The construction of orthogonalk-skeins and latink-cubes

Aequationes mathematicae -     

The Crystal and Molecular Structures of Two Acid-Catalysed Rearrangement Products of Taxochinon

The structures of two acid catalysed rearrangement products of taxochinone ( 1 ) have been determined by X-ray analysis. One of the products turned out to be a 20 (10→9) abeo-abietane ( 2 ), the other an optically inactive phenalenone ( 3 ). Crystals of the former compound, C₂₀H₂₆O₃, belong to space group P2₁2₁2₁ with four molecules per cell and the structure was refined with 879 significant reflexions to R = 0.032. Crystals of the latter compound, C₂₀H₂₂O₂, belong to space group P2₁/c with 12 molecules per cell and the structure was refined with 1823 significant reflexions to R = 0.058.     

The approach to the Boltzmann distribution in Brownian motion

The solution is obtained, in the weak-damping approximation, to the problem of the approach to the barometric distribution in Brownian motion.     

Absolute pitch among American and Chinese conservatory students: prevalence differences, and evidence for a speech-related critical period

Absolute pitch is extremely rare in the U.S. and Europe; this rarity has so far been unexplained. This paper reports a substantial difference in the prevalence of absolute pitch in two normal populations, in a large-scale study employing an on-site test, without self-selection from within the target populations. Music conservatory students in the U.S. and China were tested. The Chinese subjects spoke the tone language Mandarin, in which pitch is involved in conveying the meaning of words. The American subjects were nontone language speakers. The earlier the age of onset of musical training, the greater the prevalence of absolute pitch; however, its prevalence was far greater among the Chinese than the U.S. students for each level of age of onset of musical training. The findings suggest that the potential for acquiring absolute pitch may be universal, and may be realized by enabling infants to associate pitches with verbal labels during the critical period for acquisition of features of their native language.     

Vibrational spectra and crystal structure of the di‐amino acid peptide cyclo(L‐Met‐L‐Met): comparison of experimental data and DFT calculations

Experimental Raman and FT‐IR spectra of solid‐state non‐deuterated and N‐deuterated samples of cyclo(L ‐Met‐L ‐Met) are reported and discussed. The Raman and FT‐IR results show characteristic amide I vibrations (Raman: 1649 cm⁻¹, infrared: 1675 cm⁻¹) for molecules exhibiting a cis amide conformation. A Raman band, assigned to the cis amide II vibrational mode, is observed at ∼1493 cm⁻¹ but no IR band is observed in this region. Cyclo(L ‐Met‐L ‐Met) crystallises in the triclinic space group P1 with one molecule per unit cell. The overall shape of the diketopiperazine (DKP) ring displays a (slightly distorted) boat conformation. The crystal packing employs two strong hydrogen bonds, which traverse the entire crystal via translational repeats. B3‐LYP/cc‐pVDZ calculations of the structure of the molecule predict a boat conformation for the DKP ring, in agreement with the experimentally determined X‐ray structure. Copyright © 2009 John Wiley & Sons, Ltd.     

Families of pairs of graphs with a large number of common cards

The vertex‐deleted subgraph G?v, obtained from the graph G by deleting the vertex v and all edges incident to v, is called a card of G. The deck of G is the multiset of its unlabelled vertex‐deleted subgraphs. The number of common cards of G and H (or between G and H) is the cardinality of the multiset intersection of the decks of G and H. In this article, we present infinite families of pairs of graphs of order n ≥ 4 that have at least \begin{eqnarray*}2\lfloor\frac{1}{3}(n-1)\rfloor\end{eqnarray*} common cards; we conjecture that these, along with a small number of other families constructed from them, are the only pairs of graphs having this many common cards, for sufficiently large n. This leads us to propose a new stronger version of the Reconstruction Conjecture. In addition, we present an infinite family of pairs of graphs with the same degree sequence that have \begin{eqnarray*}\frac{2}{3}(n+5-2\sqrt{3n+6})\end{eqnarray*} common cards, for appropriate values of n, from which we can construct pairs having slightly fewer common cards for all other values of n≥10. We also present infinite families of pairs of forests and pairs of trees with \begin{eqnarray*}2\lfloor\frac{1}{3}(n-4)\rfloor\end{eqnarray*} and \begin{eqnarray*}2\lfloor\frac{1}{3}(n-5)\rfloor\end{eqnarray*} common cards, respectively. We then present new families that have the maximum number of common cards when one graph is connected and the other disconnected. Finally, we present a family with a large number of common cards, where one graph is a tree and the other unicyclic, and discuss how many cards are required to determine whether a graph is a tree. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 146–163, 2010     

