Symmetric Unit Research Articles

IN-GAP OPTICAL BISTABILITIES OF DEEP NONLINEAR BRAGG GRATING WITH SYMMETRIC THREE-LAYER UNIT CELLS

A numerical study on the hysteretic responses of deep nonlinear Bragg grating systems with symmetric three-layer unit cells has been carried out on the basis of a generalized coupled mode theory modified to accommodate deeper nonlinear refractive index modulation. The results show that the in-gap bistability offers the most favorable features in terms of switching width and threshold for optical switching application. Calculated variations of these operational features with respect to the layer thickness, operating wavelength and nonlinear index contrast provide useful guidance for the design of grating systems intended for specific optical switching applications.

Symmetrisation in the Interaction of Chloro[2‐(dimethylaminomethyl)phenyl‐C1]mercury(II) with Thiosemicarbazone Derivatives of Pyridine‐2‐carboxamide and Pyrazin‐2‐carboxamide

AbstractPyridine‐ and pyrazine‐2‐carboxamide thiosemicarbazones (HAm4DH and HAmpz4DH) or their N4,N4‐dimethyl derivatives (HAm4DM and HAmpz4DM) react with chloro[2‐(dimethylaminomethyl)phenyl‐C1]mercury(II), [Hg(damp)Cl], to give the tetrahedral [Hg(TSC)2] complexes [TSC = Am4DH (1), Am4DM (2), Ampz4DH (3) or Ampz4DM (4)]. Spectroscopic studies and a X‐ray structural analysis show that the potentially tridentate thiosemicarbazones adopt S,N coordination modes, with each deprotonated thiosemicarbazone binding to the HgII centre through the azomethine nitrogen and the thiolate sulfur atoms, whereas the heterocyclic nitrogen atoms are free of coordination. Intra‐ and intermolecular hydrogen bonding in all complexes and specific C–H···π interactions with the chelate or pyridyl rings of the complexes 1 and 2 were found in the crystal structures. Furthermore, [Hg(damp)Cl] undergoes symmetrisation to give the symmetric unit [Hg(Hdamp)2]2+ in which the Hdamp is protonated at the nitrogen. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

Dichloro[2,2′-(methylenedithio)bi-1,3-thiazole-κ2 N,N′]cobalt(II)

In the title complex, [CoCl2(C7H6N2S4)], 2,2′-(methylenedithio)bi-1,3-thiazole acts as a bidentate ligand and chelates one CoII ion through the two N atoms to give an eight-membered symmetric unit. The CoII ion is located on a twofold axis and displays a slightly distorted tetrahedral coordination environment, where the two Cl− anions occupy the remaining coordination sites. The N—Co—N and Cl—Co—Cl planes are nearly perpendicular, with a dihedral angle of 88.0 (3)°.

A copper(II) coordination polymer based on flexible spacer ligands: Synthesis, crystal structure, and magnetic properties of the adipato complex [Cu 4(bpy) 4(adip) 3](tcnp) 2 [bpy = C 10H 8N 2; [formula omitted]; [formula omitted

One-pot reaction of copper(II) chloride dihydrate CuCl 2 · 2H 2O with sodium adipate Na 2adip ( adip 2 - = O 2 C ( CH 2 ) 4 CO 2 2 - ) in the presence of 2,2′-bipyridyl (bpy = C 10H 8N 2) and potassium 1,1,3,3-tetracyano-2-ethoxypropenide ( tcnp - = ( NC ) 2 CC ( OEt ) C ( CN ) 2 - ) gives the new compound [Cu 4(bpy) 4(adip) 3](tcnp) 2 ( 1), which was characterized by single crystal X-ray diffraction analysis. Each metal ion presents an elongated square pyramidal CuN 2O 3 environment, with an oxygen atom in apical position and a base plane involving almost equivalent bond lengths. The structure can be described as a pseudo dinuclear species in which two Cu(bpy) units are triply bridged by two unsymmetrical bridging oxygen atoms of two carboxylate groups with a κ-μ-bridging mode and by an almost symmetrical OCO unit with a bidentate syn– syn κ:κ–μ-bridging mode. Such coordination modes generate the tetranuclear Cu 2(adip) 2Cu 2 units which are bound by a symmetrical adipate ligand through a κ-μ-bridging mode to lead to infinite chains involving a succession of Cu 2 units alternatively bridged by one or two aliphatic chains of adipate ligands. Magnetic measurements exhibit a maximum in the χ m versus T plot (at ∼15.2 K), which is characteristic of weak antiferromagnetic exchange interactions between the Cu(II) ions bridged by the carboxylate groups. Fit of the magnetic data with appropriate model led to J value of −7.74 cm −1 (the Hamiltonian is written as H = −2 JS a S b ).

