On Mono- and Epimorphisms in Varieties of Ordered Algebras

We study morphisms in varieties of ordered universal algebras. We prove that (i) monomorphisms are precisely the injective homomorphisms and that (ii) every regular monomorphism is an order embedding, but the converse is not true in general. We also give a necessary and sufficient condition for a morphism to be a regular epimorphism. Finally, we discuss factorizations in such varieties.     

Zigzag Theorem for Partially Ordered Monoids

While investigating the connection of absolute flatness of partially ordered monoids (briefly pomonoids) with their amalgamation, the author recently posed the question as to whether it was possible to formulate some ordered analogue of Isbell's zigzag theorem. Proving such a theorem is the primary aim of this article.     

Role of holes states on metal to insulator transition and collapse of magnetic ordering in LaFe1−xNixO3 (x = 0.0–0.5)

Polycrystalline LaFe_1?xNi_xO₃ (x = 0.0, 0.1, 0.3 and 0.5) have been prepared by the standard solid state reactions method. The phase formation has been confirmed by the powerful synchrotron X-ray diffraction experiment. In order to investigate the effects of Ni doping on the oxidation state, spin state and the magnetic ordering of the iron cations, ⁵⁷Fe Mössbauer Spectroscopy has been carried out at room temperature. Iron is present as Fe³⁺ in high spin state in LaFeO₃. Ni doping has no effect on the spin state of the Fe³⁺ cations. However, a progressive increase in the concentration of Fe⁴⁺ cations has been inferred. Relatively stronger covalent character of the Fe⁴⁺–O^?2 bond causes a progressive collapse in the magnetic ordering and delocalization of the hole states.     

Time resolved infrared spectroscopy: kinetic studies of weakly binding ligands in an iron-iron hydrogenase model compound

Solution photochemistry of (μ-pdt)[Fe(CO)(3)](2) (pdt = μ(2)-S(CH(2))(3)S), a precursor model of the 2-Fe subsite of the H-cluster of the hydrogenase enzyme, has been studied using time-resolved infrared spectroscopy. Following the loss of CO, solvation of the Fe center by the weakly binding ligands cyclohexene, 3-hexyne, THF, and 2,3-dihydrofuran (DHF) occurred. Subsequent ligand substitution of these weakly bound ligands by pyridine or cyclooctene to afford a more stable complex was found to take place via a dissociative mechanism on a seconds time scale with activation parameters consistent with such a pathway. That is, the ΔS(?) values were positive and the ΔH(?) parameters closely agreed with bond dissociation enthalpies (BDEs) obtained from DFT calculations. For example, for cyclohexene replacement by pyridine, experimental ΔH(?) and ΔS(?) values were determined to be 19.7 ± 0.6 kcal/mol (versus a theoretical prediction of 19.8 kcal/mol) and 15 ± 2 eu, respectively. The ambidentate ligand 2,3-DHF was shown to initially bind to the iron center via its oxygen atom followed by an intramolecular rearrangement to the more stable η(2)-olefin bound species. DFT calculations revealed a transition state structure with the iron atom almost equidistant from the oxygen and one edge of the olefinic bond. The computed ΔH(?) of 10.7 kcal/mol for this isomerization process was found to be in excellent agreement with the experimental value of 11.2 ± 0.3 kcal/mol.     

An experimental and in situ IR spectroscopic study of the lithiation-substitution of N-Boc-2-phenylpyrrolidine and -piperidine: controlling the formation of quaternary stereocenters

A general and enantioselective synthesis of 2-substituted 2-phenylpyrrolidines and -piperidines, an important class of pharmaceutically relevant compounds that contain a quaternary stereocenter, has been developed. The approach involves lithiation-substitution of enantioenriched N-Boc-2-phenylpyrrolidine or -piperidine (prepared by asymmetric Negishi arylation or catalytic asymmetric reduction, respectively). The combined use of synthetic experiments and in situ IR spectroscopic monitoring allowed optimum lithiation conditions to be identified: n-BuLi in THF at -50 °C for 5-30 min. Monitoring of the lithiation using in situ IR spectroscopy indicated that the rotation of the tert-butoxycarbonyl (Boc) group is slower in a 2-lithiated pyrrolidine than a 2-lithiated piperidine; low yields for the lithiation-substitution of N-Boc-2-phenylpyrrolidine at -78 °C can be ascribed to this slow rotation. For N-Boc-2-phenylpyrrolidine and -piperidine, the barriers to rotation of the Boc group were determined using density functional theory calculations and variable-temperature (1)H NMR spectroscopy. For the pyrrolidine, the half-life (t(1/2)) for rotation of the Boc group was found to be ～10 h at -78 °C and ～3.5 min at -50 °C. In contrast, for the piperidine, t(1/2) was determined to be ～4 s at -78 °C.     

