOR EFFECTIVE NONLINEAR PROPERTIES OF COMPOSITE MATERIALS

Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of linear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an effective tool to investigate the nonlinear problems.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

An ultrasound-guided percutaneous electrical nerve stimulation regimen devised using finite element modeling promotes functional recovery after median nerve transection

Percutaneous electrical nerve stimulation of an injured nerve can promote and accelerate peripheral nerve regeneration and improve function.When performing acupuncture and moxibustion,locating the injured nerve using ultrasound before percutaneous nerve stimulation can help prevent further injury to an already injured nerve.However,stimulation parameters have not been standardized.In this study,we constructed a multi-layer human forearm model using finite element modeling.Taking current density and activated function as optimization indicators,the optimal percutaneous nerve stimulation parameters were established.The optimal parameters were parallel placement located 3 cm apart with the injury site at the midpoint between the needles.To validate the efficacy of this regimen,we performed a randomized controlled trial in 23 patients with median nerve transection who underwent neurorrhaphy.Patients who received conventional rehabilitation combined with percutaneous electrical nerve stimulation experienced greater improvement in sensory function,motor function,and grip strength than those who received conventional rehabilitation combined with transcutaneous electrical nerve stimulation.These findings suggest that the percutaneous electrical nerve stimulation regimen established in this study can improve global median nerve function in patients with median nerve transection.

深厚软土区桩柱式桥墩临界荷载简化计算方法

现有桩柱式桥墩临界荷载简化计算方法在大多数情况下计算误差较大,适用性有限.在利用软土区现场桩基屈曲实验结果标定的基础上,采用基于特征值屈曲分析的有限元方法对有典型桩柱式桥墩的临界荷载进行了计算并与现有简化计算方法结果进行了对比,指出了现有简化计算方法的适用范围,发现现有简化方法不适用于软土区桩柱式桥墩计算.在大量桩柱式桥墩有限元特征值屈曲分析数据的基础上,采用随机森林算法对计算结果进行分析,得到可以计算桩柱式桥墩计算长度的随机森林模型以及各影响参数重要性指数分析结果.最后以现常用简化公式为基本形式,纳入随机森林算法给出的重要参数,通过回归分析,提出了深厚软土区桩柱式桥墩临界荷载的简化计算方法.

血清微量元素与营养素对骨坏死因果效应的孟德尔随机化分析

背景:多项临床研究观察表明血清微量元素和营养素与骨坏死之间存在密切关系,但血清微量元素和营养素与骨坏死之间是否存在遗传因果效应尚不清楚。目的:通过孟德尔随机化方法探讨血清微量元素与营养素对骨坏死的因果效应。方法:暴露因素血清微量元素和维生素的单核苷酸多态性来自已发表的UK Biobank数据库以及全基因组关联研究公开数据库。结局事件骨坏死全基因组关联研究数据来自FinnGen Biobank数据库。采用孟德尔随机化方法探讨7种微量元素和3种营养素与骨坏死之间的因果关系。利用逆方差加权、MR-Egger和加权中位数等方法进行因果推断,计算F值统计量以确保工具变量的稳健性,采用Cochran’s Q统计法和留一法进行异质性检验,采用MR-Egger回归法、MR-PRESSO进行水平多效性检验。使用PhenoScanner数据库剔除具有水平多效性的单核苷酸多态性,以确保结果的可靠性。结果与结论:经过孟德尔随机化分析发现,血清硒、磷酸盐以及维生素C、维生素E与骨坏死之间存在明显的因果关系。血清硒、维生素C、维生素E对骨坏死有保护作用,磷酸盐摄入过多会增加骨坏死的风险。研究过程中没有发现异质性和水平多效性,孟德尔随机化统计效力(Power值>80%)显示上述4项结果可靠,研究结果对于开发有针对性的预防及治疗骨坏死的措施具有重要临床意义。

弹上电子产品加固防护可靠性分析研究

提出一种弹上电子产品球栅阵列封装元器件的新型加固防护工艺方法,对使用不同加固防护方法的电子产品进行了随机振动试验与有限元仿真分析,研究对球栅阵列封装(BGA)元器件焊点可靠性的影响;采用Steinberg疲劳寿命模型分析焊点的疲劳寿命。研究表明,纳米疏水剂、四角点胶配合3D打印壳体封装的组合新型弹上电子产品加固防护方法能有效提升产品可靠性。