(dme)MCl_3(NNPh_2) (dme= dimethoxyethane; M= Nb, Ta): A Versatile Synthon for [Ta═NNPh_2] Hydrazido(2-) Complexes

Complexes (dme)TaCl_3(NNPh_2) (1) and (dme)NbCl_3(NNPh_2) (2) (dme =1,2-dimethoxyethane) were synthesized from MCl5 and diphenylhydrazine via a Lewis-acid assisted dehydrohalogenation reaction. Monomeric 1 has been characterized by X-ray, IR, UV−vis, ^(1)H NMR, and ^(13)C NMR spectroscopy and contains a κ^(1)-bound hydrazido(2-) moiety. Unlike the corresponding imido derivatives, 1 is dark blue because of an LMCT that has been lowered in energy as a result of an N_(α)−N_(β) antibonding interaction that raises the highest occupied molecular orbital (HOMO). Reaction of 1 with a variety of neutral, mono- and dianionic ligands generates the corresponding ligated complexes retaining the κ^(1)-bound [Ta−NNPh_2] moiety

Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework which is presented step-by-step with examples throughout. In this second part of two papers, we give the general categorical formulation

Grouping Individual Investment Preferences in Retirement Savings: A Cluster Analysis of a USS Members Risk Attitude Survey

Cluster analysis is used to identify homogeneous groups of members of USS in terms of risk attitudes. There are two distinct clusters of members in their 40s and 50s. One had previously ‘engaged’ with USS by making additional voluntary contributions. It typically had higher pay, longer tenure, less interest in ethical investing, lower risk capacity, a higher percentage of males, and a higher percentage of academics than members of the ‘disengaged’ cluster. Conditioning only on the attitude to risk responses, there are 18 clusters, with similar but not identical membership, depending on which clustering method is used. The differences in risk aversion across the 18 clusters could be explained largely by differences in the percentage of females and the percentage of couples. Risk aversion increases as the percentage of females in the cluster increases, while it reduces as the percentage of couples increases because of greater risk sharing within the household. Characteristics that other studies have found important determinants of risk attitudes, such as age, income and (pension) wealth, do not turn out to be as significant for USS members. Further, despite being on average more highly educated than the general population, USS members are marginally more risk averse than the general population, controlling for salary, although the difference is not significant

One size fits all: How many default funds does a pension scheme need?

In this paper, we analyse the number of default investment funds appropriate for an occupational defined contribution pension scheme. Using a unique dataset of member risk attitudes and characteristics from a survey of a large UK pension scheme, we apply cluster analysis to identify two distinct groups of members in their 40s and 50s. Further analysis indicated that the risk attitudes of the two groups were not significantly different, allowing us to conclude that a single lifestyle default fund is appropriate

Groups 5 and 6 Terminal Hydrazido(2−) Complexes: N_β Substituent Effects on Ligand-to-Metal Charge-Transfer Energies and Oxidation States

Brightly colored terminal hydrazido(2−) (dme)MCl_3(NNR_2) (dme = 1,2-dimethoxyethane; M = Nb, Ta; R = alkyl, aryl) or (MeCN)WCl_4(NNR_2) complexes have been synthesized and characterized. Perturbing the electronic environment of the β (NR_2) nitrogen affects the energy of the lowest-energy charge-transfer (CT) transition in these complexes. For group 5 complexes, increasing the energy of the N_β lone pair decreases the ligand-to-metal CT (LMCT) energy, except for electron-rich niobium dialkylhydrazides, which pyramidalize N_β in order to reduce the overlap between the Nb═Nα π bond and the Nβ lone pair. For W complexes, increasing the energy of N_β eventually leads to reduction from formally [W^(VI)≡N–NR_2] with a hydrazido(2−) ligand to [W^(IV)═N═NR_2] with a neutral 1,1-diazene ligand. The photophysical properties of these complexes highlight the potential redox noninnocence of hydrazido ligands, which could lead to ligand- and/or metal-based redox chemistry in early transition metal derivatives

Amine, Amido, and Imido Complexes of Tantalum Supported by a Pyridine-Linked Bis(phenolate) Pincer Ligand: Ta−N π-Bonding Influences Pincer Ligand Geometry

A series of tantalum imido and amido complexes supported by a pyridine-linked bis(phenolate) ligand has been synthesized. Characterization of these complexes via X-ray crystallography reveals both C_s and C_2 binding modes of the bis(phenolate)pyridine ligand, with complexes containing two or fewer strong π-donor interactions from ancillary ligands giving C_s symmetry, whereas three strong π-donor interactions (e.g., three amido ligands or one amido ligand and one imido ligand) give C_2-symmetric binding of the bis(phenolate)pyridine ligand. DFT calculations and molecular orbital analyses of the complexes have revealed that the preference for C_s-symmetric ligand binding is a result of tantalum−phenolate π-bonding, whereas in cases where tantalum−phenolate π-bonding is overridden by stronger Ta−N π-bonding, C_2-symmetric ligand binding is preferred, likely because conformationally this is the lowest-energy arrangement. This electronically driven change in geometry indicates that, unlike analogous metallocene systems, the bis(phenolate)pyridine pincer ligand is not a strong enough π-donor to exert dominant control over the electronic and geometric properties of the complex

‘Am I not a Man, whose nature is frail, and prone to error?’ An evaluation of Matthew Lewis’s The Monk as a work of tragedy

This dissertation is an argument for the re-evaluation of Matthew Lewis’s Ambrosio the Monk as a figure of tragedy instead of villainy. By identifying the characteristics of tragedy within the Gothic text, Ambrosio can be shown to fulfil the tenets of the tragic hero as established by Aristotle. Because of this, the reader can experience the tragic response of catharsis because of the pity and sympathy that Ambrosio as a tragic hero can inspire in the reader. For sympathy to be extended to the Gothic, a Romantic sensibility of the primacy of the self, analogous to that of the Renaissance humanist, must be established. The development of this Romantic Sensibility is explored with acknowledgement of the influence upon it by the Renaissance tragedians, thus establishing a chain of literary connections from the ancient tragedy to the Romantic Gothic. By recognising the shared humanity of the Gothic villain and the reader, the sympathy and pity necessary for the tragic response is extended to the Gothic villain which is transformed to a figure of tragedy

Comparing localizations across adjunctions

We show that several apparently unrelated formulas involving left or right Bousfield localizations in homotopy theory are induced by comparison maps associated with pairs of adjoint functors. Such comparison maps are used in the article to discuss the existence of functorial liftings of homotopical localizations and cellularizations to categories of algebras over monads acting on model categories, with emphasis on the cases of module spectra and algebras over simplicial operads. Some of our results hold for algebras up to homotopy as well; for example, if $T$ is the reduced monad associated with a simplicial operad and $f$ is any map of pointed simplicial sets, then $f$-localization coincides with $Tf$-localization on spaces underlying homotopy $T$-algebras, and similarly for cellularizations