Geodesically reversible Finsler 2-spheres of constant curvature

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.

The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

On homotopy spheres of low dimension

Let M be a smooth compact manifold homotopy equivalent to the 4-sphere S^4. Then M x R^1 is homeomorphism co S^4 x R^1.

Spheres of Influence: A Few Reflections on the Concept

In the frame of the Ukrainian crisis the question of spheres of influence has returned to political discourse. This may be an awkward subject, but what if we only deny the existence of such power constellations as spheres of influence? Do spheres of influence exist, or are they relics of history, and mere rhetoric? And if they exist, where can we find them? The hypothesis in this article is that instead of being a tangible reality, spheres of influence are obscure and contested political constructions, which nevertheless can have an impact on political behaviour. To demonstrate this, the article will first introduce a few examples of the current use of the concept. Secondly, a few remarks follow concerning the different IR schools of thought, and conceptual history as a method. Next, the article turns to discussing a few dictionaries and the empirical material for the present inquiry, which consists of recent textbooks, i.e. the current political science curriculum in one particular university, at the University of Tampere, Finland. More empirical cases deal with the division of Africa, the post-WWII situation, and the Hungarian revolution of 1956.

Three Spheres of Classification Research: Emergence, Encyclopedism, and Ecology

Three paths of interdisciplinary work shape the future of classification research.emergence, encyclopedism, and ecology. Each of these, in method, approach, and in substantive inquiry outline both the boundaries and the intersections of the many fields that contribute to our overall understanding of classification research. This paper outlines some high level claims of this work, ties it to current research and offers some theoretical applications of these paths.

ABSTINENCE AND ALCOHOL CONSUMPTION AMONG STUDENTS: THE INFLUENCE OF PERSONAL, FAMILY AND SOCIO-CULTURAL SPHERES

Introduction: Among young people, regular or alcohol abuse seems to ally with individual factors, which congregate to other generators behaviors health risk, in social environment, including family and school. The consumption of alcoholic beverages in the younger age groups, according to the World Development Report goes beyond 60%. In the Portuguese case, the Alentejo is the region that recorded higher consumption among schoolchildren. Objectives: This study aims to know the personal inluences of family, of belonging to the group and the school environment, on the withdrawal and consumption habits among young people. Methods: A qualitative nature of research, using comprehensive semi-structured interviews. The study was developed in a school district of Evora, Portugal. The sample consists of ten students from the 8th school grade, ive non-consumers-ive consumers aged between 13 and 15 years old. Results: The trial takes place between 12 and 14 years old as a result of curiosity, explicit or tacit motivation, “give style”, the environment, entertainment and observing behavior. Among the effects of intake indicated as motivators consumption highlight the joy of reaching states and willingness. Family members tend to encourage moderate drinking on festive occasions. family models exaggerated consumption repudiate ingestion. The elements of the group of belonging tend to motivate explicitly, the intake among consumers students. The school promotes initiatives on the theme, punctually. Conclusions: The consumption of alcohol among young people suffer the personal, family and belonging group inluences. The initiatives in school tend to have no effect.

A primer in public policy for the construction industry

The purpose of this document is to introduce non-specialists to the discipline and practice of public policy, particularly in relation to the construction sector in Australia. In order to do this, a brief overview of Australia’s government structure, and some of the main approaches to public policy analysis are outlined. Reference to construction related examples are provided to ensure issues discussed are relevant and understandable to construction professionals. Government is a significant player in the construction industry, and has multiple roles: adjudicator, regulator, constructor, purchaser and client of construction projects. Moreover there are many spheres of government that are typically engaged in construction projects at multiple stages. The machinery of government can be difficult to understand, even for long term public servants. Demystifying the processes within government can help to improve communication and therefore performance in the industry. A better understanding of how policy-making and government policies affect the construction industry will enhance communication and assist construction professionals and academics to understand and work with government. Additionally the document will provide an opportunity to demonstrate the relevance of policy analysis to inquiries of construction policies and regulation.

Performance Benchmarking of Australian Business Regulation : Submission to the Productivity Commission

