On a Conditional Cauchy-type Functional Equation Involving Powers

We solve the functional equation f(x^m + y) = f(x)^m + f(y) in the realm of polynomials with integer coefficients.

Powers and Logarithms

There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers of logarithmic and antilogarithmic mappings or powers of logarithms and antilogarithms (cf. for instance, the survey of Schinzel S[1].

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.

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

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

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

The impact of pump phase-modulation and filtering on WDM signals in a fibre optical parametric amplifier

WDM signal degradation from pump phase-modulation in a one-pump 20dB net-gain fibre optical parametric amplifier is experimentally and numerically characterised for the first time using 10x59Gb/s QPSK signals.

On two-wavelength Raman fibre laser based on spectral broadening

Raman fibre lasers and converters using the stimulated Raman scattering (SRS) in optical fibre waveguide are attractive for many applications ranging from telecommunications to bio-medical applications [1]. Multiple-wavelength Raman laser sources emitting at two and more wavelengths have been proposed to increase amplification spectrum of Raman fibre amplifiers and to improve noise characteristics [2,3]. Typically, a single fibre waveguide is used in such devices while multi-wavelength generation is achieved by employing corresponding number of fibre Bragg grating (FBG) pairs forming laser resonator. This approach, being rather practical, however, might not provide a good level of cross coherence between radiation generated at different wavelengths due to difference in FBGs and random phase fluctuations between the two wavelengths. In this work we examine a scheme of two-wavelength Raman fibre laser with high-Q cavity based on spectral intracavity broadening [3]. We demonstrate feasibility of such configuration and perform numerical analysis clarifying laser operation using an amplitude propagation equation model that accounts for all key physical effects in nonlinear fibre: dispersion, Kerr nonlinearity, Raman gain, depletion of the Raman pump wave and fibre losses. The key idea behind this scheme is to take advantage of the spectral broadening that occurs in optical fibre at high powers. The effect of spectral broadening leads to effective decrease of the FBGs reflectivity and enables generation of two waves in one-stage Raman laser. The output spectrum in the considered high-Q cavity scheme corresponds to two peaks with 0.2 - 1 nm distance between them. © 2011 IEEE.

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).

Analisi dinamica e a regime del convertitore Dickson-Charge-Pump

I circuti di tipo charge-pump trovano vasto impiego nell'elettronica moderna in quanto offrono un metodo semplice e totalmente integrato per elevare le basse tensioni di alimentazione tipiche dei circuiti digitali e trasformarle nelle alimentazioni adatte al pilotaggio di circuti di programmazione delle memorie, al pilotaggio dei mos di potenza, alla generazione della tensione di riferimento dei VCO nei PLL e in numerose altre applicazioni. Questa tesi studia il circuito charge-pump di Dickson nel suo comportamento sia a regime stazionario sia a regime dinamico. Al fine di aumentare l'efficienza è infatti importante attivare il circuito solo all'occorrenza, prestando attenzione al transitorio di accensione. Ogni aspetto teorico viene verificato per mezzo di simulazioni su LTSpice. Si è quindi potuto constatare che un dimensionamento corretto del numero di stadi ottimizza le prestazioni sia statiche che dinamiche sotto il vincolo di una massima occupazione d'area. L'impiego dei circuiti charge-pump si prevede possa essere sempre più diffuso in futuro, visto il trend verso un maggiore livello di integrazione dei sistemi elettronici e la tendenza ad utilizzare tensioni di alimentazione sempre più basse.

Woman rests aching feet by taking off high-heeled pump (these uncomfortable shoes hamper a woman's mobility)

Inscriptions: Verso: [stamped] Photograph by Freda Leinwand. [463 West Street, Studio 229G, New York, NY 10014].

Individual Proton Pump Inhibitors and Outcomes in Patients With Coronary Artery Disease on Dual Antiplatelet Therapy: A Systematic Review.

BACKGROUND: Observational studies evaluating the possible interaction between proton pump inhibitors (PPIs) and clopidogrel have shown mixed results. We conducted a systematic review comparing the safety of individual PPIs in patients with coronary artery disease taking clopidogrel. METHODS AND RESULTS: Studies performed from January 1995 to December 2013 were screened for inclusion. Data were extracted, and study quality was graded for 34 potential studies. For those studies in which follow-up period, outcomes, and multivariable adjustment were comparable, meta-analysis was performed.The adjusted odds or hazard ratios for the composite of cardiovascular or all-cause death, myocardial infarction, and stroke at 1 year were reported in 6 observational studies with data on individual PPIs. Random-effects meta-analyses of the 6 studies revealed an increased risk for adverse cardiovascular events for those taking pantoprazole (hazard ratio 1.38; 95% CI 1.12-1.70), lansoprazole (hazard ratio 1.29; 95% CI 1.09-1.52), or esomeprazole (hazard ratio 1.27; 95% CI 1.02-1.58) compared with patients on no PPI. This association was not significant for omeprazole (hazard ratio 1.16; 95% CI 0.93-1.44). Sensitivity analyses for the coronary artery disease population (acute coronary syndrome versus mixed) and exclusion of a single study due to heterogeneity of reported results did not have significant influence on the effect estimates for any PPIs. CONCLUSIONS: Several frequently used PPIs previously thought to be safe for concomitant use with clopidogrel were associated with greater risk of adverse cardiovascular events. Although the data are observational, they highlight the need for randomized controlled trials to evaluate the safety of concomitant PPI and clopidogrel use in patients with coronary artery disease.

S332 pump station, south of TS/Ph-1, Taylor Slough

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

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.