Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

An Analysis on the Decline in the Authoritative Powers of the Papacy and its Application to Challenges to Authoritative Powers Faced By the Permanent Membership of the UN Security Council

The organizational authority of the Papacy in the Roman Catholic Church and the permanent membership of the UN Security Council are unique from institutions that are commonly compared with the UN, like the Concert of Europe and the League of Nations, in that these institutional organs possessed strong authoritative and veto powers. Both organs also owe their strong authority during their founding to a need for stability: The Papacy after the crippling of Western Roman Empire and the P-5 to deal with the insecurities of the post-WWII world. While the P-5 still possesses similar authoritative powers within the Council as it did after WWII, the historical authoritative powers of the Papacy within the Church was debilitated to such a degree that by the time of the Reformation in Europe, condemnations of practices within the Church itself were not effective. This paper will analyze major challenges to the authoritative powers of the Papacy, from the crowning of Charlemagne to the beginning of the Reformation, and compare the analysis to challenges affecting the authoritative powers of the P-5 since its creation. From research conducted thus far, I hypothesize that common themes affecting the authoritative powers of the P-5 and the Papacy would include: major changes in the institutions organization (i.e. the Avignon Papacy and Japan’s bid to become a permanent member); the decline in power of actors supporting the institutional organ (i.e. the Holy Roman Empire and the P-5 members); and ideological clashes affecting the institution’s normative power (i.e. the Great Western Schism and Cold War politics).

An Analysis on the Decline in the Authoritative Powers of the Papacy and its Application to Challenges to Authoritative Powers Faced By the Permanent Membership of the UN Security Council

The organizational authority of the Papacy in the Roman Catholic Church and the permanent membership of the UN Security Council are unique from institutions that are commonly compared with the UN, like the Concert of Europe and the League of Nations, in that these institutional organs possessed strong authoritative and veto powers. Both organs also owe their strong authority during their founding to a need for stability: The Papacy after the crippling of Western Roman Empire and the P-5 to deal with the insecurities of the post-WWII world. While the P-5 still possesses similar authoritative powers within the Council as it did after WWII, the historical authoritative powers of the Papacy within the Church was debilitated to such a degree that by the time of the Reformation in Europe, condemnations of practices within the Church itself were not effective. This paper will analyze major challenges to the authoritative powers of the Papacy, from the crowning of Charlemagne to the beginning of the Reformation, and compare the analysis to challenges affecting the authoritative powers of the P-5 since its creation. From research conducted thus far, I hypothesize that common themes affecting the authoritative powers of the P-5 and the Papacy would include: major changes in the institutions organization (i.e. the Avignon Papacy and Japan’s bid to become a permanent member); the decline in power of actors supporting the institutional organ (i.e. the Holy Roman Empire and the P-5 members); and ideological clashes affecting the institution’s normative power (i.e. the Great Western Schism and Cold War politics).

Powers, liabilities and expertise in community safety: Comparative lessons for ‘urban security’ from the United Kingdom and the Republic of Ireland

This paper begins by outlining and critiquing what we term the dominant anglophone model of neo-liberal community safety and crime prevention. As an alternative to this influential but flawed model, a comparative analysis is provided of the different constitutional-legal settlements in each of the five jurisdictions across the UK and the Republic of Ireland (ROI), and their uneven institutionalization of community safety. In the light of this it is argued that the nature of the anglophone community safety enterprise is actually subject to significant variation. Summarizing the contours of this variation facilitates our articulation of some core dimensions of community safety. Then, making use of Colebatch’s (2002) deconstruction of policy activity into categories of authority and expertise, and Brunsson’s (2002) distinction between policy talk, decisions and action, we put forward a way of understanding policy activity that avoids the twin dangers of ‘false particularism’ and ‘false universalism’ (Edwards and Hughes, 2005); that indicates a path for further empirical enquiry to assess the ‘reality’ of policy convergence; and that enables the engagement of researchers with normative questions about where community safety should be heading.

