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Consider the problem of finding a point furthest from x for each point x in a metric space ([ n ] , d) , where [ n ] = { 1 , 2 , ... , n }. We prove this problem to have a deterministic O (n) -time 1 / 3 -approximation algorithm. As a corollary, the maximum spanning tree problem in metric spaces has a deterministic O (n) -time 1 / 3 -approximation algorithm. We also give a Monte Carlo O (n 1. 5 log n) -time algorithm outputting, for each x ∈ [ n ] , a point y x ∈ [ n ] satisfying d (x , y x) ≥ Δ / 2 , where Δ ≡ max x , y ∈ [ n ] d (x , y). As a corollary, we have a Monte Carlo O (n 1. 5 log n) -time algorithm for finding a spanning tree of weight at least (1 / 2 − o (1)) Δ n in ([ n ] , d). [ABSTRACT FROM AUTHOR]

Intermetallic nanocrystals are emerging materials for energy, catalysis, and biomedical applications, but combining two or more metals at the nanoscale remains challenging. The amalgamation reaction represents a convenient method for hundreds of intermetallic compositions, as it relies on fast and efficient alloying of liquid metals into presynthesized metallic seeds. Here, Pd–Zn nanocrystals, prepared via Zn amide thermolysis on the surface of Pd nanocrystals and subsequent amalgamation alloying, are investigated. Size‐uniform nanocrystals and control over a wide range of Pd–Zn compositions are achieved. This allows deriving a phase diagram at the nanoscale, in which miscibility gaps and three phases with broad solid solutions are detected. Furthermore, the formation of homogeneous ZnO shells for Pd–Zn compositions extending beyond phase solubility limits is observed. Full chemistry control for Pd–Zn nanocrystals enables a rational choice of materials for selected energy applications, achieveing an extended lifetime of Zn‐ion batteries for Zn‐rich PdZn2 stoichiometry, superior electrocatalytic properties for nearly stoichiometric PdZn halite phase, and the stability and efficiency of high‐voltage cathodes benefiting from ZnO shell protection around Pd3Zn10 nanocrystals are reported. This paper exemplifies the multifunctionality of intermetallics Pd–Zn nanocrystals, while this methodology can be extended to many other bimetallic nanomaterials. [ABSTRACT FROM AUTHOR]

The relationship between molecular structure and water dynamics is a fundamental yet often neglected subject in the field of hydrogels for drug delivery, bioprinting, as well as biomaterial science and tissue engineering & regenerative medicine (TE&RM). Water is a fundamental constituent of hydrogel systems and engages via hydrogen bonding with the macromolecular network. The methods and techniques to measure and reveal the phenomena and dynamics of water within hydrogels are still limited. In this work, differential scanning calorimetry (DSC) was used as a quantitative method to analyze freezable (including free and freezable bound) and non-freezable bound water within gelatin methacrylate (GelMA) hydrogels. Nuclear magnetic resonance (NMR) is a complementary method for the study of water behavior and can be used to measure the spin-relaxation of water hydrogen nuclei, which is related to water dynamics. In this research, nuclear magnetic resonance relaxometry was employed to investigate the molecular state of water in GelMA hydrogels using spin–lattice (T1) and spin–spin (T2) spin-relaxation time constants. The data displays a trend of increasing bound water content with increasing GelMA concentration. In addition, T2 values were further applied to calculate microviscosity and translational diffusion coefficients. Water relaxation under various chemical environments, including different media, temperatures, gelatin sources, as well as crosslinking effects, were also examined. These comprehensive physical data sets offer fundamental insight into biomolecule transport within the GelMA hydrogel system, which ultimately are important for drug delivery, bioprinting, as well as biomaterial science and TE&RM communities. [ABSTRACT FROM AUTHOR]

Consumer attitudes and behaviors are fundamentally dynamic processes; thus, understanding consumer dynamics is crucial for truly understanding consumer behaviors and for firms to formulate appropriate actions. Recent history in empirical marketing research has enjoyed increasingly richer consumer data as the result of technology and firms' conscious data collection efforts. Richer data, in turn, have propelled the development and application of quantitative methods in modeling consumer dynamics, and have contributed to the understanding of complex dynamic behaviors across many domains. In this paper, we discuss the sources of consumer dynamics and how our understanding in this area has improved over the past four decades. Accordingly, we discuss several commonly used empirical methods for conducting dynamics research. Finally, as the data evolution continues into new forms and new environments, we identify cutting-edge trends and domains, and offer directions for advancing the understanding of consumer dynamics in these emerging areas., Author(s): Jonathan Z. Zhang [sup.1] , Chun-Wei Chang [sup.2] Author Affiliations: (1) grid.47894.36, 0000 0004 1936 8083, Colorado State University, , 80523, Fort Collins, CO, USA (2) grid.467171.2, 0000 0001 [...]

Shifting from the typical 4e– pathway to H2O in electrochemical oxygen reduction to the 2e– pathway to H2O2 is increasingly recognized as an environmentally friendly approach for producing H2O2. However, the competitive 4e− pathway is a significant obstacle to the production of H2O2 since H2O is the thermodynamically favored product. Here, a series of Pt, Pd, and Rh active atoms diluted within inert‐Au matrices with precisely controlled atomic arrangements and coordination environments are synthesized via facet engineering for O2‐to‐H2O2 production. Surprisingly, individually dispersed Pt atoms within the Au surface enclosed by the square atomic arrangements exhibit superior H2O2 selectivity and achieve a maximum selectivity of 90% at 0.36 V versus the reversible hydrogen electrode. Operando synchrotron ambient pressure X‐ray photoelectron spectroscopy identifies the presence of *OOH key intermediates on these isolated Pt active sites. Grand canonical density‐functional theory also reveals that the kinetic energy barrier for the 2e− pathway (0.08 eV; OOH* + H+ + e− → H2O2) on the isolated Pt sites is significantly lower than the 4e− pathway (0.29 eV; OOH* + H+ + e− → O* + H2O). This work enables atomic‐scale control in dilute binary alloy surfaces with specific configurations of isolated active atoms and provides essential guidance for catalyst design to boost O2‐to‐H2O2 production. [ABSTRACT FROM AUTHOR]