Symmetric Unit Research Articles

Sheet resistance determination of electrically symmetric planar four-terminal devices with extended contacts

This paper reports an analytic method to determine the sheet resistance Rsq of symmetric planar four-terminal devices based on resistance measurements. Using the technique of conformal mapping it is first shown that any such device is electrically equivalent to a corresponding symmetric unit disk with the same Rsq and invariant under rotations by 90°. Two independent resistances measurable on these devices are expressed analytically as a function of Rsq and of the contact opening angle α. These two resistances fully characterize the electrical properties of such planar conductive devices. A simple procedure to extract both α and Rsq from the resistance values is then presented. These findings are corroborated by the experimental characterization of four-contact devices of ten different geometries fabricated using a commercial complementary metal oxide semiconductor process. From these widely different devices, the sheet resistance of a n-well is extracted to be 1042Ω with a relative uncertainty of only 0.45%.

Organtin complexes of 2,5‐dithiobiurea (H2dtbu): The crystal structures of (Ph3Sn)2(dtbu) and [(n‐Bu)2SnCl]2(dtbu)

AbstractA series of organotin(IV) complexes of two types, [R3Sn]2(dtbu) (R = PhCH2 1, Ph 2, n‐Bu 3, H2dtbu = 2,5‐dithiobiurea), [R2SnCl]2(dtbu) (R = PhCH2 4, Ph 5, n‐Bu 6) have been synthesized and characterized by elemental analysis, IR, and NMR (1H, 119Sn) spectroscopy. The structures of 2 and 6 have been determined by X‐ray crystallography. Crystal structures show that both complexes 2 and 6 are the symmetric dinuclear unit. Interestingly, supramolecular structures show that complex 2 has formed a linear chain through NH⋅⋅⋅S hydrogen bonding and 6 has formed a two‐dimensional network in perfect bc plane connected through NH⋅⋅⋅Cl hydrogen bonding and nonbonded S⋅⋅⋅S interactions. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:435–442, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20456

Appropriate truncation for photonic crystals

Effective properties of one-dimensional photonic crystals in the resonance domain are investigated. The obtained analytic expressions of effective permittivity and permeability lead to several results. Firstly, in the case of lossless materials, effective permittivity and permeability take, in general, complex values. It is shown that these values are governed by the truncation of the boundary layer. Considering the particular case of a symmetric unit cell, the effective permittivity and permeability become purely real and, by the way, coherent with physics. Finally, in this case with a symmetric unit cell, we show that effective permittivity and permeability can stay nearly constant in a wide range of wavevectors including propagating and evanescent waves.

Optical rectification effect in 1D metallic photonic crystal slabs with asymmetric unit cell

Photo-induced voltage due to photon drag effect is investigated for metallic photonic crystal slabs (PCS) with symmetric and asymmetric unit cells. In the symmetric structure, the signal is antisymmetric as a function of the incident angle, while in the asymmetric structure it is asymmetric. When the laser beam is normally incident to the sample, the photovoltage is observed only for PCS with asymmetric unit cells and its laser wavelength dependence is readily described in terms of uneven diffraction. The phenomenon can be referred to as optical rectification due to photonic scale asymmetry.

Molecular Conformation, Organizational Chirality, and Iron Metalation of meso-Tetramesitylporphyrins on Copper(100)

We report on the conformation and self-assembly properties of meso-tetramesitylporphyrin on Cu(100). The results show that the presence of the mesityl groups limits the interaction between the porphyrin ring and the copper surface, contributing to the high porphyrin mobility at room temperature. At low temperatures it is the substrate which determines the molecule orientation. The intermolecular interaction is also very weak, and only for high coverages do the porphyrins self-assemble to form large islands with two different mirror symmetric unit cells. The porphyrins can be Fe metalated by sublimation of Fe at room temperature on a porphyrin overlayer deposited on the copper surface.

