On the inverses of a class of toeplitz matrices of band width five

For a symmetric positive definite Toeplitz matrix of band width five and order n, those regions where the elements of the inverse alternative in sign are determined.     

Molecular and electronic structures of one-electron oxidized Ni(II)-(dithiosalicylidenediamine) complexes: Ni(III)-thiolate versus Ni(II)-thiyl radical states

The dithiosalicylidenediamine Ni II complexes [Ni(L)] (R=tBu, R'=CH2C(CH3)2CH2 1, R'=C6H4 2; R=H, R'=CH2C(CH3)2CH2 3, R'=C6H4 4) have been prepared by transmetallation of the tetrahedral complexes [Zn(L)] (R=tBu, R'=CH2C(CH3)2CH2 7, R'=C6H4 8; R=H, R'=CH2C(CH3)2CH2 9, R'=C6H4 10) formed by condensation of 2,4-di-R-thiosalicylaldehyde with diamines H2N-R'-NH2 in the presence of Zn II salts. The diamagnetic mononuclear complexes [Ni(L)] show a distorted square-planar N2S2 coordination environment and have been characterized by 1H- and 13C NMR and UV/Vis spectroscopies and by single-crystal X-ray crystallography. Cyclic voltammetry and coulombic measurements have established that complexes 1 and 2, incorporating tBu functionalities on the thiophenolate ligands, undergo reversible one-electron oxidation processes, whereas the analogous redox processes for complexes 3 and 4 are not reversible. The one-electron oxidized species, 1+ and 2+, can be generated quantitatively either electrochemically or chemically with 70 % HClO4. EPR and UV/Vis spectroscopic studies and supporting DFT calculations suggest that the SOMOs of 1+ and 2+ possess thiyl radical character, whereas those of 1(py)2 + and 2(py)2 + possess formal Ni III centers. Species 2+ dimerizes at low temperature, and an X-ray crystallographic determination of the dimer [(2)2](ClO4)2.2 CH2Cl2 confirms that this dimerization involves the formation of a S-S bond (S...S=2.202(5) A).     

Synthesis, characterisation and magnetic study of a cyano-substituted dysprosium double decker single-molecule magnet

Bis(octacyanophthalocyanine)dysprosium(III) (1) has been synthesised, characterised and magnetically studied. By the incorporation of cyano substituents on the phthalocyanine (Pc) rings, a starting point has been created for the chemical modification of double deckers for the purpose of surface self-assembly. The modification of the rings leaves the magnetic properties of the double decker largely unaffected.     

Multiple periodic solutions for a nonlinear suspension bridge equation

We investigate nonlinear oscillations in a fourth-order partialdifferential equation which models a suspension bridge. Previouswork establishes multiple periodic solutions when a parameterexceeds a certain eigenvalue. In this paper, we use Leray-Schauderdegree theory to prove that if the parameter is increased further,beyond a second eigenvalue, then additional solutions are created.     

Electron microscopic analysis of dairy microbes inactivated by ultrasound

Ultrasonication is a non-thermal method of food preservation that has the advantage of inactivating microbes in food without causing the common side-effects associated with conventional heat treatments, such as nutrient and flavour loss. The aim of this study was to evaluate the use of ultrasound as an alternative to heat pasteurisation and to assess cell damage using transmission electron microscopy (TEM). Three spoilage microbes, previously isolated from pasteurised milk, were used as "test" microbes. Saline solution (SSS) and UHT milk were used as suspension media and were inoculated with exponential growth phase "test" microbes at a microbial concentration of 1 x 10(4) cfu ml(-1). The samples were subjected to power ultrasound (20 kHz, 750 W), at 100%/124 microm wave amplitude for different time intervals. Both Escherichia coli and Saccharomyces cerevisiae were reduced by >99% (for both suspension media) after ultrasonication and Lactobacillus acidophilus was reduced by 72% and 84% in SSS and milk, respectively. Transmission electron microscope micrographs showed that ultrasonication inflicts extensive microbicidal/microbistatic external and internal damage on all three "test" microbes. In E. coli, sonication-induced emulsification caused the formation of unique minute lipopolysaccharide vesicles from the fragmenting cell envelope.     

