高体分SiC_p/Al复合材料螺纹性能的测试

从SiCp/Al复合材料性能分析着手,讨论了预置件法、焊接法和粘接法等在空间遥感器研制中常用的联接方法的优缺点,提出了在高体积分数（体分）SiCp/Al复合材料上直接加工螺纹,并加装钢丝螺套的方法来改善螺纹联接性能。对在某高体分SiCp/Al复合材料上加工的M4、M5螺纹进行了拉伸测试,结果表明：加装钢丝螺套前,复合材料螺纹有被拉脱现象;加装钢丝螺套后,M4螺纹、螺杆在3 000～4 000 N被拉断;M5螺纹、螺杆在8 000～9 000 N被拉断,测试后两种规格的螺纹状态良好,可以满足实际应用对该材料拉伸强度的要求,其已应用于工程项目中。     

Self-adjointness of unbounded tridiagonal operators and spectra of their finite truncations

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient conditions given in both cases improve and generalize previously known results. It turns out that, not only self-adjointness helps to study limit points of eigenvalues of truncated operators, but the analysis of such limit points is a key help to prove self-adjointness. Several examples show the advantages of these new results compared with previous ones. Besides, an application to the theory of continued fractions is pointed out.     

A parallel radix‐4 block cyclic reduction algorithm

A conventional block cyclic reduction algorithm operates by halving the size of the linear system at each reduction step, that is, the algorithm is a radix‐2 method. An algorithm analogous to the block cyclic reduction known as the radix‐q partial solution variant of the cyclic reduction (PSCR) method allows the use of higher radix numbers and is thus more suitable for parallel architectures as it requires fever reduction steps. This paper presents an alternative and more intuitive way of deriving a radix‐4 block cyclic reduction method for systems with a coefficient matrix of the form tridiag{ ? I,D, ? I}. This is performed by modifying an existing radix‐2 block cyclic reduction method. The resulting algorithm is then parallelized by using the partial fraction technique. The parallel variant is demonstrated to be less computationally expensive when compared to the radix‐2 block cyclic reduction method in the sense that the total number of emerging subproblems is reduced. The method is also shown to be numerically stable and equivalent to the radix‐4 PSCR method. The numerical results archived correspond to the theoretical expectations. Copyright © 2013 John Wiley & Sons, Ltd.     

参数化连分式拟合方法研究及应用

通过倒差商-连分式算法,提出了一种保端点非线性有理参数化拟合算法,通过选取中间点的参数化,利用连分式插值法,得到的拟合函数具有保端点性,规律性和灵活性.实例表明,算法减少了连分式插值迭代次数,避免插值连分式的不存在性,所得到拟合值具有更好的精度,大大提高了计算效率,拟合的误差更具有平稳性,逼近效果更好,并具有较好的预测等方面的应用.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

Effects of radiation crosslinking on structures and properties of SBS triblock copolymer

There is considerable interest in the effect of high energy radiation on triblock copolymer, SBS. Basheer and Dole have done some works about that(Basheer and Dole, 1982). In this paper, we study the effects of radiation crosslinking on the structure and mechanical properties of SBS, about which there have been no reports up to now. The following scientific problems are discussed: The variation of glass transition temperatures with dose; The effects of the ratio of B/S on the gel content; Mechanical properties of the irradiated samples.     

On the Problem of Describing Sequences of Best Trigonometric Rational Approximations

For a strictly decreasing sequence a_{n n=0} of nonnegative real numbers converging to zero, we construct a continuous 2-periodic function f such that R^T _n(f) = a_n, n=0,1,2,..., where R^T _n(f) are best approximations of the function f in uniform norm by trigonometric rational functions of degree at most n.     

A note on representations for the inverses of tridiagonal matrices

In this note, we propose an explicit representation with the nested sums for the entries of the inverses of general tridiagonal nonsingular matrices. Its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions, is considered. In addition, an analytical representation for the entries of the finite sections of the resolvent of Jacobi matrices, in terms of its related orthogonal polynomials, is observed.     

Characterizations of generalized Hermite and sieved ultraspherical polynomials

A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.