Synthesis and Biological Evaluation of Heteroaryldiamides and Heteroaryldiamines as Cytotoxic Agents, Apoptosis Inducers and Caspase‐3 Activators

The work described here involved the synthesis and biological evaluation of new heteroaryldiamides and heteroaryldiamines. A new general model in which the structures can be adjusted has been applied in this study. Three different structural units can be distinguished: a central nucleus and two symmetric terminal units. The central element is either an aliphatic chain of varying length and flexibility, piperazine, or a polyamine nucleus. However, the terminal units are pyridine, quinoline, indole, benzene or pyrido[2,3-d]pyrimidine with different substituents. The antitumoural activities of the compounds were evaluated in vitro by examining their cytotoxic effects against human breast, colon, and bladder cancer cell lines. Compounds that showed cytotoxic activity were subjected to both apoptosis and caspase-3 assays. With regard to selectivity, the cytotoxicity was also determined in cell cultures of two nontumoural lines. The most promising compounds are 4c, 5c and 7, which are amino-pyridinium, quinolyl-N-oxide, and pyridyl derivatives, respectively, and these reveal a significant in vitro cytotoxicity in at least two of the three cell lines tested. These compounds induced apoptosis and also produced a rapid dose-dependent increase in the caspase-3 level in HT-29 cells. Other encouraging profiles were found, such as those presented by 1k and 8d, which are cytotoxic and apoptotic but do not provoke an increase in the level of caspase-3, or those presented by 2f, 3c and 4a, which are slightly cytotoxic but do not show any other significant activity. The different types of behaviour of each compound are not necessarily parallel in the three cell lines tested.

On Symmetric Elements and Symmetric Units in Group Rings

ABSTRACT Let R be a commutative ring, G a group, and RG its group ring. Let ϕ: RG → RG denote the R-linear extension of an involution ϕ defined on G. An element x in RG is said to be symmetric if ϕ (x) = x. A characterization is given of when the symmetric elements (RG)ϕ of RG form a ring. For many domains R it is also shown that (RG)ϕ is a ring if and only if the symmetric units form a group. The results obtained extend earlier work of Bovdi (2001), Bovdi et al. (1996), Bovdi and Parmenter (1997), Broche Cristo (2003, to appear), Giambruno and Sehgal (1993), and Lee (1999), who dealt with the case that ϕ is the involution * mapping g ∈ G onto g−1.

Commutativity of symmetric elements in group rings

Let R be a commutative ring with unity and let G be a group. The group ring RG has a natural involution that maps each element of G to its inverse. We denote by RG + the set of symmetric elements under this involution. We study necessary and suffient conditions for RG + to be commutative or, equivalently, for RG + to be a subring of RG . We also determine all torsion groups G such that the set of symmetric units of RG is a subgroup, when char( R ) is an odd prime number.

Group algebras with symmetric units satisfying a group identity

We study group algebras FG for which the symmetric units under the natural involution: g *=g −1 satisfy a group identity. For infinite fields F of characteristic ≠2, a classification of torsion groups G whose symmetric units U +(FG) satisfy a group identity was given in [3] by Giambruno-Sehgal-Valenti. We extend this work to non torsion groups.