Bis-morpholine-substituted perylene bisimides: impact of isomeric arrangement on electrochemical and spectroelectrochemical properties

The synthesis and separation of the 1,6- and 1,7- isomers of N,N'-bis(n-butyl)dimorpholino-3,4:9,10-perylenetetracarboxylic acid bisimide are reported. Investigations of the electrochemical and spectroscopic, in particular, spectroelectrochemical, properties of the two isomers reveal a sequence of electrochemically and chemically reversible redox processes for both isomers. Importantly, the 1,7-isomer of N,N'-bis(n-butyl)dimorpholino-3,4:9,10-perylenetetracarboxylic acid bisimide was observed to undergo a two-electron oxidation process, which contrasts with the behavior of both the corresponding 1,6-isomer and other related amino-substituted perylene bis-imide species.     

Crystallographic, electrochemical, and electronic structure studies of the mononuclear complexes of Au(I)/(II)/(III) with [9]aneS2O ([9]aneS2O = 1-oxa-4,7-dithiacyclononane)

The mononuclear macrocyclic complexes [Au(I)([9]aneS2O)2]BF4 x MeCN 1a, [Au(II)([9]aneS2O)2](BF4)2 x 2 MeCN 2a, and [Au(III)([9]aneS2O)2](ClO4)6(H5O2)(H3O)2 3 ([9]aneS2O = 1-oxa-4,7-dithiacyclononane) have been prepared and structurally characterized by single crystal X-ray crystallography. The oxidation of [Au([9]aneS2O)2](+) to [Au([9]aneS2O)2](2+) involves a significant reorganization of the co-ordination sphere from a distorted tetrahedral geometry in [Au([9]aneS2O)2](+) [Au-S 2.3363(12), 2.3877(12), 2.6630(11), 2.7597(13) A] to a distorted square-planar co-ordination geometry in [Au([9]aneS2O)2](2+). The O-donors in [Au([9]aneS2O)2](2+) occupy the axial positions about the Au(II) center [Au...O = 2.718(2) A] with the S-donors occupying the equatorial plane [Au-S 2.428(8) and 2.484(8) A]. [Au([9]aneS2O)2](3+) shows a co-ordination sphere similar to that of [Au([9]aneS2O)2](2+) but with significantly shorter axial Au...O interactions [2.688(2) A] and equatorial Au-S bond lengths [2.340(4) and 2.355(6) A]. The cyclic voltammogram of 1 in MeCN (0.2 M NBu4PF6, 253 K) at a scan rate of 100 mV s(-1) shows an oxidation process at E(p)(a) = +0.74 V and a reduction process at E(p)(c) = +0.41 V versus Fc(+)/Fc assigned to the two-electron Au(III/I) couple and a second reduction process at E(p)(c) = +0.19 V assigned to the Au(I/0) couple. This electrochemical assignment is confirmed by coulometric and UV-vis spectroelectrochemical measurements. Multifrequency EPR studies of the mononuclear Au(II) complex [Au([9]aneS2O)2](2+) in a fluid solution at X-band and as frozen solutions at L-, S-, X-, K-, and Q-band reveal g(iso) = 2.0182 and A(iso) = -44 x 10(-4) cm(-1); g(xx) = 2.010, g(yy) = 2.006, g(zz) = 2.037; A(xx) = -47 x 10(-4) cm(-1), A(yy) = -47 x 10(-4) cm(-1), A(zz) = -47 x 10(-4) cm(-1); P(xx) = -18 x 10(-4) cm(-1), P(yy) = -10 x 10(-4) cm(-1), and P(zz) = 28 x 10(-4) cm(-1). DFT calculations predict a singly occupied molecular orbital (SOMO) with 27.2% Au 5d(xy) character, consistent with the upper limit derived from the uncertainties in the (197)Au hyperfine parameters. Comparison with [Au([9]aneS3)2](2+) reveals that the nuclear quadrupole parameters, P(ii) (i = x, y, z) are very sensitive to the nature of the Au(II) co-ordination sphere in these macrocyclic complexes. The observed geometries and bond lengths for the cations [Au([9]aneS2O)2](+/2+/3+) reflect the preferred stereochemistries of d(10), d(9), and d(8) metal ions, respectively, with the higher oxidation state centers being generated at higher anodic potentials compared to the related complexes [Au([9]aneS3)2](+/2+/3+).     

