Bicyclic units, Bass cyclic units and free groups

Let G be a finite group and ZG its integral group ring. We show that if alpha is a nontrivial bicyclic unit of ZG, then there are bicyclic units beta and gamma of different types, such that and are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ZG, such that < u(m), v > is a free non-abelian group for all sufficiently large positive integers m.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

Units of F5kD10

2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.

[B4O9H2] Cyclic Borate Units as the Building Unit in a Family of Zinc Borate Structures

A solvothermal reaction of ZnO, boric acid (B(OH)(3)), and aliphatic airlines in a water-pyridine mixture gave four zinc borate phases of different dimensionalities: [Zn(B4O8H2)(C3H10N2)], I (one-dimensional); [Zn(B4O8H2)(C3H10N2)] H2O, II (two-dimensional); [Zn(B5O10H3)(C10H24N4)]center dot H2O, III (two-dimensional): and [Zn-2(B8O15H2)(C3H10N2)(2)], IV (three-dimensional). The structures are formed by the connectivity involving polyborate chains and layers with Zn2+ species. In all the compounds, the amine molecules act its file ligand binding either the same or different zn centers. The formation of two different structures, II and IV, from the same amine by varying the reaction time is noteworthy. Transformation studies on II indicate that the formation of IV. from II, is facile and has been investigated for the first time. Two of file compounds, I and III, exhibit activity for second-order nonlinear optical behavior. The UV exposure of the sample indicates the absorption of all the UV radiation suggesting that the zinc borate compounds could be exploited for UV-blocking applications. The compounds have been characterized by powder X-ray diffraction, infrared spectroscopy, thermogravimetric analysis, UV-vis, photoluminescence, and NMR studies.

Cyclic AMP Increases Cell Surface Expression of Functional Na,K-ATPase Units in Mammalian Cortical Collecting Duct Principal Cells

Cyclic AMP (cAMP) stimulates the transport of Na+ and Na,K-ATPase activity in the renal cortical collecting duct (CCD). The aim of this study was to investigate the mechanism whereby cAMP stimulates the Na,K-ATPase activity in microdissected rat CCDs and cultured mouse mpkCCDc14 collecting duct cells. db-cAMP (10−3 M) stimulated by 2-fold the activity of Na,K-ATPase from rat CCDs as well as the ouabain-sensitive component of 86Rb+ uptake by rat CCDs (1.7-fold) and cultured mouse CCD cells (1.5-fold). Pretreatment of rat CCDs with saponin increased the total Na,K-ATPase activity without further stimulation by db-cAMP. Western blotting performed after a biotinylation procedure revealed that db-cAMP increased the amount of Na,K-ATPase at the cell surface in both intact rat CCDs (1.7-fold) and cultured cells (1.3-fold), and that this increase was not related to changes in Na,K-ATPase internalization. Brefeldin A and low temperature (20°C) prevented both the db-cAMP-dependent increase in cell surface expression and activity of Na,K-ATPase in both intact rat CCDs and cultured cells. Pretreatment with the intracellular Ca2+ chelator bis-(o-aminophenoxy)-N,N,N′,N′-tetraacetic acid also blunted the increment in cell surface expression and activity of Na,K-ATPase caused by db-cAMP. In conclusion, these results strongly suggest that the cAMP-dependent stimulation of Na,K-ATPase activity in CCD results from the translocation of active pump units from an intracellular compartment to the plasma membrane.

Structure and Conformation of a Cyclic Tripeptide

MANY cyclic peptides have interesting biological functions and the details of their molecular structure and conformation have been the subject of extensive investigations. Cyclic dipeptides such as diketopiperazine have been synthesised and shown to occur with the peptide units in the cis configuration1,2. In the case of a tripeptide, cyclisation can take place only if all three units are in the cis configuration3. In cyclic peptides with four units also, cis peptides are found4,5. As the number of the peptide units increases, the more stable trans configuration is generally more common6,7. We report here the main results of our X-ray crystallographic investigations of the cyclic tripeptides L-Pro-L-Pro-L-Pro and L-Pro-L-Pro-L-Hyp (hereafter called CTP 1 and CTP 2, respectively). CTP 1 was synthesised by Rothe et al. 8 and its derivatives have been prepared by Blout and his collaborators9.

