Abundant and ample straight left orders

A subsemigroup S of a semigroup Q is a straight left order in Q and Q is a semigroup of straight left quotients of S if every q ∈ Q can be written as for some with a b in Q and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a ^♯ denotes the group inverse of a in some (hence any) subgroup of Q. If S is a straight left order in Q, then Q is necessarily regular; the idea is that Q has a better understood structure than that of S. Necessary and sufficient conditions exist on a semigroup S for S to be a straight left order. The technique is to consider a pair of preorders on S. If such a pair satisfies conditions mimicking those satisfied by on a regular semigroup, and if certain subsemigroups of S are right reversible, then S is a straight left order. The conditions required for to satisfy are somewhat lengthy. In this paper we aim to circumvent some of these by specialising in two ways. First we consider only fully stratified left orders, that is, the case where (certainly the most natural choice for ) and the other is to insist that S be abundant, that is, every -class and every -class of S contains an idempotent. Our results may be used to show that the monoid of endomorphisms of a hereditary basis algebra of finite rank is a fully stratified straight left order. This revised version was published online in August 2006 with corrections to the Cover Date.     

A class of semifields of order q4

This paper gives a class of semifields of order q⁴ for any prime power q = p^r with p greater than 3. It is shown that this class has left nucleus GF(q²), and right and middle nucleus GF(q). Although it is not proved, it is believed that all the semifields in this class are new.Supported in part by NSF     

Thermal self‐initiation of styrene in the presence of TEMPO radicals: Bulk and miniemulsion

In TEMPO (2,2,6,6,‐tetramethyl‐1‐piperidinyloxy) controlled styrene radical polymerizations, the thermal self‐initiation reaction of styrene monomer is one of the main sources for the deviations from ideal living polymerization. However, it is also important because it continuously generates radicals to compensate for the loss of radicals caused by the termination reactions and thereby maintains a reasonable reaction rate. In this report, different initial TEMPO concentrations were used in styrene miniemulsion polymerizations without any added initiator. The consumption rate of TEMPO or radical generation rate was calculated from the length of the induction period and the increasing total number of polymer chains. It was found that there is little difference between the miniemulsions and the corresponding bulk systems in terms of the length of the induction period, which increases linearly with initial TEMPO concentration. After the induction period, the consumption rate of TEMPO or radical generation rate was reduced to a lower level, and a faster initial polymerization rate was found in the bulk system compared to the corresponding miniemulsion system. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4921–4932, 2004     

Solid state structure of NH-pyrazoles not easily amenable to crystal structure determinations: The case of 3(5)-phenyl-5(3)-methylpyrazole and 3,5-diphenyl-4-methylpyrazole

The structures of 3(5)-methyl-5(3)-phenylpyrazole (polymorph B ) and 3,5-diphenyl-4-methylpyrazole in the solid state cannot be determined by X-ray crystallography due to the lack of suitable monocrystals. The combined use of CPMAS nmr, DSC and powder diffraction provides information about the behaviour of these pyrazoles in the solid state, particularly, about N-H ?N intermolecular proton transfer. 3(5)-Methyl-5(3)-phenylpyrazole is an example of the influence of polymorphism on the proton exchange since polymorph A (a tetramer formed by a mixture of both tautomers) presents the phenomenon but polymorph B (formed exclusively by 3-phenyl-5-methyl tautomer) is devoid of it.     

Dynamics of a gravitationally loaded chain of elastic beads

Elastic beads repel in a highly nonlinear fashion, as described by Hertz law, when they are compressed against one another. Vertical stacking results in significant compressions of beads at finite distances from the surface of the stack due to gravity. Analytic studies that have been reported in the literature assume acoustic excitations upon weak perturbation [J. Hong et al., Phys. Rev. Lett. 82, 3058 (1999)] and soliton-like excitations upon strong perturbation [V. Nesterenko, J. Appl. Mech. Tech. Phys. 5, 733 (1983); S. Sen and M. Manciu, Physica A 268, 644 (1999)]. The present study probes the position, velocity and acceleration and selected two-point temporal correlations and their power spectra for individual beads for cases in which the system has been (i) weakly, (ii) strongly, and (iii) moderately perturbed at the surface in the sense specified in the text. Our studies reveal the existence of distinctly different dynamical behavior of the tagged beads, in contrast to conventional acoustic response, as the strength of the perturbation is varied at fixed gravitational loading. We also comment on the effects of polydispersity on system dynamics and probe the relaxation of isolated light and heavy beads in the chain. (c) 2000 American Institute of Physics.     

On an Embedding Theorem

We prove a theorem giving conditions under which a discrete-time dynamical system as (x _t ,y _t ) = (f;(x _{t – 1}, y _{t – 1}), g(x _{t – 1}, y _{t – 1})) can be reconstructed from a scalar valued time series ( _t ) _t , which depends only on x _t where _t = (x _t ). This theorem allows us to use the delay-coordinate method in this setting.     

Proper restriction semigroups – semidirect products and W-products

Fountain and Gomes [4] have shown that any proper left ample semigroup embeds into a so-called W-product, which is a subsemigroup of a reverse semidirect product ${T\ltimes {\mathcal {Y}}}$ of a semilattice ${\mathcal {Y}}$ by a monoid T, where the action of T on  ${\mathcal {Y}}$ is injective with images of the action being order ideals of  ${\mathcal {Y}}$ . Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim of this paper is to give necessary and sufficient conditions on a proper left restriction semigroup such that it embeds into a W-product. We also examine the complex relationship between W-products and semidirect products of the form ${{\mathcal {Y}}\rtimes T}$ .     

Photophysics and photochemical studies of 1,4-dihydropyridine derivatives

The absorption and fluorescence properties of nifedipine (NPDHP), felodipine (CPDHP) and a series of structurally related 1,4-dihydropyridines were studied in aqueous solution and organic solvents of different properties. The absorption and fluorescence spectra were found to depend on the chemical nature of the substituents at the position 4 of the 1,4-dihydropyridine ring (DHP) and on solvent properties. In aqueous solution, the fluorescence spectra of 4-phenyl substituted compounds are blue-shifted with respect to the alkyl substituted compounds. The more fluorescent compound is CPDHP. Nifedipine is not fluorescent. All compounds, with the exception of CPDHP, present monoexponential fluorescence decay with very short lifetime (0.2-0.4 ns). CPDHP showed a biexponential emission decay with a long-lived component of 1.7 ns; this behavior is explained in terms of different conformers because of the hindered rotation of the phenyl group by the ortho-substitution. Analysis of the solvent effect on the maximum of the absorption spectrum by using the linear solvent-energy relation solvato-chromic equation indicates the redshifts are influenced by the polarizability, hydrogen bonding ability and the hydrogen bond acceptance of the solvent. Whereas, the fluorescence characteristics (spectra, quantum yields and lifetimes) are sensitive to the polarizabilty and hydrogen bond ability of the solvents. Photo-decomposition of nifedipine is dependent on the solvent properties. Faster decomposition rates were obtained in nonprotic solvents. The 4-carboxylic derivative goes to decarboxylation. Under similar conditions, the other DHP compounds did not show appreciable photodecomposition.