Presentations of the amalgamated free product of two infinite cycles

LetH=〈a,b;a ^k =b ^l 〉, wherek,l≧2 andk+l>4. McCool and Pietrowski have proved that any pair of generators forH is Nielsen equivalent to a pairx=a ^r andy=b ^s where $$(a){\text{ }}gcd(r, s) = gcd(r, k) = gcd(s, l) = 1,$$ $$(b){\text{ }}0< 2r \leqq ks{\text{ }}and{\text{ }}0< 2s \leqq lr.$$ In terms ofx andy,H can be presented as $$G = \left\langle {x,{\text{ }}y;{\text{ }}x^{ks} = y^{lr} ,\left[ {x,{\text{ }}y^l } \right] = \left[ {x^k ,{\text{ }}y} \right] = 1} \right\rangle$$ and Zieschang has shown that ifr=1 ors=1, thenH can be defined by a single relation inx andy. We establish the exact converse of Zieschang's result, namely thatH is not defined by a single relation inx andy unlessr=1 ors=1. The proof is based on an observation of Magnus which associates polynomials with relators and some elementary facts about cyclotomic polynomials.     

Comparison of provitamin A determination by normal-phase gravity-flow column chromatography and reversed-phase high performance liquid chromatography

Summary The provitamin A content of some food samples was determined by methods involving MgO: Hyflosupercel gravityflow column chromatography (GFCC) and reversed phase high performance liquid chromatography (HPLC), the quantitation being done by external standardization (HPLC-ES) or internal standardization (HPLC-IS) with Sudan. The results obtained with - and -carotene in carrots, -carotene and -cryptoxanthin in papaya and -carotene in tomato and kale agreed well, showing that any of the these techniques can be used, provided the analysis is done under optimum conditions. Good separation of the different provitamins using GFCC depends on the analyst's skill and visual acuity. HPLC-ES required a constant supply of provitamin standards, thus the varying purity of commercially available standards and the high instability of these compounds could pose grave problems. Due to the stability of Sudan, HPLC-IS appeared to be the method of choice although passage of the extract through a MgO: Hyflosupercel minicolumn was required prior to injection to separate chlorophylls, dihydroxy- and polyoxycarotenoids which would otherwise elute with Sudan. Nonconformity of the Sudan structure to those of the provitamins did not effect the quantitative results. The chromatographic separation, identity and quantification of the provitamins could be more easily established by using HPLC-IS, complemented with GFCC.     

(18)O]-oxygen incorporation reveals novel pathways in spiroacetal biosynthesis by Bactrocera cacuminata and B. cucumis

The origins of the oxygen atoms in 1,7-dioxaspiro[5.5]undecane (1) and hydroxyspiroacetal (2) from Bactrocera cacuminata, and in 2,8-dimethyl-1,7-dioxaspiro[5.5]undecane (3) and hydroxyspiroacetal (4) from B. cucumis, have been investigated by incorporation studies from both [(18)O(2)]-dioxygen and [(18)O]-water. Combined GC-MS examination and high-field NMR analysis have demonstrated that all oxygen atoms in 1 and 2 from B. cacuminata are dioxygen derived, but in contrast, the spiroacetals 3 and 4 from B. cucumis incorporate one ring oxygen from water and one ring oxygen (and the hydroxyl oxygen in 4) from [(18)O(2)]-dioxygen. These results reveal not only the generality of monoxygenase mediation of spiroacetal formation in Bactrocera sp., but also an unexpected complexity in their biosynthesis. A general paradigm accommodating these and other observations is presented.     

Substitution reactions of [Ru(dppe)(CO)(H(2)O)(3)][OTf](2)

