Sensory arrays of covalently functionalized single-walled carbon nanotubes for explosive detection

Chemiresistive sensor arrays for cyclohexanone and nitromethane are fabricated using single-walled carbon nanotubes (SWCNTs) that are covalently functionalized with urea, thiourea, and squaramide containing selector units. Based on initial sensing results and H-1 NMR binding studies, the most promising selectors are chosen and further optimized. These optimized selectors are attached to SWCNTs and simultaneously tested in a sensor array. The sensors show a very high level of reproducibility between measurements with the same sensor and across different sensors of the same type. Furthermore, the sensors show promising long-term stability, which renders them suitable for practical applications

Dimensions of Copeland-Erdös Sequences

The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite sequence CEk(A) formed by concatenating the base-k representations of the elements of A in numerical order. This paper concerns the following four quantities. • The finite-state dimension dimFS(CEk(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. • The finite-state strong dimension DimFS(CEk(A)), a finite-state version of classical packing dimension introduced in 2004. This is a dual of dimFS(CEk(A)) satisfying DimFS(CEk(A)) ≥ dimFS(CEk(A)). • The zeta-dimension Dimζ(A), a kind of discrete fractal dimension discovered many times over the past few decades. • The lower zeta-dimension dimζ(A), a dual of Dimζ(A) satisfying dimζ(A) ≤ Dimζ(A). We prove the following. 1. dimFS(CEk(A)) ≥ dimζ(A). This extends the 1946 proof by Copeland and Erdös that the sequence CEk(PRIMES) is Borel normal. 2. DimFS(CEk(A)) ≥ Dimζ(A). 3. These bounds are tight in the strong sense that these four quantities can have (simultaneously) any four values in [0, 1] satisfying the four above-mentioned inequalities