This infinite, unanimous dissonance : a study in mathematical existentialism through the work of Jean-Paul Sartre and Alain Badiou

This thesis seeks to elucidate a motif common to the work both of Jean-Paul Sartre and Alain Badiou (with special attention being given to Being and Nothingness and Being and Event respectively): the thesis that the subject 's existence precedes and determines its essence. To this end, the author aims to explicate the structural invariances, common to both philosophies, that allow this thesis to take shape. Their explication requires the construction of an overarching conceptual framework within which it may be possible to embed both the phenomenological ontology elaborated in Being and Event and the mathematical ontology outlined in Being and Event. Within this framework, whose axial concept is that of multiplicity, the precedence of essence by existence becomes intelligible in terms of a priority of extensional over intensional determination. A series of familiar existentialist concepts are reconstructed on this basis, such as lack and value, and these are set to work in the task of fleshing out the more or less skeletal theory of the subject presented in Being and Event.

A dimensional analysis of the benzylic hydroxylase active site in mortierella isabellina

The spatial limits of the active site in the benzylic hydroxylase enzyme of the fungus Mortierella isabellina were investigated. Several molecular probes were used in incubation experiments to determine the acceptability of each compound by this enzyme. The yields of benzylic alcohols provided information on the acceptability of the particular compound into the active site, and the enantiomeric excess values provided information on the "fit" of acceptable substrates. Measurements of the molecular models were made using Cambridge Scientific Computing Inc. CSC Chem 3D Plus modeling program. i The dimensional limits of the aromatic binding pocket of the benzylic hydroxylase were tested using suitably substituted ethyl benzenes. Both the depth (para substituted substrates) and width (ortho and meta substituted substrates) of this region were investigated, with results demonstrating absolute spatial limits in both directions in the plane of the aromatic ring of 7.3 Angstroms for the depth and 7.1 Angstroms for the width. A minimum requirement for the height of this region has also been established at 6.2 Angstroms. The region containing the active oxygen species was also investigated, using a series of alkylphenylmethanes and fused ring systems in indan, 1,2,3,4-tetrahydronaphthalene and benzocycloheptene substrates. A maximum distance of 6.9 Angstroms (including the 1.5 Angstroms from the phenyl substituent to the active center of the heme prosthetic group of the enzyme) has been established extending directly in ii front of the aromatic binding pocket. The other dimensions in this region of the benzylic hydroxylase active site will require further investigation to establish maximum allowable values. An explanation of the stereochemical distributions in the obtained products has also been put forth that correlates well with the experimental observations.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

New conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow

For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional surfaces that move along fluid streamlines. Conditions are determined for which the integrals yield constants of motion for the fluid. In the case when an inviscid fluid is isentropic, these new constants of motion generalize Kelvin’s circulation theorem from closed loops to closed surfaces of any dimension.

Investigation of Frustrated Quasi-One-Dimensional Quantum Spin-Chain Materials

Copper arsenite CuAs2O4 and Copper antimonite CuSb2O4 are S=1/2 (Cu2+ 3d9 electronic configuration) quasi-one-dimensional quantum spin-chain compounds. Both compounds crystallize with tetragonal structures containing edge sharing CuO6 octahedra chains which experience Jahn-Teller distortions. The basal planes of the octahedra link together to form CuO2 ribbon-chains which harbor Cu2+ spin-chains. These compounds are magnetically frustrated with competing nearest-neighbour and next-nearest-neighbour intrachain spin-exchange interactions. Despite the similarities between CuAs2O4 and CuSb2O4, they exhibit very different magnetic properties. In this thesis work, the physical properties of CuAs2O4 and CuSb2O4 are investigated using a variety of experimental techniques which include x-ray diffraction, magnetic susceptibility measurements, heat capacity measurements, Raman spectroscopy, electron paramagnetic resonance, neutron diffraction, and dielectric capacitance measurements. CuAs2O4 exhibits dominant ferromagnetic nearest-neighbour and weaker antiferromagnetic next-nearest-neighbour intrachain spin-exchange interactions. The ratio of the intrachain interactions amounts to Jnn/Jnnn = -4.1. CuAs2O4 was found to order with a ferromagnetic groundstate below TC = 7.4 K. An extensive physical characterization of the magnetic and structural properties of CuAs2O4 was carried out. Under the effect of hydrostatic pressure, CuAs2O4 was found to undergo a structural phase transition at 9 GPa to a new spin-chain structure. The structural phase transition is accompanied by a severe alteration of the magnetic properties. The high-pressure phase exhibits dominant ferromagnetic next-nearest-neighbour spin-exchange interactions and weaker ferromagnetic nearest-neighbour interactions. The ratio of the intrachain interactions in the high-pressure phase was found to be Jnn/Jnnn = 0.3. Structural and magnetic characterizations under hydrostatic pressure are reported and a relationship between the structural and magnetic properties was established. CuSb2O4 orders antiferromagnetically below TN = 1.8 K with an incommensurate helicoidal magnetic structure. CuSb2O4 is characterized by ferromagnetic nearest-neighbour and antiferromagnetic next-nearest-neighbour spin-exchange interactions with Jnn/Jnnn = -1.8. A (H, T) magnetic phase diagram was constructed using low-temperature magnetization and heat capacity measurements. The resulting phase diagram contains multiple phases as a consequence of the strong intrachain magnetic frustration. Indications of ferroelectricity were observed in the incommensurate antiferromagnetic phase.