We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices.

The first monarch citizen science program was launched in the 1950s and, since then, thousands of volunteers have made fundamental contributions to our accumulating knowledge of monarch biology. We quantified these efforts and the degree to which citizen science has contributed to monarch scholarship. We estimate that, in 2011, volunteers spent over 72,000 hours collecting data useful for monar…

We study the homeomorphism types of manifolds h-cobordant to a fixed one. Our investigation is partly motivated by the notion of special manifolds introduced by Milnor in his study of lens spaces. In particular, we revisit and clarify some of the claims concerning h-cobordisms of these manifolds.

We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect complexes over a commutative ring without non-trivial idempotents has no proper non-zero thick subcategories that are strongly generated. The main theorem is al…

We prove that for all n, simultaneously, we can choose prime filtrations of R/In such that the set of primes appearing in these filtrations is finite.

Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of the density properties of rational points on the Kummer variety Km(Ar) of the r-fold product of A with itself. One consequence of our results is the following. Fix an abelian variety A over k, and suppose that for so…

Adult somatic cells can be reprogrammed into pluripotent stem cells, which can indefinitely proliferate in a dish and differentiate into almost all the cell types that constitute the human body. These cells hold great promise for cell therapy and regenerative medicine, as well as drug screening and disease modeling. Theoretically, we can create a source of versatile, therapeutic cells that coul…

Let G be a locally compact group, and let B(G) denote its Fourier–Stieltjes algebra. We show that B(G) is Connes-amenable if and only if G is almost abelian.

Let Hol(D) denote the space of holomorphic functions on the unit disk D. We characterize those radial weights w on D for which there exist functions f, g ∈ Hol(D) such that the sum |f| + |g| is equivalent to w. Also, we obtain similar results in several complex variables for circular, strictly convex domains with smooth boundary.

We study the stability of the standing wave solutions of a Gross–Pitaevskii equation describing Bose–Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding constrained minimization problem and establish existence, symmetry and uniqueness of the ground state solutions.