Stereochemical studies on cyclic peptides: Detailed energy minimization studies on hydrogen bonded all-trans cyclic pentapeptide backbones

Conformational studies have been carried out on hydrogenbonded all-trans cyclic pentapeptide backbone. Application of a combination of grid search and energy minimization on this system has resulted in obtaining 23 minimum energy conformations, which are characterized by unique patterns of hydrogen bonding comprising of β- and γ-turns. A study of the minimum energy conformationsvis-a-vis non-planar deviation of the peptide units reveals that non-planarity is an inherent feature in many cases. A study on conformational clustering of minimum energy conformations shows that the minimum energy conformations fall into 6 distinct conformational families. Preliminary comparison with available X-ray structures of cyclic pentapeptide indicates that only some of the minimum energy conformations have formed crystal structures. The set of minimum energy conformations worked out in the present study can form a consolidated database of prototypes for hydrogen bonded backbone and be useful for modelling cyclic pentapeptides both synthetic and bioactive in nature.

Stereochemical studies on cyclic peptides. Part XI. Conformation of cyclic pentapeptides having intramolecular 3 leads to 1 hydrogen bonds.

Conformational analysis of cyclic pentapeptides having two intra-ring 3 leads to 1 hydrogen bonds has been carried out. It is found that the structure can easily be formed with trans planar peptide units without causing significant angular strain at the alpha-carbon atoms. Four different types of conformations designated Types I--IV are possible for the backbone structure. Details of these four types of conformations and also the accommodating possibility of these types for allglycyl and all-alanyl residues are presented. Three of the four types have relatively low energies for glycyl residues whereas the other one has a slightly higher energy. When alanyl residues are introduced at the five alpha-carbon atoms, the types that are energetically favourable depend upon the sequence of isomers. Energy calculations have also been carried out for the combinations of glycyl, L- and D-alanyl residues. The theoretical results are compared with available experimental observations both from solution and solid state studies.

Self-assembly of discrete metallamacrocycles employing half-sandwich octahedral diruthenium(II) building units and imidazole-based ligands

Equimolar combination of a series of binuclear half-sandwich p-cymene ruthenium(II) building units Ru-2(mu-eta(4)-C2O4)(MeOH)(2)(eta(6)-p-cymene)(2)](OTf)(2) 1a](OTf)(2), Ru-2(mu-eta(4)-N,N'-diphenyloxamidato)( MeOH)(2)(eta(6)-p-cymene)(2)](OTf)(2) 1b](OTf)(2) and Ru-2(mu-eta(4)-C6H2O4)(MeOH)(2)(eta(6)-p-cymene)(2)](OTf)(2) 1c](OTf)(2) separately with imidazole-based ditopic ligands (L-1-L-2) in methanol yielded a series of tetranuclear metallamacrocycles 2-7](OTf)(4), respectively L-1 = 1,4-bis(imidazole-1-yl)benzene; L-2 = 4,4'-bis(imidazole-1-yl)biphenyl; OTf- = O3SCF3-]. Similarly, the reaction of Ru-2(mu-eta(4)-C2O4)(MeOH)(2)(eta(6)-p-cymene)2](OTf)(2) 1a](OTf)(2) with a triazine-based tritopic ligand 1,3,5-tris(imidazole-1-yl) triazine (L3) in 3: 2 M ratio afforded an unexpected tetranuclear macrocycle 8](OTf)(4) instead of an expected trigonal prismatic cage 8a](OTf)(6). All the self-assembled macrocycles 2-8](OTf)(4) were isolated in moderate to high yields and were fully characterized by multinuclear H-1, F-19] NMR, IR and electrospray ionization mass spectrometry (ESI-MS). In addition, X-ray diffraction study on the single crystals of 3](OTf)(4) and 8](OTf)(4) also indicated the formation 2 + 2] self-assembled macrocycles. Despite the possibility of formation of different conformational isomeric macrocycles (syn-and anti) and polymeric product due to free rotation of ligand sites of imidazole linkers, the selective formation of single conformational isomer (anti) as the only product is quite interesting. Furthermore, the photo-and electrochemical properties of these assemblies have been studied using UV/Vis absorption and cyclic voltammetry analysis. (c) 2013 Elsevier B.V. All rights reserved.