The labile nature of the coordinated water ligands in the organometallic aqua complex [Ru(dppe)(CO)(H(2)O)(3)][OTf](2) (1) (dppe = Ph(2)PCH(2)CH(2)PPh(2); OTf = OSO(2)CF(3)) has been investigated through substitution reactions with a range of incoming ligands. Dissolution of 1 in acetonitrile or dimethyl sulfoxide results in the facile displacement of all three waters to give [Ru(dppe)(CO)(CH(3)CN)(3)][OTf](2) (2) and [Ru(dppe)(CO)(DMSO)(3)][OTf](2) (3), respectively. Similarly, 1 reacts with Me(3)CNC to afford [Ru(dppe)(CO)(CNCMe(3))(3)][OTf](2) (4). Addition of 1 equiv of 2,2'-bipyridyl (bpy) or 4,4'-dimethyl-2,2'-bipyridyl (Me(2)bpy) to acetone/water solutions of 1 initially yields [Ru(dppe)(CO)(H(2)O)(bpy)][OTf](2) (5a) and [Ru(dppe)(CO)(H(2)O)(Me(2)bpy)][OTf](2) (6a), in which the coordinated water lies trans to CO. Compounds 5a and 6a rapidly rearrange to isomeric species (5b, 6b) in which the ligated water is trans to dppe. Further reactivity has been demonstrated for 6b, which, upon dissolution in CDCl(3), loses water and coordinates a triflate anion to afford [Ru(dppe)(CO)(OTf)(Me(2)bpy)][OTf] (7). Reaction of 1 with CH(3)CH(2)CH(2)SH gives the dinuclear bridging thiolate complex [[(dppe)Ru(CO)](2)(mu-SCH(2)CH(2)CH(3))(3)][OTf] (8). The reaction of 1 with CO in acetone/water is slow and yields the cationic hydride complex [Ru(dppe)(CO)(3)H][OTf] (9) via a water gas shift reaction. Moreover, the same mechanism can also be used to account for the previously reported synthesis of 1 upon reaction of Ru(dppe)(CO)(2)(OTf)(2) with water (Organometallics 1999, 18, 4068).     

Anatoxins and degradation products, determined using hybrid quadrupole time-of-flight and quadrupole ion-trap mass spectrometry: forensic investigations of cyanobacterial neurotoxin poisoning

The potent neurotoxins from cyanobacteria, anatoxin-a (AN), its methyl analogue, homoanatoxin-a (HMAN), and their degradation products, have been studied using nano-electrospray hybrid quadrupole time-of-flight mass spectrometry (QqTOF-MS). The anatoxin degradation products, which are readily produced in vivo by either reduction or epoxidation, were also examined in this study. The high mass accuracy QqTOF-MS data was used to confirm formula assignments for major product ions and quadrupole ion-trap (QIT)-MS was used to construct fragmentation pathways for anatoxins. Significant differences between these fragmentation pathways were observed. Comparisons between the spectra of compounds that differ in side-chain length (the AN and HMAN series) were used to identify ions that are characteristic of the homologues. The application to forensic samples in which the principal neurotoxin had undergone rapid biodegradation has been demonstrated and used to confirm anatoxin poisoning of dogs.     

Dihydrogen complexes of rhodium: [RhH2(H2)x (PR3)2]+ (R = Cy, iPr; x = 1, 2)

Addition of H2 (4 atm at 298 K) to [Rh(nbd)(PR3)2][BAr(F)4] [R = Cy, iPr] affords Rh(III) dihydride/dihydrogen complexes. For R = Cy, complex 1a results, which has been shown by low-temperature NMR experiments to be the bis-dihydrogen/bis-hydride complex [Rh(H)2(eta2-H2)2(PCy3)2][BAr(F)4]. An X-ray diffraction study on 1a confirmed the {Rh(PCy3)2} core structure, but due to a poor data set, the hydrogen ligands were not located. DFT calculations at the B3LYP/DZVP level support the formulation as a Rh(III) dihydride/dihydrogen complex with cis hydride ligands. For R = iPr, the equivalent species, [Rh(H)2(eta2-H2)2(P iPr3)2][BAr(F)4] 2a, is formed, along with another complex that was spectroscopically identified as the mono-dihydrogen, bis-hydride solvent complex [Rh(H)2(eta2-H2)(CD2Cl2)(P iPr3)2][BAr(F)4] 2b. The analogous complex with PCy3 ligands, [Rh(H)2(eta2-H2)(CD2Cl2)(PCy3)2][BAr(F)4] 1b, can be observed by reducing the H2 pressure to 2 atm (at 298 K). Under vacuum, the dihydrogen ligands are lost in these complexes to form the spectroscopically characterized species, tentatively identified as the bis hydrides [Rh(H)2(L)2(PR3)2][BAr(F)4] (1c R = Cy; 2c R = iPr; L = CD2Cl2 or agostic interaction). Exposure of 1c or 2c to a H2 atmosphere regenerates the dihydrogen/bis-hydride complexes, while adding acetonitrile affords the bis-hydride MeCN adduct complexes [Rh(H)2(NCMe)2(PR3)2][BAr(F)4]. The dihydrogen complexes lose [HPR3][BAr(F)4] at or just above ambient temperature, suggested to be by heterolytic splitting of coordinated H2, to ultimately afford the dicationic cluster compounds of the type [Rh6(PR3)6(mu-H)12][BAr(F)4]2 in moderate yield.     

