604 research outputs found
Galois-theoretical groups
A group G is called Galois-theoretical if CGCA(H)=H for any subgroup H of G and CACG(B)=B for any subgroup B of A=Aut(G). This paper shows that a group G is Galois-theoretical if and only if G is isomorphic to the trivial group, to the cyclic group of order 3, or to the symmetric group of degree 3
FOREIGN CAPITAL AND GENDER DIFFERENCES IN PROMOTIONS: EVIDENCE FROM THE BRAZILIAN TRANSFORMATION INDUSTRY
The Effects of Conditional Cash Transfer Programmes on Adult Labour Supply: An Empirical Analysis Using a Time-Series-Cross-Section
Spectroscopic Probes of Low-Barrier Proton-Transfer Dynamics
The diverse discipline of molecular spectroscopy, which has profited tremendously from the advent of tunable laser sources, has transformed the scientific community’s knowledge of the microscopic world, allowing the study of perplexing quantum-chemical phenomena. Classically-hindered proton transfer, a multidimensional process mediated by nuclear-quantum effects (e.g., potential-barrier tunneling), is a chemical transformation that forms the crux of all acid/base chemistry. Although extensive research efforts have aimed to establish the paradigms that govern this transformation, a full understanding has proven elusive with questions continuing to emerge.Exploring the proton-transfer reaction, and the related concept of hydrogen bonding, has benefitted greatly from investigations of model systems where the hydron migration is facilitated by a symmetric double-minimum potential well. In such molecular species, the spectroscopic signature of tunneling-induced bifurcations gives a direct measure of reaction rates, thus enabling the extraction of dynamical information. This thesis focuses on a relatively unexplored member of this group, 6-hydroxy-2- formylfulvene or HFF, which exhibits a quasi-linear reaction site on a conjugated framework – a structural arrangement that engenders a low-barrier hydrogen bonding (LBHBing) motif. Additionally, HFF has been suggested to experience a drastic quenching in dynamics accompanying π*←π electronic excitation that has been attributed to a substantial change in reaction mechanism whereby the strictly planar reaction coordinate in the X1A1 state transforms into an out-of-plane pathway involving substantial heavy- atom motion in the A1B2 (π∗π) state. The unique structural and dynamical characteristics of HFF create a potent platform for studying the effects of isotopic substitution and vibrational excitation on tunneling phenomena as presented in this thesis. The origin band of HFF and its monodeuterated isotopolog, HFF-d, were probed using polarization-resolved degenerate four-wave mixing (DFWM), an absorption-based technique that provides near-rotational resolution. This enabled the measurement of tunneling-induced bifurcations for the vibrationless A1B2 states of HFF and HFF-d, yielding Δ = 0.1009(43) cm-1 and Δ = 0.074(10) cm-1, respectively. These values imply a small deuterium kinetic isotope effect (DKIE) of Λ = 1.36 (relative to the analogous ground-state value of Λ = 3.44) that can be rationalized by considering the substantial heavy-atom motion (and the corresponding large effective mass) that is involved in the excited-state proton-transfer process, which dominates the reaction and makes the change in the mass of the shuttling hydron less consequential. Similar DFWM studies also were performed for two higher-energy vibronic bands of A1B2 (π∗π) HFF and HFF-d, ν4(a1), a chelate-ring breathing mode, and ν7(b2), a chelate-ring deformation mode. Although vibrational excitation can have a substantial effect on proton-transfer dynamics, the two studied modes did not couple effectively to the reaction coordinate and, therefore, resulted in minimal changes to measured tunneling splittings, thereby highlighting the distinct nature of the multidimensional out-of-plane tunneling mechanism that governs the π * ← π excited state
On dominant contractions and a generalization of the zero-two law
Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to
L^1(X,{\cf},\m) be two positive contractions such that . If
then for all n\in\bn. In the present paper we
generalize this result to multi-parameter contractions acting on . As an
application of that result we prove a generalization of the "zero-two" law.Comment: 10 page
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