Generalized slant Toeplitz operators on H2

For an integer k ≥ 2, k^th‐order slant Toeplitz operator U_φ [1] with symbol φ in L^∞(??), where ?? is the unit circle in the complex plane, is an operator whose representing matrixM = (α_ij ) is given by α_ij = 〈φ, z^ki–j〉, where 〈. , .〉 is the usual inner product in L²(??). The operator V_φ denotes the compression of U_φ to H²(??) (Hardy space). Algebraic and spectral properties of the operator V_φ are discussed. It is proved that spectral radius of V_φ equals the spectral radius of U_φ, if φ is analytic or co‐analytic, and if T_φ is invertible then the spectrum of V_φ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the production of slow particles in high energy heavy ion collisions

The mechanism for producing slow, target associated particles in high energy heavy ion collisions is investigated. It is shown that the same mechanism which was proposed for hadron induced interactions is likely to appear also for heavy-ion reactions. The results indicate however a much weaker correlation between impact parameter and yield of slow particles.     

The 2-characters of a group and the group determinant

A new look at Frobenius' original papers on character theory has produced the following: (a) the group determinant determines the group (Formanek-Sibley); (b) the group is determined by the 1-, 2- and 3-characters of the irreducible representations (Hoehnke-Johnson); and (c) pairs of non-isomorphic groups exist with the same irreducible 1- and 2-characters (Johnson-Sehgal). The examples produced in Johnson and Sehgal have large orders but, recently, McKay and Sibley have proved that the ten Brauer pairs of order 256 have the same irreducible 2-characters. It is shown here that the pairs of non-isomorphic groups of order p³, p and odd prime, have the same irreducible 2-characters. Further results are given on the k-characters of the regular representation/rod a shorter proof of the result mentioned in (c) is indicated. A criterion is given which is sufficient for the 3-character of an arbitrary representation to determine the group.     

Regioselective synthesis of symmetrical pyridyl selenium compounds by bromine–magnesium exchange of bromopyridines using isopropyl magnesium chloride: X‐ray crystal structure of 2,2′,5,5′‐tetrabromo‐3,3′‐dipyridyldiselenide

2,2′‐Dipyridyl‐3,3′‐dipyridyl,5,5′‐dipyridyl‐diselenides have been synthesized by a convenient method employing non‐cryogenic conditions. Various bromopyridines (2‐Bromopyridine, 2,5‐dibromopyridines and 2,3,5‐Tribromopyridines) undergo selective monobromine–magnesium exchange to yield the corresponding pyridyl magnesium chlorides at room temperature upon treatment with ⁱPrMgCl. The resulting pyridyl magnesium chloride is quenched with elemental selenium, which upon further oxidation affords the above diselenides in good yields. The compounds prepared using this methodology have been characterized by elemental analysis, IR, NMR (¹H, ¹³C, ⁷⁷Se) and mass spectral analysis. The molecular structure of 2,2′,5,5′‐Tetrabromo‐3,3′‐dipyridyldiselenide has been established by single‐crystal X‐ray diffraction analysis. It exists as a dimeric form due to the non‐bonding interactions between the selenium of one pyridine moiety and the hydrogen of the other. Copyright © 2004 John Wiley & Sons, Ltd.     

Transmission performance of 20 × 10 Gb/s WDM signals using cascaded optimized SOAs with OOK and DPSK modulation formats

We investigated 20 channels at 10 Gb/s wavelength division multiplexing (WDM) transmission over 1190 km single mode fiber and dispersion compensating fiber using cascaded inline semiconductor optical amplifier at a span of 70 km for RZ-DPSK (return zero differential phase-shift keying) modulation format by using same channel spacing, i.e. 100 GHz. We show for RZ-OOK (return zero on-off keying) format a transmission distance of up to 1050 km with Q factor more than 15 dB, without any power drops. We developed the SOA model for inline amplifier having minimum cross-talks and ASE (amplified spontaneous emission) noise power with sufficient gain. At optimal bias current of 400 mA, a high constant gain of 36.5 dB is obtained up to a saturation power of 21.36 mW. So reduction of cross-talk and distortion is possible by decreasing the bias current at appropriate amplification factor.The DPSK modulation format has less cross-talk as compared to OOK format for nonlinearities and saturation case. The impact of optical power received and Q factor at different distance for both RZ-OOK and RZ-DPSK modulation format has been illustrated. We have shown the optical spectrum and clear Eye diagram at the transmission distance of 1190 km in RZ-DPSK system and 1050 km in RZ-OOK systems.The bit error rate (BER) for all channels observed is less than 10⁻¹⁰ up to gain saturation for both DPSK and OOK systems. Finally, we investigated that the transmission distance decreases with a decrease in channel spacing of up to 20 GHz.     

Performance of YBaCuO thick film rf SQUIDs at 77 K

RF SQUID behaviour has been observed at 77 K in YBaCuO thick films prepared by screen printing technique. A hole shunted with a microbridge type of geometry is patterned manually for observing rf SQUID behaviour. Flux noise spectrum is also studied and it is found to depend on the quality of the film. The spectral density of the flux noise in the white noise region is 1.7×10⁻³ Φ₀/√Hz at 77 K.     

Electron paramagnetic resonance, optical and electrical properties of vanadyl doped alkali germanoborate glasses

Glasses with composition xGeO₂.(0.30−x)M₂O.0.70B₂O₃ (M=Li, K) containing 2.0 mol% of V₂O₅ have been prepared in the range 0.00≤x≤0.15 by normal melt quenching method. Electron paramagnetic resonance (EPR), optical transmission and absorption spectra and dc conductivity of these glasses have been studied. Spin Hamiltonian parameters (SHPs) of VO²⁺ ions, dipolar hyperfine coupling parameter, P, Fermi contact interaction parameter, K and molecular orbital coefficients (α² and γ²) have been calculated. In GeO₂·Li₂O·B₂O₃ glasses there is no change in the tetragonality of the V⁴⁺O₆ complex and the size of 3d_xy orbit also remains unchanged with increase in GeO₂ content. In GeO₂·K₂O·B₂O₃ glasses, there is an increase in the tetragonality of the V⁴⁺O₆ complex and the 3d_xy orbit expands with increase in GeO₂ content. Values of the theoretical optical basicity, Λ_th, have also been reported. Optical band gap decreases with increase in GeO₂ content. The dc conductivity of these glasses decreases and the activation energy increases with increase in GeO₂:M₂O ratio.     

First passage time for a class of one-dimensional stochastic systems

We consider the time evolution of a class of stochastic systems of finite size with polynomial nearest neighbor transition rates. We obtain analytical expressions for the first passage time (FPT) and its moments. We show that the mean FPT, averaged over a uniform initial distribution, shows a simple asymptotoc behavior with the system size and the parameters of the transition rates.