Crystal Structures and Characterizations of (Nitrato-O)(Nitrato-O,O′)(η6-Hexamethylbenzene)Ruthenium(II) and Di(Trifluoroacetato-O)(H2O-O)(η6-Hexamethylbenzene) Ruthenium(II)

The title complexes [(HMB)Ru(NO3)2] (HMB=η6-C6Me6) (1) and [(HMB)Ru(O2CCF3)2(H2O)] (2) were spectroscopically characterized and their structures were determined by single-crystal diffraction analysis. In both compounds, the Ru atom is η6-coordinated to a hexamethylbenzene ring and three oxygen donor atoms in a “three-legged piano stool” arrangement. In the asymmetric unit of 1, ruthenium atom is coordinated to two nitrato ligands, one of which is η1-O coordinated and the second bidentate via both oxygen atoms; while in the symmetric unit of 2, two disordered trifluoroacetate ligands are monodentate, symmetrically bound to the ruthenium atom, and the pseudo-octahedral geometry is completed by an oxygen atom from a H2O molecule, which is hydrogen-bonded to both acetate ligands. Crystallographic data for 1 and 2 have been deposited at the Cambridge Crystallographic Data Centre with CCDC numbers 270839 and 270840, respectively. Copies of the information can be obtained free of charge from The Director, CCDC, 12 Union Road, Cambridge CB2 1EZ, UK (fax: +44(0)1223-336033; e-mail: deposit@ccdc.cam.ac.uk or http://www.ccdc.cam.ac.uk).

Dimethyl-, diphenyl- and cyclotetramethylene silylchloride derivatives of guanidine, their synthesis and structure. Formation of pentacoordinated silicon compounds and an unexpected diionic disila-diguanidinium dichloride

The reaction of 1,3,4,6,7,8-hexahydro-2 H-pyrimido[1,2 a]pyrimidinyl potassium, [hpp] −K + ( 1), with dimethyldichlorosilane, diphenyldichlorosilane or cyclotetramethylenedichlorosilane (1,1-dichloro silolane) in THF resulted in the formation of the in solid-state unexpected diionic dimer λ 4 Si-[Me 2SiCl(hpp)] 2 ( 2) (76%), as well as λ 5 Si-Ph 2SiCl(hpp) ( 3) (87%) and λ 5 Si-(CH 2) 4SiCl(hpp) ( 4) (28%). Compounds 3 and 4 are the first synthesised examples of four ring (–λ 5 Si–N–C N–) guanidine structures. 1H and 13C NMR show the compounds to have a symmetric guanidine unit in solution. 29Si NMR analysis shows the structures, in selected solvents, to be of λ 5 Si-type for 3 and to the major part for 2. Compound 4, on the other hand, is of ionic λ 4 Si-type. The syntheses and molecular structures of the compounds are discussed.

Complexes of the heavier alkaline earth metals containing β-diketiminato and iodide ligand sets

Treatment of [ ( 2 , 6 - i Pr 2 C 6 H 3 ) NC ( t Bu ) CH 2 C ( t Bu ) N ( 2 , 6 - i Pr 2 C 6 H 3 ) ] ( L Ar ′ H ) with potassium hydride in tetrahydrofuran afforded K ( η 1 - L Ar ′ ) ( THF ) 3 (89%) as a yellow crystalline solid after workup. The crystal structure of K ( η 1 - L Ar ′ ) ( THF ) 3 revealed an open monomeric molecule in which the potassium ion is bonded to three tetrahydrofuran ligands and one η 1-β-diketiminato ligand through one of the nitrogen atoms. Treatment of K ( η 1 - L Ar ′ ) ( THF ) 3 with equimolar amounts of MI 2 (M = Ca, Ba) afforded [ Ca ( η 5 - L Ar ′ ) ( μ - I ) ( THF ) ] 2 (62%) and [ Ba ( η 2 - L Ar ′ ) ( μ - I ) ] 2 (27%) as yellow crystalline solids. Treatment of M(η 5-L tBu ) 2 (M = Ca, Sr, Ba, L tBu = tBuNC(CH 3)CHC(CH 3)N tBu −) with the corresponding metal iodide in tetrahydrofuran afforded [Ca(η 5-L tBu )(μ-I)(THF)] 2 (68%), [Sr(η 5-L tBu )(μ-I)(THF)] 2 (53%), and [(η 5-L tBu )Ba(μ-I)(μ-η 2:η 5-L tBu )Ba(η 5-L tBu )] 2(24%). Structural assignments for these complexes were based on spectral and analytical data as well as X-ray crystallography. [Ca(η 5-L tBu )(μ-I)(THF)] 2 and [Sr(η 5-L tBu )(μ-I)(THF)] 2 are dimers that are held together by bridging iodide ligands, while [Ba(η 5-L tBu )(μ-I)(μ-η 2:η 5-L tBu )Ba(η 5-L tBu )] 2 is a tetramer containing two symmetrical dimeric units that are linked by two bridging iodide ligands. In benzene- d 6 solution, [ Ca ( η 5 - L Ar ′ ) ( μ - I ) ( THF ) ] 2 and [ Ba ( η 2 - L Ar ′ ) ( μ - I ) ] 2 are stable toward ligand redistribution. [Ca(η 5-L tBu )(μ-I)(THF)] 2 exists as mixtures of three species in toluene- d 8, but the mixed ligand complex is strongly favored under the conditions studied. At 31.3 °C, the equilibrium constant for ligand redistribution of [Sr(η 5-L tBu )(μ-I)(THF)] 2 to Sr(η 5-L tBu ) 2 and SrI 2(THF) 2 in toluene- d 8 was 5.3 × 10 −5 M.

