Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

MSC 2010: 26A33, 34D05, 37C25

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Fractional Korovkin Theory Based on Statistical Convergence

2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.

Fractional Trigonometric Korovkin Theory in Statistical Sense

2000 Mathematics Subject Classification: 41A25, 41A36.

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).

Table 1 Core site, fractional abundance of individual isoprenoid GDGTs and TEX86 values

TEXL86 and TEXH86 are organic palaeothermometers based on the lipids of Group 1 Crenarchaeota, recently proposed as a modified version of the original TEX86 index, but with significantly improved geographical coverage. Since few data from the global core top calibration are from the Pacific, this study was carried out to assess whether the global core top calibration is regionally biased or not. The result of principal components analysis of the fractional abundance of GDGTs, an analysis of variance (ANOVA) and the comparison of the residuals of TEXH 86 derived sea surface temperature (SST) estimates of the Pacific subset with that of the global data set suggest that the Pacific subset has a similar TEXH 86-SST relationship with the global data set. However, the regression line through the Pacific data and an ANOVA on the residuals of TEXL 86 derived SST estimates suggest otherwise. The contradictory findings are likely to stem from the large scatter in the Pacific TEXL 86 values in the mid temperature range. While regionality does not seem to exert a strong bias on TEXL 86 and TEXH 86 calibration, it appears that there is a strong need to resolve the large scatter in the global data set, especially in the mid and high latitudes, in order to improve the calibration for a better SST estimation.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Fractional order of poling period for broadly tunable second harmonic generation

We demonstrate the possibility to use a fractional order of poling period of nonlinear crystal waveguides for tunable second harmonic generation. This approach allows one to extend wavelength coverage in the visible spectral range by frequency doubling in a single crystal waveguide.

Fractional abundances of isoprenoid and branched glycerol dialkyl glycerol tetraethers (GDGT) of cores SO201-2-12KL and SO201-2-114KL

It has been proposed that North Pacific sea surface temperature (SST) evolution was intimately linked to North Atlantic climate oscillations during the last glacial-interglacial transition. However, during the early deglaciation and the Last Glacial Maximum, the SST development in the subarctic northwest Pacific and the Bering Sea is poorly constrained as most existing deglacial SST records are based on alkenone paleothermometry, which is limited prior to 15 ka B.P. in the subarctic North Pacific realm. By applying the TEXL86 temperature proxy we obtain glacial-Holocene-SST records for the marginal northwest Pacific and the Western Bering Sea. Our TEXL86-based records and existing alkenone data suggest that during the past 15.5 ka, SSTs in the northwest Pacific and the Western Bering Sea closely followed millennial-scale climate fluctuations known from Greenland ice cores, indicating rapid atmospheric teleconnections with abrupt climate changes in the North Atlantic. Our SST reconstructions indicate that in the Western Bering Sea SSTs drop significantly during Heinrich Stadial 1 (HS1), similar to the known North Atlantic climate history. In contrast, progressively rising SST in the northwest Pacific is different to the North Atlantic climate development during HS1. Similarities between the northwest Pacific SST and climate records from the Gulf of Alaska point to a stronger influence of Alaskan Stream waters connecting the eastern and western basin of the North Pacific during this time. During the Holocene, dissimilar climate trends point to reduced influence of the Alaskan Stream in the northwest Pacific.

An investigation of lower limb joint powers as a predictive measure of countermovement vertical jump height.

Measuring and tracking athletic performance is crucial to an athlete’s development and the countermovement vertical jump is often used to measure athletic performance, particularly lower limb power. The linear power developed in the lower limb is estimated through jump height. However, the relationship between angular power, produced by the joints of the lower limb, and jump height is not well understood. This study examined the contributions of the kinetic value of angular power, and its kinematic component, angular velocity, of the lower limb joints to jump height in the countermovement vertical jump. Kinematic and kinetic data were gathered from twenty varsity-level basketball and volleyball athletes as they performed six maximal effort jumps in four arm swing conditions: no-arm involvement, single-non-dominant arm swing, single-dominant arm swing, and two-arm swing. The displacement of the whole body centre of mass, peak joint powers, peak angular velocity, and locations of the peaks as a percentage of the jump’s takeoff period, were computed. Linear regressions assessed the relationship of the variables to jump height. Results demonstrated that knee peak power (p = 0.001, ß = 0.363, r = 0.363), its location within takeoff period (p = 0.023, ß = -0.256, r = 0.256), and peak knee peak angular velocity (p = 0.005, ß = 0.310, r = 0.310) were moderately linked to increased jump height. Additionally, the location, within the takeoff period, of the peak angular velocities of the hip (p = 0.003, ß = -0.318, r = 0.419) and ankle (p = 0.011, ß = 0.270, r = 0.419) were positively linked to jump height. These results highlight the importance of training the velocity and timing of joint motion beyond traditional power training protocols as well as the importance of further investigation into appropriate testing protocol that is sensitive to the contributions by individual joints in maximal effort jumping.

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.