In this paper, by msss_mappings, the relations between metric spaces and spaces with σ _locally countable cs_networks or spaces with σ _locally countable weak bases are established. These are some answers to A...In this paper, by msss_mappings, the relations between metric spaces and spaces with σ _locally countable cs_networks or spaces with σ _locally countable weak bases are established. These are some answers to Alexandroff’s problems.展开更多
A method of controllable internal perturbation inside the chaotic map is proposed to solve the problem in chaotic systems caused by finite precision.A chaotic system can produce large amounts of initial-sensitive,non-...A method of controllable internal perturbation inside the chaotic map is proposed to solve the problem in chaotic systems caused by finite precision.A chaotic system can produce large amounts of initial-sensitive,non-cyclical pseudo-random sequences.However,the finite precision brings short period and odd points which obstruct application of chaos theory seriously in digital communication systems.Perturbation in chaotic systems is a possible efficient method for solving finite precision problems,but former researches are limited in uniform distribution maps.The proposed internal perturbation can work on both uniform and non-uniform distribution chaotic maps like Chebyshev map and Logistic map.By simulations,results show that the proposed internal perturbation extends sequence periods and eliminates the odd points,so as to improve chaotic performances of perturbed chaotic sequences.展开更多
A new algorithm for a novel hash function, based on chaotic tent map with changeable parameter, is proposed and analyzed. The one dimensional and piecewise tent map with changeable parameters decided by the position i...A new algorithm for a novel hash function, based on chaotic tent map with changeable parameter, is proposed and analyzed. The one dimensional and piecewise tent map with changeable parameters decided by the position index of blocked messages is chosen, and blocked massages translated into ASCII code values are employed as the iteration time of the chaotic tent map. The final 128-bit hash value is generated by logical XOR operation on intermediate hash values. Theoretical analysis and computer simulation indicate that the proposed algorithm can satisfy the performance requirements of hash function.展开更多
This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are thekno...This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are theknown generators in the terms whose internal degree are 4(p - 1) + 1, 2pn+1(p-1),展开更多
This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.
文摘In this paper, by msss_mappings, the relations between metric spaces and spaces with σ _locally countable cs_networks or spaces with σ _locally countable weak bases are established. These are some answers to Alexandroff’s problems.
基金Supported by the National Basic Research Program of China(No.2007CB310606)
文摘A method of controllable internal perturbation inside the chaotic map is proposed to solve the problem in chaotic systems caused by finite precision.A chaotic system can produce large amounts of initial-sensitive,non-cyclical pseudo-random sequences.However,the finite precision brings short period and odd points which obstruct application of chaos theory seriously in digital communication systems.Perturbation in chaotic systems is a possible efficient method for solving finite precision problems,but former researches are limited in uniform distribution maps.The proposed internal perturbation can work on both uniform and non-uniform distribution chaotic maps like Chebyshev map and Logistic map.By simulations,results show that the proposed internal perturbation extends sequence periods and eliminates the odd points,so as to improve chaotic performances of perturbed chaotic sequences.
基金Supported by the National Natural Science Foundation of China （No. 61173178, 61003247, 61070246） and the Fundamental Research Funds for the Central University （No. COJER1018002,cdjerl018003）.
文摘A new algorithm for a novel hash function, based on chaotic tent map with changeable parameter, is proposed and analyzed. The one dimensional and piecewise tent map with changeable parameters decided by the position index of blocked messages is chosen, and blocked massages translated into ASCII code values are employed as the iteration time of the chaotic tent map. The final 128-bit hash value is generated by logical XOR operation on intermediate hash values. Theoretical analysis and computer simulation indicate that the proposed algorithm can satisfy the performance requirements of hash function.
文摘This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are theknown generators in the terms whose internal degree are 4(p - 1) + 1, 2pn+1(p-1),
基金Project supported by the National Natural Science Foundation of China (No.10171003, No.10231040) the Doctoral Education Program Foundation of China.
文摘This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.