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.

Reliability and discriminatory power of methods for dental plaque quantification

OBJECTIVE: This in situ study evaluated the discriminatory power and reliability of methods of dental plaque quantification and the relationship between visual indices (VI) and fluorescence camera (FC) to detect plaque. MATERIAL AND METHODS: Six volunteers used palatal appliances with six bovine enamel blocks presenting different stages of plaque accumulation. The presence of plaque with and without disclosing was assessed using VI. Images were obtained with FC and digital camera in both conditions. The area covered by plaque was assessed. Examinations were done by two independent examiners. Data were analyzed by Kruskal-Wallis and Kappa tests to compare different conditions of samples and to assess the inter-examiner reproducibility. RESULTS: Some methods presented adequate reproducibility. The Turesky index and the assessment of area covered by disclosed plaque in the FC images presented the highest discriminatory powers. CONCLUSION: The Turesky index and images with FC with disclosing present good reliability and discriminatory power in quantifying dental plaque.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

Joint forces and torques when walking in shallow water

This study reports for the first time an estimation of the internal net joint forces and torques on adults` lower limbs and pelvis when walking in shallow water, taking into account the drag forces generated by the movement of their bodies in the water and the equivalent data when they walk on land. A force plate and a video camera were used to perform a two-dimensional gait analysis at the sagittal plane of 10 healthy young adults walking at comfortable speeds on land and in water at a chest-high level. We estimated the drag force on each body segment and the joint forces and torques at the ankle, knee, and hip of the right side of their bodies using inverse dynamics. The observed subjects` apparent weight in water was about 35% of their weight on land and they were about 2.7 times slower when walking in water. When the subjects walked in water compared with walking on land, there were no differences in the angular displacements but there was a significant reduction in the joint torques which was related to the water`s depth. The greatest reduction was observed for the ankle and then the knee and no reduction was observed for the hip. All joint powers were significantly reduced in water. The compressive and shear joint forces were on average about three times lower during walking in water than on land. These quantitative results substantiate the use of water as a safe environment for practicing low-impact exercises, particularly walking. (C) 2011 Elsevier Ltd. All rights reserved.

Communism and Public Opinion in Queensland, 1939-1951 : An Explanation of Queensland's Vote in the 1951 Anti-Communist Referendum

The starting point of this thesis was a desire to explain the rapid demise in the popularity which the Communist Party enjoyed in Queensland during the second world war. Wartime Queensland gave the Australian Communist Party its highest state vote and six years later Queensland again gave the Communist Party its highest state vote - this time however, to ban the Party. From this I was led into exploring the changing policies, beliefs and strategies of the Party, as well as the many sub-groups on its periphery, and the shifts in public response to these. In 1939 Townsville elected Australia's first Communist alderman. Five years later, Bowen elected not only Australia's first but also the British Empire's first, Communist state government member. Of the five electorates the Australian Communist Party contested in the 1944 Queensland State elections, in none did the Party's candidate receive less than twenty per-cent of the formal vote. Not only was the Party seemingly enjoying considerable popular support but this was occurring in a State which, but for the Depression years (May 1929 - June 1932) had elected a Labor State Government at every state election since 1915. In the September 1951 Constitution Alteration Referendum, 'Powers To Deal With Communists and Communism', Queensland regist¬ered the nation's highest "Yes" majority - 55.76% of the valid vote. Only two other states registered a majority in favour of the referendum's proposals, Western Australia and Tasmania. As this research was undertaken it became evident that while various trends exhibited at the time, anti-Communism, the work of the Industrial Groups, Labor opportunism, local area feelings, ideological shifts of the Party, tactics of Communist-led unions, etc., were present throughout the entire period, they were best seen when divided into three chronological phases of the Party's history and popularity. The first period covers the consolidation of the Party's post-Depression popularity during the war years as it benefited from the Soviet Union's colossal contribution to the Allied war efforts, and this support continued for some six months or so after the war. Throughout the period Communist strength within the trade union movement greatly increased as did total Party membership. The second period was marked by a rapid series of events starting in March 1946, with Winston Churchill's "Official Opening" of the Cold War by his sweeping attack on Communism and Russia, at Fulton. Several days later the first of a series of long and bitter strikes in Communist-led unions occurred, as the Party mobil¬ized for what it believed would be a series of attacks on the working class from a ruling class, defending a capitalist system on the verge of an economic collapse. It was a period when the Party believed this ruling class was using Labor reformism as a last desperate 'carrot' to get workers to accept their lot within a capitalist economic framework. Out of the Meat Strike emerged the Industrial Groups, who waged not only a determined war against Communist trade union leadership but also encouraged the A.W.U.-influenced State Labor apparatus to even greater anti-Communist antagonisms. The Communist Party's increasing militancy and Labor's resistance to it, ended finally in the collapse of the Chifley Labor government. Characteristically the third period opens with the Communist Party making an another about-face, desperately trying to form an alliance with the Labor Party and curbing its former adventurist industrial policy, as it prepared for Menzies' direct assault. The Communist Party's activities were greatly reduced, a function of both a declining member-ship and, furthermore, a membership reluctant to confront an increasingly hostile society. In examining the changing policies, beliefs and strategies of the Party and the shifts in public response to these, I have tried to distinguish between general trends occurring within Australia and the national party, and trends peculiar to Queensland and the Queensland branch of the Party, The Communist Party suffered a decline in support and membership right across Australia throughout this period as a result of the national policies of the Party, and the changing nature of world politics. There were particular features of this decline that were peculiar to Queensland. I have, however, singled out three features of particular importance throughout the period for a short but more specifically detailed analysis, than would be possible in a purely chronological study: i.e. the Party's structure, the Party's ideological subservience to Moscow, and the general effect upon it of the Cold War.

Osmoregulation of the Australian freshwater crocodile, Crocodylus johnstoni, in fresh and saline waters

An unusual saltwater population of the "freshwater" crocodilian, Crocodylus johnstoni, was studied in the estuary of the Limmen Bight River in Australia's Northern Territory and compared with populations in permanently freshwater habitats. Crocodiles in the river were found across a large salinity gradient, from fresh water to a salinity of 24 mg.ml-1, more than twice the body fluid concentration. Plasma osmolarity, concentrations of plasma Na+, Cl-, and K+, and exchangeable Na+ pools were all remarkably constant across the salinity spectrum and were not substantially higher or more variable than those in crocodiles from permanently freshwater habitats. Body fluid volumes did not vary; condition factor and hydration status of crocodiles were not correlated with salinity and were not different from those of crocodiles from permanently fresh water. C. johnstoni clearly has considerable powers of osmoregulation in waters of low to medium salinity. Whether this osmoregulatory competence, extends to continuously hyperosmotic environments is not known, but distributional data suggest that C. johnstoni in hyperosmotic conditions may require periodic access to hypoosmotic water. The study demonstrates a physiological capacity for colonisation of at least some estuarine waters by this normally stenohaline freshwater crocodilian.

An everyday nostalgia: Memory and the fictions of belonging

In 1984, George Orwell presented the future as a dystopian vision, where everyday existence was governed and redefined by an oppressive regime. Winston Smith's daily duties at the Ministry of Truth involved the invention, rewriting and erasing of fragments of history as a means of perpetuating contentment, uniformity and control. History, as Orwell described it in the novel 'was a palimpsest, scraped clean and reinscribed exactly as often as was necessary.' More that a quarter of a century after the publication of 1984, Michel Foucault discussed the cinematic representation and misrepresentation of French history and identity in terms of what he called the manipulation of 'popular memory'. In what was tantamount to a diluted version of Orwell's palimpsestic histories, Foucault stated that 'people are not shown what they were, but what they must remember having been.' This paper will investigate notions of memory, identity and the everyday through a discussion of the community of Celebration in Florida. Conceived in the 1990s, Celebration was designed around a fictionalised representation of pre 1940s small town America, using nostalgia for a mythologised past to create a sense of comfort, community and conformity among its residents. Adapting issues raised by Orwell, Foucault and Baudrillard, this paper will discuss the way in which architecture, like film and literature, can participate in what Foucault discussed as the manipulation of popular memory, inducing and exploiting a nostalgia for an everyday past that that never really existed.

