Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

Individual difference factors and men's attraction to female body features /

Existing research on attraction to body features has suggested that men show general preferences for women with lower waist-to-hip ratios (WHR), larger breasts, and slender body weights. The present study intended to expand on this research by investigating several individual difference factors and their potential contribution to variation in what men find attractive in female body features. Two hundred and seventy-three men were assessed for sex-role identity, 2D:4D digit ratios (a possible marker of prenatal exposure to androgens, and thus masculinization), physical attractiveness, early sexual experiences (as indices of early sexual conditioning), and early family attitudes toward body features, as well as their current preferences for WHR, breast size, weight, and height in women. For WHR, as predicted, physical attractiveness, early sexual experiences, and lower (more masculine) right-hand 2D:4D ratios significantly predicted current preferences for more feminine (lower) WHR. Early sexual experiences significantly predicted later preferences for breast size; in addition, more masculine occupational preferences and lower (more masculine) left-hand 2D:4D ratios predicted preferences for larger breasts. Participants' height, education level, Unmitigated Agency (masculinity) scores, and early sexual experiences significantly predicted current preferences for height. Finally, early sexual experiences significantly predicted current preferences for weight. The results suggest that variation in preferences for women's bodily features can be uniquely accounted for by a number of individual difference factors. Strengths and weaknesses of the study, along with implications for future research, are discussed.

Biotransformations of water insoluble substrates in aqueous, two-phase and encapsulated systems /

The biotransformation of water insoluble substrates by mammalian and bacterial cells has been problematic, since these whole cell reactions are primarily performed in an aqueous environment The implementation of a twophase or encapsulated system has the advantages of providing a low water system along with the physiological environment the cells require to sustain themselves. Encapsulation of mammalian cells by formation of polyamide capsules via interfacial polymerization illustrated that the cells could not survive this type of encapsulation process. Biotransformation of the steroid spironolactone [3] by human kidney carcinoma cells was performed in a substrate-encapsulated system, yielding canrenone [4] in 70% yield. Encapsulation of nitrile-metabolizing Rhodococcus rhodochrous cells using a polyamide membrane yielded leaky capsules, but biotransformation of 2-(4- chlorophenyl)-3-methylbutyronitrile (CPIN) [6] in a free cell system yielded CPIN amide [7] in 40% yield and 94% ee. A two-phase biotransformation of CPIN consisting of a 5:1 ratio of tris buffer, pH 7.2 to octane respectively, gave CPIN acid [8] in 30% yield and 97% ee. It was concluded that Rhodococcus rhodochrous ATCC 17895 contained a nonselective nitrile hydratase and a highly selective amidase enzyme.

Bis-and tris (amidine) fluoroboron cations and related systems studies by Multinuclear NMR and fast atom bombardment mass spectometry

The formation and the isolation of fluoroboron salts, (D2BF2+)(PF6-), (DD'BF2+)(PF6-) and (D3BF2+)(PF6-)2, have been carried out. 1,8-Diazabicyclo [5,4.0]undec-7-ene (DBU) and 1,5-diazabicyclo[4,3,O]non-5-ene (DBN), extremely strong organic bases, were introduced into the fluoroboron cation systems and induced a complicated redistribution reaction in the D/BF3/BC13 systems. The result was the formation of all BFnCI4-n-, D.BFnCI3-n and fluoroboron cation species which were detected by 19p and 11B NMR spectrometry. The displacement reaction of CI- from these D.BFnCI3-n (n = 1 and 2) species by the second entering ligand is much faster than in other nitrogen donor containing systems which have been previously studied. Tetramethylguanidine, oxazolines and thiazolines can also produce similar reactions in D/BF3/BCI3 systems, but no significant BFnC4-n- species were observed. As well as influences of their basicity and their steric hindrance, N=C-R(X) (X = N, 0 or S) and N=C( X)2 (X = N or S) structures of ligands have significant effects on the fonnationof fluoroboron cations and the related NMR parameters. D3BF2+ and some D2BF2+ show the expected inertness, but (DBU)2BF2+ shows an interestingly high reactivity. (D2BF2+)(X-) formed from weak organic bases such as pyridine can react with stronger organic bases and form DD'BF2+ and D'2BF2+ in acetone or nitromethane. Fast atom bombardment mass spectrometry is doubly meaningful to this work. Firstly, FABMS can be directly applied to the complicated fluoroboron cation containing solution systems as an excellent complementary technique to multinuclear NMR. Secondly, the gas-phase ion substitution reaction of (D2BF2+)(PF6-) with the strong organic bases is successfully observed in a FABMS ion source when the B-N bond is not too strong in these cations.

Interactions between the cholinergic and dopaminergic systems during the production of ultrasonic vocalizations in rats

Rats produce ultrasonic vocalizations that can be categorized into two types of ultrasonic calls based on their sonographic structure. One group contains 22-kHz ultrasonic vocalization (USVs), characterized by relatively constant (flat) frequency with peak frequency ranging from 19 to 28-kHz, and a call duration ranging between 100 – 3000 ms. These vocalization can be induced by cholinomimetic agents injected into the ascending mesolimbic cholinergic system that terminates in the anterior hypothalamic-preoptic area (AH-MPO) and lateral septum (LS). The other group of USVs contains 50-kHz USVs, characterized by high peak frequency, ranging from 39 to 90-kHz, short duration ranging from 10-90 ms, and varying frequency and complex sonographic morphology. These vocalizations can be induced by dopaminergic agents injected into the nucleus accumbens, the target area for the mesolimbic dopaminergic system. 22-kHz USVs are emitted in situations that are highly aversive, such as proximity of a predator or anticipation of a foot shock, while 50 kHz USVs are emitted in rewarding and appetitive situations, such as juvenile play behaviour or anticipation of rewarding electrical brain stimulation. The activities of these two mesolimbic systems were postulated to be antagonistic to each other. The current thesis is focused on the interaction of these systems indexed by emission of relevant USVs. It was hypothesized that emission of 22 kHz USVs will be antagonized by prior activation of the dopaminergic system while emission of 50 kHz will be antagonized by prior activation of the cholinergic system. It was found that injection of apomorphine into the shell of the nucleus accumbens significantly decreased the number of carbachol-induced 22 kHz USVs from both AH-MPO and LS. Injection of carbachol into the LS significantly decreased the number of apomorphine-induced 50 kHz USVs from the shell of the nucleus accumbens. The results of the study supported the main hypotheses that the mesolimbic dopaminergic and cholinergic systems function in antagonism to each other.

Educational Leadership: Exploring the Influence of Managed and Living Systems in Educational Leadership Discourse

A conceptual analysis of educational leadership explored the influence of managed and living systems on 21st century leadership discourse. Drawing on a detailed understanding of managed and living systems theory compiled from the work of Capra (2002), Morgan (1997), Mitchell and Sackney (2009), and Wheatley (2007), this study draws attention to the managed systems systemic concepts of efficiency, control, and standardization, and the living systems concepts of collaboration, shared meaning, change, and interconnection as markers of systems theory that find resonance within leadership literature. Using these systemic concepts as a framework, this study provides important insights into the espousal of managed and living systems concepts within the leadership discourse.