The need to “reduce red tape” and regulatory inconsistencies is a desirable outcome (OECD 1997) for developed countries. The costs normally associated with regulatory regimes are compliance costs and direct charges. Geiger and Hoffman (1998) have noted that the extent of regulation in an industry tends to be negatively associated with firm performance. Typically, approaches to estimation of the cost of regulations examine direct costs, such as fees and charges, together with indirect costs, such as compliance costs. However, in a fragmented system, such as Australia, costs can also be incurred due to procedural delays, either by government, or by industry having to adapt documentation for different spheres of government; lack of predictable outcomes, with variations occurring between spheres of government and sometimes within the same government agency; and lost business opportunities, with delays and red tape preventing realisation of business opportunities (OECD 1997). In this submission these costs are termed adaptation costs. The adaptation costs of complying with variations in regulations between the states has been estimated by the Building Product Innovation Council (2003) as being up to $600 million per annum for building product manufacturers alone. Productivity gains from increased harmonisation of the regulatory system have been estimated in the hundreds of millions of dollars (ABCB 2003). This argument is supported by international research which found that increasing the harmonisation of legislation in a federal system of government reduces what we have termed adaptation costs (OECD 2001). Research reports into the construction industry in Australia have likewise argued that improved consistency in the regulatory environment could lead to improvements in innovation (PriceWaterhouseCoopers 2002), and that research into this area should be given high priority (Hampson & Brandon 2004). The opinion of industry in Australia has consistently held that the current regulatory environment inhibits innovation (Manley 2004). As a first step in advancing improvements to the current situation, a summary of the current costs experienced by industry needs to be articulated. This executive summary seeks to outline these costs in the hope that the Productivity Commission would be able to identify the best tools to quantify the actual costs to industry.

Public Perceptions of Elections: An Australia-New Zealand Comparison

his collection of essays honouring the late Emeritus Keith Jackson addresses the public interest in New Zealand. This subject is of increasing importance at a time when politicians are grappling with serious issues that call into question the boundaries between the private and public spheres. The essays, by leading scholars and acknowledged experts in their field, reflect Keith's own preoccupations with institutional politics and with communication

