Study on computer perception of topological symmetry

A new algorithm for computer perception of topological symmetry is proposed. A node library containing various kinds of nodes is built, and the index number of the library is used as initial atom class identifier (CI) to discriminate the different types of non-hydrogen atoms. The path index (PI) and ringindex (RI) are calculated from the CI, and the global topological enviroment is defined as the sum of PIs and RIs. The topological symmetry can be detected by the iterative calculation of the global topological enviroment.

A NEW SCHEME FOR ASSIGNMENT OF A CANONICAL CONNECTION TABLE

A new algorithm for deriving canonical numbering of atoms in a molecular graph has been developed. Some graph invariants, such as node properties, degree (connectivity), topological path, the smallest node ring index, etc., are encoded together to partit

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].

Voter behaviour and constitutional change in Australia since 1967

Australian Constitutional referendums have been part of the Australian political system since federation. Up to the year 1999 (the time of the last referendum in Australia), constitutional change in Australia does not have a good history of acceptance. Since 1901, there have been 44 proposed constitutional changes with eight gaining the required acceptance according to section 128 of the Australian Constitution. In the modern era since 1967, there have been 20 proposals over seven referendum votes for a total of four changes. Over this same period, there have been 13 federal general elections which have realised change in government just five times. This research examines the electoral behaviour of Australian voters from 1967 to 1999 for each referendum. Party identification has long been a key indicator in general election voting. This research considers whether the dominant theory of voter behaviour in general elections (the Michigan Model) provides a plausible explanation for voting in Australian referendums. In order to explain electoral behaviour in each referendum, this research has utilised available data from the Australian Electoral Commission, the 1996 Australian Bureau of Statistics Census data, and the 1999 Australian Constitutional Referendum Study. This data has provided the necessary variables required to measure the impact of the Michigan Model of voter behaviour. Measurements have been conducted using bivariate and multivariate analyses. Each referendum provides an overview of the events at the time of the referendum as well as the =yes‘ and =no‘ cases at the time each referendum was initiated. Results from this research provide support for the Michigan Model of voter behaviour in Australian referendum voting. This research concludes that party identification, as a key variable of the Michigan Model, shows that voters continue to take their cues for voting from the political party they identify with in Australian referendums. However, the outcome of Australian referendums clearly shows that partisanship is only one of a number of contributory factors in constitutional referendums.

The constitutional power to make war: domestic legal issues raised by Australia's action in Iraq

The legal power to declare war has traditionally been a part of a prerogative to be exercised solely on advice that passed from the King to the Governor-General no later than 1942. In 2003, the Governor- General was not involved in the decision by the Prime Minister and Cabinet to commit Australian troops to the invasion of Iraq. The authors explore the alternative legal means by which Australia can go to war - means the government in fact used in 2003 - and the constitutional basis of those means. While the prerogative power can be regulated and/or devolved by legislation, and just possibly by practice, there does not seem to be a sound legal basis to assert that the power has been devolved to any other person. It appears that in 2003 the Defence Minister used his legal powers under the Defence Act 1903 (Cth) (as amended in 1975) to give instructions to the service head(s). A powerful argument could be made that the relevant sections of the Defence Act were not intended to be used for the decision to go to war, and that such instructions are for peacetime or in bello decisions. If so, the power to make war remains within the prerogative to be exercised on advice. Interviews with the then Governor-General indicate that Prime Minister Howard had planned to take the matter to the Federal Executive Council 'for noting', but did not do so after the Governor-General sought the views of the then Attorney-General about relevant issues of international law. The exchange raises many issues, but those of interest concern the kinds of questions the Governor-General could and should ask about proposed international action and whether they in any way mirror the assurances that are uncontroversially required for domestic action. In 2003, the Governor-General's scrutiny was the only independent scrutiny available because the legality of the decision to go to war was not a matter that could be determined in the High Court, and the federal government had taken action in March 2002 that effectively prevented the matter coming before the International Court of Justice

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Constitutional legitimacy : an international ill and gap in the literature?

The central argument of this work is that “democratic constitutional legitimacy”[2] probably does not currently exist in the politics of any country internationally. This inherent problem in constitutionalism is an endemic governance problem most citizenries should be dealing with, only that we are not in a large extent doing so and haven’t been historically. This position was ascertained using a form of Beck and Grande’s (2010) cosmopolitan methodology in my doctoral thesis (which we shall return to). It is argued that every constitution is in need of considerable rethinking so as to bring its statutes in line with the interests of the plurality of individuals it oversees. Finally, this work attempts to show that research in this area of democratic constitutional legitimacy is lacking in the literature as only a few scholars presently engage the issue (namely Simone Chambers).

