Normal Criterion Concerning Shared Values

The value distribution of f + a(f ) and normal families of meromorphic functions

In this paper, we obtain a normal criterion of meromorphic functions concerning shared values. Let D be a domain in C and F be a family of meromorphic functions in D. Let k, n,m ∈ N, n ≥ mk+m+1, and a, b two finite complex numbers with a 6= 0. Suppose that every f ∈ F has all its zeros of multiplicity at least k+ 1 . If f + a(f ) and g + a(g)share the value b IM for every pair of functions (f, ...

A Note on Normal Families of Meromorphic Functions Concerning Shared Values

Normal families of meromorphic functions sharing values or functions

* Correspondence: jiangyunbo@ss. buaa.edu.cn School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, People’s Republic of China Abstract In this paper, we investigate the normal families of meromorphic functions concerning shared values and shared analytic functions and prove some normal criteria that generalize or extend some results obtained by Q. C. Zhang, Y....

Normal Criteria of Function Families Concerning Shared Values

Construction of a Shared Secret Key Using Continuous Variables ( Full Text Report )

Motivated by recent advances in quantum cryptography with continuous variables, we study the problem of extracting a shared digital secret key from two correlated real values. Alice has access to a real value XA, and Bob to another value XB such that the mutual information I(XA;XB) is nonzero. They wish to convert their values into a shared secret digital information while leaking as little inf...