Synthesis,Characterization, and Reactivity of a Uranium(VI) Carbene Imido Oxo Complex

We report the uranium(VI) carbene imido oxo complex [U(BIPM^TMS)(NMes)(O)(DMAP)₂] ( 5 , BIPM^TMS=C(PPh₂NSiMe₃)₂; Mes=2,4,6‐Me₃C₆H₂; DMAP=4‐(dimethylamino)pyridine) which exhibits the unprecedented arrangement of three formal multiply bonded ligands to one metal center where the coordinated heteroatoms derive from different element groups. This complex was prepared by incorporation of carbene, imido, and then oxo groups at the uranium center by salt elimination, protonolysis, and two‐electron oxidation, respectively. The oxo and imido groups adopt axial positions in a T‐shaped motif with respect to the carbene, which is consistent with an inverse trans‐influence. Complex 5 reacts with tert‐butylisocyanate at the imido rather than carbene group to afford the uranyl(VI) carbene complex [U(BIPM^TMS)(O)₂(DMAP)₂] ( 6 ).     

Synthesis of a uranium(VI)-carbene: reductive formation of uranyl(V)-methanides, oxidative preparation of a [R2C═U═O]2+ analogue of the [O═U═O]2+ uranyl ion (R = Ph2PNSiMe3), and comparison of the nature of U(IV)═C, U(V)═C, and U(VI)═C double bonds

We report attempts to prepare uranyl(VI)- and uranium(VI) carbenes utilizing deprotonation and oxidation strategies. Treatment of the uranyl(VI)-methanide complex [(BIPMH)UO(2)Cl(THF)] [1, BIPMH = HC(PPh(2)NSiMe(3))(2)] with benzyl-sodium did not afford a uranyl(VI)-carbene via deprotonation. Instead, one-electron reduction and isolation of di- and trinuclear [UO(2)(BIPMH)(μ-Cl)UO(μ-O){BIPMH}] (2) and [UO(μ-O)(BIPMH)(μ(3)-Cl){UO(μ-O)(BIPMH)}(2)] (3), respectively, with concomitant elimination of dibenzyl, was observed. Complexes 2 and 3 represent the first examples of organometallic uranyl(V), and 3 is notable for exhibiting rare cation-cation interactions between uranyl(VI) and uranyl(V) groups. In contrast, two-electron oxidation of the uranium(IV)-carbene [(BIPM)UCl(3)Li(THF)(2)] (4) by 4-morpholine N-oxide afforded the first uranium(VI)-carbene [(BIPM)UOCl(2)] (6). Complex 6 exhibits a trans-CUO linkage that represents a [R(2)C═U═O](2+) analogue of the uranyl ion. Notably, treatment of 4 with other oxidants such as Me(3)NO, C(5)H(5)NO, and TEMPO afforded 1 as the only isolable product. Computational studies of 4, the uranium(V)-carbene [(BIPM)UCl(2)I] (5), and 6 reveal polarized covalent U═C double bonds in each case whose nature is significantly affected by the oxidation state of uranium. Natural Bond Order analyses indicate that upon oxidation from uranium(IV) to (V) to (VI) the uranium contribution to the U═C σ-bond can increase from ca. 18 to 32% and within this component the orbital composition is dominated by 5f character. For the corresponding U═C π-components, the uranium contribution increases from ca. 18 to 26% but then decreases to ca. 24% and is again dominated by 5f contributions. The calculations suggest that as a function of increasing oxidation state of uranium the radial contraction of the valence 5f and 6d orbitals of uranium may outweigh the increased polarizing power of uranium in 6 compared to 5.