Synthesis and modifications of metal oxide nanostructures and their applications

Transition metal oxides are functional materials that have advanced applications in many areas, because of their diverse properties (optical, electrical, magnetic, etc.), hardness, thermal stability and chemical resistance. Novel applications of the nanostructures of these oxides are attracting significant interest as new synthesis methods are developed and new structures are reported. Hydrothermal synthesis is an effective process to prepare various delicate structures of metal oxides on the scales from a few to tens of nanometres, specifically, the highly dispersed intermediate structures which are hardly obtained through pyro-synthesis. In this thesis, a range of new metal oxide (stable and metastable titanate, niobate) nanostructures, namely nanotubes and nanofibres, were synthesised via a hydrothermal process. Further structure modifications were conducted and potential applications in catalysis, photocatalysis, adsorption and construction of ceramic membrane were studied. The morphology evolution during the hydrothermal reaction between Nb2O5 particles and concentrated NaOH was monitored. The study demonstrates that by optimising the reaction parameters (temperature, amount of reactants), one can obtain a variety of nanostructured solids, from intermediate phases niobate bars and fibres to the stable phase cubes. Trititanate (Na2Ti3O7) nanofibres and nanotubes were obtained by the hydrothermal reaction between TiO2 powders or a titanium compound (e.g. TiOSO4·xH2O) and concentrated NaOH solution by controlling the reaction temperature and NaOH concentration. The trititanate possesses a layered structure, and the Na ions that exist between the negative charged titanate layers are exchangeable with other metal ions or H+ ions. The ion-exchange has crucial influence on the phase transition of the exchanged products. The exchange of the sodium ions in the titanate with H+ ions yields protonated titanate (H-titanate) and subsequent phase transformation of the H-titanate enable various TiO2 structures with retained morphology. H-titanate, either nanofibres or tubes, can be converted to pure TiO2(B), pure anatase, mixed TiO2(B) and anatase phases by controlled calcination and by a two-step process of acid-treatment and subsequent calcination. While the controlled calcination of the sodium titanate yield new titanate structures (metastable titanate with formula Na1.5H0.5Ti3O7, with retained fibril morphology) that can be used for removal of radioactive ions and heavy metal ions from water. The structures and morphologies of the metal oxides were characterised by advanced techniques. Titania nanofibres of mixed anatase and TiO2(B) phases, pure anatase and pure TiO2(B) were obtained by calcining H-titanate nanofibres at different temperatures between 300 and 700 °C. The fibril morphology was retained after calcination, which is suitable for transmission electron microscopy (TEM) analysis. It has been found by TEM analysis that in mixed-phase structure the interfaces between anatase and TiO2(B) phases are not random contacts between the engaged crystals of the two phases, but form from the well matched lattice planes of the two phases. For instance, (101) planes in anatase and (101) planes of TiO2(B) are similar in d spaces (~0.18 nm), and they join together to form a stable interface. The interfaces between the two phases act as an one-way valve that permit the transfer of photogenerated charge from anatase to TiO2(B). This reduces the recombination of photogenerated electrons and holes in anatase, enhancing the activity for photocatalytic oxidation. Therefore, the mixed-phase nanofibres exhibited higher photocatalytic activity for degradation of sulforhodamine B (SRB) dye under ultraviolet (UV) light than the nanofibres of either pure phase alone, or the mechanical mixtures (which have no interfaces) of the two pure phase nanofibres with a similar phase composition. This verifies the theory that the difference between the conduction band edges of the two phases may result in charge transfer from one phase to the other, which results in effectively the photogenerated charge separation and thus facilitates the redox reaction involving these charges. Such an interface structure facilitates charge transfer crossing the interfaces. The knowledge acquired in this study is important not only for design of efficient TiO2 photocatalysts but also for understanding the photocatalysis process. Moreover, the fibril titania photocatalysts are of great advantage when they are separated from a liquid for reuse by filtration, sedimentation, or centrifugation, compared to nanoparticles of the same scale. The surface structure of TiO2 also plays a significant role in catalysis and photocatalysis. Four types of large surface area TiO2 nanotubes with different phase compositions (labelled as NTA, NTBA, NTMA and NTM) were synthesised from calcination and acid treatment of the H-titanate nanotubes. Using the in situ FTIR emission spectrescopy (IES), desorption and re-adsorption process of surface OH-groups on oxide surface can be trailed. In this work, the surface OH-group regeneration ability of the TiO2 nanotubes was investigated. The ability of the four samples distinctively different, having the order: NTA > NTBA > NTMA > NTM. The same order was observed for the catalytic when the samples served as photocatalysts for the decomposition of synthetic dye SRB under UV light, as the supports of gold (Au) catalysts (where gold particles were loaded by a colloid-based method) for photodecomposition of formaldehyde under visible light and for catalytic oxidation of CO at low temperatures. Therefore, the ability of TiO2 nanotubes to generate surface OH-groups is an indicator of the catalytic activity. The reason behind the correlation is that the oxygen vacancies at bridging O2- sites of TiO2 surface can generate surface OH-groups and these groups facilitate adsorption and activation of O2 molecules, which is the key step of the oxidation reactions. The structure of the oxygen vacancies at bridging O2- sites is proposed. Also a new mechanism for the photocatalytic formaldehyde decomposition with the Au-TiO2 catalysts is proposed: The visible light absorbed by the gold nanoparticles, due to surface plasmon resonance effect, induces transition of the 6sp electrons of gold to high energy levels. These energetic electrons can migrate to the conduction band of TiO2 and are seized by oxygen molecules. Meanwhile, the gold nanoparticles capture electrons from the formaldehyde molecules adsorbed on them because of gold’s high electronegativity. O2 adsorbed on the TiO2 supports surface are the major electron acceptor. The more O2 adsorbed, the higher the oxidation activity of the photocatalyst will exhibit. The last part of this thesis demonstrates two innovative applications of the titanate nanostructures. Firstly, trititanate and metastable titanate (Na1.5H0.5Ti3O7) nanofibres are used as intelligent absorbents for removal of radioactive cations and heavy metal ions, utilizing the properties of the ion exchange ability, deformable layered structure, and fibril morphology. Environmental contamination with radioactive ions and heavy metal ions can cause a serious threat to the health of a large part of the population. Treatment of the wastes is needed to produce a waste product suitable for long-term storage and disposal. The ion-exchange ability of layered titanate structure permitted adsorption of bivalence toxic cations (Sr2+, Ra2+, Pb2+) from aqueous solution. More importantly, the adsorption is irreversible, due to the deformation of the structure induced by the strong interaction between the adsorbed bivalent cations and negatively charged TiO6 octahedra, and results in permanent entrapment of the toxic bivalent cations in the fibres so that the toxic ions can be safely deposited. Compared to conventional clay and zeolite sorbents, the fibril absorbents are of great advantage as they can be readily dispersed into and separated from a liquid. Secondly, new generation membranes were constructed by using large titanate and small ã-alumina nanofibres as intermediate and top layers, respectively, on a porous alumina substrate via a spin-coating process. Compared to conventional ceramic membranes constructed by spherical particles, the ceramic membrane constructed by the fibres permits high flux because of the large porosity of their separation layers. The voids in the separation layer determine the selectivity and flux of a separation membrane. When the sizes of the voids are similar (which means a similar selectivity of the separation layer), the flux passing through the membrane increases with the volume of the voids which are filtration passages. For the ideal and simplest texture, a mesh constructed with the nanofibres 10 nm thick and having a uniform pore size of 60 nm, the porosity is greater than 73.5 %. In contrast, the porosity of the separation layer that possesses the same pore size but is constructed with metal oxide spherical particles, as in conventional ceramic membranes, is 36% or less. The membrane constructed by titanate nanofibres and a layer of randomly oriented alumina nanofibres was able to filter out 96.8% of latex spheres of 60 nm size, while maintaining a high flux rate between 600 and 900 Lm–2 h–1, more than 15 times higher than the conventional membrane reported in the most recent study.