Classical limit of the tensor product of holomorphic discrete series representations

For three coadjoint orbits \(\mathcal {O}_1, \mathcal {O}_2\) and \(\mathcal {O}_3\) in \(\mathfrak {g}^*\) , the Corwin–Greenleaf function \(n(\mathcal {O}_1 \times \mathcal {O}_2, \mathcal {O}_3)\) is given by the number of \(G\) -orbits in \(\{(\lambda , \mu ) \in \mathcal {O}_1 \times \mathcal {O}_2 \, : \, \lambda + \mu \in \mathcal {O}_3 \}\) under the diagonal action. In the case where \(G\) is a simple Lie group of Hermitian type, we give an explicit formula of \(n(\mathcal {O}_1 \times \mathcal {O}_2, \mathcal {O}_3)\) for coadjoint orbits \(\mathcal {O}_1\) and \(\mathcal {O}_2\) that meet \(\left( [\mathfrak {k}, \mathfrak {k}] + \mathfrak {p}\right) ^{\perp }\) , and show that the formula is regarded as the ‘classical limit’ of a special case of Kobayashi’s multiplicity-free theorem (Progr. Math. 2007) in the branching law to symmetric pairs.     

Mapping the spatial overlap of excitons in a photosynthetic complex via coherent nonlinear frequency generation

We experimentally demonstrate a nonlinear spectroscopic method that is sensitive to exciton-exciton interactions in a Frenkel exciton system. Spatial overlap of one-exciton wavefunctions leads to coupling between them, resulting in two-exciton eigenstates that have the character of many single-exciton pairs. The mixed character of the two-exciton wavefunctions gives rise to a four-wave-mixing nonlinear frequency generation signal. When only part of the linear excitation spectrum of the complex is excited with three spectrally tailored pulses with separate spatial directions, a frequency-shifted third-order nonlinear signal emerges in the phase-matched direction. We employ the nonlinear response function formalism to show that the emergence of the signal is mediated by and carries information about the two-exciton eigenstates of the system. We report experimental results for nonlinear frequency generation in the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex. Our theoretical analysis of the signal from FMO confirms that the emergence of the frequency-shifted signal is due to the interaction of spatially overlapped excitons. In this method, the signal intensity is directly measured in the frequency domain and does not require scanning of pulse delays or signal phase retrieval. The wavefunctions of the two-exciton states contain information about the spatial overlap of excitons and can be helpful in identifying coupling strengths and relaxation pathways. We propose this method as a facile experimental means of studying exciton correlations in systems with complicated electronic structures.     

Effect of morphology of thin DNA films on the electron stimulated desorption of anions

We present a comparison between the electron stimulated desorption (ESD) of anions from DNA samples prepared by lyophilization (an example of poorly organized or nonuniform films) and molecular self-assembly (well-ordered films). The lyophilization (or freeze- drying) method is perhaps the most frequently employed technique for forming DNA films for studies of low-energy electron (LEE) interactions leading to DNA damage; however, this technique usually produces nonuniform films with considerable clustering which may affect DNA configuration and enhance sample charging when the film is irradiated. Our results confirm the general validity of ESD measurements obtained with lyophilized samples, but also reveal limitations of lyophilization for LEE studies on DNA films. Specifically we observe some modulation of structures, associated with dissociative electron attachment, in the anion yield functions from different types of DNA film, confirming that conformational factors play a role in the LEE induced damage to DNA.     

Ab Initio Calculations of the Conformational Preferences of 1,3-Oxathiane S-Oxide and its Analogs Containing S and SE Atoms—Evidence for Stereoelectronic Interactions Associated with the Anomeric Effects