Synthesis and Crystal Structure of a Dimethyltin Derivative of 1,4-Dithioerythritol

The title complex, [(CH3)2(HOC2H5)Sn(C4H6O2S2)Sn(HOC2H5)(CH3)2], was synthesized starting from dimethyltin dichloride, 1,4-dithioerythritol and sodium ethoxide. The crystal structure was determined by single-crystal X-ray diffraction. It crystallizes in the monoclinic system, space group P21/n with a = 7.9282(6)A, b = 11.3888(9)A, c = 11.0228(9)A, β = 99.594(3)°, Z = 2, V = 981.36(13)A3. Its crystal structure was determined and refined to a final R = 0.0232 for 1730 independent reflections. The complex is the symmetric dinuclear unit made up of two distorted trigonal bipyramids.

1,1'-Binaphthalene-2,2'-diyl hydrogen phosphate.

The title compound, racemic bnppa, C20H13O4P, crystallizes with four mol­ecules in the asymmetric unit. Two independent centrosymmetric O—H⋯O hydrogen-bonded tetra­mers, each involving two of the symmetry-independent mol­ecules in the asymmetric unit generate the packing motif in the crystal structure. The hydro­phobic parts of the tetra­mers connect to their neighbours via C—H⋯π and π–π inter­actions [3.899 (2), 3.895 (2) and 3.803 (2) Å within the symmetric unit, 3.851 (2), 4.000 (2), 3.988 (2) and 3.905 (2) Å across centres of symmetry].

Diaqua(2,9-dimethyl-1,10-phenanthroline-κ2N,N′)(3-hydroxybenzoato-κ2O,O′)cobalt(II) nitrate

In the symmetric unit of the title compound, [Co(C7H5O3)(C14H12N2)(H2O)2]NO3, the Co2+ cation is coordinated by a bidentate 2,9-dimethyl-1,10-phenanthroline (dmphen) ligand, a bidentate 3-hydroxy­benzoate anion and two water mol­ecules in a distorted octa­hedral environment. The 3-hydroxy­benzoate ligand, Co atom and nitrate anion are situated on a crystallographic twofold rotation axis. The OH group of the benzoate anion is disordered over two symmetry-related positions with site-occupancy factors of 0.5. An extensive series of O—H⋯O hydrogen bonds, involving water mol­ecules and 3-hydroxy­benzoate and nitrate anions, and weak C—H⋯O hydrogen bonds lead to a supra­molecular network structure.

Common occurrence of internal repeat symmetry in membrane proteins

Symmetry plays significant roles in protein structure and function. Particularly, symmetric interfaces are known to act as switches for two-state conformational change. Membrane proteins often undergo two-state conformational change during the transport process of ion channels or the active/inactive transitions in receptors. Here, we provide the first comprehensive analyses of internal repeat symmetry in membrane proteins. We examined the known membrane protein structures and found that, remarkably, nearly half of them have internal repeat symmetry. Moreover, we found that the conserved cores of these internal repeats are positioned at the interface of symmetric units when they are mapped on structures. Because of the large sequence divergence that occurs between internal repeats, the inherent symmetry present in protein sequences often has only been detected after structure determination. We therefore developed a sensitive procedure to predict the internal repeat symmetry from sequence information and identified 4653 proteins that are likely to have internal repeat symmetry.

Over-rejections by the weighted symmetric unit root test in multiple structural breaks

This study investigates the behaviour of the weighted symmetric unit root test (Pantula et al., 1994) when the data generating process has a unit root and multiple structural breaks in the level of its trend function. The results obtained from this study reveal that the test can be biased towards over-rejections of the unit root null hypothesis in large samples as well as small samples.