Signs of Ancient and Modern Exon-Shuffling Are Correlated to the Distribution of Ancient and Modern Domains Along Proteins

Exon-shuffling is an important mechanism accounting for the origin of many new proteins in eukaryotes. However, its role in the creation of proteins in the ancestor of prokaryotes and eukaryotes is still debatable. Excess of symmetric exons is thought to represent evidence for exon-shuffling since the exchange of exons flanked by introns of the same phase does not disrupt the reading frame of the host gene. In this report, we found that there is a significant correlation between symmetric units of shuffling and the age of protein domains. Ancient domains, present in both prokaryotes and eukaryotes, are more frequently bounded by phase 0 introns and their distribution is biased towards the central part of proteins. Modern domains are more frequently bounded by phase 1 introns and are present predominantly at the ends of proteins. We propose a model in which shuffling of ancient domains mainly flanked by phase 0 introns was important in the ancestor of eukaryotes and prokaryotes, during the creation of the central part of proteins. Shuffling of modern domains, predominantly flanked by phase 1 introns, accounted for the origin of the extremities of proteins during eukaryotic evolution.

Abstract passive interferometers with applications to conservative logic

Interferometers with two complex inputs and two complex outputs can be viewed as state machines over a 4-D hyperspace, where the relationship between outputs and inputs are transition functions. In the simplest case, there is full symmetry between inputs and between outputs. The nonzero inputs, the origin and the outputs define a 2-D plane in the 4-D space. The interferometer rotates the input vectors by π / 4 in the hyperspace. Cascading the symmetric units defines a simple Hamiltonian path of length 8 in a 2-D subspace. Breaking symmetry by introducing a relative phase shift in the input leads to more complex Hamiltonian paths that can require all four dimensions to describe. The special symmetry breaking caused by a π 2 phase shift in one of the input arms leads to outputs which, upon detection, are recognizable as Boolean and other simple operations on properly encrypted and interpreted inputs!

Demetallation of a Ni(II) tetraazamacrocyclic complex by cyanoxime resulting in the formation of a stereospecific trinuclear compound [Na(H2O)6]+[NaNi2L6]− (L = NC-C(NO)-C(O)NH)

The reaction between the NiA(ClO4)2 and NaHL2 {where A = 14ane[N4], the macrocyclic ligands derived from the product of template condensation of 2,6-diacetylpyridine with aliphatic 3,3′-diaminodipropylamine, NH2(CH2)3NH(CH2)3NH2; and L = 2-cyano-2-isonitrosoacetamide anion, ACO− (amidecyanoxime, NC-C(NO)-C(O) )} has led to the formation of a highly unusual trimetallic bis-[ fac-(triscyanoximato) nickel(II)] anionic complex anion instead of the expected Ni(II) macrocyclic complex with coordinated cyanoxime ligands. Two equivalent and symmetric trigonal-prismatic NiL units are connected to form the [NaNi2L6]− anion by the presence of a central sodium cation. The latter is located between two NiL anions and has an octahedral NaO6 geometry comprised of oxygen atoms of the nitroso group of the cyanoxime ligand. The oxime ligand is planar and adopts a cis-anti configuration in the complex.

