Finding the αn-th largest element

We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

Production of indigotin in submerged culture using morchella nov. ES-1

A new strain of the fungusMorchella nov. ES-1 (ATCC 20951) that produces blue pigment in submerged culture has been isolated. The blue pigment was extracted by chloroform or ethyl acetate treatment. The crude extract when chromatographed yielded three fractions; a blue one has been identified by mass spectrometry as indigotin. Fermentation studies using enriched media revealed that maximum accumulation of indigotin in culture was approx 24 mg/L in 168 h.     

Solvation thermodynamics: theory and applications

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.     

Size‐dependent mechanical properties of glassy polymer nanofibers via molecular dynamics simulations

The microstructure of polymer matrix under cylindrical confinement is key to understanding the size‐dependent thermomechanical behavior of electrospun nanofibers. Coarse‐grained molecular dynamics simulation was applied here to probe polymer systems under cylindrical confinement, prepared with or without pre‐stretching. Simulation results showed that below a certain radius, a noticeable increase of the elastic modulus is observed with the decrease of the radius of cylindrical confinement. This size‐dependent mechanical behavior correlated to the degree of polymer chain orientation. Modulation of density and bond orientation in the radial direction was observed: the density and bond orientation began to oscillate, increasing the oscillation amplitudes with decreases in the radius. Such behavior suggests that the cylindrical confinement enhances the bond alignment of the entire fiber and not in the near‐surface layers only. The unstretched fibers had uniform density distribution along the fiber axis, while the stretched fibers demonstrated a fluctuation in density distribution. The crossover radius of size‐dependent behavior was two orders of magnitude smaller than observed in real experiments, demonstrating that the confinement affects some internal fiber scale, which exceeds the scale of individual macromolecules, and this internal scale may be related to supramolecular structures of the polymer matrix rather than the individual macromolecules. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 506–514     

Seeing chance: perceptual reasoning as an epistemic resource for grounding compound event spaces

The mathematics subject matter of probability is notoriously challenging, and in particular the content of random compound events. When students analyze experiments, they often omit to discern variations as distinct events, e.g., HT and TH in the case of flipping a pair of coins, and thus infer erroneous predictions. Educators have addressed this conceptual difficulty by engaging students in actual experiments whose outcomes contradict the erroneous predictions. Yet whereas empirical activities per se are crucial for any probability design, because they introduce the pivotal contents of randomness, variance, sample size, and relations among them, empirical activities may not be the unique or best means for students to accept the logic of combinatorial analysis. Instead, learners may avail of their own pre-analytic perceptual judgments of the random generator itself so as to arrive at predictions that agree rather than conflict with mathematical analysis. I support this view first by detailing its philosophical, theoretical, and didactical foundations and then by presenting empirical findings from a design-based research project. Twenty-eight students aged 9?C11 participated in tutorial, task-based clinical interviews that utilized an innovative random generator. Their predictions were mathematically correct even though initially they did not discern variations. Students were then led to recognize the formal event space as a semiotic means of objectifying these presymbolic notions. I elaborate on the thesis via micro-ethnographic analysis of key episodes from a paradigmatic case study.     

Thermo-mechanical behavior of electrospun thermoplastic polyurethane nanofibers

Analysis of the thermo-mechanical behavior of electrospun thermoplastic polyurethane (TPU) block co-polymer nanofibers (glass transition temperature ∼−50 °C) is presented. Upon heating, nanofibers began to massively contract, at ∼70 °C, whereas TPU cast films started to expand. Radial wide-angle X-ray scattering (WAXS) profiles of the nanofibers and the films showed no diffraction peaks related to crystals, whereas their amorphous halo had an asymmetric shape, which can be approximated by two components, associated with hard and soft segments. During heating, noticeable changes in the contribution of these components were only observed in nanofibers. These changes, which were accompanied with an endothermic DSC peak, coinciding with the start of the nanofibers contraction, can be attributed to relaxation of an oriented stretched amorphous phase created during electrospinning. Such structure relaxation becomes possible when a portion of the hard segment clusters, forming an effective physical network, is destroyed upon heating.