Experimental Study on the Pore Structure Fractals and Seepage Characteristics of a Coal Sample Around a Borehole in Coal Seam Water Infusion

In this study, a two-dimensional fully coupled computational model is developed for simulation of proppant settlement in hydro-fractures with the use of the extended finite element framework. The porous domain is governed by the well-known \((\mathbf{u}-p)\) formulation, which consists of the momentum balance equation of the bulk, in conjunction with the momentum balance and continuity equations of the pore fluid. The hydro-fracture inflow is modeled as a 1D flow on the basis of the Darcy law, in which fracture permeability is incorporated by means of the cubic law. Contact constraints are elaborated to eliminate the overlap of fracture edges and the leak-off flow. Proppant settlement is conducted on the basis of Stokes’ law for particle terminal velocity, in which the effects of fracture walls, concentration, viscosity and bridging are incorporated into the model. A fixed-point algorithm is introduced to achieve the optimum combination for the proppant injection. Using the extended finite element method, the strong discontinuity in the displacement field due to crack body, as well as the weak discontinuity in the pressure field due to leakage, is included in the model with the use of the Heaviside and modified level set enrichment functions, respectively. The robustness and versatility of the proposed numerical algorithm in determining the optimum proppant injection is examined through several numerical simulations.     

Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty

The flight control problem of a flexible air-breathing hypersonic vehicle is presented in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, where aerodynamic uncertainty and the strong couplings between the engine and flight dynamics are included, is derived to reduce the complexity of controller design. The flexible dynamics are viewed as perturbations of the model. They are not taken into consideration at the level of control design, the influence of which is evaluated through simulation. The control-oriented model is decomposed into velocity subsystem and altitude subsystem, which are controlled separately. Then robust adaptive controller is developed for the velocity subsystem, while the controller which combines dynamic surface control and radial basis function neural network is designed for the altitude subsystem. The unknown nonlinear function is approximated by the radial basis function neural network. Minimal-learning parameter technique is utilized to estimate the maximum norm of ideal weight vectors instead of their elements to reduce the computational burden. To handle input constraints, additional systems are constructed to analyze their impact, and the states of the additional systems are employed at the level of control design and stability analysis. Besides, “explosion of terms” problem in the traditional backstepping control is circumvented using a first-order filter at each step. By means of Lyapunov stability theory, it is proved theoretically that the designed control law can assure that tracking error converges to an arbitrarily small neighborhood around zero. Simulations are performed to demonstrate the effectiveness of the presented control scheme in coping with input constraint and aerodynamic uncertainty.     

The Explicit Computations of the Bergman Kernels on Generalized Hua Domains

The Bergman kernel function plays an important role in several complex variables. Thereexists the Bergman kernel function on any bounded domain in Cn. But we can get the Bergmankernel functions in explicit formulas for a few types of domains only, for instance, the boundedhomogeneous domains and the egg domains in some cases.Yin Weiping defined four types of generalized Hua domainsGHE1(N1,… Nr; m, n,p1…,pr, k)where wj = (wi1,…, wjNj ),j = 1, 2,…, r. RI(m, n), RⅡ(p), RⅢ(q), and RⅣ…     

Convergence rates in the law of logarithm of random elements

1. IntroductionLet {Xu, n 2 1} be a sequence of r.v.IS in the same probability space and put Sa =nZ Xi, n 2 1; L(x) = mad (1, logx).i=1Since the definition of complete convergence is illtroduced by Hsu and Robbins[6], therehave been many authors who devote themselves to the study of the complete convergence forsums of i.i.d. real-valued r.v.'s, and obtain a series of elegys results, see [3,7]. Meanwhile,the convergence rates in the law of logarithm of i.i.d. real-vained r.v.'s have also be…     

Empirical tail conditional allocation and its consistency under minimal assumptions

Annals of the Institute of Statistical Mathematics - Under minimal assumptions, we prove that an empirical estimator of the tail conditional allocation (TCA), also known as the marginal expected...     

邻域并和[a,b]-因子

设ａ＜ｂ是整数,Ｇ＝（Ｖ（Ｇ）,Ｅ（Ｇ））是一个图．Ｇ的一个支撑子图Ｆ称为Ｇ的一个［ａ,ｂ］－因子,若对任意的υ∈ＥＶ（Ｇ）,有ａ≤ｄ_Ｆ（υ）≤ｂ．本文得到了下列结果：设１≤ａ≤ｂ是整数,Ｇ是一个阶为ｎ的图,最小度δ（Ｇ）≥ａ且＞（ａ＋ｂ）（２ａ＋２ｂ－３）如果对于Ｇ的任意两个不相邻的顶点ｕ,υ有Ｎ_Ｇ（ｕ）ＵＮ_Ｇ（υ）≥ａｎ,则Ｇ有一个［ａ,ｂ］－因子．     

Determination of Fatty Acid Methyl Esters in Biodiesel Produced from Yellow Horn Oil by LC

A simple and accurate HPLC method with refractive index detection was developed to determine the main fatty acid methyl esters in biodiesel produced from yellow horn oil. Methyl linoleate, methyl linolenate, methyl arachidate, methyl stearate, methyl palmitate and methyl oleate were separated on a HIQ SIL C18W column using methanol as mobile phase. The method has good repeatability and precision, the intraday and interday RSD for both retention time and peak area was less than 3.2%. The LOD (S/N = 3) and LOQ (S/N = 9) were less than 0.004 and 0.015 mg mL⁻¹, respectively.