Atomic structure of [0001]-tilt grain boundaries in ZnO: A high-resolution TEM study of fiber-textured thin films

The atomic structure of [0001]-tilt grain boundaries in ZnO was investigated using high-resolution transmission electron microscopy (HRTEM) and atomistic calculations. HRTEM observation was conducted for [0001] fiber-textured ZnO thin films grown on quartz-glass substrates by the pulsed-laser deposition. The [0001]-tilt boundaries observed in the films can be classified into three types: low-angle boundaries composed of irregular dislocation arrays, boundaries with ${10\overline{1}0}$ facet structures, and near-low $\ensuremath{\Sigma}$ boundaries represented by symmetric periodicity units. The atomic structure of the boundaries is discussed with a focus on a $\ensuremath{\Sigma}=7$ boundary in conjunction with atomistic calculations and HRTEM image simulations. The $\ensuremath{\Sigma}=7$ boundary consists of multiple structural units that are very similar to the core structures of edge dislocations. Straight or zigzag arrangements of the dislocationlike structural units constitute other high-angle boundaries with symmetric and ${10\overline{1}0}$ facet structures as well. It is suggested that [0001]-tilt boundaries in ZnO are generally described as an array of the dislocationlike units.

Types of internal structure and external morphology of submarine dunes under the influence of tide- and wind-driven processes (Dover Strait, northern France)

The expression of tide- and wind-driven processes in the internal architecture and external morphology of very large submarine dunes is investigated at a dune field located in the central part of the Dover Strait (Southern North Sea). Current measurements and sediment transport calculations enable quantification of the dominant tide- and wind-driven processes, and very high resolution seismic recordings are used to analyse internal structure and external morphology of dunes. In the study area, moderate to storm winds induce temporary currents that can lead to the reversal of sediment transport direction and induced erosive processes on the seabed. Dune master-bedding consists of extended erosive surfaces with 9–11° slopes that bound storm-generated sets of cross-beds, 1.5–4.85 m thick (2.65 m on average). Three types of architectures are observed within the dune field, and occasionally within single dunes. These types, which display a strong linkage between internal structure and external morphology, consist of: (1) asymmetric dunes with cosets, which dip in the direction of the marked external asymmetry of the dunes; (2) dunes with a complex external morphology composed of mega-herringbone structures, each displaying an opposing progradation direction; and (3) dunes with a symmetric megaripple bedding unit at their summit. The diversity of the internal architecture and external morphology results from the variable combinations of tide- and wind-driven processes occurring in the study area. The asymmetry of tidal peak current velocity and the relative strength of wind-driven currents are the parameters that have the most important influence on dune architecture. Asymmetric dunes with cosets result from a strong asymmetry in tidal peak current velocity, which is reversed only slightly during storms. Dunes with mega-herringbone structures and dunes with symmetric megaripple units at their summit are observed in areas where the asymmetry of the tidal peak current velocity is negligible, allowing reversal of the sediment transport and dune migration directions each time moderate winds blow. The latter architectural type is specific to sand-rich areas. The different dune architecture types display strong geometrical similarities to structures observed in dunes from other shelf environments where driving processes are different. This implies that a study based only on a geometric description of internal structures will not enable the reconstitution of ancient depositional environments. A better discriminant criteria seems to be the thickness of the second-order sets of cross-beds which is correlated with specific hydro-sedimentary processes. Dune height also probably has an important influence on the thickness of second-order sets of cross-beds, as dune height and set thickness display a clear relationship in the present study.

