素理想(p)在Q(μ~1~(l/m))中的分解

设Q为有理数域,令φ为由奇素数p生成的有理数域Q的p-adic赋值,R为与其相对应的赋值环,(p)为R的极大理想(素理想).本文用扩张平移的方法讨论了lm)(μ∈R)中的分解问题,并完全解决了该问题.素理想(p)在Q的lm次根扩张Q(μ1     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅲ):时间二阶精度的全离散格式

In this paper, a fully discrete format of nonlinear Galerkin mixed element method with two-step discretization of time for the non stationary conduction-convection problems is presented. The existence and the convergence of the fully discrete mixed element solution are shown. On the basis of [9] and [10], we have proved that the schemes have second-order convergence accuracy for the time discretization.     

关于“复合型积分因子的存在定理及应用”的一个注记

对“复合型积分因子的存在定理及应用”中给出的微分方程M(x,y)dx+N(x,y)dy=0复合型积分因子的定义进行剖析,得到了一般性复合型积分因子的定义及其存在的充要条件和计算公式.     

TC4钛合金自然破片的引燃机理分析

对两种热处理条件不同的ＴＣ４钛合金圆筒在内部爆轰加载下的自然破片形成过程作了研究，并对破片的宏观断裂特征和细观断裂机理进行了分析。研究结果表明，一些引燃战斗部采用钛合金壳体的根本原因在于利用壳体破裂时形成的高温绝热剪切带和钛元素本身在高温下的剧烈氧化性。     

应力约束下薄板结构的拓扑优化

研究了应力约束下薄板结构的拓扑优化问题，分析了极限应力的影响，建立了拓扑优化的数学模型，讨论了若干优化过程中的技术问题，最后，进行了实例计算。     

纯相稀土硫化物红色发光材料的高温微波合成及其光谱性质

采用工业频率为2.45 GHz的高温微波法制备了纯基质相的CaS∶Eu2+红色发光材料,激发波段为410~580 nm,发射峰值波长为654 nm。在微波输入功率为1.0~1.1 k W的条件下,可以获得纯基质相CaS∶Eu2+发光材料;在1.2~1.3 k W功率范围,获得的样品中含有Ca O杂质相,且颗粒团聚严重。其中,1.1 k W制备的CaS∶Eu2+样品相纯度最高,发光性能最优。微波功率的变化本质上揭示了固体颗粒的介电损耗因子及其加热特性的变化,体系涉及的非平衡反应机制促使了纯基质相的形成,并影响材料晶相结构、粒径、形貌和发光性能。结果显示,高温微波制备技术通过控制输入功率及其物料的介电损耗性质,能够获得纯基质相并且颗粒小、团聚少的荧光粉。     

Superconvergence analysis of finite element method for Poisson–Nernst–Planck equations

This article concerns with the superconvergence analysis of bilinear finite element method (FEM) for nonlinear Poisson–Nernst–Planck (PNP) equations. By employing high accuracy integral identities together with mean value technique, the superclose estimates in H¹‐norm are derived for the semi‐discrete and the backward Euler fully‐discrete schemes, which improve the suboptimal error estimate in L²‐norm in the previous literature. Furthermore, the global superconvergence results in H¹‐norm are obtained through interpolation postprocessing approach. Finally, a numerical example is provided to confirm the theoretical analysis.     

A posteriori error analysis of an augmented fully mixed formulation for the nonisothermal Oldroyd–Stokes problem

In this article, we consider an augmented fully mixed variational formulation that has been recently proposed for the nonisothermal Oldroyd–Stokes problem, and develop an a posteriori error analysis for the 2‐D and 3‐D versions of the associated mixed finite element scheme. More precisely, we derive two reliable and efficient residual‐based a posteriori error estimators for this problem on arbitrary (convex or nonconvex) polygonal and polyhedral regions. The reliability of the proposed estimators draws mainly upon the uniform ellipticity of the bilinear forms of the continuous formulation, suitable assumptions on the domain and the data, stable Helmholtz decompositions, and the local approximation properties of the Clément and Raviart–Thomas operators. On the other hand, inverse inequalities, the localization technique based on bubble functions, and known results from previous works are the main tools yielding the efficiency estimate. Finally, several numerical results confirming the properties of the a posteriori error estimators and illustrating the performance of the associated adaptive algorithms are reported.     

A Lie symmetry analysis and explicit solutions of the two‐dimensional ∞‐Polylaplacian

In this work, we consider the Lie point symmetry analysis of a strongly nonlinear partial differential equation of third order, the ∞‐Polylaplacian, in two spatial dimensions. This equation is a higher order generalization of the ∞‐Laplacian, also known as Aronsson's equation, and arises as the analog of the Euler–Lagrange equations of a second‐order variational principle in L^∞. We obtain its full symmetry group, one‐dimensional Lie subalgebras and the corresponding symmetry reductions to ordinary differential equations. Finally, we use the Lie symmetries to construct new invariant ∞‐Polyharmonic functions.     

A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators

A priori estimates for finite-difference approximations for the first and second-order derivatives are obtained for solutions of parabolic equations described in the title.