The alternating semigroups: Generators and congruences

The idea of an even permutation has recently been generalized, via path notation, to one-one partial transformations (charts) in the symmetric inverse semigroupsC _n. The even charts form the alternating semigroupA _n ^c ⊂C _n . Generators ofA _n ^c are identified: It then follows that forn≥5,A _n ^c is the collection of restrictions of the even permutations (of rankn). Like theC _n case, the congruences ofA _n ^c form a chain. Part of this research was supported by a Mary Washington College faculty development grant.     

Kinetics of the γ-radiation-induced polymerization of methyl methacrylate in the solid state

Studies have been made of the γ-radiation-induced polymerization of methyl methacrylate in bulk, in the solid state at a temperature of ?65°C. and a radiation intensity of 346,000 rad/hr. The reaction was found to have an extremely long induction period (～50 hr.) when pure monomer was used, and to be first-order with respect to polymer concentration. This first-order dependency was confirmed by a series of irradiations in which 0.6% poly(methyl methacrylate) was dissolved in the monomer before irradiation. These irradiations showed no induction period. Nuclear magnetic resonance spectroscopy indicated a much more heterotactic polymer than that obtained in the liquid state at ?49°C.     

The melt hollow fiber spinning process: steady-state behavior,sensitivity and stability

The rheology of the melt hollow fiber spinning process is examined in the thin filament limit. The resulting thin filament equations are also applicable to single-phase and two-phase extensional flows. Using a novel numerical solution procedure, the sensitivity of the fiber spinning equations to material property and process variations is investigated. Fiber geometry is directly controlled by the mass flowrates of the core and clad fluids while the spinline tension is most strongly influenced by clad viscosity. A maximum can occur in the clad stress profile if a core liquid is used and the ratio of core to clad viscosity increases greatly with temperature. Isothermal spinning of high viscosity clad liquids with either a core gas or liquid is unstable for draw ratios greater than 20.2 as found for solid fibers.     

The structure of 2,4-dibromomenthone

A three-dimensional X-ray diffraction study has shown that the product obtained by bromination of - or -menthone is 2,4-dibromomenthone [2(a), 6(e)-dibromo-2(e)-isopropyl-5(e)methyl cyclohexanone]. The two Br atoms are trans, and the isopropyl and methyl groups are also trans. There are four molecules in the unit cell, which has symmetry P2₁2₁2₁ and dimensions a = 13·58, b = 13·81 and c = 6·25 Å. One intermolecular Br … Br contact of 3·52 ± 0·01 Å occurs, a distance which is about 0·4 Å shorter than the van der Waals distance.     

Centralizers in symmetric inverse semigroups: Structure and order

The representation [5] of the centralizerC(x) of a permutationx in (a symmetric inverse semigroup)C _n involves direct products of wreath products. Indeed, this semigroup case extends its group theory counterpart. Here, the last case (forx nilpotent) is addressed: A quotient of a wreath product is introduced and used to obtain a representation of the correspondingC(x). It follows that, for anyx∈C _n ,C(x) can be imbedded in a direct product of wreath products with a quotient of a wreath product. A formula for calculating the order ofC(x) is given. The independent parameters in the formula are precisely those that define the path structure ofx∈C _n . Part of this research was supported by a Mary Washington College faculty development grant.     

Cyclic subsemigroups of symmetric inverse semigroups

A generalization of the cycle notation for permutations is introduced for partial one-one transformations (charts). Notational representation theorems for charts that generalize those of permutations are given. Notational multiplication of charts is developed and then applied to yield a transparent proof of Frobenius' result which bounds the idempotent in the cyclic subsemigroup. Lastly, the well known result that the structure of the cyclic subgroups of the finite symmetric groups is determined from combinations of disjoint cycles is generalized to the cyclic subsemigroups of the finite symmetric inverse semigroups.     

ENDOR studies of the ligation and structure of the non-heme iron site in ACC oxidase

Ethylene is a plant hormone involved in all stages of growth and development, including regulation of germination, responses to environmental stress, and fruit ripening. The final step in ethylene biosynthesis, oxidation of 1-aminocyclopropane-1-carboxylic acid (ACC) to yield ethylene, is catalyzed by ACC oxidase (ACCO). In a previous EPR and ENDOR study of the EPR-active Fe(II)-nitrosyl, [FeNO],(7) complex of ACCO, we demonstrated that both the amino and the carboxyl moieties of the inhibitor d,l-alanine, and the substrate ACC by analogy, coordinate to the Fe(II) ion in the Fe(II)-NO-ACC ternary complex. In this report, we use 35 GHz pulsed and CW ENDOR spectroscopy to examine the coordination of Fe by ACCO in more detail. ENDOR data for selectively (15)N-labeled derivatives of substrate-free ACCO-NO (E-NO) and substrate/inhibitor-bound ACCO-NO (E-NO-S) have identified two histidines as protein-derived ligands to Fe; (1,2)H and (17)O ENDOR of samples in D(2)O and H(2)(17)O solvent have confirmed the presence of water in the substrate-free Fe(II) coordination sphere (E-NO). Analysis of orientation-selective (14,15)N and (17)O ENDOR data is interpreted in terms of a structural model of the ACCO active site, both in the presence (E-NO-S) and in the absence (E-NO) of substrate. Evidence is also given that substrate binding dictates the orientation of bound O(2).