Discrete groups of slow subgroup growth

It is known that the subgroup growth of finitely generated linear groups is either polynomial or at least $n^{\frac{{\log n}}{{\log \log n}}} $ . In this paper we prove the existence of a finitely generated group whose subgroup growth is of type $n^{\frac{{\log n}}{{(\log \log n)^2 }}} $ . This is the slowest non-polynomial subgroup growth obtained so far for finitely generated groups. The subgroup growth typen ^logn is also realized. The proofs involve analysis of the subgroup structure of finite alternating groups and finite simple groups in general. For example, we show there is an absolute constantc such that, ifT is any finite simple group, thenT has at mostn ^{c logn} subgroups of indexn.     

Charge neutralization of ions from benzene

Cross-sections have been measured for the charge neutrilization if ions from benzene in kiloelectron-volt collisions with benezene target molecules. Measured values range from 65 Ų for the symmetric [C₆H₆]⁺? C₆H₆ resonant reactions to 8 Ų for [C₃H₃]⁺? C₆H₆ reactions. Cross-sections computed using a simple resonance charge transfer model compare favourably with experimental data for the symmetric reactions. The cross-sections for asymmetric reactions are smaller that those for they symmetric system and magnitudes of the asymmetric cross-sections are correlated with recombination energies of the respective ions.     

Synthesis of (pyridinyl)-1,2,4-triazolo[4,3-a]pyridines

Methods for the synthesis of (pyridinyl)-1,2,4-triazolo[4,3-a]pyridines were developed. The principal route to the required intermediate 2-chloropyridines was based on rearrangements of mono N-oxides of 2,2′-bipyridine, 2,3′-bipyridine, 3,3′-bipyridine, 2,4′-bipyridine and 4,4′-bipyridine with phosphorus oxychloride. Reaction of 3,3′-bipyridine 1-oxide or 2,2′-bipyridine 1-oxide with phosphorus oxychloride gave mixtures of chloro isomers. Reaction with acetic anhydride, 3,3′-bipyridine 1-oxide and 2,2′-bipyridine 1-oxide gave exclusively [3,3′-bipyridine]-2(1H)-one and [2,2′-bipyridine]-6(1H)-one, respectively. 1,2,4-Triazolo[4,3-a]pyridines with pyridinyl groups at the 5,6,7 and 8 positions were synthesized.     

Partial-filling affinity capillary electrophoresis

Partial-filling affinity capillary electrophoresis (PFACE) is used to examine the binding interactions between two model biological systems: D-Ala-D-Ala terminus peptides to the glycopeptide antibiotic vancomycin (Van) from Streptomyces orientalis, and arylsulfonamides to carbonic anhydrase B (CAB, EC 4.2.1.1, bovine erythrocytes). Using these two systems, modifications in the PFACE technique are demonstrated including flow-through PFACE (FTPFACE), competitive flow-through PFACE (CFTPFACE), on-column ligand synthesis PFACE (OCLSPFACE), and multiple-step ligand injection PFACE (MSLIPFACE). In PFACE small plugs of sample are injected into the capillary column and an equilibrium is established between receptor and ligand during electrophoresis. Binding constants are then obtained by Scatchard analysis using changes in the migration time of the receptor/ligand on changing the concentration of the ligand/receptor. Data demonstrating the quantitative potential of these methods are presented. This review focuses on the unique capabilities of the different PFACE techniques as applied to two model biological systems.     

On the viability of small endohedral hydrocarbon cage complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, AND X@C16H16

