岩石爆破破碎时间及微差起爆延时优化

利用分形理论分析岩石爆破的破碎时间，提出了岩石爆破破碎时间的计算方法和微差起爆延时优化的一种途径。     

基于水声信道传播时延排序的分层空时信号检测

基于分层空时编码的多输入多输出技术是一种极具潜力的高速水声通信技术, 但要实现这种潜力需要复杂的空时信号处理方法, 以抵消来自水声信道的多径干扰和异步到达干扰, 以及叠加在接收端的各层信号之间的干扰. 对低复杂度的空时信号处理方案进行了研究, 提出了一种基于子信道传播时延排序的有序连续干扰抵消信号检测算法, 利用子信道间的传播时延差, 实现可使差错概率最小的最佳检测排序; 给出了利用信道估计, 以极低的计算量确定排序的方法, 从而可以大幅降低信号检测的计算复杂度. 采用低复杂度的单载波频域均衡来抵消水声信道中的码间干扰和异步到达干扰. 仿真结果表明, 基于时延排序的信号处理算法可以获得检测性能的改善, 而且性能增益在高数据率时更加显著. 研究结果表明, 采用有效的信号处理方法可使水声信道中造成信号检测干扰的传播时延成为改善系统性能的有利因素.     

Smooth extension of functions on a certain class of non-separable Banach spaces

Let us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C¹-smooth function g with Lip(g)?CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of c₀(Γ), for some set Γ, such that the coordinate functions of the homeomorphism are C¹-smooth (Hájek and Johanis, 2010 [10]). Then, we prove that for every closed subspace Y⊂X and every C¹-smooth (Lipschitz) function f:Y→R, there is a C¹-smooth (Lipschitz, respectively) extension of f to X. We also study C¹-smooth extensions of real-valued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of non-separable Banach spaces satisfying the above property.     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.     

Pedogogical perspectives on the method of Wilmer III and Costa for solving second-order differential equations

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive approximations. We show how applying the method of approximations naturally leads to the constructed approximation of Wilmer III and Costa. The new link is important because it enables us to respond to several challenges posed by Wilmer III and Costa. This includes addressing issues raised therein with convergence of their recursively constructed sequence of functions, and responding to their call regarding more mathematical rigour when relaxing the polynomial condition on the coefficients in the differential equation. Furthermore, the new link is pedagogically significant because it also opens up new pedagogical points of view. For example, the results in this paper provide potentially alternate, but overlapping, perspectives that are suitable for, and jointly inform, the learning and teaching of solution methods to differential equations. The value of this is supported by the presumption of Tisdell that teaching multiple ways to solve the same problem has academic and social value.     

多集分裂等式问题的逐次松弛投影算法

多集分裂等式问题是分裂可行性问题的拓展问题,在图像重建、语言处理、地震探测等实际问题中具有广泛的应用。为了解决这个问题,提出了逐次松弛投影算法,设计了变化的步长,使其充分利用当前迭代点的信息且不需要算子范数的计算,证明了算法的弱收敛性。数值算例验证了算法在迭代次数与运行时间等方面的优越性。     

Influence of Successive Washing on Porous Structure of Pseudoboehmite

1. Introduction As we know, the structure and performance of γ-Al2O3 are determined by the pore structure of its precursor, namely, the pseudoboehmite. Some factors influencing the pore structure of the pseudoboehmite have been reported, and among them the washing process is one of the important factors because: (1) the adsorbing on the surface of the pseudoboehmite acts as a stabilizing factor for amorphous particles [1], and washing can remove the Cl- anions, thus enhanc- ing the transform…     

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.

     

On the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids

Abstract We analyze mathematical models governing planar flow of chemical reaction from unburnt gasesto burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction aresignificant. These models can be then formulated as the Navier-Stokes equations for exothermically reactingcompressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, andlarge-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations withconstant adiabatic exponent γ and specific heat C_v. Our approach for the existence and regularity is to combinethe difference approximation techniques with the energy methods, total variation estimates, and weak conver-gence argumeots to deal with large jump discontinuities; and for large-time behavior is an a posteriori argumentdirectly from the weak form of the equations. The approach and ideas we develop here can be applied to solvinga more complicated model where γ     

Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay

A distributed control problem for the parabolic operator withan infinite number of variables and time delay is considered.The performance index has an integral form. Constraints on controlsare imposed. To obtain optimality conditions for the Neumannproblem, the generalization of the Dubovitskii–Milyutintheorem given by Walczak in WALCZAK, S. Folia Mathematics, 1,187–196 and WALCZAK, S. J. Optim. Theory Appl., 42, 561–582was applied.