Ferroelectric order in highly disordered molecular-ionic crystals

The ordering of the anionic sublattice at the coexisting high orientational disorder of the cationic sublattice produces spontaneous polarization in imidazolium tetrafluoroborate $[{\mathrm{C}}_{3}{\mathrm{N}}_{2}{\mathrm{H}}_{5}{]}^{+}[{\mathrm{BF}}_{4}{]}^{\ensuremath{-}}.$ This ferroelectric crystal exhibits the Curie point at 297.0 K and undergoes two other polymorphic phase transitions at 213.6 and 187.8 K. In spite of its pentagonal ring the dynamically disordered polar cation is localized at a special position on the threefold axis of the highly symmetrical rhombohedral unit cell. Thus it does not contribute immediately to the spontaneous polarization which originates predominantly from the behavior of the distorted tetrahedral fluoroborate anion.

Synthesis, crystal structure and electrical characterization of Cs 4[(UO 2) 2(V 2O 7)O 2], a uranyl divanadate with chains of corner-sharing uranyl square bipyramids

A new cesium uranyl vanadate Cs 4[(UO 2) 2(V 2O 7)O 2] has been synthesized by solid-state reaction and its structure determined from single-crystal X-ray diffraction data. It crystallizes in the orthorhombic symmetry with space group Pmmn and following cell parameters: a=8.4828(15) Å, b=13.426(2) Å and c=7.1366(13) Å, V=812.8(3) Å 3, Z=2 with ρ mes=5.39(2) g/cm 3 and ρ cal=5.38(1) g/cm 3. A full-matrix least-squares refinement on the basis of F 2 yielded R 1=0.027 and w R 2=0.066 for 62 parameters with 636 independent reflections with I⩾2 σ( I) collected on a BRUKER AXS diffractometer with Mo Kα radiation and a charge-coupled device detector. The crystal structure is characterized by ∞ 2[(UO 2) 2(V 2O 7)O 2] 4− corrugated layers parallel to (001). The layers are built up from distorted (UO 2)O 4 octahedra and divanadate V 2O 7 units resulting from two VO 4 tetrahedra sharing corner. The distorted uranyl octahedra (UO 2)O 4 are linked by corners to form infinite ∞ 1[UO 5] 4− chains parallel to the a-axis. These chains are linked together by symmetrical divanadate units sharing two corners with each chain, the two last corners being oriented towards the same interlayer. The cohesion of the structure is assured by interlayer Cs + ions. Their mobility within the interlayer space gives rise to a cationic conductivity with an important jump between 635°C and 680°C. Cs 4[(UO 2) 2(V 2O 7)O 2] is readily decomposed by water at 60°C to form the Cs-carnotite analog Cs 2(UO 2) 2(V 2O 8) compound.

Solvothermal Synthesis and Characterization of Zn(NH3)CO3 Single Crystal

AbstractA new 3-dimensional zinc carbonate Zn(NH3)CO3 has been synthesized from a glycol system with urea and zinc acetate as raw materials. The crystal structure and photoluminescent properties have been investigated using X-ray diffraction, smart CCD and FL. The compound had an orthorhombic system with space group of Pna21 with M = 142.41, a = 9.1449(18) Å, b = 7.5963(15) Å, c = 5.4982(11) Å, V = 381.95(13) Å3, Z = 4, R = 0.0285 and RW = 0.0745. The NH3 and CO32- were connected through the Zn-N bond and Zn-O bond in the symmetric unit. Photoluminescent property was observed in the compound at room temperature and the exited and emission peaks were located at about 350 nm and 426 nm, respectively.

Determination of the degree of randomness in condensation copolymers containing both symmetrical and unsymmetrical monomer units: a theoretical study

Abstract Expressions for the degree of randomness, B, and for the number- and weight-average block lengths of condensation copolymers containing both symmetrical (AA + BB) and unsymmetrical (AB) monomer units are established through an approach based on functional group probabilities. Several parameters introduced in literature to characterize randomness in AA + BB condensation copolymers are also calculated using this approach and compared to B, showing that they are simple linear or rational functions of B. A method for calculating functional group probabilities from the dyad and triad number-fractions determined by NMR spectroscopy is described for poly(ethylene terephthalate)-poly(ε-caprolactone) copolyesters. This method obviously applies to any AA + BB + AB polycondensation and is easily generalizable to other types of condensation copolymers.