It is possible to generalize the fruitful interaction between (real or complex) Jacobi matrices, orthogonal polynomials and Padé approximants at infinity by considering rational interpolants, (bi-)orthogonal rational functions and linear pencils zB − A of two tridiagonal matrices A, B, following Spiridonov and Zhedanov. In the present paper, beside revisiting the underlying generalized Favard t...

We present a design principle to develop new categories of telluride-based thermoelectric nanowire heterostructures through rational solution-phase reactions. The catalyst-free synthesis yields Te-Bi(2)Te(3) "barbell" nanowire heterostructures with a narrow diameter and length distribution as well as a rough control over the density of the hexagonal Bi(2)Te(3) plates on the Te nanowire bodies, ...

Gas sensors based on metal oxide semiconductors (MOSCs) and reduced graphene (rGO) for sensing of organic volatile compounds often suffer from high operation temperature, low responses, poor selectivity, or narrow detection range. Herein, we design fabricate Bi-doped rGO/Co3O4 (BGCO) nanohybrids with a flower morphology, which have been applied as layer an ethanol sensor. This BGCO sensor exhib...

A generalization of Patterson’s work (Patterson, 1985), on the invariants of the rational Bézier curves, to the case of surfaces is presented. An equation for the determination of the invariants for surfaces of degree (n, n) is derived and solved for the bi-quadratics – for which it is shown that seven independent, invariant functions exist. Explicit forms of the invariants are derived and a nu...

In this paper, an attempt has been made to construct a shape preserving rational bi-cubic interpolant (cubic/quadratic) with twelve free parameters to depict a more pleasant and smooth display of positive surface through positive data. Simple data dependent constraints are derived for four free parameters to preserve the positivity of data while the remaining eight are left free for designer’s ...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

We give a variant of Barvinok’s algorithm for computing a short rational generating function for the integer points in P := {x ∈ Rn : Ax ≤ b}; a use of which is to count the number of integer points in P . We use an algebraic perturbation, replacing each bi with bi + τ i, where τ > 0 is an arbitrarily small indeterminate. Hence, our new right-hand vector has components in the ordered ring Q[τ ]...

For each odd prime p, we prove the existence of infinitely many real quadratic fields which are p-rational. Explicit imaginary and bi-quadratic p-rational also given for p. Using a recent method developed by Greenberg, deduce Galois extensions Q with group isomorphic to an open subgroup GLn(Zp), n=4 n=5 at least all primes p<192.699.943.

Theorem A. Let A be an abelian variety over a number field k and X a subvariety of A. Then there are a finite number of translated abelian subvarieties B1, . . . , Bn over k such that Bi ⊂ X and the closure X(k) of X(k) in X is contained in ⋃ i Bi. In this short note, as applications of the above Faltings’ theorem, we will give several remarks on rational points of varieties whose cotangent bun...

In this paper we investigate some questions about coordination and interpretation which have been addressed by bidirectional Optimality Theory (Bi–OT). We consider examples from anaphora resolution, and there especially the role of epistemic contexts and expectations. We look at communicative acts as joint projects following H.H. Clark (1996) and model them by using multi–agent systems with joi...