Science China Mathematics

The Blaschke tensor and the Möbius form are two of the fundamental invariants in the Möbius geometry of submanifolds; an umbilic-free immersed submanifold in real space forms is called Blaschke parallel if its Blaschke tensor is parallel. We prove a theorem which, together with the known classification result for Möbius isotropic submanifolds, successfully establishes a complete classification of the Blaschke parallel submanifolds in S n with vanishing Möbius form. Before doing so, a broad class of new examples of general codimensions is explicitly constructed.

In this paper, we generalize the concept of Type II codes to arbitrary finite rings. We focus on Type II codes over finite chain rings and use the Chinese Remainder Theorem on these codes to study Type II codes over principal ideal rings.

In this paper, we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (abbr. elliptic SPDEs) driven by space white noises with homogeneous Dirichlet boundary conditions for two and three space dimensions. We also establish L 2 error estimates for the scheme. In particular, a numerical test for d = 2 is presented at the end of the article.

This paper reported the effect of the weak damage in the Al0.25Ga0.75As/GaAs epitaxial layer induced by 0.8 MeV Si ions implantation with ion dose from 1 × 1014 to 5 × 1015 cm-2. The Raman spectra measured on these samples showed that there were two kinds of phonon modes existing in the epitaxial Al0.25Ga0.75As films. The strains induced in the implanted layer and the corresponding lattice parameters were also evaluated as a function of the implanted dose. In addition, the Rutherford backscattering spectrometry/channeling (RBS/C) was also measured on these samples. These two measurement techniques all confirmed that the implantation only induced weak damage in the material.

The paper is devoted to the analysis of certain dynamical properties of a family of iterative Newton type methods used to find roots of non-linear equations. We present a procedure for constructing polynomials in such a way that superattracting cycles of any prescribed length occur when these iterative methods are applied. This paper completes the study begun in Amat, Bermúclez, Busquier, et al., (2009).

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.

Trong bài báo này, chúng tôi định nghĩa một hàm L Rankin-Selberg gắn liền với các biểu diễn tự động cusp của GL m ( $$ \mathbb{A} $$ E ) × GL m′ ( $$ \mathbb{A} $$ F ) trên các trường số đại số tuần hoàn E và F, những trường này giữ nguyên dưới tác động của nhóm Galois, bằng cách khai thác một kết quả đã được chứng minh bởi Arthur và Clozel, và chứng minh một định lý số nguyên tố cho hàm L này.

Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many biological and soft matter materials solvable in solvents. The appropriate treatment of long-range electrostatic interaction is essential for these charged systems, but remains a challenging problem for large-scale simulations. We have developed an efficient Barnes-Hut treecode algorithm for electrostatic evaluation in Monte Carlo simulations of Coulomb many-body systems. The algorithm is based on a divideand-conquer strategy and fast update of the octree data structure in each trial move through a local adjustment procedure. We test the accuracy of the tree algorithm, and use it to perform computer simulations of electric double layer near a spherical interface. It has been shown that the computational cost of the Monte Carlo method with treecode acceleration scales as log N in each move. For a typical system with ten thousand particles, by using the new algorithm, the speed has been improved by two orders of magnitude from the direct summation.

In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical results show that the methods of single-shot (common-shot) migration and synthesized-shot migration are of practical values and can be applied to field data processing of 3D prestack depth migration.