Inverse ambiguous functions on some finite non-abelian groups

In Schmitz (Aequ Math 91:373–389, 2017), the first author defines an “inverse ambiguous function” on a group G to be a bijective function \(f:G \rightarrow G\) satisfying the functional equation \(f^{-1}(x) = (f(x))^{-1}\) for all \(x \in G\). Using a simple criterion involving the number of elements in G not equal to their own inverse, the classification of finite abelian groups admitting inverse ambiguous functions is achieved. In this paper we aim to extend the results from (2017) to determine the existence of inverse ambiguous functions on members of certain families of non-abelian groups, namely the symmetric groups \(S_n\), the alternating groups \(A_n\), and the general linear groups GL(2, q) over a finite field \(\mathbb {F}_q\).     

Efficient clustering of cyclic sulfonium salts applying liquid secondary ion mass spectrometry

Salt-like cluster ions of the ([cation](n)[anion](n-1))(+) type are commonly composed of mono-atomic, inorganic components. Clusters containing organic ions are also known, with nitrogen-centred cations being particularly prominent. However, sulphur-centred analogues, such as organic sulphonium salts, represent a notable exception. Fast atom bombardment and liquid secondary ion mass spectrometry of such compounds show, in general, a low tendency towards the formation of clusters. The present study reveals that sputtering of cyclic sulphonium salts leads to the efficient formation of cluster ions beyond previous observations. Cluster ions are characterised by isotopic pattern analysis and collision-induced dissociation.     

High-spin structure of yrast-band in 78Kr

Lifetime of levels up to 22⁺, have been measured in ⁷⁸Kr and an oblate shape is assigned to the ground state using the CSM and the configuration dependent shell correction calculations. Calculations further show that ⁷⁸Kr is highly γ-soft nucleus. The experimental Q _t values coupled with theoretical calculations indicate an oblate shape for ⁷⁸Kr at low spins and triaxial shape at higher spins     

Kinetic analysis of complex decomposition reactions using evolved gas analysis

For complex decomposition reactions, traditional methods, such as TG and DSC cannot fully resolve all of the steps in the reaction. Evolved gas analysis (EGA) offers another tool to provide more information about the decomposition mechanism. The decomposition of sodium bicarbonate was studied by TG, DSC and EGA using a simultaneous thermal analysis unit coupled to a FTIR. The decomposition of sodium bicarbonate involves two reaction products H₂O and CO₂, which are not evident from either TG or DSC measurements alone. A comparison of the reaction kinetics from TG, DTG and EGA data were compared.     

An allylstannane reagent on non-cross-linked polystyrene support

[reaction: see text] A new allylstannane reagent on non-cross-linked polystyrene was developed for the first time. This support differs markedly from standard cross-linked polymers because it is completely soluble in organic solvents; moreover, the reactions can be conveniently monitored directly by standard 1H NMR methods. The allylstannane underwent a free radical reaction with an alkyl halide to form a new allyl appendage. Tin byproducts can be easily recovered from cold methanol as white crystalline solids.     

Synthesis of two fluoro analogues of the nicotinic acetylcholine receptor agonist UB-165

Two racemic fluoropyridine analogues 4 and 5 of the potent nicotinic agonist UB-165 have been synthesized. Halogenated pyridines 7 and 12 provided the organometallic reagents needed for the Negishi and Suzuki coupling reactions used for the preparation of 4 and 5, and the N-vinyloxycarbonyl protecting group of 8 and 15 was cleaved using a novel trifluoroacetic acid-mediated deprotection protocol. Analogue 4 retained high binding affinity at rat brain alpha4beta2 and alpha7 nicotinic receptors.     

Synthesis of 4-hydroxy-6,9-difluorobenz[g]isoquinoline-5,10-diones and conversions to 4-hydroxy-6,9-bis[(aminoalkyl)amino]-benz[g]isoquinoline-5,10-diones

Synthetic procedures have been developed which lead to 4-hydroxy-6,9-difluorobenz[g]isoquinoline-5,10-dione ( 4a ) and its 3-methyl analogue 4b . Attempts to displace the fluorides from 4a with N,N-dimethylethylenediamine were unsuccessful. Analogue 4a on treatment with N-(t-butoxycarbonyl)ethylene diamine led to 15 , formed from addition of the nucleophilic amine to C-3. On the other hand, analogue 4b , on treatment with N,N-dimethylethylenediamine led to the anticipated difluoride displacement product 3c . The protection of the hydroxy group of 4a by benzylation with phenyldiazomethane led to 4c which on treatment with N-(t-butoxycarbonyl)ethylene diamine or N,N-dimethylethylenediamine led to the corresponding 6,9-bis-substituted analogues 18a and 18b , respectively. Reductive debenzylations of 18a and 18b by hydrogenation over Pearlman's catalyst also effected partial reductions of the quinone. However, air oxidation of the over reduced products led to 3a and 3b , respectively. Treatment of 3a with hydrogen chloride gas led to the hydrochloride salt of 3d . Addition of O-p-Methoxybenzyl-N,N'-diisopropylurea to 4a led to the p-methoxybenzyl analogue 4d . Treatment of 4d with N,N-dimethylethylene diamine or N-(t-butoxycarbonyl)ethylene diamine led to displacements of the fluorides to yield 18c and 18d , respectively. Deprotection of 18c to 3b was accomplished using methanesulfonic acid. Treatment of 18d with trifluoroacetic acid followed by addition of maleic acid led to dimaleate salt of 3d .     

Synthesis of regioisomeric 6,9-(chlorofluoro)-substituted benzo[g]quinoline-5,10-diones,benzo[g] isoquinoline-5,10-diones and 6-chloro-9-fluorobenzo[g]quinoxaline-5,10-dione

Treatment of difluoro or chloro fluoro-substituted benzyl bromides 5a-c with zinc dust in tetrahydro-furan leads to the corresponding benzylic zinc bromides 6a-c. These organometallics on treatment with chlorosubstituted heterocyclic esters 4A and 4B mediated by nickel catalysis undergo couplings to yield dihalobenzyl substituted heterocyclic esters 7Aa-c and 7Ba-c. Treatment of 4c with 6c under Pd catalysis leads to 7Cc. The acids 8, prepared by hydrolysis of these esters, with treatment of fuming sulfuric acid undergo cyclizations and oxidations to yield the desired regioisomeric dihalo-substituted heterocyclic quinones 2.