From lamellar net to bilayered-lamella and to porous pillared-bilayer: reversible crystal-to-crystal transformation, CO2 adsorption, and fluorescence detection of Fe3+, Al3+, Cr3+, MnO4-, and Cr2O72- in water.

An aqua-coordinated lamellar net [Zn(5-NH2-1,3-bdc)(H2O)] (1, 5-NH2-1,3-H2bdc = 5-amino-1,3-benzenedicarboxylic acid) has been found to undergo a reversible stimuli-responsive 2D-to-2D crystal-to-crystal transformation with a water-free bilayered-lamellar net [Zn(5-NH2-1,3-bdc)] (1') upon removal and rebinding of aqua ligands, whereas a 2D porous pillared-bilayer [Zn2(5-NH2-1,3-bdc)2(NI-bpy-44)]·DMF (2, NI-bpy-44 = N-(pyridin-4-yl)-4-(pyridin-4-yl)-1,8-naphthalimide) has been tailored by introducing NI-bpy-44 to replace the coordinated aqua ligands. Pillared-bilayer 2 displayed a moderate CO2 uptake of 79.1 cm3 g-1 STP at P/P0 = 1 and 195 K with an isosteric heat of CO2 adsorption (Qst) of 37.0 kJ mol-1 at zero-loading. It is noteworthy that the water suspensions of 1 and 2 both displayed good fluorescence performances, which were effectively quenched by Fe3+, MnO4-, and Cr2O72- ions and shifted to long wavelengths by Fe3+, Al3+, and Cr3+, even with the coexistence of equal amounts of most other interfering ions. Taking the Stern-Volmer quenching constant, limit of detection, quenching efficiency, anti-interference ability, and visual observation into consideration, it is clear that both 1 and 2 are promising and excellent fluorescent sensors for highly sensitive detection of Fe3+, MnO4-, and Cr2O72-.

Fast Algorithms for Computing Path-Difference Distances.

Tree comparison metrics are an important tool for the study of phylogenetic trees. Path-difference distances measure the dissimilarity between two phylogenetic trees (on the same set of taxa) by comparing their path-length vectors. Various norms can be applied to this distance. Three important examples are the $l_{1}\text{-},\;l_{2}\text{-}$l1-,l2-, and $l_{{\infty }}$l∞-norms. The previous best algorithms for computing path-difference distances all have $O(n^{2})$O(n2) running time. In this paper, we show how to compute the $l_{1}$l1-norm path-difference distance in $O(n\;{\log}^{2}\;n)$O(nlog2n) time and how to compute the $l_{2}$l2- and $l_{{\infty }}$l∞-norm path-difference distances in $O(n\;{\log}\;n)$O(nlogn) time. By extending the presented algorithms, we also show that the $l_{p}$lp-norm path-difference distance can be computed in $O(pn\;{\log}^{2}\;n)$O(pnlog2n) time for any positive integer $p$p. In addition, when the integer $p$p is even, we show that the distance can be computed in $O(p^{2}n\;{\log}\;n)$O(p2nlogn) time as well.