Simulation of scattering and phase behavior around the isotropic-nematic transition of discotic particles

The detailed study of the isotropic-nematic phase transition in a system of discotic particles of aspect ratios L/D≤0.1 presented here is relevant to a broad range of colloidal suspensions of chemically modified clay particles. Using Monte Carlo simulation techniques the equation of state, radial distribution functions, structure factors and normalized scattering intensities are calculated for each phase. The results are interpreted and related to previously reported free energy calculations [Fartaria and Sweatman, Chem. Phys. Lett. 478 (2009) 150], suggesting a nearly continuous isotropic-nematic transition for lower aspect ratios. Given this behavior we examined the structural information for each phase to determine how experimental scattering data might be used to distinguish the two phases. The radial distribution functions in each phase depend strongly on aspect ratio, and for larger aspect ratios a dramatic increase in the local ordering of discotic particles (represented here as cut-spheres) is observed just before the phase transition. However, this nearest-neighbor ordering seen in g(r) around r/D=0.1 would hardly be discernible in experimental scattering data subject to usual statistical errors. The structure factors and scattering intensities were calculated for L/D=0.1, 0.04 and 0.01 for the isotropic and nematic phases at and away from the isotropic-nematic transition. While the isotropic-nematic phase transition can be detected from the height and shape of the first scattering peak around 7QD for larger aspect ratios, this feature becomes much less discriminatory with decreasing aspect ratio. Instead, scattering intensities at low scattering vector amplitudes (Q→0) can be used for detection of the phase transition at low aspect ratios. These results provide useful insight to guide interpretation of X-ray and light scattering measurements for colloidal dispersions of thin platelets undergoing isotropic-nematic transitions.     

Effect of methanol quality on the ionisation of herbicides,insecticides and fungicides using gradient elution liquid chromatography

This paper explores the changes in the electrospray signal response of 39 structurally different compounds caused by the quality of the methanol, when used as a component in a gradient elution mobile phase. When three batches of LC–MS grade methanol from one manufacturer were evaluated, the largest variation in the electrospray signal responses of the 39 compounds examined was 18%. However, significant enhancement of the electrospray signals of up to 106% were observed among different brands of LC–MS grade methanol from different manufacturers. The effect of methanol quality on signal response was found to be compound dependent. This study also demonstrated that the senescence of the methanol was important. Using an expired batch of LC–MS grade methanol, electrospray signals were suppressed by as much as 95% for all compounds measured using positive mode electrospray. Conversely, the negative mode electrospray signals of compounds such as 4-octyl benzoic acid showed an enhancement of up to 96% when using the same batch of methanol. Linuron was used as a model compound to examine the change in the electrospray response, during gradient elution, when the proportion of an expired batch of methanol was varied. An infusion experiment showed that the linuron signal intensity decreased as the proportion of expired methanol increased in the mobile phase, which was in direct contrast to the increase in linuron signal observed with a non-expired batch of methanol. A series of isocratic experiments also showed that the linuron signal decreased as the proportion of expired methanol increased in the mobile phase. The ion ratios of several of the compounds studied changed significantly when using the expired batch of LC–MS methanol. The change in the ion ratios accentuates the difficulty of identifying compounds from in-source spectral libraries. A protocol is recommended for assessing the quality of methanol for LC–MS applications.     

Examples concerning absolute flatness and amalgamation in pomonoids

Flatness properties of acts over monoids have been studied for almost four decades and a substantial literature is now available on the subject. Analogous research dealing with partially ordered monoids acting on posets was begun in the 1980s in two papers by S.M. Fakhruddin, and, after a dormancy period of some 20 years, has recently been rekindled with the appearance of several research articles. In comparing flatness properties of S-acts and S-posets, it has been noted that the imposition of order results in severe restrictions as far as absolute flatness is concerned. For example, whereas every inverse monoid is absolutely flat (meaning all of its left and right acts are flat), even the three-element chain in its natural order, considered as a pomonoid, fails to have this property. It has long been understood that absolutely flat monoids, in particular, inverse monoids, are amalgamation bases in the class of all monoids. The purpose of the present article is to further investigate absolute flatness of pomonoids and to begin to study its connection with amalgamation in that context. T.E. Hall’s results, that amalgamation bases in the class of all monoids have the so-called representation extension property (REP), which in turn implies the right congruence extension property, are first adapted to the ordered context. A detailed study of the compatible orders (of which there are exactly 13) on the three-element chain semilattice U then reveals a wide range of possibilities: exactly four of these orders render U absolutely flat as a pomonoid, two more give it the right order-congruence extension property in every extension (RCEP) (but fail to make it an amalgamation base because of the failure of the ordered analogue of (REP)), and for the remaining seven, even (RCEP) fails.     

Two-color three-photon resonant excitation spectrum of strontium in the autoionization region

We report new studies of the odd parity autoionizing Rydberg series of strontium attached to the 4d( ² D _{3/2, 5/2}) ionic limits possessing J = 1-3 based on the two-color three photon resonant excitation technique in conjunction with an atomic beam apparatus. Using the 4d ²³ P ₀ intermediate levels, we have been able to record the autoionizing Rydberg series of J = 1 whereas, from the 4d ²³ P ₂ intermediate level the series of Rydberg levels possessing J = 1, 2 and 3 have been observed. The level assignments and the line shapes simulations of the autoionizing resonances have been made using the multichannel quantum defect theory. Received 21 November 2001 / Received in final form 2 May 2002 Published online 19 July 2002