Equality cases in matrix norm inequalities of golden-thompson type

The equality cases in several matrix norm (trace) inequalities are characterized. Norm inequalities of Golden-Thompson type and of its complement type are treated as well as a logarithmic trace inequality and norm inequalities for matrix exponentials.     

A Simple Chaotic Circuit with Impulsive Switch Depending on Time and State

This paper presents a simple chaotic circuit consisting of two capacitors, one linear two-port VCCS and one time-state-controlled impulsive switch. The impulsive switch causes rich chaotic and periodic behavior. The circuit dynamics can be simplified into a one-dimensional return map that is piecewise linear and piecewise monotone. Using the return map, we clarify parameter conditions for existence of chaotic and periodic attractors and coexistence state of attractors.     

Time-resolved EPR studies on magnetic interactions between excited triplet (tetraphenylporphinato) zinc and doublet nitroxide radical

By time-resolved electron paramagnetic resonance (TREPR), four (tetraphenylporphinato) zinc (ZnTPP) complexes coordinated by an axial ligand containing a nitroxide radical (NRX; X=4, 5, 8, and 10, denotes the bond number from zinc to nitroxide nitrogen) have been studied in terms of magnetic interactions between the photoexcited triplet state of ZnTPP and NRX. The TREPR spectrum of ZnTPP coordinated by NR10 is almost the same as the one of ZnTPP coordinated by pyridine, indicating that the electron exchange interaction,J, between ZnTPP and the doublet nitroxide is negligibly small. On the other hand, TREPR spectra of the NR4 and NR5 complexes are assigned to the Q₁ state constituted by the ZnTPP and the nitroxide radical. In the case of the ZnTPP-NR8 complex, both T₁ and Q₁ TREPR signals are seen, which may originate from two conformations or degenerate T₁ states of ZnTPP. This EPR study is useful for understanding the photophysical and photochemical properties of chromophores.     

Optical properties of new organic conductors based on the BEDT-TSeF molecule (the κ-(BETS)4Hg2.84Br8 superconductor and κ-(BETS)4Hg3Cl8 Metal) in the range 300–15 K

Polarized reflectance and optical conductivity spectra of single crystals of two new isostructural organic conductors based on the BEDT-TSeF molecule, namely, the κ-(BETS)₄Hg_2.84Br₈ superconductor (T _c =2 K) and the κ-(BETS)₄Hg₃Cl₈ metal, which undergoes a smooth transition to the dielectric state near 35 K, have been obtained in the spectral region 700–6500 cm⁻¹ at temperatures of 300–15 K. At 300 K, the spectra of both compounds are nearly identical and differ from the Drude spectrum characteristic of metals. The nature of the observed difference is discussed, and the spectra are described in terms of a cluster approach with inclusion of electron-electron correlations in the Hubbard approximation combined with the Drude model. The parameters of the theory were determined, including the electron transfer integrals between molecules in a cluster. The spectra in the conducting plane of the crystals were found to be essentially anisotropic, which should be assigned to specific features of in-plane interaction between molecules. The spectra of the superconductor and the metal become increasingly different as the temperature is lowered. The spectra of the metal obtained for T<150 K exhibit splitting of the broad electronic maximum in the mid-IR region into two bands, which is accompanied by a splitting of a vibronic feature deriving from electron interaction with intramolecular BETS vibrations of ν₃(A _g ) symmetry. No such splitting is observed in the superconductor spectra with decreasing temperature. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 11, 2004, pp. 1921–1929. Original Russian Text Copyright ? 2004 by Vlasova, Drichko, Petrov, Semkin, Zhilyaeva, Lyubovskaya, Olejniczak, A. Kobayashi, H. Kobayashi.     

Synthesis and chiroptical properties of optically active poly(ethynylcarbazole) derivatives: Substituent effect on the helix formation

Novel chiral acetylene monomers containing carbazole, 2‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 1 ), 3‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 2 ), 2‐ethynyl‐9‐[(S)‐2‐methylbutyl]carbazole ( 3 ), and 2‐ethynyl‐9‐[(S)‐4‐methylhexyl]carbazole ( 4 ) were synthesized and polymerized with [(nbd)RhCl]₂? Et₃N. The corresponding polyacetylenes with number‐average molecular weights ranging from 68,700 to 310,000 were obtained in good yields. Poly( 1 ) exhibited a large specific rotation and an intense Cotton effect in toluene, indicating that it formed a helix with predominantly one‐handed screw sense, while the other three polymers showed no evidence for taking a helical structure. Poly( 1 ) largely decreased the CD intensity upon heating from ?10 to 60 °C. Poly( 1 ) showed a Cotton effect in film state in a manner similar to solution state. No chiral amplification was observed in the copolymerization of 1 with achiral 2‐ethynyl‐9‐tert‐butoxycarbonylcarbazole ( 5 ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4450–4458, 2007     

Quasi-monocyclic near-infrared pulses with a stabilized carrier-envelope phase characterized by noncollinear cross-correlation frequency-resolved optical gating.

Precise characterization of noncollinear optical parametric amplifier idler pulses that have bandwidths of more than an octave with a center wavelength at 990 nm was demonstrated. The method employed was cross-correlation frequency-resolved optical gating with broadband sum-frequency mixing to take advantage of the idler's angular dispersion. Compression to near the transform limit was achieved to produce quasi-monocyclic near-infrared pulses by use of a deformable membrane mirror.