This review article demonstrates the zero to one innovation capability of fullerene nanoarchitectonics in material advances.

A plausible conjecture states that an element of the Jacobson radical of the endomorphism ring of an abelian p-group increases the height of any non-zero element of the socle. I construct a counter-example.

The nonleptonic two-body decays of mesons are conventionally evaluated under the factorization hypothesis. In the factorization approach, the decay amplitude is expressed in terms of factorizable hadronic matrix elements multiplied by some combinations of Wilson coefficient functions. To be more specific, the factorization hypothesis assumes that the 3-body hadronic matrix element 〈h1h2|O|M〉 fo...

Charles Pepe-Ranney1, Chantal Koechli 2, Ruth Potrafka 3, Cheryl Andam 2, Erin Eggleston 2, Ferran Garcia-Pichel 3, Daniel H Buckley1,∗ 1Cornell University, Department of Crop and Soil Sciences, Ithaca, NY, USA 2Cornell University, Department of Microbiology, Ithaca, NY, USA 3Arizona State University, School of Life Sciences, Tempe, AZ 85287, USA. Correspondence*: Daniel H Buckley Cornell Unive...

A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeys the zero-one law if and only if its syntactic monoid has a zero element, by means of Eilenberg’s variety theoretic approach. Our proof gives an effective automata characterisation of the zero-one law ...

Let L be the zero set of a nonconstant monic polynomial with complex coe¢ cients. In the context of constructive mathematics without countable choice, it may not be possible to construct an element of L. In this paper we introduce a notion of distance from a point to a subset, more general than the usual one, that allows us to measure distances to subsets like L. To verify the correctness of th...

We present a triangular six-node shell element that represents an important improvement over a recently published element [1]. The shell element is formulated, like the original element, using the MITC procedure. The element has the attributes to be spatially isotropic, to pass the membrane and bending patch tests, to contain no spurious zero energy mode, and is formulated without an artificial...

A ring is a set R with two binary operations usually called addition, denoted as +, and multiplication, denoted as ·, such that (R, +) satisfies the five axioms of closure, associativity, commutativity, identity element (called zero, 0), and inverse element; and (R, ·) satisfies the three axioms of closure, associativity, and identity element (called one, 1). Furthermore, multiplication (·) dis...

A posteriori error estimation and related adaptive mesh-refining algorithms have themselves proven to be powerful tools in nowadays scientific computing. Contrary to adaptive finite element methods, convergence of adaptive boundary element schemes is, however, widely open. We propose a relaxed notion of convergence of adaptive boundary element schemes. Instead of asking for convergence of the e...