Abstract

Stereoelectronic interactions associated with the AE and also the conformational and structural properties of 1,3-oxathiane S-oxide (1), 1,3-dithiane S-oxide (2), 1,3-thiaselenane S-oxide (3), 1,3-oxaselenane Se-oxide (4), 1,3-thiaselenane Se-oxide (5), and 1,3-diselenane Se-oxide (6) were investigated using quantum mechanical methods. These compounds were fully optimized at the B3LYP/6 – 311 + G** and HF/6 – 311 + G** levels of theory. The Gibbs Free Energy, Enthalpy, and Entropy differences (i.e., ΔG, ΔH, and ΔS) between the axial and equatorial conformations were calculated at the B3LYP/6 – 311 + G** and HF/6 – 311 + G** levels of theory. The decrease of the AE is corresponding to the decreases of calculated Δ(G _ax – G _eq) value of the above mentioned compounds. The calculated AE values are more significant for the justification of the conformational dominances of the compounds than steric effects. In this work, the relations between the Anomeric Effects, donor and acceptor orbital energies, occupancies, structural parameters, dipole–dipole interactions, and conformational behavior of the compounds have been studied.     

Synthesis of Imidazolato and 2-Methyl-Imidazolato Derivatives of Tellurium(IV)

INTRODUCTION

The chemistry of S-N compounds has been well established^[1] in the past few years and the stability was accounted in terms of extensive π bonding^[2,3]. The diversity of these compounds tempted chemsits to explore analogous Se-N and Te-N compounds. However, the poor or even absence of π bonding with heavier Se and Te posed problem to synthesize such compounds in the past. The chemistry of Se-N and Te-N compounds has been developed extensively by introducing new synthetic precursors^[4] in the last decade or so. We have observed that N-trimethyl silylimidazole and 2-methyl silylimidazole are potential reagents for peperation of monomeric transition metal imidazolates and Tin(IV) imidazolate^[5,6]. We, therefore, thought worthwhile to synthesize amido derivatives of Te(IV) incorporating these π delocalised heterocycles which acts as potential 4e (both σ and π) donors.     

Two-grid finite element method for the dual-permeability-Stokes fluid flow model

In this paper, two-grid finite element method for the steady dual-permeability-Stokes fluid flow model is proposed and analyzed. Dual-permeability-Stokes interface system has vast applications in many areas such as hydrocarbon recovery process, especially in hydraulically fractured tight/shale oil/gas reservoirs. Two-grid method is popular and convenient to solve a large multiphysics interface system by decoupling the coupled problem into several subproblems. Herein, the two-grid approach is used to reduce the coding task substantially, which provides computational flexibility without losing the approximate accuracy. Firstly, we solve a global problem through standard P_k ? P_k??1 ? P_k ? P_k finite elements on the coarse grid. After that, a coarse grid solution is applied for the decoupling between the interface terms and the mass exchange terms to solve three independent subproblems on the fine grid. The three independent parallel subproblems are the Stokes equations, the microfracture equations, and the matrix equations, respectively. Four numerical tests are presented to validate the numerical methods and illustrate the features of the dual-permeability-Stokes model.

     

A redox series of aluminum complexes: characterization of four oxidation states including a ligand biradical state stabilized via exchange coupling

Electrophilic activation and subsequent reduction of substrates is in general not possible because highly Lewis acidic metals lack access to multiple redox states. Herein, we demonstrate that transition metal-like redox processes and electronic structure and magnetic properties can be imparted to aluminum(III). Bis(iminopyridine) complexes containing neutral, monoanionic, and dianionic iminopyridine ligands (IP) have been characterized structurally and electronically; yellow (IP)AlCl(3) (1), deep green (IP(-))(2)AlCl (2) and (IP(-))(2)Al(CF(3)SO(3)) (3), and deep purple [(IP(2-))Al](-) (5) are presented. The mixed-valent, monoradical complex (IP(-))(IP(2-))Al is unstable toward C-C coupling, and [(IP(2-))Al](2-)(μ-IP-IP)(2-) (4) has been isolated. Variable-temperature magnetic susceptibility and EPR spectroscopy measurements indicate that the biradical character of the ligand-based triplet in 2 is stabilized by strong antiferromagnetic exchange coupling mediated by aluminum(III): J = -230 cm(-1) for ? = -2J(?(L(1))·?(L(2))). Coordination geometry-dependent (IP(-))-(IP(-)) communication through aluminum(III) is observed electrochemically. The cyclic voltammogram of trigonal bipyramidal 2 displays successive ligand-based oxidation events for the two IP(1-/0) processes, at -0.86 and -1.20 V vs SCE. The 0.34 V spacing between redox couples corresponds to a conproportionation constant of K(c) = 10(5.8) for the process (IP(-))(2)AlCl + (IP)(2)AlCl → 2(IP(-))(IP)AlCl consistent with Robin and Day Class II mixed-valent behavior. Tetrahedral 5 displays localized, Class I behavior as indicated by closely spaced redox couples. Furthermore, CV's of 2 and 5 indicate that changes in the coordination environment of the aluminum center shift the potentials for the IP(1-/0) and IP(2-/1-) redox couples by up to 0.9 V.     

