Let X be a smooth projective scheme of dimension d ≥ 1 over the field k, and let C be an indecomposable coherent sheaf on X . Then there is an Auslander-Reiten sequence in the category of quasi-coherent sheaves on X , 0 → (ΣC)⊗ ω −→ B −→ C → 0. Here ΣC is the (d−1)’st syzygy in a minimal injective resolution of C, and ω is the dualizing sheaf of X . 0. Introduction This note shows that Auslande...

Ayache has recently proved that if R is an integrally closed domain such that each overring of R is treed, then R is a locally pseudo-valuation domain. We investigate the extent to which the analogue (in which one concludes that R is a locally pseudo-valuation ring) holds if R is generalized to a commutative ring. A positive result is obtained if R is an idealization D(+)K where D is an integra...

We develop the symbolic representation method to derive the hierarchies of (2+1)-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and noncommutative cases in the sense that the dependent variable takes its values in C or a noncommutative associative algebra. We prove that these hierarchies are indeed qu...

We carry out general relativistic ray-tracing radiative-transfer calculations to study whether a localized emission from $e^{\pm}$ plasma rings created at the stagnation surface in jet funnel, which we refer as rings, can explain ring image of M87 observed by Event Horizon Telescope (EHT) 2017. The resultant images consist direct and formed via strong deflection black-hole (BH) gravity, "quasi ...

We introduce the Singleton bounds for codes over a finite commutative quasi-Frobenius ring.

We study the stability of a viscous incompressible fluid ring on a partially wetting substrate within the framework of long-wave theory. We discuss the conditions under which a static equilibrium of the ring is possible in the presence of contact angle hysteresis. A linear stability analysis (LSA) of this equilibrium solution is carried out by using a slip model to account for the contact line ...

Among structured Peer-to-Peer systems, Chord has a general popularity due to its salient features like simplicity, high scalability, small path length with respect to network size, and flexibility on node join and departure. However, Chord doesn’t take into account the topology of underlying physical network when a new node is being added to the system, thus resulting in high routing late...