Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

Géniuszok párharca. Milton Friedman és J. M. Keynes vitája Tim Congdon és Robert Skidelsky előadásában = War of the geniuses. The debate between Milton Friedman and J. M. Keynes as presented by Tim Congdon and Robert Skidelsky

Tavaly ünnepelte a közgazdász-társadalom Milton Friedman Nobel-díjas közgazdász születésének századik évfordulóját. A jubileumi megemlékezésnek különös aktualitást ad, hogy a 2008 óta tartó pénzügyi világválság hátterében ismét fellobbant a 20. századi közgazdaságtan két meghatározó irányzata - a Friedman nevével fémjelzett monetarizmus és a Keynes és követői által követett keynesizmus - közötti vita. E szerteágazó vitasorozat egyik "gyöngyszeme" két nemzetközileg ismert és elismert közgazdász, Tim Congdon és Robert (Lord) Skidelsky, összecsapása a Standpoint hasábjain 2009-ben. A szerző megmutatja, hogy a vita valójában nem a pénz fontosságáról vagy a mennyiségi pénzelmélet igazságáról folyt, hanem egyrészt egy sokkal elvontabb fogalomról: a bizonytalanság közgazdasági szerepéről, másrészt gyakorlati, gazdaságpolitikai kérdésekről: a monetáris és a fiskális politika lehetséges hatékonyságáról. A máig is tartó vitában "az inga többször kilengett", hol a keynesiánusok, hol a monetaristák javára, de még semmi nem dőlt el. ____ Last year economists marked the centenary of the birth of genius among them, Milton Friedman. The commemoration was especially topical because the world financial crisis that erupted in 2008 has brought sharply into focus again the old division in 20th-century economics between monetarism and Keynesianism. One highlight in this series of disputes was the 2009 clash between two internationally known and appreciated economists Tim Congdon and Robert (Lord) Skidelsky in the columns of Standpoint. The central element in the discussion is the role of money: what kind of economic policy to pursue, monetary or fiscal, to pull troubled economies out of crisis. The question closely resembles a decisive dilemma for Keynes in the 1930s. Though Keynes turned against some basic propositions of neoclassical economics, he never challenged the importance of money to the functioning of the economy, or the validity of the quantity theory of money. The author argues here that the issue is not about the formal category of money or demand for it, but about the far deeper economic concept of the role of uncertainty in economics. Another aspect concerns the relative efficiency of various kinds of economic policy, i. e. the strengths and weaknesses of monetary and fiscal policies.

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.