The fourth virial coefficient is calculated exactly for a fluid of hard spheres in even dimensions. For this purpose the complete star cluster integral expressed as sum two three-folded integrals only involving spherical angular coordinates. These are solved anallytically any dimension d and working with existing expressions other terms we obtain an expression B4(d) that sums finite number simp...

— In this article we review some recent work on fourth order equations in conformal geometry of three and four dimensions. We discuss an existence result for a Yamabe-type equation in dimension three. We examine a generalization of the Cohn-Vossen inequality to dimension four. Finally, we review an application of the fourth order equation to a fully nonlinear equation in dimension four that inv...

We show that there is a unique extremal even unimodular lattice of dimension 48 which has an automorphism of order 5 of type 5− (8, 16)− 8. Since the three known extremal lattices do not admit such an automorphism, this provides a new example of an extremal even unimodular lattice in dimension 48.

In 1993, based on my original 1981 research on serial sections of human embryos, I proposed that vision may have three components, rather than just 2—the rods and cones. I termed the third component nonvisual retinal ganglion cells (NVRGCs)(ipRGCs: intrinsically photosensitive retinal ganglion cells NVRGCs: nonvisual retinal ganglion cells, PACAP: pituitary adenylate cyclase-activating polypept...

Conall M. O’Seaghdha* and Caroline S. Fox*** *National Heart, Lung, and Blood Institute’s Framingham Offspring Study and the Center for Population Studies, Framingham, Massachusetts; Division of Intramural Research, National Heart, Lung, and Blood Institute, Bethesda, Maryland; Renal Division and Division of Endocrinology, Brigham and Women’s Hospital, Boston, Massachusetts; Renal Division, Mas...