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).

Should the fiscal powers of the Northern Ireland Assembly be enhanced?

Northern Ireland has been characterised by an inability to narrow the persistent economic gap relative to Britain. Some commentators have suggested that regional Corporation Tax variation may be the “game changer” in closing this gap. This paper draws on a range of papers that help us better understand the historical and institutional context. However, the analysis of tax variation is broader than this. Consideration is given as to which taxes might be the most suitable candidates for devolution. While greater tax variations could certainly complement an emphasis on increased competitiveness aimed at improving economic outcomes, they are no substitute for such a focus. As is often the case in institutional and economic development, issues of sequencing and policy capacity are salient.

Health Care Power of Attorney FAQ, May 28, 2015

Health Care Power of Attorney questions and answers on common questions.

Health Care Power of Attorney FAQ, May 30, 2013

Information regarding questions and answers for Health Care Power of Attorney

Durable (Financial) Power of Attorney, July 28, 2014

What is a financial power of attorney (FPOA)? A FPOA is a document authorizing an agent to make financial management decisions for the principal. The agent is the person that will be managing the principal’s finances, so it is important to choose someone trustworthy; someone who will not abuse or exploit this power, will listen to the principal’s wishes included in the document or otherwise communicated to the agent, and will look out for the principal’s best interests.

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.

Assessing testamentary and decision-making competence/capacity in the Australian context

Australia lacks a satisfactory, national paradigm for assessing competence and capacity in the context of testamentary, enduring power of attorney and advance care directive documents. Competence/capacity assessments are currently conducted on an ad hoc basis by legal and/or medical professionals. The reliability of the assessment process is subject to the skill set and mutual understanding of the legal and/or medical professional conducting the assessment. There is a growth in the prevalence of diseases such as dementia. Such diseases impact upon cognition which increasingly necessitates collaboration between the legal and medical professions when assessing the effect of mentally disabling conditions upon competency/capacity. Miscommunication and lack of understanding between legal and medical professionals involved could impede the development of a satisfactory paradigm. A qualitative study seeking the views of legal and medical professionals who practise in this area has been conducted. This incorporated surveys and interviews of 10 legal and 20 medical practitioners. Some of the results are discussed here. Practitioners were asked whether there is a standard approach and whether national guidelines were desirable. There was general agreement that uniform guidelines for the assessment of competence/capacity would be desirable. The interviews also canvassed views as to the state of the relationship between the professions. The results of the empirical research support the hypothesis that relations between the professions could be improved. The development of a national paradigm would promote consistency and transparency of process, helping to improve the professional relationship and maximising the principles of autonomy, participation and dignity.

Reading Elizabeth Bishop's "Artifact of [Words]"

As Emerson noted in his essay 'The Poet' "we are not pans and barrows, not even porters of the fire and torch-bearers, but children of the fire, made of it, and only the same divinity transmuted, and at two or three removes, when we least know about it." For Emerson, the fire is poetry, an elemental force capable of transmutation, transformation and enduring relevance. Moving from Emerson, Elizabeth Bishop rises as the twentieth-century poet most aligned with the possibility of poetry and the powers of its practice, as 'At The Fishhouses' indicates in her clear referencing of Emerson:

"If you should dip your hand in,
your wrist would ache immediately,
your bones would begin to ache and your hand would burn
as if the water were a transmutation of fire
that feeds on stones and burns with a dark gray flame."

This essay will look in detail at Bishop's understanding of the possibility of poetry and how art functions as a multi-dimensional structure that is unsettled as much as it unsettles. In particular, Bishop's poem 'The Monument' will be unpicked as testament both to the practice of Bishop's art and also the role of the poet critic responding to what they uncover

Political Posturing or Real Powers: Control of Genetically Modified Crops by the Member States and their Regions

The cultivation of genetically modified (GM) crops in the EU is highly harmonised, involving a central authorisation procedure that aims to ensure a high level of environmental and human health protection. However conflicts over authority persist and the Commission has responded to a combination of internal and external pressures with a more flexible approach to coexistence, a proposed opt-out clause and recently a promise by the head of the Commission to review the existing EU GM legislative regime, providing an opportunity to consider and suggest paths of development. In light of the significance of multilevel governance and subsidiarity for GM cultivation, this paper considers the policy-making powers of the Member States and subnational regions in this regime, focussing upon post-authorisation options in particular. A number of core mechanisms exist, including voluntary measures, safeguard clauses, coexistence measures, a proposed express opt-out and Article 4(2) TEU on ‘national identity. These mechanisms are examined in light of the goals and challenges of multilevel governance, in order to consider whether the relevant powers are located at the appropriate level. Overall, it is apparent that the developments occurring at the EU level are strengthening multilevel governance, but with significant opportunities to improve it further through focussing on the supporting roles and the regional levels in particular.