Enhanced antibacterial performance of hybrid semiconductor nanomaterials: ZnO/SnO2 nanocomposite thin films

The nano-sized coupled oxides ZnO/SnO₂ thin films in a molar ratio of 2:1 (Z2S), 1:1 (ZS) and 1:2 (ZS2) were prepared using sol-gel dip coating method and characterized with X-ray diffraction (XRD), scanning electron microscopy (SEM) and UV-vis spectroscopy. Escherichia coli (E. coli, ATCC 25922) was selected as a model for the Gram-negative bacteria to evaluate antibacterial property of composite samples compared with single ZnO (Z) and single SnO₂ (S) films. The antibacterial activity has been studied applying the so-called antibacterial drop test under UV illumination. The bactericidal activity was estimated by relative number of bacteria survived calculated from the number of viable cells which form colonies on the nutrient agar plates. The influence of the SnO₂-ZnO nanocomposite composition on the structural features and on the antibacterial properties of the thin films are reported and discussed. It is found that all coatings exhibited a high antibacterial activity. The coupled oxide photocatalyst Z2S has better photocatalytic activity to bacteria inactivation than ZS, ZS2, Z and S films. Furthermore, nanostructured films were active even in the absence of irradiation.     

Differential Pulse Voltammetric Determination of 2‐Methyl‐4,6‐Dinitrophenol using Bismuth Bulk Electrode

This work reports the application of bismuth bulk electrode (BiBE) for the determination of 2‐methyl‐4,6‐dinitrophenol (MDNP) by differential pulse voltammetry (DPV) in Britton‐Robinson buffer of pH 12.0 as an optimal medium. BiBE was prepared by transferring molten bismuth into a glass tube under constant stream of nitrogen. The linear concentration dependences were measured from 1 to 10 μmol ? L^?1 and from 10 to 100 μmol ? L^?1 by using optimum accumulation potential of ?0.7 V and optimum accumulation time 30 s. Under these conditions limit of determination and limit of quantification was 0.45 and 1.5 μmol ? L^?1, respectively. The developed method was successfully applied for the analysis of tap water as a model sample.     

Modeling and optimization of simultaneous degradation of rhodamine B and acid red 14 binary solution by homogeneous Fenton reaction: a chemometrics approach

This study aimed to propose a mathematical method to investigate and optimize the simultaneous elimination process of multiple organic pollutants using the Fenton process. Hence, the treatment of rhodamine B (RB) and acid red 14 (AR14) dyes in their binary solution was studied. Multivariate curve resolution alternating least square (MCR-ALS), a novel chemometric method, was applied along with correlation constraints to resolute the UV-Vis spectrophotometric data, enabling quantification of investigated dyes despite a high spectral overlapping. Response surface methodology was adopted to assess the model and optimize individual and interactive effects of three independent factors (Fe²⁺, H₂O₂ and initial pH) on the simultaneous elimination of RB and AR14. The values of the regression coefficient for RB and AR14 were determined as 98.48 and 98.67 percent, respectively, revealing the reliability of the obtained polynomial models to predict decolorization efficiencies. Desirability function was employed to optimize the independent variables to attain the highest possible degradation performance for both dyes in their binary solution. At the optimum point of operation ([Fe²⁺] = 143.88 mg/L, [H₂O₂] = 126.89 mg/L and pH = 3.71), degradation efficiencies of RB and AR14 were found as 81.58% and 80.22%, respectively, which were nearly identical to the experimental results.