"The Changing Contributions of Men and Women to the Level and Distribution of Family Income, 1968-1988"

In the past twenty years, the labor force participation and earnings of women, especially married women, have risen dramatically. Over the same period, men's earnings have increased only modestly, and the distribution of family income has grown less equal. In this paper, we analyze the impact of changes in the level and distribution of earnings of men and women in the distribution of family income. We emphasize the contributions due to the increased work effort and real earnings of wives, as they account for a major portion of growth in family income over these two decades. Working wives have taken the place of economic growth as the factor that raises the standard of living of families across the entire income distribution. We analyze Current Population Survey data for white, black and Hispanic families in 1968, 1978, and 1988. Our results show that the primary factor contributing to rising income inequality was the increased inequality in the distribution of husbands' earnings. Wives' earnings both raised family income and lowered inequality.

A survey on constructive methods for the Oberwolfach problem and its variants

The generalized Oberwolfach problem asks for a decomposition of a graph $G$ into specified 2-regular spanning subgraphs $F_1,\ldots, F_k$, called factors. The classic Oberwolfach problem corresponds to the case when all of the factors are pairwise isomorphic, and $G$ is the complete graph of odd order or the complete graph of even order with the edges of a $1$-factor removed. When there are two possible factor types, it is called the Hamilton-Waterloo problem. In this paper we present a survey of constructive methods which have allowed recent progress in this area. Specifically, we consider blow-up type constructions, particularly as applied to the case when each factor consists of cycles of the same length. We consider the case when the factors are all bipartite (and hence consist of even cycles) and a method for using circulant graphs to find solutions. We also consider constructions which yield solutions with well-behaved automorphisms.Comment: To be published in the Fields Institute Communications book series. 23 pages, 2 figure

Resolvability of infinite designs

In this paper we examine the resolvability of infinite designs. We show that in stark contrast to the finite case, resolvability for infinite designs is fairly commonplace. We prove that every t-(v,k,Λ) design with t finite, v infinite and k,λ<v is resolvable and, in fact, has α orthogonal resolutions for each α<v. We also show that, while a t-(v,k,Λ) design with t and λ finite, v infinite and k=v may or may not have a resolution, any resolution of such a design must have v parallel classes containing v blocks and at most λ−1 parallel classes containing fewer than v blocks. Further, a resolution into parallel classes of any specified sizes obeying these conditions is realisable in some design. When k<v and λ=v and when k=v and λ is infinite, we give various examples of resolvable and non-resolvable t-(v,k,Λ) designs

On the minisymposium problem

The generalized Oberwolfach problem asks for a factorization of the complete graph $K_v$ into prescribed $2$-factors and at most a $1$-factor. When all $2$-factors are pairwise isomorphic and $v$ is odd, we have the classic Oberwolfach problem, which was originally stated as a seating problem: given $v$ attendees at a conference with $t$ circular tables such that the $i$th table seats $a_i$ people and ${\sum_{i=1}^t a_i = v}$, find a seating arrangement over the $\frac{v-1}{2}$ days of the conference, so that every person sits next to each other person exactly once. In this paper we introduce the related {\em minisymposium problem}, which requires a solution to the generalized Oberwolfach problem on $v$ vertices that contains a subsystem on $m$ vertices. That is, the decomposition restricted to the required $m$ vertices is a solution to the generalized Oberwolfach problem on $m$ vertices. In the seating context above, the larger conference contains a minisymposium of $m$ participants, and we also require that pairs of these $m$ participants be seated next to each other for $\left\lfloor\frac{m-1}{2}\right\rfloor$ of the days. When the cycles are as long as possible, i.e.\ $v$, $m$ and $v-m$, a flexible method of Hilton and Johnson provides a solution. We use this result to provide further solutions when $v \equiv m \equiv 2 \pmod 4$ and all cycle lengths are even. In addition, we provide extensive results in the case where all cycle lengths are equal to $k$, solving all cases when $m\mid v$, except possibly when $k$ is odd and $v$ is even.Comment: 25 page

Decompositions of complete graphs into bipartite 2-regular subgraphs

It is shown that if G is any bipartite 2-regular graph of order at most n/2 or at least n – 2, then the obvious necessary conditions are sufficient for the existence of a decomposition of the complete graph of order n into a perfect matching and edge-disjoint copies of G

Five Years of Mid-Infrared Evolution of the Remnant of SN 1987A: The Encounter Between the Blast Wave and the Dusty Equatorial Ring

We have used the Spitzer satellite to monitor the mid-IR evolution of SN 1987A over a 5 year period spanning the epochs between days 6000 and 8000 since the explosion. The supernova (SN) has evolved into a supernova remnant (SNR) and its radiative output is dominated by the interaction of the SN blast wave with the pre-existing equatorial ring (ER). The mid-IR spectrum is dominated by emission from ~180 K silicate dust, collisionally-heated by the hot X-ray emitting gas with a temperature and density of ~5x10^6 K and 3x10^4 cm-3, respectively. The mass of the radiating dust is ~1.2x10^(-6) Msun on day 7554, and scales linearly with IR flux. The infrared to soft-X-ray flux ratio is roughly constant with a value of 2.5. Gas-grain collisions therefore dominate the cooling of the shocked gas. The constancy of of this ratio suggests that very little grain processing or gas cooling have occurred throughout this epoch. The shape of the dust spectrum remained unchanged during the observations while the total flux increased with a time dependence of t^(0.87), t being the time since the first encounter between the blast wave and the ER. These observations are consistent with the transitioning of the blast wave from free expansion to a Sedov phase as it propagates into the main body of the ER.Comment: Accepted for publication in the ApJ, 11 pages, 11 figure