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...

The California Stem Cell Research and Cures Act, also called Proposition 71 [5], was a ballot initiative proposed by California voters in 2004 to allocate three billion dollars of state funds for stem cell research over ten years. Endorsed by California scientists and patient-advocates, Prop 71 passed on 2 November 2004, amending the state constitution to make stem cell research a constitutiona...

Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [6]. This leads to a classification problem. For example, in [3], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ...