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1
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A class of extensions of Restricted (s,t)-Wythoff’s game

100%
Liu S., Li H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
281-295
EN
Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.
2
Content available remote

Dual-stage adaptive finite-time modified function projective multi-lag combined synchronization for multiple uncertain chaotic systems

100%
Li Q., Liu S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1035-1047
EN
In this paper, for multiple different chaotic systems with unknown bounded disturbances and fully unknown parameters, a more general synchronization method called modified function projective multi-lag combined synchronization is proposed. This new method covers almost all of the synchronization methods available. As an advantage of the new method, the drive system is a linear combination of multiple chaotic systems, which makes the signal hidden channels more abundant and the signal hidden methods more flexible. Based on the finite-time stability theory and the sliding mode variable structure control technique, a dual-stage adaptive variable structure control scheme is established to realize the finite-time synchronization and to tackle the parameters well. The detailed theoretical derivation and representative numerical simulation is put forward to demonstrate the correctness and effectiveness of the advanced scheme.
3
Content available remote

Corrigendum to: Dual-stage adaptive finite-time modified function projective multi-lag combined synchronization for multiple uncertain chaotic systems

100%
Li Q., Liu S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1256-1257
4
Content available remote

Outcome space range reduction method for global optimization of sum of affine ratios problem

81%
Jiao H., Liu S., Yin J., Zhao Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
736-746
EN
Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.
5
Content available remote

A new branch and bound algorithm for minimax ratios problems

81%
Zhao Y., Liu S., Jiao H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
840-851
EN
This study presents an efficient branch and bound algorithm for globally solving the minimax fractional programming problem (MFP). By introducing an auxiliary variable, an equivalent problem is firstly constructed and the convex relaxation programming problem is then established by utilizing convexity and concavity of functions in the problem. Other than usual branch and bound algorithm, an adapted partition skill and a practical reduction technique performed only in an unidimensional interval are incorporated into the algorithm scheme to significantly improve the computational performance. The global convergence is proved. Finally, some comparative experiments and a randomized numerical test are carried out to demonstrate the efficiency and robustness of the proposed algorithm.
6
Content available remote

Complete convergence for weighted sums of pairwise independent random variables

81%
Ge L., Liu S., Miao Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
467-476
EN
In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.
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