DESIGN,CALIBRATION, AND INITIAL RESULTS ON A COLOR/TEMPERATURE-MAPPING GOLD-FILM HEATER

The goal of this article is to present a new heater design which combines a thin-film resistometry technique with a double-incident liquid-crystal film in the form of a coated (printed) sheet to provide both a spatial mean surface temperature and a color/ temperature map. The heater is demonstrated to yield spatial temperature results consistent with those of other boiling studies in the literature while providing the additional functionality of a mean temperature measurement. The heater design and calibration are outlined and four boiling tests are presented to show the applicability of such a neater for fundamental boiling research, including some information in the conduction and convection regimes, electric-field-enhanced boiling research, and microgravity boiling research.     

Learning Interactions via Hierarchical Group-Lasso Regularization

We introduce a method for learning pairwise interactions in a linear regression or logistic regression model in a manner that satisfies strong hierarchy: whenever an interaction is estimated to be nonzero, both its associated main effects are also included in the model. We motivate our approach by modeling pairwise interactions for categorical variables with arbitrary numbers of levels, and then show how we can accommodate continuous variables as well. Our approach allows us to dispense with explicitly applying constraints on the main effects and interactions for identifiability, which results in interpretable interaction models. We compare our method with existing approaches on both simulated and real data, including a genome-wide association study, all using our R package glinternet.     

Chemoselectivity of Tertiary Azides in Strain-Promoted Alkyne-Azide Cycloadditions

The strain-promoted alkyne-azide cycloaddition (SPAAC) is the most commonly employed bioorthogonal reaction with applications in a broad range of fields. Over the years, several different cyclooctyne derivatives have been developed and investigated in regard to their reactivity in SPAAC reactions with azides. However, only a few studies examined the influence of structurally diverse azides on reaction kinetics. Herein, we report our investigations of the reactivity of primary, secondary, and tertiary azides with the cyclooctynes BCN and ADIBO applying experimental and computational methods. All azides show similar reaction rates with the sterically non-demanding cyclooctyne BCN. However, due to the increased steric demand of the dibenzocyclooctyne ADIBO, the reactivity of tertiary azides drops by several orders of magnitude in comparison to primary and secondary azides. We show that this chemoselective behavior of tertiary azides can be exploited to achieve semiorthogonal dual-labeling without the need for any catalyst using SPAAC exclusively.     

Computational and NMR Studies on the Complexation of Lithium Ion to 8-Crown-4

Lithium ion selective crown ethers have been the subject of much research for a multitude of applications. Current research is aimed at structurally rigidifying crown ethers, as restructuring of the crown ether ring upon ion binding is energetically unfavorable. In this work, the lithium ion binding ability of the relatively rigid 8-crown-4 was investigated both computationally by density functional theory calculations and experimentally by ¹H and ⁷Li NMR spectroscopy. Although both computational and experimental results showed 8-crown-4 to bind lithium ion, this binding was found to be weak compared to larger crown ethers. The computational analysis revealed that the complexation is driven by enthalpy rather than entropy, illustrating that rigidity is only of nominal importance. To elucidate the origin of the favorable interaction of lithium ion with crown ethers, activation strain analyses and energy decomposition analyses were performed pointing to the favorable interaction being mainly electrostatic in nature. 8-crown-4 presents the smallest crown ether reported to date capable of binding lithium ion, possessing two distinct conformations from which it is able to do so.