Calculation of nondifferential properties for atomic ground states /

A new method for sampling the exact (within the nodal error) ground state distribution and nondiflPerential properties of multielectron systems is developed and applied to firstrow atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (the 6 operator). For this purpose, new simple trial functions are developed and optimized. First, using Hydrogen as a test case, we demonstrate the accuracy of our algorithm and its sensitivity to error in the trial function. Applications to first row atoms are then described. We obtain results which are more satisfactory than the ones obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. Also, a comparison is made with results of highly accurate post-Hartree Fock calculations, thereby illuminating the nodal error in our estimates. Taking into account the CPU time spent, our results, particularly for the 8 operator, have a relatively large variance. Several ways of improving the eflSciency together with some extensions of the algorithm are suggested.

Diatoms as indicators of lake trophic status

Relationships between surface sediment diatom assemblages and lake trophic status were studied in 50 Canadian Precambrian Shield lakes in the Muskoka-Haliburton and southern Ontario regions. The purpose of this study was to develop mathematical regression models to infer lake trophic status from diatom assemblage data. To achieve this goal, however, additional investigations dealing with the evaluation of lake trophic status and the autecological features of key diatom species were carried out. Because a unifying index and classification for lake trophic status was not available, a new multiple index was developed in this study, by the computation of the physical, chemical and biological data from 85 south Ontario lakes. By using the new trophic parameter, the lake trophic level (TL) was determined: TL = 1.37 In[1 +(TP x Chl-a / SD)], where, TP=total phosphorus, Chl-a=chlorophyll-a and SD=Secchi depth. The boundaries between 7 lake trophic categories (Ultra-oligotrophic lakes: 0-0.24; Oligotrophic lakes: 0.241-1.8; Oligomesotrophic lakes: 1.813.0; Mesotrophic lakes: 3.01-4.20; Mesoeutrophic lakes: 4.21-5.4; Eutrophic lakes: 5.41-10 and Hyper-eutrophic lakes: above 10) were established. The new trophic parameter was more convenient for management of water quality, communication to the public and comparison with other lake trophic status indices than many of the previously published indices because the TL index attempts to Increase understanding of the characteristics of lakes and their comprehensive trophic states. It is more reasonable and clear for a unifying determination of true trophic states of lakes. Diatom specIes autecology analysis was central to this thesis. However, the autecological relationship of diatom species and lake trophic status had not previously been well documented. Based on the investigation of the diatom composition and variety of species abundance in 30 study lakes, the distribution optima of diatom species were determined. These determinations were based on a quantitative method called "weighted average" (Charles 1985). On this basis, the diatom species were classified into five trophic categories (oligotrophic, oligomesotrophic, mesotrophic, mesoeutrophic and eutrophic species groups). The resulting diatom trophic status autecological features were used in the regressIon analysis between diatom assemblages and lake trophic status. When the TL trophic level values of the 30 lakes were regressed against their fi ve corresponding diatom trophic groups, the two mathematical equations for expressing the assumed linear relationship between the diatom assemblages composition were determined by (1) uSIng a single regression technique: Trophic level of lake (TL) = 2.643 - 7.575 log (Index D) (r = 0.88 r2 = 0.77 P = 0.0001; n = 30) Where, Index D = (0% + OM% + M%)/(E% + ME% + M%); 4 (2) uSIng a' multiple regressIon technique: TL=4.285-0.076 0%- 0.055 OM% - 0.026 M% + 0.033 ME% + 0.065 E% (r=0.89, r2=0.792, P=O.OOOl, n=30) There was a significant correlation between measured and diatom inferred trophic levels both by single and multiple regressIon methods (P < 0.0001, n=20), when both models were applied to another 20 test lakes. Their correlation coefficients (r2 ) were also statistically significant (r2 >0.68, n=20). As such, the two transfer function models between diatoms and lake trophic status were validated. The two models obtained as noted above were developed using one group of lakes and then tested using an entirely different group of lakes. This study indicated that diatom assemblages are sensitive to lake trophic status. As indicators of lake trophic status, diatoms are especially useful in situations where no local trophic information is available and in studies of the paleotrophic history of lakes. Diatom autecological information was used to develop a theory assessing water quality and lake trophic status.

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.

Forgiveness in Two Minds: Understanding Forgiveness Through Dual-Process Theory

In this thesis, I examined the relevance of dual-process theory to understanding forgiveness. Specifically, I argued that the internal conflict experienced by laypersons when forgiving (or finding themselves unable to forgive) and the discrepancies between existing definitions of forgiveness can currently be best understood through the lens of dual-process theory. Dual-process theory holds that individuals engage in two broad forms of mental processing corresponding to two systems, here referred to as System 1 and System 2. System 1 processing is automatic, unconscious, and operates through learned associations and heuristics. System 2 processing is effortful, conscious, and operates through rule-based and hypothetical thinking. Different definitions of forgiveness amongst both lay persons and scholars may reflect different processes within each system. Further, lay experiences with internal conflict concerning forgiveness may frequently result from processes within each system leading to different cognitive, affective, and behavioural responses. The study conducted for this thesis tested the hypotheses that processing within System 1 can directly affect one's likelihood to forgive, and that this effect is moderated by System 2 processing. I used subliminal conditioning to manipulate System 1 processing by creating positive or negative conditioned attitudes towards a hypothetical transgressor. I used working memory load (WML) to inhibit System 2 processing amongst half of the participants. The conditioning phase of the study failed and so no conclusions could be drawn regarding the roles of System 1 and System 2 in forgiveness. The implications of dual-process theory for forgiveness research and clinical practice, and directions for future research are discussed.

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.