Interocular symmetry in myopic anisometropia

Purpose: To investigate the interocular symmetry of optical, biometric and biomechanical characteristics between the fellow eyes of myopic anisometropes. Methods: Thirty-four young, healthy myopic anisometropic adults (≥ 1 D spherical equivalent difference between eyes) without amblyopia or strabismus were recruited. A range of biometric and optical parameters were measured in both eyes of each subject including; axial length, ocular aberrations, intraocular pressure (IOP), corneal topography and biomechanics. Ocular sighting dominance was also measured. Results: Mean absolute spherical equivalent anisometropia was 1.70 ± 0.74 D and there was a strong correlation between the degree of anisometropia and the interocular difference in axial length (r = 0.81, p < 0.001). The more and less myopic eyes displayed a high degree of interocular symmetry for the majority of biometric, biomechanical and optical parameters measured. When the level of anisometropia exceeded 1.75 D, the more myopic eye was more likely to be the dominant sighting eye than for lower levels of anisometropia (p=0.002). Subjects with greater levels of anisometropia (> 1.75 D) also showed high levels of correlation between the dominant and non-dominant eyes in their biometric, biomechanical and optical characteristics. Conclusions: Although significantly different in axial length, anisometropic eyes display a high degree of interocular symmetry for a range of anterior eye biometrics and optical parameters. For higher levels of anisometropia, the more myopic eye tends to be the dominant sighting eye.

Symmetry of in-shoe force signatures in athletes under field conditions : an application for injury prevention

The aetiology behind overuse injuries such as stress fractures is complex and multi-factorial. In sporting events where the loading is likely to be uneven (e.g. hurdling and jumps), research has suggested that the frequency of stress fractures seems to favour the athlete’s dominant limb. The tendency for an individual to have a preferred limb for voluntary motor acts makes limb selection a possible factor behind the development of unilateral overuse injuries, particularly when repeatedly used during high loading activities. The event of sprint hurdling is well suited for the study of loading asymmetry as the hurdling technique is repetitive and the limb movement asymmetrical. Of relevance to this study is the high incidence of Navicular Stress Fractures (NSF) in hurdlers, with suggestions there is a tendency for the fracture to develop in the trail leg foot, although this is not fully accepted. The Ground Reaction Force (GRF) with each foot contact is influenced by the hurdle action, with research finding step-to-step loading variations. However, it is unknown if this loading asymmetry extends to individual forefoot joints, thereby influencing stress fracture development. The first part of the study involved a series of investigations using a commercially available matrix style in-shoe sensor system (FscanTM, Tekscan Inc.). The suitability of insole sensor systems and custom made discrete sensors for use in hurdling-related training activities was assessed. The methodology used to analyse foot loading with each technology was investigated. The insole and discrete sensors systems tested proved to be unsuitable for use during full pace hurdling. Instead, a running barrier task designed to replicate the four repetitive foot contacts present during hurdling was assessed. This involved the clearance of a series of 6 barriers (low training hurdles), place in a straight line, using 4 strides between each. The second part of the study involved the analysis of "inter-limb" and "within foot loading asymmetries" using stance duration as well as vertical GRF under the Hallux (T1), the first metatarsal head (M1) and the central forefoot peak pressure site (M2), during walking, running, and running with barrier clearances. The contribution to loading asymmetry that each of the four repetitive foot contacts made during a series of barrier clearances was also assessed. Inter-limb asymmetry, in forefoot loading, occurred at discrete forefoot sites in a non-uniform manner across the three gait conditions. When the individual barrier foot contacts were compared, the stance duration was asymmetrical and the proportion of total forefoot load at M2 was asymmetrical. There were no significant differences between the proportion of forefoot load at M1, compared to M2; for any of the steps involved in the barrier clearance. A case study testing experimental (discrete) sensors during full pace sprinting and hurdling found that during both gait conditions, the trail limb experienced the greater vertical GRF at M1 and M2. During full pace hurdling, increased stance duration and vertical loading was a characteristic of the trail limb hurdle foot contacts. Commercially available in-shoe systems are not suitable for on field assessment of full pace hurdling. For the use of discrete sensor technology to become commonplace in the field, more robust sensors need to be developed.