Eigenvalues of the Dirac Operator on Manifolds¶with Boundary

Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized by the existence of real Killing spinors and the minimality of the boundary. Received: 22 August 2000 / Accepted: 15 March 2001     

Isobutene Polymerization Using [CuII(NCMe)6]2+ with Non‐Coordinating Anions as Catalysts

Cu^II compounds coordinated octahedrally with nitriles and associated with bulky, non‐coordinating counter ions can be applied in the polymerization of isobutene at 30 °C. High yields and a high content of terminal double bonds are reached in the resulting highly reactive polyisobutylenes, while the molecular masses are moderate. Two of the coordinating nitriles are more weakly coordinated than the other four, as can be concluded from an exemplary X‐ray structure and from vibrational spectra, thus providing easily accessible sites for substrate coordination.

     

Bis(μ‐pyrrolidine‐N:N)bis(dibromoboron), [(Br)2B(pyrrolidine)2B(Br)2]

The B atoms in the title compound, C₈H₁₆B₂Br₄N₂, bridge between the two monomeric moieties, forming a (BN)₂ four‐membered ring with partial bond orders of the B—N bonds.     

Λ b →Λ c +a 1 decay in the heavy quark effective theory

Using the heavy quark approximation, we have studied the nonleptonic decay mode Λ _b →Λ _c a ₁. We have included nonfactorizable contributions as well as factorizable ones in our analysis. The estimated branching ratio for this process is (1.4±0.1)% and the asymmetry parameter α found to be −0.8.     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

Fabrication and characterization of enhanced hydrazine electrochemical sensor based on gold nanoparticles decorated on the vanadium oxide,ruthenium oxide nanomaterials,and carbon nanotubes composites

This work describes the synthesis of mixed oxide film of vanadium and ruthenium by pulsed deposition technique on multiwall carbon nanotubes and the decoration of gold nanoparticles on the mixed film. A ternary electrocatalyst has been developed for the electrochemical oxidation of hydrazine by combining two metal oxide mixtures with Au nanoparticles. Surface morphology and chemical composition of the electrode have been examined with SEM, EDX, HRTEM, EIS, and XRD. The peak current of hydrazine increased 9 times at the AuNPs/(VOx-RuOx)/CNT/GCE compared to the bare GCE, and the peak potential shifted to negative 848 mV. Linear sweep voltammetry (LSV) and amperometric techniques revealed that the AuNPs/(VOx-RuOx)/CNT/GCE displays linear concentration range 2.5–10000 µM (LSV) and the concentration range 0.03–100 µM (amperometry). The limit of detection (LOD) is 0.5 μM and 0.1 μM at (S/N = 3) for LSV and amperometric technique, respectively. The results obtained show a good RSD% of 2.1%–3.2% and reasonable recovery of 97%–108% of hydrazine detection.     

Full Thermal Switching of Enzymes by Thermoresponsive Poly(2-oxazoline)-Based Enzyme Inhibitors

Controlling the activity of enzymes is an important feature for many processes in medicine, bioanalytics, and biotechnology. So far, it has not been possible to fully switch biocatalysts on and off by thermoresponsive enzyme inhibitors. Herein, we present poly(2-oxazoline)s with iminodiacetic acid end groups (POx-IDA) that are lower critical solution temperature (LCST) polymers and thus thermosensitive. They are capable of reversibly inhibiting the activity of horse radish peroxidase and laccase by more than 99 %. Increasing the temperature makes the POx-IDA precipitate, which leads to 100 % recovery of the enzyme activity. This switching cycle is fully reversible. The LCST of the POx-IDA can be tuned by varying the polymer composition to generate a wide range of switching windows.     

A conformal lower bound for the smallest eigenvalue of the Dirac operator and killing spinors

On a Riemannian spin manifold, we give a lower bound for the square of the eigenvalues of the Dirac operator by the smallest eigenvalue of the conformal Laplacian (the Yamabe operator). We prove, in the limiting case, that the eigenspinor field is a killing spinor, i.e., parallel with respect to a natural connection. In particular, if the scalar curvature is positive, the eigenspinor field is annihilated by harmonic forms and the metric is Einstein.     

Synthesis,characterization and biological properties of mixed ligand complexes of cobalt(II/III) valproate with 2,9‐dimethyl‐1,10‐phenanthroline and 1,10‐phenanthroline

The synthesis of mononuclear cobalt(II/III) complexes with two different ligands (complex 2: [Co(valp)₂(2,9‐dmp)] and complex 3: [Co(valp)₂(H₂O)(1,10‐phen)]) was investigated and the characterization of both complexes was achieved using IR, UV–Vis, and single crystal X‐ray diffraction. Using single crystal X‐ray diffraction, the crystal structure of each of the complexes was determined. Additionally, the biological activity of these complexes was studied in five gram‐positive and four gram‐negative bacterial strains. Whereas in all gram‐negative bacteria tested, cobalt valproate complexes did not show any anti‐bacterial activity, both complexes had effects on gram positive bacteria. Complex 2 demonstrated good anti‐bacterial activity against all gram‐positive bacteria with inhibition zone diameter (IZD) ranging between 15–28 mm. Complex 3 exhibited low inhibition activity against all gram‐positive bacteria except E. faecalis with IZD ranging between 11.3–13.7 mm. Moreover, as an indication of its uses as industrial catalyst, the rate of bis(p‐nitrophenyl) phosphate (BNPP) hydrolysis when catalyzed by these complexes was measured at different temperatures, concentrations and pH. Complex 2 proved to be a better catalyst to induce the hydrolysis of BNPP.