The Structure of the Prokaryotic Cyclic Nucleotide-Modulated Potassium Channel MloK1 at 16 Å Resolution

The gating ring of cyclic nucleotide-modulated channels is proposed to be either a two-fold symmetric dimer of dimers or a four-fold symmetric tetramer based on high-resolution structure data of soluble cyclic nucleotide-binding domains and functional data on intact channels. We addressed this controversy by obtaining structural data on an intact, full-length, cyclic nucleotide-modulated potassium channel, MloK1, from Mesorhizobium loti, which also features a putative voltage-sensor. We present here the 3D single-particle structure by transmission electron microscopy and the projection map of membrane-reconstituted 2D crystals of MloK1 in the presence of cAMP. Our data show a four-fold symmetric arrangement of the CNBDs, separated by discrete gaps. A homology model for full-length MloK1 suggests a vertical orientation for the CNBDs. The 2D crystal packing in the membrane-embedded state is compatible with the S1-S4 domains in the vertical "up" state.

Gain Improvement of a Microstrip Composite Right/Left-Handed Leaky Wave Antenna Using Symmetrical Unit Cells with Short Stubs

In order to improve the antenna gain, a composite right/left-handed (CRLH) leaky-wave (LW) antenna composed of symmetrical unit cells with short stubs terminated by vertical vias is designed. The use of symmetrical unit cells suppresses the cross-polarization of radiation to less than 23 dB. By comparing the measured radiation characteristics to that of a conventional CRLH LW antenna without short stub in the X-band, it is shown that the presented CRLH LW antenna with 51 unit cells offers a narrower beam and the antenna gain improves 4.1, 2.2 and 3.1 dB in the backward, broadside and forward directions of radiation, respectively.

Microstructure based model for permeability predictions of open-cell metallic foams via homogenization

To predict effective permeabilities of open-cell foams, produced by a SlipReactionFoamSintering (SRFS)-process, a multi-scale approach based on the homogenization method is applied. This formulation allows to calculate effective Darcy permeabilities by solving special Stokes flow problems on a unit cell. Starting from a detailed foam description by tomographic images, a new procedure based on a spectral analysis of the foam microstructure is presented in order to derive symmetric and non-symmetric unit cell models of the foam. Effective permeabilities are determined by using these unit cell models for a representative iron-based SlipReaction (SR)-foam sample. The analysis of these predictions leads to define one, rather simple, unit cell model suitable for further stochastic homogenization simulations.

New coordination polymer based on a triply bridged dicarboxylate ligand: Synthesis, structure, and magnetic properties of the adipato complex [Cu 4(bpy) 4(adip) 3](tcnoet) 2 · 2H 2O {bpy = C 10H 8N 2; adip 2− = [O 2C(CH 2) 4CO 2] 2−; tcnoet − = [(NC) 2CC(OEt)C(CN) 2] −}

One-pot reaction of copper(II) chloride dihydrate CuCl 2 · 2H 2O with 2,2′-bipyridyl (bpy = C 10H 8N 2) in the presence of sodium adipate Na 2adip (adip 2− = [O 2C(CH 2) 4CO 2] 2−) and potassium 1,1,3,3-tetracyano-2-ethoxypropenide (tcnoet − = [(NC) 2CC(OEt)C(CN) 2] −) gives the new compound [Cu 4(bpy) 4(adip) 3](tcnoet) 2 · 2H 2O ( 1), which was characterized by single crystal X-ray diffraction analysis. The Cu(II) 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 and by an almost symmetrical OCO unit with a bidentate syn– syn bridging mode. Each Cu 2 dinuclear unit is triply bonded by aliphatic chains of the three adipate ligands to generate a ladder-like infinite chain. Magnetic measurements exhibit a maximum in the χ m versus T plot (at ∼5.0 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 −3.26(1) cm −1 (the Hamiltonian is written as H = −2 JS a S b ).

Group rings whose symmetric units are nilpotent

Let K be an infinite field of characteristic different from 2, and G a group containing elements of infinite order. We classify the groups G such that the symmetric units of KG satisfy the identity (x1, x2, …, xn) = 1, for some n.