Women drivers' behaviour, socio-demographic characteristics and accidents

The purpose of this study was to examine factors which affect driving behaviour and accident rates in women in Australia. Two groups of women (aged 18-23 and 45-50 years) participating in the Australian Longitudinal Study on Women's Health, completed a mailed questionnaire on driver behaviour and road accidents. Self reported accident rates in the last 3 years were 1.87 per 100 000 km for the young drivers (n = 1199) and 0.59 per 100 000 km for the mid-age drivers (n = 1564); most accidents involved damage only, not injury. Mean scores for lapses obtained using the Driver Behaviour Questionnaire, were similar in the two age groups and similar to those found in other studies. In contrast, scores for errors and violations for the young women were higher than for the mid-age group and previous reports using the same instruments. Riskier driving behaviour among young women was associated with stress and habitual alcohol consumption. In the mid-age group, poorer driver behaviour scores were related to higher levels of education, feeling rushed, higher habitual alcohol consumption and lower life satisfaction scores. Accident rates in both groups were significantly related to lapses. Women born in non-English speaking countries had significantly higher risk of accidents compared to Australian-born women: relative risk = 3.40, 95% confidence interval (1.93, 5.98) for the young drivers; relative risk = 1.77, 95% confidence interval (1.11, 2.83) for mid-age drivers. These findings support the need for road safety campaigns targeted at young women to reduce dangerous driving practices, such as speeding,'tail gating' and overtaking on the inside. There is also a need for further research to understand how lifestyle characteristics are associated with higher risk of accidents and to explore factors which might account for the higher risk for women drivers who were born overseas. (C) 1999 Elsevier Science Ltd. All rights reserved.

Endorsement of CIDI psychosis screening items in the Australian Survey of Mental Health and Well being

This paper presents preliminary analysis of the endorsement of the CIDI Psychosis Screening items in a large Australian community sample. CIDI interviews were completed on a representative sample of 10,641 individuals living in private dwellings in Australia. The items examined constructs related to thought control/interference (G1), ideas of reference (G2), and special powers (G3). If endorsed, each item had a follow-up probe (G1A telepathy; G2A things arranged with special meaning; G3A -- group acceptability). The final item (G4) asked if the respondent had been told that they had schizophrenia. This paper presents the frequency of endorsement, and examines the impact of age and sex on these items. Endorsement of the items was G1 =5.86°/,,, G1A=0.70%, G2=4.84%, G2A=l.31%, G3=3.41%, G3A=2.65%, and G4=0.65%. If screen-positives are defined as two or more 'hits', then 0.41% of the sample met this criterion. Younger participants were significantly more likely to be screen-positive. Items G1, G1A, G2 and G2A were endorsed more frequently by younger participants while there were no significant age effects identified in items G3 or G4. There was a nonsignificant trend for females to endorse item G1 more frequently than males (p = 0.07), but there were no signficant gender differences on the other items. Many individuals who were 'screen-negative' for psychosis endorsed CIDI items related to thought controls, ideas of reference and special powers, suggesting that there may be a 'continuum' of experiences in the population. The impact of age on the distribution of these measures suggests either differential biological vulnerability to these experiences and/or differential cultural factors influencing endorsement of the items. The implications of these findings on our understanding of the symptoms of psychosis will be discussed. The survey was funded by the Commonwealth Dept. of Health and Family Services. The Stanley Foundation supported this project.