On the convergence for PNQD sequences with general moment conditions

Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].

Numerical simulation of groundwater under complex karst conditions and the prediction of roadway gushing in a coal mine:a case study in the Guang'an Longtan Reservoir in Sichuan Province, China

Numerical simulation of groundwater in karst areas has long been restricted by the difficulty of generalizing the hydrogeological conditions of reservoirs and of determining the relevant parameters due to the anisotropy and discontinuity of the karst water-bearing media in these areas. In this study, we used the Guang'an Longtan Coal mine in Sichuan as an example, and generalized the complex hydrogeological conditions in the reservoir area. A finite element numerical flow model was used to simulate current and future scenarios of roadway gushing at the bottom of the coal mine at pile number 1 + 700 m. The results show that the roadway section corresponding to valleys has a gushing quantity of 4323.8–4551.25 m^3/d before impoundment. Modeled water inflow after impoundment increased to 1.6 times the water inflow before impoundment, which threatens the impoundment as well as the roadway's normal operation. Therefore, roadway processing measures are needed to guarantee the safety of the impoundment and of the mining operation.

A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions

In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.

The Inner Structure of the Intrinsic Electron and the Origin of Self-Mass

A brief review and analysis of two historical models of the electron, the charged spinning sphere and Goudsmit and Uhlenbeck’s concept, is presented. It is shown that the enormous potential of classical electrodynamics has been underutilized in particle physics. Such observation leads to discovery of a principal component in the electron inner structure—the charged c-ring. The intrinsic (fundamental) electron model based on the charged c-ring successfully explains the ontology of the charge fractionation in quantum chromodynamics and the formation of Cooper pairs in superconductivity. The c-ring properties are explained on the basis of the General Compton Conditions as defined. Properties of the charged c-ring include the explanation of the boundary conditions, electro-magnetostatic field configuration, self-mass, spin, magnetic moment, and the gyromagnetic ratio. The self-mass of the intrinsic electron is 100% electro-magnetostatic and it is shown how to compute its value. The classical-quantum divide no longer exists. Relation between the intrinsic electron and the electron is fundamentally defined. The electron is the composite fermion consisting of the intrinsic electron and the neutrino. The ontology of the anomaly in the electron magnetic moment is demonstrated—it is due to the addition of the neutrino magnetic moment to the overall electron magnetic moment. The intrinsic electron replaces the W? boson in particle physics, resulting in a fundamental implication for the Standard Model.

Numerical Modelling of Standing Waves with Three-Dimensional Non-Linear Wave Propagation Model

Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.

Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.

A semi-analytical method for forced vibration analysis of cracked laminated composite beam with general boundary condition

In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solution is solved using the Jacobi-Ritz method.The boundary conditions(BCs)at both ends of the CLCB are generalized by the application of artificial elastic springs,the CLCB is separated into two elements along the crack,the flexibility coefficient of fracture theory is used to model the essential continuous condition of the connective interface.All the allowable displacement functions used to analyze dynamic characteristics of CLCB are expressed by classical Jacobi orthogonal polynomials in a more general form.The accuracy of the proposed method is verified through the compare with results of the finite element method(software ABAQUS is used in this paper).On this basis,the parametric study for dynamic analysis characteristics of CLCB is performed to provide reference datum for engineers.

Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

This paper presents a unified approach for predicting the free and forced (steady-state and transient) vibration analyses of annular sector and annular plates with various combinations of classical and non-classical boundary supports. In spite of the types of the boundary restraints and the shapes of the plates, the admissible displacement function is described as a modified trigonometric series expansion, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. Mathematically, the unification of various boundary value problems for annular sector and annular plates is physically realized by setting a set of coupling springs to ensure appropriate continuity conditions along the radial edges of concern. Numerous examples are presented for the free vibration analyses of annular sector and annular plates with different boundary restraints. With regard to the forced vibration analysis, annular sector and annular plates with different external excitations are examined. The accuracy, convergence and numerical robustness of the current approach are extensively demonstrated and verified through numerical examples which involve plates with various shapes and boundary conditions. © 2017, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.

NONLINEAR SEMIGROUP APPROACH TOTRANSPORT EQUATIONS WITH DELAYED NEUTRONS

This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.

Detecting Lags in Nonlinear Models Using General Mutual Information

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.

Multidimensional BSDEs with Weak Monotonicity and General Growth Generators

This paper aims at solving a multidimensional backward stochastic differential equation （BSDE） whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonieity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonieity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results.