I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is the...I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.展开更多
The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the tech...The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product （IWOP） of operators, the new completeness and orthogonMity relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.展开更多
基金Project supported by the National Natural Science Foundation of China the Doctoral Progamme Foundation of China and the Foundation of Wuhan University.
文摘I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.
文摘The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product （IWOP） of operators, the new completeness and orthogonMity relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.
