摘要：首先应用反连续极限法讨论一类具有饱和非线性项的离散薛定谔方程孤立子的存在性。通过计算扩散系数 ε 的精确范围，给出离散孤立子存在的充分条件，并证明该孤立子是按指数衰减的。结合正则扰动定理以及指标理论我们获得了反连续极限法下孤立子谱稳定性与不稳定性结果。最后，利用指数展开法以及数值模拟我们展示了多种不同类型的孤立子。并给出了稳定性问题特征值的近似估计。
2、题目：Strong edge-colorings of graphs
摘要：A strong edge-coloring of a graph G is a proper edge-coloring of G such that the edges of any path of length 3 use three different colors. The strong chromatic index of a graph G is the smallest integer k such that G can be strongly edge-colored with k colors. In this paper, we obtain the strong chromatic index of some classes of graphs.
3、题目：Block-based characterization of protease specificity from substrate sequence profile
摘要：The mechanism of action of proteases has been widely studied based on substrate specificity. Prior research has been focused on the amino acids at a single amino acid site, but rarely on combinations of amino acids around the cleavage bond. We propose a novel block-based approach to reveal the potential combinations of amino acids which may regulate the action of proteases. After quantitative analysis, we discovered a number of prominent blocks, each of which consists of successive amino acids near a cleavage bond, intuitively characterizing the site cooperation of the substrate sequences.
4、题目: On constructions and applications of deterministic encoding functions into elliptic curves
摘要：We summarize deterministic encodings from finite fields into elliptic curves. Based on these encodings, various hash functions from bit-strings into elliptic curves are constructed, which are indifferentiable from random oracles. Such hash functions can be applied in plenty of cryptographic protocols. For instance, some identity-based cryptosystems can utilize hash functions to generate public-keys efficiently. On the other side, by constructing injective maps from large subset of a finite field to elliptic curves, one can present points on curves as strings with distribution indistinguishable from uniform distribution of bit strings, hence censorship circumventions can be achieved when transmitting public-keys. For some hyperelliptic curves, deterministic encodings can also be constructed.
5、题目：Robust H-infty control of space craft rendezvous on elliptical orbit
摘要: We consider the robust H-infty control problem of spacecraft rendezvous on elliptical orbit. Based on Lyapunov theory, a sufficient condition for the existence of the robust H-infty controller is given in terms of the periodic Riccati differential equation(RDE).Then, a stabilizable controller design method based on a fast multi-shot algorithm is proposed. With the controller obtained,the spacecraft rendezvous mission can be accomplished. An illustrative example is provided to show the effectiveness of the proposed control design method.