Performance Analysis of Heat Sinks With Phase-Change Materials Subjected to Transient and Cyclic Heating

Phase-change cooling technique is a suitable method for thermal management of electronic equipment subjected to transient or cyclic heat loads. The thermal performance of a phase-change based heat sink under cyclic heat load depends on several design parameters, namely, applied heat flux, cooling heat transfer coefficient, thermophysical properties of phase-change materials (PCMs), and physical dimensions of phase-change storage system during melting and freezing processes. A one-dimensional conduction heat transfer model is formulated to evaluate the effectiveness of preliminary design of practical PCM-based energy storage units. In this model, the phase-change process of the PCM is divided into melting and solidification subprocesses, for which separate equations are written. The equations are solved sequentially and an explicit closed-form solution is obtained. The efficacy of analytical model is estimated by comparing with a finite-volume-based numerical solution for both transient and cyclic heat loads.

Soluble, saturated-red-light-emitting poly(p-phenylenevinylene) containing triphenylamine units and cyano groups

A conjugated poly(p-CN-phenylenevinylene) (PCNPV) containing both electron-donating triphenylamine units and electron-withdrawing cyano groups was prepared via Knoevenagel condensation in a good yield. Gel permeation chromatography suggested that the soluble polymer had a very high weight-average molecular weight of 309,000. A bright and saturated red emission was observed under UV excitation in solution and film. Cyclic voltammetry showed that the polymer presented quasi-reversible oxidation with a relatively low potential because of the triphenylamine unit. A single-layer indium tin oxide/PCNPV/Mg-Ag device emitted a bright red light (633 nm).

Novel bipolar conjugated polymer containing both triphenylamine and oxadizole units

A novel bipolar conjugated polymer containing triphenylamine and 1, 3, 4-oxadiazole units was synthesized by Suzuki reaction. Its structure and properties were characterized by NMR, IR, UV-Vis, PL spectroscopy and electrochemical measurement. The photo luminescent spectroscopy and cyclic voltammograms measurement demonstrated that the resulting polymer shows blue emission (477 nm) and possesses both electron and hole-transporting property.

Novel macrocyclic precursors of poly{aryl ether ketone (sulfone)} containing hexafluoroisopropylidene units: Synthesis, characterization, and polymerization

Cyclic oligomers containing hexafluoroiso-propylidene(HFIP) units were prepared in excellent yields by a nucleophilic aromatic substitution reaction of 4,4(7)- (hexafluoroisopropylidene) diphenol with difluoro-monomers in the presence of anhydrous potassium carbonate under pseudo high dilution conditions. A combination of GPC, MALDI-TOF MS and NMR analysis confirmed the structure of the cyclic oligomers. All macrocyclic oligomers are crystalline and undergo facile melt polymerization to give high molecular weight fluorinated polyethers.

Synthesis and characterization of novel bipolar PPV-based copolymer containing triazole and carbazole units

Two new blue light-emitting PPV-based conjugated copolymers containing both an electron-withdrawing unit (triazole-TAZ) and electron-rich moieties (carbazole-CAR and bicarbazole-BCAR) were prepared by Wittig condensation polymerization between the triazole diphosphonium salt and the corresponding dialdehyde monomers. Their structures and properties were characterized by FT-IR, TGA, DSC, UV-Vis, PL spectroscopy and electrochemical measurements. The resulting copolymers are soluble in common organic solvents and thermally stable with a T-g of 147degreesC for TAZ-CAR-PPV and of 157degreesC for TAZ-BCAR-PPV. The maximum photoluminescence wavelengths of TAZ-CAR-PPV and TAZ-BCAR-PPV film appear at 460 nm and 480 nm, respectively. Cyclic voltammetry measurement demonstrates that TAZ-BCAR-PPV has good electrochemical reversibility, while TAZ-CAR-PPV exhibits the irreversible redox process. The triazole unit was found to be an effective pi-conjugation interrupter and can play the rigid spacer role in determining the emission colour of the resulting copolymer.