Geometry and combinatorics of Julia sets of real quadratic maps

For real a correspondence is made between the Julia setB forz(z–)², in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325.     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

Theoretical Study of Weakly Bound Dimers between Hydrogen Fluoride and Some Polar Molecules

Weakly bound linear and bent dimers, FH—X (where X = CO, OC, CNH, NCH, N₂O and ON₂), are investigated using the DFT B3LYP and ab initio MP2 methods with the same basis sets (6–311++G(3df,2pd)). The strengths of the H—C or H—N H‐bonds in dimers FH—CO, FH—CNH, and FH—N₂O are compared with those of the H—O or H—N H‐bonds in dimers FH—OC, FH—NCH, and FH—ON₂. The results obtained for the H‐bond distances, the elongation effect of the HF bond, the red shift of the HF stretching frequency, and the energy difference between the dimer and the charge transfer reveal that the H‐bonds of the first group of dimers are stronger than those of the second. The Gibbs energies calculated for the six dimer formations indicate that the weakly bound dimers are unstable at room temperature (T = 298 K) (FH—X's → FH + X's, ΔG < 0).     

Ionization thresholds and positions of avoided crossing of potassium Stark Rydberg states: a Stark-adapted quantum defect orbital treatment

We have calculated the positions of the avoided level crossings between (n+2)s, np states and nd, k Stark states in the Rydberg Stark states of the potassium atom with principal quantum number n comprised between 12 and 17. We have also studied the adiabatic electric field ionization thresholds for the above Rydberg states. Both the ionization thresholds and the positions of avoided crossings have been calculated using the recently developed Stark-adapted quantum defect orbital (SQDO) formalism. The presently reported values appear to be in very good agreement with the available theoretical and experimental data.     

分次环的分次Jacobson根

本文通过引入弱拟正则元的概念，对一般Ｍｏｎｏｉｄ分次环Ａ（未必有１）给出以内部元素刻划的分次Ｊａｃｏｂｓｏｎ根ＪＧ（Ａ）．证明当Ａ有１时，ＪＧ（Ａ）与通常定义的Ｊｇ（Ａ）相等．对ＪＧ（Ａ）性质的讨论，推广了最近的许多结果．作为应用，我们给出了Ａｒｔｉｎ分次环的全部基本结构定理．     

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Derivation of invariant varieties of periodic points from singularity confinement in the case of Toda map

We have shown in [1] that the invariant varieties of periodic points (IVPP) of all periods of some higher dimensional rational maps can be derived, iteratively, from the singularity confinement (SC). We generalize this algorithm, in this paper, to apply to any birational map, which has more invariants than the half of the dimension.     

Efficient one‐pot synthesis of water‐compatible and photoresponsive molecularly imprinted polymer nanoparticles by facile RAFT precipitation polymerization

A facile, general, and highly efficient one‐pot approach to obtain azobenzene (azo)‐containing molecularly imprinted polymer (MIP) nanoparticles with photoresponsive template binding and release properties in aqueous media is described, which involves the combined use of hydrophilic macromolecular chain transfer agent‐mediated reversible addition‐fragmentation chain transfer precipitation polymerization and easily available water‐insoluble azo functional monomers. The resulting azo‐containing MIPs were characterized with dynamic laser scattering (DLS), SEM, FTIR, static contact angle and water dispersion studies, and equilibrium binding experiments. They have proven to be nanoparticles (their diameters being around 104–397 nm, as determined by DLS in methanol) with surface‐grafted hydrophilic polymer brushes and exhibit excellent pure water‐compatible template binding properties. Moreover, obvious photoregulated template binding behaviors were observed for such azo‐containing MIP nanoparticles, which led to their largely accelerated template release in the aqueous media under the UV light irradiation. Furthermore, the general applicability of the strategy was also demonstrated. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1941–1952