The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .     

Distributionally robust stochastic programs with side information based on trimmings

Mathematical Programming - We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the...     

Exo conformers of N‐(pyridin‐2‐yl)‐ and N‐(pyridin‐3‐yl)norbornene‐5,6‐dicarboximide crystals

Two isomeric pyridine‐substituted norbornenedicarboximide derivatives, namely N‐(pyridin‐2‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (I), and N‐(pyridin‐3‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (II), both C₁₄H₁₂N₂O₄, have been crystallized and their structures unequivocally determined by single‐crystal X‐ray diffraction. The molecules consist of norbornene moieties fused to a dicarboximide ring substituted at the N atom by either pyridin‐2‐yl or pyridin‐3‐yl in an anti configuration with respect to the double bond, thus affording exo isomers. In both compounds, the asymmetric unit consists of two independent molecules (Z′ = 2). In compound (I), the pyridine rings of the two independent molecules adopt different conformations, i.e. syn and anti, with respect to the methylene bridge. The intermolecular contacts of (I) are dominated by C—H...O interactions. In contrast, in compound (II), the pyridine rings of both molecules have an anti conformation and the two independent molecules are linked by carbonyl–carbonyl interactions, as well as by C—H...O and C—H...N contacts.     

An approximation to the minimum traveling wave for the delayed diffusive Nicholson's blowflies equation

In this work, we study the approximation of traveling wave solutions propagated at minumum speeds c ₀(h ) of the delayed Nicholson's blowflies equation: In order to do that, we construct a subsolution and a super solution to (?). Also, through that construction, an alternative proof of the existence of traveling waves moving at minimum speed is given. Our basic hypothesis is that p /δ ∈(1,e ] and then, the monostability of the reaction term. Copyright © 2017 John Wiley & Sons, Ltd.     

Bonding and Acidity of the Formal Hydride in the Prototypical Au9(PPh3)8H2+ Nanocluster

The role of hydrogen atoms as surface ligands on metal nanoclusters is of profound importance but remains difficult to directly study. While hydrogen atoms often appear to be incorporated formally as hydrides, evidence suggests that they donate electrons to the cluster's delocalized superatomic orbitals and may consequently behave as acidic protons that play key roles in synthetic or catalytic mechanisms. Here we directly test this assertion for the prototypical Au₉(PPh₃)₈H²⁺ nanocluster, formed by addition of a hydride to the well-characterized Au₉(PPh₃)₈³⁺. Using gas-phase infrared spectroscopy, we were able to unambiguously isolate Au₉(PPh₃)₈H²⁺ and Au₉(PPh₃)₈D²⁺, revealing an Au−H stretching mode at 1528 cm⁻¹ that shifts to 1038 cm⁻¹ upon deuteration. This shift is greater than the maximum expected for a typical harmonic potential, suggesting a potential governing cluster-H bonding that has some square-well character consistent with the hydrogen nucleus behaving as a metal atom in the cluster core. Complexing this cluster with very weak bases reveals a redshift of 37 cm⁻¹ in the Au−H vibration, consistent with those typically seen for moderately acidic groups in gas phase molecules and providing an estimate of the acidity of Au₉(PPh₃)₈H²⁺, at least with regard to its surface reactivity.     

Sponge-nested polymer monoliths: Versatile materials for the solid-phase extraction of bisphenols

Polymer monoliths are promising materials for sample preparation due to their high porosity, pH stability, and simple preparation. The use of melamine formaldehyde foams has been reported as an effective support to prepare highly robust silica and polymer monoliths. Herein, divinylbenzene monoliths based on a 50:50 (%, w/w) crosslinker/porogen ratio have been nested within a melamine-formaldehyde sponge, resulting in monoliths with a surface area higher than 400 m²/g. The extraction performance of these monoliths was evaluated for the extraction of endocrine-disrupting bisphenols from aqueous solutions. We evaluated for the first time the versatility of sponge-nested polymer monoliths by comparing three different extraction modes (vortex mixing, magnetic stirring, and orbital shaking). Vortex mixing showed a comparable recovery of bisphenols (39%–81%) in a shorter extraction time (30 min, instead of 2 h). In addition, the robustness of the sponge-nested polymer monoliths was demonstrated for the first time by reshaping a larger monolithic cube (0.125 cm³) into four smaller pieces (4 × 0.03125 cm³) leading to a 16%–21% increase in extraction efficiency. This effect was attributed to an increase in the effective contact area with the sample, obtaining a higher analyte extraction capacity.     

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term . © 2014 Wiley Periodicals, Inc.     

Photoelectrochemical Hydrogen Production in Alkaline Solutions Using Cu2O Coated with Earth‐Abundant Hydrogen Evolution Catalysts

The splitting of water into hydrogen and oxygen molecules using sunlight is an attractive method for solar energy storage. Until now, photoelectrochemical hydrogen evolution is mostly studied in acidic solutions, in which the hydrogen evolution is more facile than in alkaline solutions. Herein, we report photoelectrochemical hydrogen production in alkaline solutions, which are more favorable than acidic solutions for the complementary oxygen evolution half‐reaction. We show for the first time that amorphous molybdenum sulfide is a highly active hydrogen evolution catalyst in basic medium. The amorphous molybdenum sulfide catalyst and a Ni–Mo catalyst are then deposited on surface‐protected cuprous oxide photocathodes to catalyze sunlight‐driven hydrogen production in 1 M KOH. The photocathodes give photocurrents of ?6.3 mA cm^?2 at the reversible hydrogen evolution potential, the highest yet reported for a metal oxide photocathode using an earth‐abundant hydrogen evolution reaction catalyst.