The conjugacy problem for Dehn twist automorphisms of free groups

A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which is induced by a Dehn twist homeomorphism of the surface. For , a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn twist automorphisms of . Received: February 12, 1996.     

Random Features of the Fatigue Limit

The classical fatigue limit is often an important characteristic in fatigue design regarding metallic material. The limit is usually obtained from a staircase test in combination with some assumption about the statistical distribution of the limit. This distribution can be of a normal, log-normal or of extreme value type and no particular physical argument gives favor to any specific distribution. This leads to a certain ambiguity in the evaluation of test results which forces the designer to introduce large safety factors. In order to find a physically based statistical distribution for use in staircase tests to determine the fatigue limit we present here a random model for the fatigue limit based on the following assumptions; (i) The square root area model according to Murakami and co-workers is valid, (ii) the randomness in the fatigue limit is induced by the randomness of the maximum defect size, (iii) the random maximum defect size has an extreme value distribution of Gumbel type. This leads to the fatigue limit distribution based on Gumbel (FLG), which is recommended to replace the normal distribution in the evaluation of staircase fatigue tests in case of hard materials. It turns out that the skewness of the resulting distribution depends on the coefficient of variation; with a normal-like non-skewed distribution at the coefficient of variation of five percent.     

Reduction of Theoretical Uncertainty in Quantum Computing

A theoretical framework is developed to evaluatethe amount of intrinsic uncertainty, as distinguishedfrom operational uncertainty (noise), inherent inquantum computation. The temporal evolution of states in quantum computing is analyzeddiagramatically, providing a visual tool for therefining of quantum algorithms to help achieve minimaluncertainty and maximal efficiency, as well as forbetter understanding of the quantum entanglements crucial to quantumcomputing.     

Note on the Kaplan–Yorke Dimension and Linear Transport Coefficients

A number of new relations between the Kaplan–Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport coefficients in terms of the Kaplan–Yorke dimension is derived. Alternatively, the Kaplan–Yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.     

Treatment of intralocular diseases with poly(ortho ester)‐based drug delivery systems

A poly(ortho ester) (POE) has been investigated as a carrier for controlled delivery in intraocular therapy. The intraocular biocompatibility of POE was assessed in the rabbit after intravitreal as well as suprachoroidal injections. In both cases, the injection was feasible and reproducible, and the tolerance of POE was good, with no clinical or cellular signs of inflammation. The polymer degraded slowly within 2 to 3 weeks, with total bioresorption. POE allowed to sustain the release of an antifibroblastic agent in a model of glaucoma filtering surgery in the rabbit. A formulation based on POE and 5‐fluorouracil was administered to prevent the failure of the surgery. This POE formulation was effective in inhibiting the fibrotic response, allowing a local and controlled release of a small amount of the antiproliferative drug, while reducing its toxicity. Based on these results, POE appears to be a promising carrier for sustained drug delivery in treatment of intraocular affections.     

Gauss point mass lumping schemes for Maxwell's equations

Finite element and finite difference methods for approximating the Maxwell system propagate numerical waves with slightly incorrect velocities, and this results in phase error in the computed solution. Indeed this error limits the type of problem that can be solved, because phase error accumulates during the computation and eventually destroys the solution. Here we propose a family of mass-lumped finite element schemes using edge elements. We emphasize in particular linear elements that are equivalent to the standard Yee FDTD scheme, and cubic elements that have superior phase accuracy. We prove theorems that allow us to perform a dispersion analysis of the two common families of edge elements on rectilinear grids. A result of this analysis is to provide some justification for the choice of the particular family we use. We also provide a limited selection of numerical results that show the efficiency of our scheme. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 63–88, 1998     

The action of a few permutations on r-tuples is quickly transitive

We prove that for every r and d≥2 there is a C such that for most choices of d permutations π₁, π₂,…,π_d of S_n, the following holds: for any two r-tuples of distinct elements in {1,…,n}, there is a product of less than C log n of the π_is which map the first r-tuple to the second. Although we came across this problem while studying a rather unrelated cryptographic problem, it belongs to a general context of which random Cayley graph quotients of S_n are good expanders. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12: 335–350, 1998     

Determination of the isomerization rate constant HOCH2CH2CH2CH(OO·)CH3 →HOC·HCH2CH2CH(OOH)CH3. Importance of intramolecular hydroperoxy isomerization in tropospheric chemistry

The rate constant of the title reaction is determined during thermal decomposition of di-n-pentyl peroxide C₅H₁₁O( )OC₅H₁₁ in oxygen over the temperature range 463–523 K. The pyrolysis of di-n-pentyl peroxide in O₂/N₂ mixtures is studied at atmospheric pressure in passivated quartz vessels. The reaction products are sampled through a micro-probe, collected on a liquid-nitrogen trap and solubilized in liquid acetonitrile. Analysis of the main compound, peroxide C₅H₁₀O₃, was carried out by GC/MS, GC/MS/MS [electron impact EI and NH₃ chemical ionization CI conditions]. After micro-preparative GC separation of this peroxide, the structure of two cyclic isomers (3S*,6S*)3α-hydroxy-6-methyl-1,2-dioxane and (3R*,6S*)3α-hydroxy-6-methyl-1,2-dioxane was determined from ¹H NMR spectra. The hydroperoxy-pentanal OHC( )(CH₂)₂( )CH(OOH)( )CH₃ is formed in the gas phase and is in equilibrium with these two cyclic epimers, which are predominant in the liquid phase at room temperature. This peroxide is produced by successive reactions of the n-pentoxy radical: a first one generates the CH₃C·H(CH₂)₃OH radical which reacts with O₂ to form CH₃CH(OO·)(CH₂)₃OH; this hydroxyperoxy radical isomerizes and forms the hydroperoxy HOC·H(CH₂)₂CH(OOH)CH₃ radical. This last species leads to the pentanal-hydroperoxide (also called oxo-hydroperoxide, or carbonyl-hydroperoxide, or hydroperoxypentanal), by the reaction HOC·H(CH₂)₂CH(OOH)CH₃+O₂→O()CH(CH₂)₂CH(OOH)CH₃+HO₂. The isomerization rate constant HOCH₂CH₂CH₂CH(OO·)CH₃→HOC·HCH₂CH₂CH(OOH)CH₃ (k₃) has been determined by comparison to the competing well-known reaction RO₂+NO→RO+NO₂ (k₇). By adding small amounts of NO (0–1.6×10¹⁵ molecules cm⁻³) to the di-n-pentyl peroxide/O₂/N₂ mixtures, the pentanal-hydroperoxide concentration was decreased, due to the consumption of RO₂ radicals by reaction (7). The pentanal-hydroperoxide concentration was measured vs. NO concentration at ten temperatures (463–523 K). The isomerization rate constant involving the H atoms of the CH₂( )OH group was deduced: or per H atom: The comparison of this rate constant to thermokinetics estimations leads to the conclusion that the strain energy barrier of a seven-member ring transition state is low and near that of a six-member ring. Intramolecular hydroperoxy isomerization reactions produce carbonyl-hydroperoxides which (through atmospheric decomposition) increase concentration of radicals and consequently increase atmospheric pollution, especially tropospheric ozone, during summer anticyclonic periods. Therefore, hydrocarbons used in summer should contain only short chains (<C₄) hydrocarbons or totally branched hydrocarbons, for which isomerization reactions are unlikely. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 875–887, 1998