A well-known theorem by Becker states that if a normalized univalent function \(f\) in the unit disk \(\mathbb{D}\) can be embedded as initial element into Loewner chain \((f_t)_{t\geqslant 0}\) such Herglotz \(p\) Loewner-Kufarev PDE \(\partial f_t(z)/\partial f=zf'_t(z)p(z,t)\), \(z\in\mathbb{D}\), a.e. \(t\ge0\),satisfies \(\big|(p(z,t)-1)/(p(z,t)+1)\big|\le k<1\), then admits \(k\)-q.c. ...

© Springer Science+Business Media New York 2015 S. Grossbard, The Marriage Motive: A Price Theory of Marriage, DOI 10.1007/978-1-4614-1623-4_2 This chapter and the following are adapted from “A Theory of Allocation of Time in Markets for Labor and Marriage,” Economic Journal, Vol. 94, pp. 863–882, December 1984. While writing it I benefited from helpful comments from Gary Becker, Jerry Green (f...

In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies $a_0(z)=1$. In this paper, we prove Becker's conjecture in the best-possible form; we show that the rational function $R(z)$ can be...

Three new cecidogenous species of Palaeomystella Fletcher (Lepidoptera, Momphidae) from the Brazilian Atlantic Rain Forest are described. Larvae of P. fernandesi Moreira & Becker, sp. n., P. rosaemariae Moreira & Becker, sp. n. and P. tavaresi Becker & Moreira, sp. n. induce galls, respectively, on Tibouchina sellowiana (Cham.) Cogn., T. asperior (Cham.) Cogn. and T. fissinervia (Schrank & Mart...