On trivial words in finitely presented groups

We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of such groups by finding the cogrowth series for Baumslag-Solitar groups $\mathrm{BS}(N,N) =$ and prove that their cogrowth rates are algebraic numbers.Comment: This article has been rewritten as two separate papers, with improved exposition. The new papers are arXiv:1309.4184 and arXiv:1312.572

Generalized Fragmentation Functions for Fractal Jet Observables

We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.Comment: 37+18 pages, 24 figure

Pyrolysis of Lignocellulosic Materials. Phenolic Constituents of A Wood Pyrolytic Oil

Liquid pyrolytic products have been examined qualitatively and quantitatively for the presence of phenols. The liquid was solvent-extracted and examined by gas chromatography/mass spectrometry. The phenolic fraction contained phenol, o-cresol, guaiacol, m,p-cresol, 2,4-dimethylphenol, 4-meth-ylguaiacol, 4-ethylguaiacol, 4-propylguaiacol, eugenol, and isoeugenol. The total phenolic content was found to be 13.34% gravimetrically, but only 3.1% could be accounted for by chromatographic means, indicating the presence of a large proportion of nonvolatile, possibly polymeric material

Chemical Comparison of Two Ecotypes of Loblolly Pine (Pinus Taeda L.)

Loblolly pine from the continuous range in east Texas was compared with an apparently drought-resistant ecotype, the so-called "Lost pines" or "Bastrop pines." The Bastrop pines are found in a small area of central Texas isolated from the rest of the loblolly range, and in a region receiving considerably less rainfall. Determinations made were: holocellulose, alpha cellulose, ash, specific gravity, and percentages of earlywood and latewood. Nutrient analyses for levels of sodium, potassium, calcium, magnesium, zinc, manganese, and copper were also performed. It was found that the earlywood of the east Texas population had significantly greater levels of holocellulose and alpha cellulose. Regression analyses were performed relating the nutrient values to the chemical components. The appearance of potassium and magnesium in these equations, for the Bastrop pines, may indicate physiological adaptation to the more xeric environment

The Application of Molecular Orbital Calculations to Wood Chemistry. II. The Protonation of Beta-Methyl Glucopyranoside

The protonation step in the acid hydrolysis reaction of beta-methyl glucopyranoside was studied by molecular orbital techniques. The semi-empirical, self-consistent fields method of modified neglect of diatomic overlap (MNDO) was used to calculate energetic and electronic information in an attempt to determine the site of initial protonation

Retinoid regulation of heparin-binding EGF-like growth factor gene expression in human keratinocytes and skin *

Retinoic acid (RA) has profound effects on epidermal homeostasis; however, the molecular mechanisms by which retinoids regulate keratinocyte cell proliferation and differentiation are not well understood. Here we report that mRNA expression of heparin-binding EGF-like growth factor (HB-EGF), a member of the EGF family of growth factors, is induced by RA in human keratinocytes and skin, and is overexpressed in the context of epidermal hyperplasia in vivo. Treatment of normal adult human keratinocytes with micromolar concentrations of RA significantly induced the expression of HB-EGF. The response was efficiently blocked by specific inhibitors of ErbB tyrosine kinase activity, MAP kinase kinase (MEK), or p38 stress-activated protein kinase. RA also enhanced the induction of HB-EGF mRNA in human skin organ culture, an ex vivo model system displaying many similarities to wound healing in vivo. HB- EGF transcripts were markedly increased in human skin by topical treat- ment with RA under conditions known to provoke epidermal hyperplasia. HB-EGF transcripts were also markedly overexpressed in the hyperplas- tic epidermis of psoriatic lesions, relative to normal skin. These results support the hypothesis that the effects of RA on epidermal hyperplasia are mediated at least in part by HB-EGF, and suggest that signal transduction mechanisms other than or in addition to nuclear RA receptors contribute to this effect.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72809/1/j.1600-0625.1998.tb00339.x.pd

Properties of Char Produced from Pyrolysis of Southern Pine

Bench scale pyrolyses were carried out on southern pine at conditions of 250, 350, 400, 500, and 800 C for 1, 2, and 4 hours in a flowing nitrogen atmosphere at flow rates of 135 and 405 milliliters per minute. Data presented in this paper represent work on the properties of the chars produced under these conditions. Results of oxygen bomb calorimetry, density and specific gravity measurements, carbon and hydrogen analyses, and gravimetric yields were statistically analyzed to determine the influence of process conditions on char properties. In general, char yield and percentage of hydrogen and oxygen decreased, while the carbon percentage increased with increasing temperature

On groups and counter automata

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.Comment: 18 page

Dynamical transitions and sliding friction of the phase-field-crystal model with pinning

We study the nonlinear driven response and sliding friction behavior of the phase-field-crystal (PFC) model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed layers on a substrate under the action of an external driving force at finite temperatures, allowing for both elastic and plastic deformations. We derive general stochastic dynamical equations for the particle and momentum densities including both thermal fluctuations and inertial effects. The resulting coupled equations for the PFC model are studied numerically. At sufficiently low temperatures we find that the velocity response of an initially pinned commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The main features of the nonlinear response in the PFC model are similar to the results obtained previously with molecular dynamics simulations of particle models for adsorbed layers.Comment: 7 pages, 8 figures, to appear in Physcial Review