Enumeration and Generating Functions of Rota–Baxter Words

In this paper, we prove results on enumerations of sets of Rota–Baxter words ( ${{{\tt RBWs}}}$ ) in a single generator and one unary operator. Examples of operators are integral operators, their generalization to Rota–Baxter operators, and Rota–Baxter type operators. ${{{\tt RBWs}}}$ are certain words formed by concatenating generators and images of words under the operators. Under suitable conditions, they form canonical bases of free Rota–Baxter type algebras which are studied recently in relation to renormalization in quantum field theory, combinatorics, number theory, and operads. Enumeration of a basis is often a first step to choosing a data representation in implementation. We settle the case of one generator and one operator, starting with the idempotent case (more precisely, the exponent 1 case). Some integer sequences related to these sets of ${{{\tt RBWs}}}$ are known and connected to other sequences from combinatorics, such as the Catalan numbers, and others are new. The recurrences satisfied by the generating series of these sequences prompt us to discover an efficient algorithm to enumerate the canonical basis of certain free Rota–Baxter algebras.     

Internal energy content of n-butylbenzene, bromobenzene, iodobenzene and aniline molecular ions generated by two-photon ionization at 266 nm. A photodissociation study

A technique to investigate photodissociation kinetics on a nanosecond time scale has been devised for molecular ions generated by multiphoton ionization (MPI) using mass-analyzed ion kinetic energy spectrometry. The branching ratio or rate constant has been determined for the photodissociation of the n-butylbenzene, bromobenzene, iodobenzene, and aniline molecular ions generated by MPI at 266 nm. The ion internal energies have been estimated by comparing the measured kinetic data with the previous energy dependence data. The analysis has shown that only those molecular ions generated by two-photon ionization contribute to the photodissociation signals. Around half of the available energy has been found to remain as molecular ion internal energy in the two-photon ionization process. Copyright 1999 John Wiley & Sons, Ltd.     

Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

The neuroblast and angioblast chemotaxic factor SDF-1 (CXCL12) expression is briefly up regulated by reactive astrocytes in brain following neonatal hypoxic-ischemic injury

Background  

Stromal cell-derived factor 1 (SDF-1 or CXCL12) is chemotaxic for CXCR4 expressing bone marrow-derived cells. It functions in brain embryonic development and in response to ischemic injury in helping guide neuroblast migration and vasculogenesis. In experimental adult stroke models SDF-1 is expressed perivascularly in the injured region up to 30 days after the injury, suggesting it could be a therapeutic target for tissue repair strategies. We hypothesized that SDF-1 would be expressed in similar temporal and spatial patterns following hypoxic-ischemic (HI) injury in neonatal brain.     

Selective visible light reduction of carbon dioxide over iridium(III)-terpyridine photocatalysts

The CO₂ reduction reaction is an imperative piece of technology that closes the carbon cycle in many critical energy conversion and chemical manufacturing processes. Here, we report two new iridium (III) terpyridine-based photocatalysts capable of selective reduction of CO₂ to CO under visible light (λ ≥ 420 nm). The first photocatalyst, [Ir–COOH], was functionalized with the carboxyl group on the phenylpyridine, whereas the second, [Ir-PhCOOH], was attached to a phenyl spacer on the terpyridine. The [Ir-PhCOOH] was characterized by a higher extinction coefficient than [Ir–COOH], thus allowing more absorption of photons. Although both photocatalysts require two-electron activation, the [Ir-PhCOOH] is more readily activated as a result of the more negatively charged Ir center. These photocatalysts show exclusive selectivities in the production of CO. The turnover frequencies for [Ir–COOH] and [Ir-PhCOOH] were 19 and 10 h^?1, respectively, under visible light irradiation. The e-e-H-H pathway was identified as the most favorable, consisting of the rate-limiting step in the conversion of 1COOH to 1CO, and where the barrier is significantly lower for [Ir-PhCOOH] than for [Ir–COOH].     

An efficient (1)H/(31)P double-resonance solid-state NMR probe that utilizes a scroll coil

The construction and performance of a scroll coil double-resonance probe for solid-state NMR on stationary samples is described. The advantages of the scroll coil at the high resonance frequencies of (1)H and (31)P include: high efficiency, minimal perturbations of tuning by a wide range of samples, minimal RF sample heating of high dielectric samples of biopolymers in aqueous solution, and excellent RF homogeneity. The incorporation of a cable tie cinch for mechanical stability of the scroll coil is described. Experimental results obtained on a Hunter Killer Peptide 1 (HKP1) interacting with phospholipid bilayers of varying lipid composition demonstrate the capabilities of this probe on lossy aqueous samples.     

Forbush decreases recorded by the URAGAN muon hodoscope in 2006–2011

Variations in the cosmic ray muon flux on Earth’s surface during Forbush decreases (FD) recorded by the URAGAN muon hodoscope in 2006–2011 are investigated. The dependence of the rate of amplitude reduction on the primary particle energy in a range above 10 GeV at different phases of FD development is studied by analyzing the variations in the cosmic ray muon flux recorded with the hodoscope. Analytical data on the spatial and angular dynamics of the muon flux are used to estimate variations in the spatial anisotropy of the muon flux during FDs.