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H(+), H, He, Ne, Ar, Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,+,2+)) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C(4)H(4), T(d)()) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C(8)H(8), O(h)()) and bicyclo[2.2.2]octane (C(8)H(14), D(3)(h)()) minima are limited to encapsulating species smaller than Ne and Na(+). Despite its intermediate size, adamantane (C(10)H(16), T(d)()) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li(0,+), Be(0,+,2+), Na(0,+), and Mg(2+). In contrast, the truncated tetrahedrane (C(12)H(12), T(d)()) encapsulates fewer species, while the D(4)(d)() symmetric C(16)H(16) hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg(+) species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C-C bonding and C-H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E(endo)) to the sum of their isolated components (E(inc) = E(endo) - E(cage) - E(x)) and to their exohedral isomer energies (E(isom) = E(endo) - E(exo)). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E(isom) is always exothermic), Be(2+)@C(10)H(16) (T(d)(); -235.5 kcal/mol), Li(+)@C(12)H(12) (T(d)(); 50.2 kcal/mol), Be(2+)@C(12)H(12) (T(d)(); -181.2 kcal/mol), Mg(2+)@C(12)H(12) (T(d)(); -45.0 kcal/mol), Li(+)@C(16)H(16) (D(4)(d)(); 13.3 kcal/mol), Be(+)@C(16)H(16) (C(4)(v)(); 31.8 kcal/mol), Be(2+)@C(16)H(16) (D(4)(d)(); -239.2 kcal/mol), and Mg(2+)@C(16)H(16) (D(4)(d)(); -37.7 kcal/mol) are relatively stable as compared to experimentally known He@C(20)H(20) (I(h)()), which has an E(inc) = 37.9 kcal/mol and E(isom) = -35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.     

Development of a flexible approach to Nuphar alkaloids via two enantiospecific piperidine-forming reactions

In this paper we describe the stereoselective synthesis of functionalized lactam 7 via two enantiospecific piperidine-forming techniques and its employment in a general synthetic approach to Nuphar alkaloids. Specifically, the formation of piperidine 18 by formal [3 + 3] cycloaddition and stepwise annelation processes is described; the latter technique was found to be significantly more efficient than the Pd-catalyzed TMM addition process. Finally, exploitation of the exocyclic alkene installed in the piperidine-forming reaction in the transformation of 18 to (-)-deoxynupharidine ((-)-2), (-)-castoramine ((-)-3), and (-)-nupharolutine ((-)-4) via intermediate lactam 7 is delineated.     

Observations on maximum entropy processing of MR images

A maximum entropy (MAXENT) criteria for MR image processing optimizations has previously shown poor performance, but this note observes that there are two entirely different kinds of "data transmission" applications which appear to have been intermixed. In the two cases, "image entropy" actually refers to different kinds of data variables. The previous literature formulations are for transfer of data in which pixel-locations are the transmitted variable, and these pixels may be neither uniform nor constant. The second application concerns the MRI data set for display. Its data variables are image pixel-values of magnetization intensity, and the data transfer mode has the sense of visual display. When MAXENT criteria are modified to address an array of pixel-value intensities, and use a pixel-value information entropy rather than pixel-locations entropy, then successful data processing results. Restoring display visualization from highly nonuniform surface coils for lumbar spine scans are demonstrated, as an example of MAXENT usefulness.     

A Novel, Simple and Efficient Synthesis of Ferrocenyl Enones and Alkynols

Propargylic alcohols are versatile precursors to many organic molecules including natural products and pharmaceutical compounds.[1] In our continuing interest in the development of practical methods for synthesis of ferrocene derivatives, we decided to investigate the efficiencies of ferrocenylacetylene addition to aromatic aldehydes under t-BuOKcatalyzed condition.[2] Interestingly, we found that the usually reliable coupling reaction between terminal alkyne of type 1 and aromatic aldehydes of type 2 does not furnish the expected propargylic alcohols, but that the isomeric aryl enones 3are found in high yield and very short reaction time (10～20 min). This provided a promising protocol for preparation of ferrocenyl chalcones in a practical, economical and mild sense compared with the traditional method. To the best of our knowledge, this unusual reaction was first observed for the addition of ferrocenylacetylene to aldehyde in a base-catalyzed manner (Eq. 1).     

Reactions of tertiary propargyl alcohols with sodium halides under oxidative conditions

The study of the reactions of tertiary propargyl alcohols with sodium halides under oxidative conditions is presented. With sodium iodide, α-iodoenones were formed, however, with sodium bromide or chloride the α-haloenones were only formed in low yields under anhydrous conditions. Conversely, upon addition of water to the reaction mixtures, α,α-dibromoketones and α,α-dichloroketones were formed in good yields, but α,α-diiodoketones were not observed.