170,567 research outputs found
Slice-polynomial functions and twistor geometry of ruled surfaces in CP 3
No full textIn the present paper we introduce the class of slice-polynomial functions: slice regular functions defined over the quaternions, outside the real axis, whose restriction to any complex half-plane is a polynomial. These functions naturally emerge in the twistor interpretation of slice regularity introduced in Gentili et al. (J Eur Math Soc 16(11):2323–2353, 2014) and developed in Altavilla (J Geom Phys 123:184–208, 2018). To any slice-polynomial function P we associate its companionP ∨ and its extension to the real axis P R , that are quaternionic functions naturally related to P. Then, using the theory of twistor spaces, we are able to show that for any quaternion q the cardinality of simultaneous pre-images of q via P, P ∨ and P R is generically constant, giving a notion of degree. With the brand new tool of slice-polynomial functions, we compute the twistor discriminant locus of a cubic scroll C in CP 3 and we conclude by giving some qualitative results on the complex structures induced by C via the twistor projection
-exponential of Slice Regular Functions
No full textAs in [Entire slice regular functions, Springer, 2016] we define the ∗-exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for exp ∗ (f) are provided, also in terms of suitable sine and cosine functions. We completely classify under which conditions the ∗-exponential of a function is either slice-preserving or C J -preserving for some J ∈ S and show that exp ∗ (f) is never-vanishing. Sharp necessary and sufficient conditions are given in order that exp ∗ (f + g) = exp ∗ (f) ∗ exp ∗ (g), finding an exceptional and unexpected case in which equality holds even if f and g do not commute. We also discuss the existence of a square root of a slice-preserving regular function, characterizing slice-preserving functions (defined on the circularization of simply connected domains) which admit square roots. Square roots of this kind of function are used to provide a further formula for exp ∗ (f). A number of examples are given throughout the paper
Non-linear dynamic of real wages over the business cycles
No full textThis paper aims at analysing the dynamic properties of real wages over the business cycle. We apply a Bayesian vector autoregressive (BVAR) model and analyse the possible asymmetric behaviour of real wages in response to different macroeconomic shocks. Finally, we use the NBER business cycle periodisation to evaluate how real wages interact with the different shocks during contractions and booms. The results indicate that real wages cyclicality substantially depends on the driving forces of business cycle fluctuations. Different time periods are dominated by different types of shocks. When the business cycle is mainly driven by supply-side shocks real wages present a pro-cyclical behaviour. On the contrary, when the business cycle is driven by aggregate demand shocks real wages move counter-cyclically
Asymmetric Effects of National-based Active Labour Market Policies
No full textAsymmetric effects of national-based active labour market policies, Regional Studies. Labour market policies settled at the national level imply a ‘one-size-fits-all’ labour market strategy. This strategy might not sufficiently take into account region-specific economic structures. Whether active labour market programmes might asymmetrically affect
labour markets at the regional level is evaluated. The results for Italy suggest that while in the South employment is mainly
driven by social and economic context variables, in the North the employment dynamics are significantly explained by policy interventions. Two policy implications are suggested. First, the success of active policies depends on the regional labour market
conditions. Second, policy-makers should adjust labour policy strategy to regional economic structures
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