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In this article, we study the evolution of the two-qubit system with Ising spin-chain environment by choosing the Lindblad equation to describe this process. First, we expand the Hamiltonian of a two-qubit system with its eigenstates and give the Lindblad equation for the evolution of the two-qubit system with Ising spin-chain as the environment. Compared with directly calculating the differential equation between elements of density matrix, we choose a method to solve the Lindblad equation with a smaller calculation dimension. Finally, by constructing an operator solution with operators, we obtain the dynamics of the two-qubit system with Ising spin-chain environment. [ABSTRACT FROM AUTHOR]

In this paper, we prove that ζ cannot be a solution to any nontrivial algebraic differential equation whose coefficients are polynomials in Γ , Γ (n) and Γ (ℓ n) over the ring of polynomials in C , where ℓ , n ≥ 1 are positive integers. [ABSTRACT FROM AUTHOR]

We investigate several quantitative properties of entire and meromorphic solutions to some differential-difference equations and generalised delay differential-difference equations. Our results are sharp in a certain sense as illustrated by several examples. [ABSTRACT FROM AUTHOR]

Abstract: By emplying the main ideas from G. Brosch, two results of R. Nevanlinna''s Four Value Theorem type on the unicity of meromorphic functions in the open complex plane sharing three distinct values, and a fourth value or a pair of values weakly are proved, which extend and generalize previous results of R. Nevanlinna, G.G. Gundersen, H. Ueda and G. Brosch. [Copyright &y& Elsevier]