Conservative Polarimetric Scatterers and Their Role in Incorrect Extensions of the Cameron Decomposition

The properties of symmetric polarimetric scatterer scattering matrices are examined. It is shown that the unambiguous rotation angle for conservative symmetric polarimetric scatterers is the interval (-pi/4,+pi/4] as compared with (-pi/2,+pi/2] for nonconservative symmetric scatterers. Errors relating to the Cameron decomposition, which are recently introduced into the literature, are discussed. It is demonstrated that these errors arise from a faulty symmetric scatterer scattering matrix distance measure. This, in turn, leads to an improper mapping of the symmetric scatterer unit disk to a hemisphere. The correct mapping of the symmetric scatterer unit disk to the symmetric scatterer unit sphere is described

Cation Exchange in Lipophilic G-Quadruplexes: Not All Ion Binding Sites Are Equal

Lipophilic guanosine derivatives that form G-quadruplexes are promising building blocks for ionophores and ion channels. Herein, cation exchange between solvated cations (K+ and NH4+) and bound cations in the G-quadruplex [G1]16.4Na+.4DNP- was studied by electrospray ionization mass spectrometry and solution 1H, 15N NMR spectroscopy. The ESI-MS and 1H NMR data provided evidence for the formation of mixed-cationic Na+, K+ G-quadruplexes. The use of 15NH4+ cations in NMR titrations, along with 15N-filtered 1H NMR and selective NOE experiments, identified two mixed-cationic intermediates in the cation exchange pathway from [G1]16.4Na+.4DNP- to [G1]16.4NH4+.4DNP-. The central Na+, bound between the two symmetry-related G8-Na+ octamers, exchanges with either K+ or NH4+ before the two outer Na+ ions situated within the C4 symmetric G8 octamers. A structural rationale, based on differences in the cations' octahedral coordination geometries, is proposed to explain the differences in site exchange for these lipophilic G-quadruplexes. Large cations such as Cs+ can be exchanged into the central cation binding site that holds the two symmetry-related C4 symmetric G8 octamer units together. The potential relevance of these findings to both supramolecular chemistry and DNA G-quadruplex structure are discussed.

Symmetric units satisfying a group identity

Let K be an infinite field of characteristic p ≠ 2 , G a locally finite group and KG its group algebra. Let φ : KG → KG denote the K-linear extension of an involution φ defined on G. In this paper we prove, under some assumptions, that if the set of φ-symmetric units of KG satisfies a group identity then KG satisfies a polynomial identity. Moreover, in case the prime radical of KG is nilpotent we characterize the groups for which the φ-symmetric units satisfy a group identity.

Synthesis and Crystal Structure of A New Dinuclear Cu(II) Complex

A new dinuclear copper(II) complex was synthesized by reaction of 5,5‐diphenylimidazoline‐2,4‐dione (phenytoin, PHT), 3‐amino‐1‐propanol(PA) and copper acetate. Its crystal structure was determined by single crystal X‐ray diffraction. The compound crystallizes in the monoclinic system, space group C2/c with a=28.429(10), b=8.328(3), c=17.863(7) Å, β=111.189(6)°; V=3943(2) Å3, Mr=833.87, Z=4, F(000)=1736, Dc=1.405 g/cm3, μ=1.137 mm−1, the final R=0.0699 and wR=0.1737. The symmetric unit is comprised of four molecules. The complex is a centrosymmetric plane in which each copper(II) is coordinated in the quadrilateral plane to the ligand phenytoin through the deprotonated oxygen atom of 3‐amino‐1‐propanol as well as the nitrogen atoms of imine and amine. The Cu(II)…Cu(II) average distance is 3.005 (19) Å.

Symmetric Units in Alternative Loop Rings

Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. For α = ∑ αℓℓ in a loop ring RL, define α♯= ∑ αℓℓ-1and call α symmetric if α♯= α. We find necessary and sufficient conditions under which the symmetric units are closed under multiplication (and hence form a subloop of the loop of units in RL) when R has characteristic two and when R= Z, the ring of rational integers.