Well‐Defined Single‐Site Monohydride Silica‐Supported Zirconium from Azazirconacyclopropane

The silica‐supported azazirconacyclopropane ?SiOZr(HNMe₂)(η²‐NMeCH₂)(NMe₂) ( 1 ) leads exclusively under hydrogenolysis conditions (H₂, 150 °C) to the single‐site monopodal monohydride silica‐supported zirconium species ?SiOZr(HNMe₂)(NMe₂)₂H ( 2 ). Reactivity studies by contacting compound 2 with ethylene, hydrogen/ethylene, propene, or hydrogen/propene, at a temperature of 200 °C revealed alkene hydrogenation.     

Fast frequency modulation optical code division multiple access communication system

An optical fast frequency modulation code division multiple access communication system is proposed. In this system, an electrically controlled tunable optical filter (TOF) is used to encode the modulated broadband light source. The code depends on the function set to the controller. Two-dimensional code named functional code is also proposed based on a shifted sine function. The function defines the dynamic coding pattern of the central wavelength of the transmitted narrowband optical signal. Thus, the system will allow for an easy reconfiguration of the transmitter without the need for sophisticated encoder. At the receiver, a synchronized TOF with the same function is used as a decoder. The performance of this system is shown to be better compared with a fast frequency hopping and a spectral amplitude coding systems.     

Photolysis of xylylbischromones

Photoreorganisation of xylylbischromones occurring through 1,4-biradical is described. In these bischromones, the two chromophores have been found to behave independently.     

Attempted polymerization of substituted pipecolic acid NCA's: Dimerization and mechanism

Racemic and optically active N-carboxyanhydrides (NCA)s of 2-methyl- and cis-6-methylpipecolic acid, when subjected to polymerization conditions in solution or in bulk whether with “weak” or “strong” base initiators, resisted polymerization under all conditions tried. Instead, the NCA of 2-methylpipecolic acid gave the corresponding cyclic dipeptide and the NCA of cis-6-methylpipecolic acid formed the cyclic dipeptide derived from trans-6-methylpipecolic acid. The mechanism of dimerization of these NCA's was investigated. Evidence was provided for the proposed mechanism in which the active moiety is not a carbamate ion but an amino group. Methyl 2-methylpipecolate underwent an intermolecular S_N2-type reaction upon heating, yielding equimolar quantities of methyl N-methyl-2-methylpipecolate and 2-methylpipecolic acid.     

Metrization and Semimetrization Theorems with Applications to Manifolds

This paper is a study of conditions under which a space with S₂ is metrizable, o-semimetrizable or semimetrizable. It is shown that: a wMN, w-space is metrizable if and only if it has S₂, a quasi--space is metrizable if and only if it is a pseudo wN-space with S₂, a separable manifold is metrizable if and only if it has S₂ with property (*), a perfectly normal manifold with q quasi-G ^* diagonal is metrizable and a separable manifold is a hereditarily separable metrizable if and only if it has -S₂.     

Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.     

Algebraic approach to electronic spectroscopy and dynamics

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponential operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a(+). While exp(a(+)) translates coherent states, exp(a(+)a(+)) operation on coherent states has always been a challenge, as a(+) has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F(tau(1),tau(2),tau(3),tau(4)), of which the optical nonlinear response function may be procured, as evaluating F(tau(1),tau(2),tau(3),tau(4)) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.     

Investigation of structural and textural properties of Ge<Subscript> <Emphasis Type="Italic">x</Emphasis> </Subscript>MoO<Subscript>3</Subscript> system,promising catalyst for photocatalytic applications

The main objective of this work is to control the structural, textural and electrical properties of the system prepared by mixing molybdenum oxide with different amounts of germanium. The system is expected to be suitable as a catalyst for the photodegradation of methyl red (one of the dyes group) and the results of this study can throw some light on the relationship between the properties of this system and the extent of the dye degradation as indicated by the measurements of the photocatalytic activity. The composite materials (Ge_xMoO₃) were prepared by solid-state reaction between germanium and molybdenum oxide. The mixtures were made in Ge/MoO₃ molar ratios of 0.01, 0.05, 0.1, 0.2, 0.5, and 1.0. The reaction was conducted in air at 700°C. The prepared samples were characterized by X-ray powder diffraction, micro-Raman spectroscopy, nitrogen adsorption measurements, diffuse reflectance spectrometry and UV-Vis absorption spectrophotometry. The addition of germanium has affected the photocatalytic activity of MoO₃ as evidenced by an increase in the degradation extent of methyl red from about 14% (for pure oxide) to about 97% for Ge_xMoO₃ (x = 1). An enhancement in the photocatalytic activity was attributed to the change in the band gap and modification of the textural properties associated with the formation of Ge_xMoO₃ composites.