The energy operator for infinite statistics

We construct the energy operator for particles obeying infinite statistics defined by aq-deformation of the Heisenberg algebra.The aim of this paper is to construct the energy operator for particles which obey the so-called infinite statistics defined by theq-deformation of the Heisenberg algebra. This topic was studied in the previous article [1], where a conjecture was formulated concerning the form of the energy operator. Our main result is a proof of this conjecture in a slightly modified form (cf. Remark 1).     

Imaging Nanometre‐Sized Hot Spots on Smooth Au Films with High‐Resolution Tip‐Enhanced Luminescence and Raman Near‐Field Optical Microscopy

A novel near‐field optical microscope based on a parabolic mirror is used for recording high‐resolution tip‐enhanced photoluminescence (PL) and Raman images with unprecedented sensitivity and contrast. The measurements reveal small islands on the Au surface with dimensions of only a few nanometres with locally enhanced Au PL. These islands appear as nanometre‐sized hot spots in tip‐enhanced Raman microscopy when benzotriazole molecules adsorbed on the Au surface serve as local sensors for the optical field. The spectra show that localized plasmons are the cause of both the locally enhanced Au PL and enhanced Raman scattering. This finding suggests that the dispersive background in the surface‐enhanced Raman spectra can be explained simply by the enhanced Au PL in the gap. Furthermore, our results show that the surface flatness must be better than 1 nm, to provide an optically homogeneous substrate for near‐field enhanced PL and Raman spectroscopy.     

Bonding and metal-atom dynamics in two unique Sn(I)-Sn(III) complexes

Two recently reported tin complexes, which incorporate both Sn(I) and Sn(III) sites in their structure, have been examined by temperature-dependent 119Sn M?ssbauer effect (ME) spectroscopy. The distinct hyperfine parameters of the two sites make it possible to assign relative occupancies of the two sites (at 90 K) on the basis of the recoil-free fraction data extracted from the ME spectra. The temperature dependencies of the recoil-free fractions, elucidated from the ME spectra, show that the metal-atom dynamics are very similar for the two sites in the temperature range 90相似文献   

Interpenetrating Networks Obtained by Crosslinking in the Vinylacetate (VAc)-Triethoxyvinylsilane (VTES)-Tetraethoxysilane (TEOS) System

In the present work the sol-gel process in the ternary system VAc-VTES-TEOS was approached. The monomer that ensures the crosslinking of the obtained networks is VTES, which could react with VAc by free-radical polymerisation and with TEOS by hydrolysis-polycondensation. The early stage evolution of the process was monitored by gas chromatography coupled with mass spectrometry (GC-MS). The gels obtained were characterised by IR spectroscopy, DTA/TG analysis and DSC measurements. Important differences in the gelling process and in the properties of the obtained gels could be noticed, related to the presence of VAc and VTES in the reaction mixtures. The investigation allowed to establish the compositions and the experimental conditions in which gels with high degree of crosslinking could be obtained.     

Congruences for modular forms of weights two and four

We prove a conjecture of Calegari and Stein regarding mod p congruences between modular forms of weight four and the derivatives of modular forms of weight two.     

Parametrized Gröbner–Shirshov bases

We consider the problem of describing Gröbner–Shirshov bases for free associative algebras in finite terms. To this end we consider parametrized elements of an algebra and give methods for working with them which under favorable conditions lead to a basis given by finitely many patterns. On the negative side we show that in general there can be no algorithm. We relate our study to the problem of verifying that a given set of words in certain groups yields Bokut’ normal forms (or groups with a standard basis).     

Gold-Catalyzed C−H Functionalization Polycondensation for the Synthesis of Aromatic Polymers

Homogeneous gold (Au) complexes have demonstrated tremendous utility in modern organic chemistry; however, their application for the synthesis of polymers remains rare. Herein, we demonstrate the first catalytic application of Au complexes toward the polycondensation of alkyne-containing comonomers and heteroarene nucleophiles. Polymerization occurs through successive intermolecular hydroarylation reactions to produce high molecular weight aromatic copolymers with 1,1-disubstituted alkene backbone linkages. Clear correlations between the rate and degree of polymerization (DP) were established based on catalyst structure and counterion pairing, thus enabling polymerization reactions that proceeded with remarkable efficiency, high reactivity, and exceptional DPs. The reactivity is broad in scope, enabling the copolymerization of highly functionalized aromatic and aliphatic monomers. These results highlight the untapped utility of Au catalysis in providing access to new macromolecular constructs.     

Optical imaging of excited-state tautomerization in single molecules

Tautomerism process of single fluorescent molecules was studied by means of confocal microscopy in combination with azimuthally or radially polarized laser beams. During a tautomerism process the transition dipole moment (TDM) of a molecule changes its orientation which can be visualized by the fluorescence excitation image of the molecule. We present experimental and theoretical studies of two porphyrazine-type molecules and one type of porphyrin molecule: a symmetrically substituted metal-free phthalocyanine and porphyrin, and nonsymmetrically substituted porphyrazine. In the case of phthalocyanine the fluorescence excitation patterns show that the angle between the transition dipole moments of the two tautomeric forms is near 90°, in agreement with quantum chemical calculations. For porphyrazine we find that the orientation change of the TDM is less than 60° or larger than 120°, as theoretically predicted. Most of the porphyrin molecules show no photoinduced tautomerization, while for 7% of the total number of investigated molecules we observed excitation patterns of two different trans forms of the same single molecule. We demonstrate for the first time that a molecule, undergoing a tautomerism process stays in one tautomeric trans conformation during a time comparable with the acquisition time of one excitation pattern. This allowed us to visualize the existence of each of the two trans forms of one single porphyrin molecule, as well as the sudden switching between these tautomers.