Square-bounded partitions and Catalan numbers

For each integer k≥1, we define an algorithm which associates to a partition whose maximal value is at most k a certain subset of all partitions. In the case when we begin with a partition λ which is square-bounded, i.e. λ=(λ ₁≥⋅⋅⋅≥λ _k ) with λ ₁=k and λ _k =1, applying the algorithm ℓ times gives rise to a set whose cardinality is either the Catalan number c _ℓ−k+1 (the self dual case) or twice that Catalan number. The algorithm defines a tree and we study the propagation of the tree, which is not in the isomorphism class of the usual Catalan tree. The algorithm can also be modified to produce a two-parameter family of sets and the resulting cardinalities of the sets are the ballot numbers. Finally, we give a conjecture on the rank of a particular module for the ring of symmetric functions in 2ℓ+m variables.     

Chrysanthemyl 2-acetoxy-3-methylbutanoate: the sex pheromone of the citrophilous mealybug, Pseudococcus calceolariae

Headspace volatiles collected from virgin females of the citrophilous mealybug, Pseudococcus calceolariae, contain three compounds not present in the headspace of control samples. The main female-specific compound is identified as [2,2-dimethyl-3-(2-methylprop-1-enyl)cyclopropyl]methyl 2-acetoxy-3-methylbutanoate (chrysanthemyl 2-acetoxy-3-methylbutanoate). The other two compounds are identified as [2,2-dimethyl-3-(2-methylprop-1-enyl)cyclopropyl]methanol (chrysanthemol) and [2,2-dimethyl-3-(2-methylprop-1-enyl)cyclopropyl]methyl 2-hydroxy-3-methylbutanoate (chrysanthemyl 2-hydroxy-3-methylbutanoate). Traps baited with 100 μg and 1000 μg of chrysanthemyl 2-acetoxy-3-methylbutanoate captured 4- and 20-fold more males than traps baited with virgin females.     

Mapping prehistoric ghosts in the synchrotron

The detailed chemical analysis of fossils has the potential to reveal great insight to the composition, preservation and biochemistry of ancient life. Such analyses would ideally identify, quantify, and spatially resolve the chemical composition of preserved bone and soft tissue structures, but also the embedding matrix. Mapping the chemistry of a fossil in situ can place constraints on mass transfer between the enclosing matrix and the preserved organism(s), and therefore aid in distinguishing taphonomic processes from original chemical zonation remnant within the fossils themselves. Conventional analytical methods, such as scanning electron microscopy (SEM) and pyrolysis–gas chromatography/mass spectrometry (Py-GC/MS) have serious limitations in this case, primarily, an inability to provide large (i.e., decimeter) scale chemical maps. Additionally, vacuum chamber size and the need for destructive sampling preclude analysis of large and precious fossil specimens. However, the recent development of Synchrotron Rapid Scanning X-ray Fluorescence (SRS-XRF) at the Stanford Synchrotron Radiation Lightsource (SSRL) allows the non-destructive chemical analysis and imaging of major, minor, and trace element concentrations of large paleontological and archeological specimens in rapid scanning times. Here we present elemental maps of a fossil reptile produced using the new SRS-XRF method. Our results unequivocally show that preserved biological structures are not simply impressions or carbonized remains, but possess a remnant of the original organismal biochemistry. We show that SRS-XRF is a powerful new tool for the study of paleontological and archaeological samples.     

Protonation Sequence Study of the Solution Structure of DTPA by 1H NMR

The protonation sequence of DTPA is evaluated using a 300 MHz H NMR instrument. A terminal nitrogen is protonated first (pK_a1,2=10.02, 8.45). Upon the first protonation a dynamic hydrogen bonded five membered ring is formed between the terminal nitrogen and the central nitrogen. The second equivalent of protons protonates the opposite terminal amine and causes the ring to open. The third protonation (pK_a3=4.65) takes place on the central acetate and forms a ring with the central amine. The fourth protonation is assigned to a terminal acetate. The formation of five membered rings involving hydrogen bonding gives a better quantitative and qualitative account for the unusual shifts observed in the H NMR spectra than previous explanations.     

Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses

We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles, which readily permit variation of the sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in the packing fraction. The experimental results suggest that low-frequency quasilocalized phonon modes in colloidal glasses, i.e., modes that present low energy barriers for system rearrangements, are spatially correlated with rearrangements in this thermal system.     

Observation of the first excited transverse mode in guided matter waves

In direct analogy to the textbook example of light guided in a few-mode fiber (FMF), we report the observation of the first excited mode of an optically guided atomic beam. We selectively excite the atomic analog of the LP?? optical mode by controlling the energy distribution of ultracold atoms loaded into the guide, resulting in a modal structure dominated by a 47(2)% population in the first excited transverse mode. The ability to guide lower-order modes has been essential to demonstrating optical effects such as multimode interferometry, slow light, and entanglement, and an atomic analog to a FMF may lead to similarly useful applications.     

Organometallic Polymers. XXVII. Radical-Initiated Polymerization and Copolymerization of π-(2, 4-Hexadien-1-yl Acrylate) tricarbonyliron

The novel monomer, π-(2, 4-hexadiene- l-yl acrylate) tricarbonyliron (HATI), has been prepared by two routes. It was homopolymerized and copolymerized with acrylonitrile, vinyl acetate, styrene, and methyl acrylate in benzene solutions. In all cases azobisisobutyronitrile was the initiator. The relative reactivity ratios, where HATI is defined as M₁, were determined: r₁ = 0.34, r₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = vinyl acetate; r₁ = 0.26, r₂ = 1.81, M₂ = styrene; and r₁ = 0.30, r₂ = 0.74, M₂ = methyl acrylate. The homo-and copolymers had high values of T_g. When polymerizations are carried out at high concentrations, a very high molecular weight tail is observed in HATI hompolymerizations and in HATI-methyl acrylate copolymerizations. The polymers were characterized by IR, gel permeation chromatography, viscosity, and differential scanning calorimetry studies. Finally, thermal decompositions carried out in air resulted in decomposition of the Fe(CO)₃ group, producing Fe₂O₃ as a fine powder. Thermal decomposition under nitrogen (in solution and on solids ground into KBr pellets) resulted in slow destruction of the Fe(CO)₃ groups but the resulting polymer mass was insoluble, and the question of what form the iron exists in (Fe metal, oxides, carbides, etc.) has not been answered.     

Polymerization of Methane and Olefin Mixtures over Fluosulfonic Acid and Antimony Pentafluoride

Mixtures of methane and olefins (ethylene, propylene, butenes, butadiene, and styrene) have been polymerized over HSO₃ F-SbF₃ to yield an oily oligomer with a molecular weight ranging from 100 to 700. The NMR spectra of each polymer showed a sharp peak at or near 1.25 &, suggesting the presence of block methylene in the polymer. The formation of block methylene is surprising considering the fact that the polymerization reaction is carbonium ion in nature. A primary cation has been invoked to explain the results. The formation of this primary cation must involve some extraordinary stabilization by some component in the acid.     

Nanostructures in Physical Materials Chemistry: An Exploratory Laboratory

The blend of nanotechnology and material science is often beyond the scope of undergraduate laboratories. Through undergraduate research, graphite-intercalated compounds have been incorporated in the production of carbon-based nanostructures. Based on this work a series of exploratory exercises were designed for the undergraduate physical chemistry laboratory emphasizing nanostructure material science. This rapidly expanding area of science and technology can be introduced at an undergraduate level using a high temperature oven to produce nanostructure samples that are analyzed by Raman spectroscopy, scanning electron microscopy, and transmission electron microscopy at research university laboratories, infrared spectroscopy, and a bomb calorimeter. In these experiments we use samples of pure graphite, fluorinated graphite, and lanthanum oxide to induce the formation of nanostructures. An overview of fullerenes, nanotubes, boron nitride and Si nanostructures, other carbon forms, graphite-intercalated compounds, and the storage of hydrogen in nanotubes are provided in an appendix. Several extensions of the laboratory are proposed.     

A Short Existence Proof for Correlation Dimension

The Grassberger–Hentschel–Procaccia correlation dimension has been put on a rigorous basis by Pesin and Tempelman. We simplify their proof that this dimension is given in terms of the measure of neighborhoods of the diagonal.