Annual report of the Attorney General to the Governor of the state of Ohio for the year ending .

Includes opinions of the Attorney General.

Acts of Congress, treaties, proclamations, decisions of the Supreme Court of the United States, and opinion of the attorney general relating to noncontiguous territory, Cuba and Santo Domingo, and to military affairs ... Comp. in the Bureau of insular affairs, War department ...

This edition contains legislation March 4, 1911-March 3, 1913; Supreme Court cases June 1, 1911-May 31, 1913; Opinions of attorney general March 4, 1911-March 3, 1913; Executive orders of the President March 4, 1898-March 3, 1913; List of officials January 1, 1913.

Biennial report of the attorney general of the state of Michigan.

Mode of access: Internet.

Vibrational spectroscopic studies of wool

Fourier transfonn (FT) Raman, Raman microspectroscopy and Fourier transform infrared (FTIR) spectroscopy have been used for the structural analysis and characterisation of untreated and chemically treated wool fibres. For FT -Raman spectroscopy novel methods of sample presentation have been developed and optimised for the analysis of wool. No significant fluorescence was observed and the spectra could be obtained routinely. The stability of wool keratin to the laser source was investigated and the visual and spectroscopic signs of sample damage were established. Wool keratin was found to be extremely robust with no signs of sample degradation observed for laser powers of up to 600 m W and for exposure times of up to seven and half hours. Due to improvements in band resolution and signal-to-noise ratio, several previously unobserved spectral features have become apparent. The assignment of the Raman active vibrational modes of wool have been reviewed and updated to include these features. The infrared spectroscopic techniques of attenuated total reflectance (ATR) and photoacoustic (P A) have been used to examine shrinkproofed and mothproofed wool samples. Shrinkproofing is an oxidative chemical treatment used to selectively modifY the surface of a wool fibre. Mothproofing is a chemical treatment applied to wool for the prevention of insect attack. The ability of PAS and A TR to vary the penetration depth by varying certain instrumental parameters was used to obtain spectra of the near surface regions of these chemically treated samples. These spectra were compared with those taken with a greater penetration depth, which therefore represent more of the bulk wool sample. The PA and ATR spectra demonstrated that oxidation was restricted to the near-surface layer of wool. Extensive curve fitting of ATR spectra of untreated wool indicated that cuticle was composed of a mixed protein conformation, but was predominately that of an a.-helix. The cortex was proposed to be a mixture of both a.helical and ~-pleated sheet protein conformations. These findings were supported by PAS depth profiling results. Raman microspectroscopy was used in an extensive investigation of the molecular structure of the wool fibre. This included determining the orientation of certain functional groups within the wool fibre and the symmetry of particular vibrations. The orientation ofbonds within the wool fibre was investigated by orientating the wool fibre axis parallel and then perpendicular to the plane of polarisation of the electric vector of the incident radiation. It was experimentally determined that the majority of C=O and N-H bonds of the peptide bond of wool lie parallel to the fibre axis. Additionally, a number of the important vibrations associated with the a-helix were also found to lie parallel to the fibre axis. Further investigation into the molecular structure of wool involved determining what effect stretching the wool fibre had on bond orientation. Raman spectra of stretched and unstretched wool fibres indicated that extension altered the orientation ofthe aromatic rings, the CH2 and CH3 groups of the amino acids. Curve fitting results revealed that extension resulted in significant destruction of the a-helix structure a substantial increase in the P-pleated sheet structure. Finally, depolarisation ratios were calculated for Raman spectra. The vibrations associated with the aromatic rings of amino acids had very low ratios which indicated that the vibrations were highly symmetrical.