Chromatographic and column stability at pH 7 of a C18 dimethylurea polar stationary phase

Chromatographic evaluations of a C18 dimethylurea phase in 150 mm x 3.9 mm HPLC columns were performed using the Tanaka and Engelhardt test mixtures. The applicability of the new C18 dimethylurea phase was also evaluated with a mixture of some herbicides and their metabolites. An artificial aging procedure was also performed by passing a potassium phosphate mobile phase buffered at pH 7.0 through C18 50 mm x 3.9 mm dimethylurea columns. The column stability was evaluated by means of the chromatographic parameters obtained for the separation of some compounds from the Neue test mixture, using apolar, polar and highly basic analytes.     

Effects in high-performance liquid chromatography of a high pH in the mobile phase on poly(methyloctylsiloxane) immobilized by gamma-radiation on titanium-grafted silica

Effects of high-pH environments on a stationary phase prepared by gamma-radiation immobilization of poly(methyloctylsiloxane) on titanium-grafted silica were investigated by HPLC testing with standard sample mixtures. The HPLC parameters indicate good stationary phase stability to 10000 column volumes each of mobile phases with pH of 7, 9 and 12. At pH 13, the efficiency decreases slowly, although reasonably good separations are still possible until increasing flow resistance no longer allows easy passage of the mobile phase.     

Viability of the antigen determines whether DNA or urocanic acid act as initiator molecules for UV-induced suppression of delayed-type hypersensitivity

UV radiation suppresses the immune response, and UV-induced immune suppression contributes to UV-induced photocarcinogenesis. For UV-induced immune suppression to occur, electromagnetic energy (i.e. UV radiation) must be converted to a biological signal. Two photoreceptors have been identified in the skin that serves this purpose, epidermal DNA and trans-urocanic acid (UCA). Although compelling evidence exists to support a role for each pathway (UV-induced DNA damage or photoisomerization of UCA) in UV-induced immune suppression, it is not clear what determines which photoreceptor pathway is activated. To address this question, we injected UV-irradiated mice with a monoclonal antibody with specificity for cis-UCA or applied liposomes containing DNA repair enzymes to the skin of UV-irradiated mice. The effect that each had on UV-induced suppression of delayed-type hypersensitivity was measured. We asked whether the light source used (FS-40 sunlamps vs solar-simulated UV radiation) altered whichever pathway of immune suppression was activated. Different doses of UV radiation and the viability of the antigen were also considered. Neither the dose of UV nor the light source had any influence on determining which pathway was activated. Rather, we found that the viability of the antigen was the critical determinant. When live antigens were used, UV-induced immune suppression was blocked with monoclonal anti-cis-UCA but not with T4 endonuclease V-containing liposomes. The reverse was observed when formalin-fixed or killed antigens were used. Our findings indicate that antigen viability dictates which photoreceptor pathway predominates after UV exposure.     

Rapid method for evaluating reversed-phase high-performance liquid chromatography column stability

A procedure is presented for the rapid evaluation of HPLC stationary phase stability at pH 8.4 or 10.1 using a temperature of 60 degrees C. Mobile phase (MeOH-0.1 mol l(-1) aqueous NaHCO3, 50:50, v/v) is continuously passed through the column with periodic injections of a test solution until the several chromatographic parameters of the resulting chromatograms are degraded. The tests were applied to several commercial and laboratory-made stationary phases. After degradation two of these phases, one commercial and one laboratory-made, were examined by elemental analysis and scanning electron microscopy to elucidate the degradation process.