An Example of Embedded Singular Continuous Spectrum for One-Dimensional Schrödinger Operators

We present a new example of a potential such that the corresponding Schrödinger operator in the halfaxis has singular continuous spectrum embedded in the absolutely continuous spectrum. The singular part is supported in an essentialy dense set. This generalizes a result of C. Remling [3].Mathematics Subject Classification: 34L40, 81Q10.     

Photooxidation of Histidine by 3,3′,4,4′-Benzophenone Tetracarboxylic Acid in Aqueous Solution: Time-Resolved and Field-Dependent CIDNP Study

The photooxidation reaction between 3,3′,4,4′-benzophenone tetracarboxylic acid (TCBP) and l-histidine (His) has been investigated in neutral aqueous solution using the technique of chemically induced dynamic nuclear polarization (CIDNP). Relative values of ¹³C isotropic hyperfine couplings in the TCBP and His radicals were obtained from the ¹³C-time-resolved CIDNP spectrum, recorded during the photoreaction of TCBP with His at natural abundance of the magnetic isotope ¹³C. Good agreement was found for the hyperfine coupling constants of the TCBP ketyl radical calculated using methods of density functional theory, and those obtained from the ¹³C-time-resolved CIDNP spectrum. The mechanism of the quenching reaction of triplet-excited TCBP by His in neutral aqueous solution was established. ¹H CIDNP field dependencies for the photoreaction of TCBP with His were obtained and the g-factor of the histidyl radical was found.     

On Integrability of the Kontsevich Non-Abelian ODE System

We consider systems of ODEs with the right-hand side being Laurent polynomials in several non-commutative unknowns. In particular, these unknowns could be matrices of arbitrary size. An important example of such a system was proposed by M. Kontsevich (private communication). We prove the integrability of the Kontsevich system by finding a Lax pair, corresponding first integrals and commuting flows. We also provide a pre-Hamiltonian operator which maps gradients of integrals for the Kontsevich system to symmetries.     

Stable bright and vortex solitons in photonic crystal fibers with inhomogeneous defocusing nonlinearity

We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright solitons and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber. The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear.     

A Curtin–Hammett pentamethylene chain symmetrization process in the Bergman cyclization of an 11‐membered ring enediyne

Pentamethylene chain conformational effects for the Bergman cyclization of the 11‐membered ring enediyne, (3Z)‐3‐cycloundecene‐1,5‐diyne, 2, are examined theoretically with unrestricted Becke, three‐parameter, Lee–Yang–Parr/6‐31 G(d,p) calculations. A C₁ symmetric enediyne conformation was found to be the global minimum, where its nonsymmetric pentamethylene chain prevented π‐orbital alignment of the acetylene groups for C–C σ bond product formation. The Bergman cyclization of 2 was found to be conformationally dependent. In a Curtin–Hammett type process, the C₁ symmetric 2 inverts to one of the C_S or C₂ symmetric conformers required for the Bergman cyclization, which produced a C_S or C₂ symmetric 1,4‐diradical intermediate. The activation energy for the cyclization is slightly higher to reach the C₂ symmetry diradical compared with the C_S symmetry diradical. Copyright © 2012 John Wiley & Sons, Ltd.     

Antiproton and charged kaon production in \sqrt {s_{NN} } = 130 GeV Au+Au collisions at RHICGeV Au+Au collisions at RHIC

Preliminary results on antiproton and charged kaon spectra and the net-proton number at mid-rapidity are reported for Au+Au collisions at $\sqrt {s_{NN} } = 130$ GeV as measured by the STAR experiment at RHIC. Inverse slope parameters of the transverse mass distributions increase with the collision centrality, consistent with a strong radial flow. The antiproton and charged kaon extrapolated yields, normalized to the uncorrected negatively charged hadron yield, increase with the collision centrality. A finite but small number of net-baryons is found to be present at mid-rapidity.     

CdxHg(1−x)Te Alloy Colloidal Quantum Dots: Tuning Optical Properties from the Visible to Near‐Infrared by Ion Exchange

The energy gap between valence and conduction levels in colloidal semiconductor quantum dots can be tuned via the nanoparticle diameter when this is comparable to or less than the Bohr radius. In materials such as cadmium mercury telluride, which readily forms a single phase ternary alloy, this quantum confinement tuning can also be augmented by compositional tuning, which brings a further degree of freedom in the bandgap engineering. Here it is shown that compositional control of 2.3 nm diameter Cd_xHg_(1?x)Te nanocrystals by exchange of Hg²⁺ in place of Cd²⁺ ions can be used to tune their optical properties across a technologically useful range, from 500 nm to almost 1200 nm. Data on composition‐dependent changes in the optical properties are provided, including bandgap, extinction coefficient, emission energy and spectral shape, Stokes shift, quantum efficiency, and radiative lifetimes as the exchange process occurs, which are highly relevant for those seeking to use these technologically important QD materials.     

Effect of π-Extended Substituents on Photophysical Properties of BODIPY Dyes in Solutions

Four boron-dipyrrine (BODIPY) based dyes with π-extended substituents in 8-position of dipyrrin ligand have been synthesized and characterized. Photophysical properties of the obtained compounds have been investigated in different individual solvents. Deposits of solvent polarity and viscosity were evaluated. BODIPY with 8-biphenyl substituent was found to be the fluorescent molecular rotor in contrast to more extended substituents. The complex nature of solvent-solute interactions leads to the poor applicability of standard multiparameter approaches to BODIPY solvatochromic properties. Fluorescence intensity was found to increase in case of solvent polarity growth, it is not typical for BODIPY. Taking that into account the BODIPY with π-extended substituents could be used for fluorescence viscosity measurements, and as the fluorescent media polarity indicators in analytical chemistry and biochemistry.     

Wave Function in Classical Statistical Mechanics

The possibility to formulate classical statistical mechanics in terms of the complex wave function and density matrix obeying the evolution equation is discussed. It is shown that the modulus squared of the introduced wave function of the classical particle has the same physical meaning as the modulus squared of the wave function of the quantum particle. The tomographic probabilities are studied for both classical and quantum states. Integrals of motion and their relation to the propagators are discussed.     

Solid-Phase Luminescence Determination of Ciprofloxacin and Norfloxacin in Biological Fluids

A simple, rapid, and sensitive luminescence test method for the determination of ciprofloxacin (CIP) and norfloxacin (NOR) has been described. The method is based on the intramolecular energy transfer from organic acid to terbium (Tb³⁺) ion. Luminescence of terbium (III) complex with CIP (NOR), sorbed on the zeolite has been studied. Under optimized conditions the detection limit is 1 g/mL in urine and human plasma.