Recent zbMATH articles in MSC 30D30https://www.zbmath.org/atom/cc/30D302022-05-16T20:40:13.078697ZWerkzeugHomeomorphisms of \(S^1\) and factorizationhttps://www.zbmath.org/1483.300152022-05-16T20:40:13.078697Z"Dalthorp, Mark"https://www.zbmath.org/authors/?q=ai:dalthorp.mark"Pickrell, Doug"https://www.zbmath.org/authors/?q=ai:pickrell.dougSummary: For each \(n>0\) there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations ``conjugated by \(z\to z^n\)''. We show that these families are free of relations, which determines the structure of ``the group of homeomorphisms of finite type''. We next consider factorization for more robust groups of homeomorphisms. We refer to this as root subgroup factorization (because the factors correspond to root subgroups). We are especially interested in how root subgroup factorization is related to triangular factorization (i.e., conformal welding) and correspondences between smoothness properties of the homeomorphisms and decay properties of the root subgroup parameters. This leads to interesting comparisons with Fourier series and the theory of Verblunsky coefficients.On meromorphic solutions of nonlinear delay-differential equationshttps://www.zbmath.org/1483.300632022-05-16T20:40:13.078697Z"Mao, Zhiqiang"https://www.zbmath.org/authors/?q=ai:mao.zhiqiang"Liu, Huifang"https://www.zbmath.org/authors/?q=ai:liu.huifangSummary: Using Cartan's second main theorem and Nevanlinna's theorem concerning a group of meromorphic functions, we obtain the growth and zero distribution of meromorphic solutions of the nonlinear delay-differential equation \(f^n(z) + P(z) f^{( k )}(z + \eta) = H_0(z) + H_1(z) e^{\omega_1 z^q} + \cdots + H_m(z) e^{\omega_m z^q}\), where \(n, k, q, m\) are positive integers, \( \eta, \omega_1, \cdots, \omega_m\) are complex numbers with \(\omega_1 \cdots \omega_m \neq 0\), and \(P, H_0, H_1, \cdots, H_m\) are entire functions of order less than \(q\) with \(P H_1 \cdots H_m \not\equiv 0\). Especially for \(\eta = 0\), some sufficient conditions are given to guarantee the above equation has no meromorphic solutions of few poles.