Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The 'catenary of eq...

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a f...

The catenary is the curve that a free-hanging chain assumes under its own weight, and thought to be a "true mathematical and mechanical form" in architecture by Robert Hooke in the 1670s, with nevertheless no significant phenomena observed in optics. We show that the optical catenary can serve as a unique building block of metasurfaces to produce continuous and linear phase shift covering [0, 2...

Nonunique factorization in cancellative commutative semigroups is often studied using combinatorial factorization invariants, which assign to each semigroup element a quantity determined by the factorization structure. For numerical semigroups (additive subsemigroups of the natural numbers), several factorization invariants are known to admit predictable behavior for sufficiently large semigrou...

Railway traction model is a complex mix of electrical and mechanical parameters. Pantograph acts as an active link between the catenary and electric drive used for driving the electric loco. It collects the current from the catenary and supplies it to loco transformer for feeding to the drive. Stable current collection is one of the foremost requirements for the efficient and reliable operation...

We study in detail the algebra Sn in the title which is an algebra obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. The algebra Sn is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is proved that the classical Krull dimen...

Changes in shape of the mandibular dental arch were demonstrated in a developmentally representative sample of human embryos. Each reconstructed arch was described in terms of a conformance to a reference geometric curve; ie, catenary. Cross-sectional sample trends showed that the initial dental lamina is anteroposteriorly flattened during the sixth week and begins a progressive elongation and ...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

Let A be a Noetherian local domain, N be a finitely generated torsion-free module, and M a proper submodule that is generically equal to N . Let A[N ] be an arbitrary graded overdomain of A generated as an A-algebra by N placed in degree 1. Let A[M ] be the subalgebra generated by M . Set C := Proj(A[M ]) and r := dimC. Form the (closed) subset W of Spec(A) of primes p where A[N ]p is not a fin...