Temperature evolution associated with dynamic phase transformation in shape-memory TiNi alloys

In this paper, temperature evolution in shape-memory TiNi alloys was in situ measured in the process of phase transition under shock loading tests. It was shown that the temperature increased during loading, while unloading, it would keep the maximum value constant or decreased, depending on the strain rate. The corresponding dynamic response indicated that the hardening property is related to phase transition strain and the transformation path has remarkable strain-rate effect. The reason for this phenomenon is essentially due to the temperature dependence of the phase transformation stress. Moreover, the evolution of temperature was consistent with the change of stress, suggesting that this dynamic phase transition deformation is uniform. The theoretical calculation shows that the mechanism of temperature evolution results from the release of latent heat and the hysteresis dissipated energy. The results of this investigation provide insight into intriguing strain-rate-dependent phenomena intrinsic of TiNi alloys.     

Sorting Using Complete Subintervals and the Maximum Number of Runs in a Randomly Evolving Sequence

We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a string of 0’s, and then evolves by changing each 0 to 1, with the n changes done in random order. What is the maximal number of runs of 1’s? We give asymptotic results for the distribution and mean. It turns out that, as in many problems involving a maximum, the maximum is asymptotically normal, with fluctuations of order n ^1/2, and to the first order well approximated by the number of runs at the instance when the expectation is maximized, in this case when half the elements have changed to 1; there is also a second order term of order n ^1/3. We also treat some variations, including priority queues and sock-sorting. The proofs use methods originally developed for random graphs.     

Isometric Extension Problem Between Strictly Convex Two-dimensional Normed Spaces

In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case.     

New Exact Travelling Wave Solutions to Kundu Equation

Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.     

非线性发展方程非局部初值问题解的存在性

本文讨论非线性方程的非局部初值问题，利用半群理论、单调算子理论以及Banach不动点定理，分别得到两个问题的温和解和弱解的存在唯一性定理．     

Approximation of Solutions of Nonlinear Equations of Monotone and Hammerstein Type

Let X be a real uniformly smooth and uniformly convex Banach space with dual X ^*. Let A: X → X ^* be a bounded uniformly submonotone map. It is proved that a Mann-type approximation sequence converges strongly to Jx ^* where x ^* ∈ N(A). Furthermore, as an application of this result an iterative sequence which converges strongly to a solution of the Hammerstein equation u+KFu = 0 is constructed where, F:X→X^* and K:X^*→X are monotone-type mappings. No invertibility assumption is imposed on K. Moreover, neither K nor F need be compact. Finally, our method is of independent interest.     

Optimal coordination of directional over-current relays using informative differential evolution algorithm

Growing interconnection in distribution system creates new problem for protection engineers. Particularly the design of overcurrent relay coordination in such system is an independent area of research. With the availability of new artificial based optimization algorithm relay coordination research gain a new momentum. Well established artificial based optimization algorithm such as genetic and particle swam optimization are successfully applied for such applications. This paper discusses the application of informative differential evolution algorithm with self adaptive re-clustering technique for selection of TDS and PSM for optimal coordination of directional overcurrent relays. Both continuous as well as discrete version of informative differential evolution algorithm are used for optimization of relay setting. Proper combination of backup relays for each primary relay are identified by using LINKNET graph theory approach. Coordination of directional overcurrent is developed for 9 bus and IEEE 30 bus distribution systems. The aim of problem is to minimize the total operating time of primary relays and eliminate the miscoordination among the primary and backup relay pairs. Discrete types of settings for electromechanical types of relay are also discussed in this paper. Moreover, the relay coordination problem is modified for providing optimal coordination time interval between 0.2 and 0.8 s among all primary and backup relays pairs. The results are compared with hybrid of genetic algorithm – nonlinear programming and sequential quadratic programming. Digsilient power factory software is used for verification of result.