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When will the human population peak? In this article, we build on classical results by Ansley Coale, who showed that when fertility declines steadily, births reach their maximum before fertility reaches replacement level, and the decline in total population size does not occur until several decades after fertility has reached that level. We extend Coale's results by modeling longevity increases, net immigration, and a slowdown in fertility decline that resembles current projections. With these extensions, our models predict a typical lag between replacement-level fertility and population decline of about 35 to 40 years, consistent with projections by the United Nations and about 15 years longer than the lag predicted by Coale. Our analysis helps reveal underlying factors in the timing of peak population.

This paper explores the potential for co-design to link sustainable consumption and production in the fashion industry. We review relevant research and perspectives and propose a co-design platform and an ideation toolkit in which users are encouraged to explore sustainability as a way of thinking at the early stages of the fashion design development process. We explain the rationale behind the ideation toolkit, its structure and demonstrate how to apply the toolkit to fashion design through a case study. Finally, we discuss both opportunities and challenges of co-designing the fashion system and its implementation in sustainable fashion and textile design education.

AbstractA deformation U, of a graded K-algebra Ais said to be of PBW type if gr Uis A. It has been shown for Koszul and N-Koszul algebras that the deformation is PBW if and only if the relations of Usatisfy a Jacobi type condition. In particular, for these algebras the determination of the PBW property is a finiteand explicitly determined linear algebra problem. We extend these results to an arbitrary graded K-algebra, using the notion of central extensions of algebras and a homological constant attached to Awhich we call the complexityof A.

This paper classifies central and normal extensions from global dimension 3 Artin–Schelter regular algebras to global dimension 4 Artin–Schelter regular algebras. Let Abe an AS regular algebra of global dimension 3, and let Dbe an extension of Aby a normal graded element z, i.e., D/〈z〉=A. The algebra Afalls under a classification due to Artin, Schelter, Tate, and Van den Bergh [Artin and Schelter, Adv. Math.66(1987), pp. 171–216; Artin et al., in“The Grothendieck Festschrift,” Vol. 1, pp. 33–85, Birkhäuser, Basel, 1990; Artin et al., Invent Math.106(1991), pp. 335–388] and is either quadratic or cubic. The quadratic algebras Aare Koszul, and this fact was used by Le Bruyn, Smith, and Van den Bergh [Le Bruyn et al., Math. Z.222(1996), 171–212] to classify the four-dimensional AS regular algebras Dwhen Ais quadratic and deg(z)=1. Alternative methods are needed when Ais cubic or deg(z)>1. We prove in all such cases that the regularity of Dand zis equivalent to the regularity of zin low degree (e.g., 2 or 3) and this is equivalent to easily verifiable matrix conditions on the relations for D.

1.The effects of placebo and of LSD-25 at two dose levels (0.5 and 1.5 meg/kg), all injected intramuscularly, on pupil diameter (photographic method) and kneejerk threshold (pendulum hammer) were measured in 5 chronic schizophrenic and 5 nonpsychotic control subjects matched as closely as possible for age and weight.2.No significant differences were found between the two groups as regards extent of pupil dilation or of decrease in kneejerk threshold produced by either dose of LSD-25, or with respect to the differences in magnitudes of effect of the two doses.3.For the two groups combined (N=10), significant negative correlations were found between age and initial (pre-injection) pupil diameter, and between age and pupillary response to LSD-25, while the latter was found to correlate positively with initial pupil diameter.4.In contrast, no significant correlations were found between age and initial kneejerk threshold, age and decrease in threshold produced by either dose of LSD-25, or between the latter and initial kneejerk threshold.5.It is concluded that some as yet unknown factors involved in the aging process influence not only initial pupil size but also pupillary responsivity to LSD-25, and that control of the age variable is particularly important in any study on autonomic functioning.